imfstaffpapers...imfstaffpapers robert flood editor and committee chair ayhan kose co-editor david...

IMFstaffpapersRobert Flood

Editor and Committee Chair

Ayhan KoseCo-Editor

David EinhornAssistant Editor

Jelena KmezicResearch Assistant

Rosalind OliverAdministrative Coordinator

Editorial Committee

The objective of IMF Staff Papers is to publish high-quality research on a variety of topics of interest to a broad audience including academics and policymakers in the member countries of the Fund. IMF Staff Papers is open to outside submissions. The papers selected for publication in the journal are subject to an extensive review process using both internal and external referees. IMF Staff Papers also welcomes outside comments, criticisms, and interesting replications of published work. The views presented in published papers are those of the authors and should not be attributed to or reported as reflecting the position of the IMF, its Executive Board, or any other organization mentioned herein.

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International Monetary Fund

Volume 55 Number 2

IMFstaffpapers2008


EDITOR’S NOTE

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Volume 55 Number 2

Contents2008

Special Global Economy Model Issue

ForewordRobert P. Floo d K 211

Getting to Know the Global Economy Model and Its PhilosophyDougla s Laxto n K 213

The Global Economy Model: Theoretical FrameworkPaolo Pesen ti K 243

The Impact on the United States of the Rise in Energy Prices:Does the Source of the Energy Market Imbalance Matter?

Jared Be bee and Ben Hunt K 285

Oil Price Movements and the Global Economy: A Model-Based AssessmentSelim Elekdag, Rene Lalon de, Dougla s Laxton, Dirk Muir, and Paolo Pesen ti K 297

Productivity and Global Imbalances: The Role of Nontradable Total FactorProductivity in Advanced Economies

Pietro Co va, Massim iliano Pisani, Nico letta Batini, and Alessa ndro Rebu cci K 312

Inflation Targeting and Price-Level-Path Targeting in the Global Economy Model:Some Open Economy Considerations

Donald Co letti, Rene Lalonde, and Dirk Mui r K 326

The Macroeconomic Costs and Benefits of Adopting the EuroPhilip pe Ka ram, Dougla s Laxt on, Da vid Rose, and Natali a Tamir isa K 339

Why It Pays to Synchronize Structural Reforms in the Euro AreaAcross Markets and Countries

Luc Everaert and Werner Schule K 356


Underline

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Foreword

Robert P. FloodEditor

IMF Staff Papers (2008) 55, 211–212. doi:10.1057/imfsp.2008.10

This special issue of IMF Staff Papers, edited by Douglas Laxton,is devoted to the Global Economy Model (GEM). The GEM and the

IMF’s other dynamic stochastic general equilibrium models—the GlobalFiscal Model and the Global Integrated Monetary and Fiscal Model—arenow used widely inside the Fund and in a number of central banksworldwide.

The issue consists of eight papers. In the first paper, Douglas Laxtondiscusses the philosophy of GEM and explains, in some examples, howGEM modelers find solutions to their systems of nonlinear equations. In thesecond paper, Paolo Pesenti lays out in detail the structure of GEM,explaining how the various equations in GEM are derived from individualand firm-level self-interested maximizing behavior and how individualdecisions interact with government policy rules. The remaining six papersare specific applications of the GEM structure to a variety of real problemsand policy issues.

While the Laxton and Pesenti papers are reasonably self-contained, thesix application papers, which make no effort to be self-contained, representa publishing experiment for IMF Staff Papers. The application papersare much-condensed versions of working papers with identical titles allavailable on the IMF Staff Papers website. In the working papers, theauthors lay out in more detail the models with which they are working

IMF Staff PapersVol. 55, No. 2

& 2008 International Monetary Fund

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and there is a considerable repetition concerning model setup acrosspapers, as they all start from the same basic model laid out by Pesenti.In the versions published here, authors explain the ways in whichtheir models deviate from the GEM standard and present their mainexperimental results. Full replication instructions can be found inthe working paper versions. Data and programs are available on the IMFStaff Papers website.

Robert P. Flood

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Getting to Know the Global Economy Modeland Its Philosophy

DOUGLAS LAXTON�

This paper provides a nontechnical introduction to the IMF’s Global EconomyModel (GEM). GEM is a modern dynamic stochastic general equilibrium(DSGE) model that has been designed for studying a range of issues that cannotbe adequately addressed with reduced-form econometric models or an earliergeneration of macromodels whose dynamic equations were not based on strongchoice-theoretic foundations. Unlike earlier models, which were viewed as blackboxes by many outsiders, GEM’s theoretical structure is much better connectedwith work in the academic community, making it considerably easier for outsideresearchers to apply it and extend it for their own work. To understand the basicphilosophy behind GEM, we start by using the issue of exchange rate pass-throughto understand how adding additional features to the model allows one to betterunderstand issues related to the magnitude of exchange rate pass-through. We thenprovide a nontechnical introduction to what needs to be known to develop a steady-state calibration of the model. Finally, we end by summarizing other work onDSGE modeling at the IMF and lay out a few major priorities for the future.

[JEL C51, E31, E52]

IMF Staff Papers (2008) 55, 213–242; doi:10.1057/imfsp.2008.11

�Douglas Laxton is assistant to the director of the IMF Research Department. Theauthor thanks all the people involved in the development of the Global Economy Model(GEM) and the IMF’s other DSGE models. We owe a great debt to Ken Rogoff for invitingPaolo Pesenti to the IMF and focusing our attention on getting the job done quickly. We alsothank Raghuram Rajan, Simon Johnson, and others for making further development of thesetypes of models a priority and supporting outreach efforts in creating a DSGE modelingnetwork. Finally, we acknowledge the invaluable help from Laura Leon in preparing the paperand Peter Hollinger, Michel Juillard, Dirk Muir, and Susanna Mursula in developingprocedures used in model simulations. Thanks as well to our Econometric Support Team whohave helped with training and getting the models used. Finally, we appreciate comments fromRobert Flood, Peter Hollinger, and Turgut Kisinbay on an earlier draft.



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The Global Economy Model (GEM) is a modern dynamic stochasticgeneral equilibrium (DSGE) model that is based on the new open-

economy literature pioneered by Obstfeld and Rogoff (1995 and 1996).1

GEM’s modular structure has been designed to make it relatively easy forresearchers to simplify the model’s structure by turning off certain features.Although different versions of GEM have been published in several papers,no single paper has documented the general structure of GEM or provided adetailed motivation for many of its features and options. The main purposeof this volume is to document GEM and to provide a flavor for some recentapplications and extensions of the model.

The first two-country version of GEM was developed in 2001 and waslater published in the Journal of Monetary Economics. Within a few monthsthere was a small team of economists working on the model, which grewin size over time and later became a network of researchers from bothinside and outside the IMF. Today, variants of GEM are used extensivelyat the central bank in Canada, Italy, Japan, and the Norges Bank. Buildingon the success of the GEM project, the IMF Research Department’sModeling Unit has developed other DSGE models to address issues thatrequire more elaborate theoretical structures. This includes the Global FiscalModel (GFM), which focuses on medium- and long-term fiscal issues,and the Global Integrated Monetary Fiscal Model (GIMF), which hasbeen designed for issues that involve both monetary and fiscal policy.2 Thesetwo models as well as GEM are now used extensively within the Fundfor supporting our surveillance activities.3 Figure 1 provides a graphicalrepresentation of the number of papers that have been generated withGEM, GFM, and GIMF as well as some smaller DSGE models that weredeveloped to look at specific issues that required a more specialized modelstructure.

Much of the success of GEM and the other DSGE models has been a resultof their strong links to the academic literature. Indeed, before models like GEMmacromodeling at the IMF and in other policymaking institutions was to alarge extent disconnected with modeling in the academic community. However,with the emergence of the new open-economy literature and the general interestin developing models with better choice-theoretic foundations, there has beenmuch more effective collaboration between researchers in academia andmodelers in policymaking institutions. Indeed, a few other policymakinginstitutions have already replaced their earlier generation of macroeconometric

1See Laxton and Pesenti (2003) for the first version of the GEM and Botman and others(2007) for a summary of applications and extensions of the model.

2See Botman and others (2006) for a description of GFM and Kumhof and Laxton (2007)for a description of GIMF. Both these models are based on the finite-planning horizonparadigm, which can give rise to strong non-Ricardian behavior—see Blanchard (1985).

3See Botman and others (2007) for a summary of applications and extensions based onGEM, GFM, and GIMF.

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models with these types of models for production work and several institutionsare currently in the process of doing it.4

Arguably the benefits of this cooperation are just beginning. In fact, asdiscussed at the end of the paper, recent work in both academia andpolicymaking institutions on developing a better empirical methodologybased on Bayesian theory has already made significant progress ineliminating the enormous gap between econometric theory and appliedmacromodeling. By supporting the development of tools like the DYNAREproject, the IMF and a few other policymaking institutions have made a veryuseful investment that may make it possible in a matter of years to graduallyretire an older generation of models that have been either calibrated orestimated with very unreliable estimation procedures.5

The main purpose of this volume is to document GEM and to providea few applications and extensions of the model. This first paper in thevolume has a few objectives. First, it is meant to provide a summary of

Figure 1. Papers Using or Extending the Modeling Unit’s DSGE Models

2002 2003 2004 2005 2006 20070

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GEMGETMGFMGIMFOther

4For some recent examples of modern DSGE models in central banks, see Erceg,Guerrieri, and Gust (2005); Murchison and Rennison (2006); and Adolfson and others(forthcoming).

5See Sims (2002) for a critique of the methods that were used to parameterize the earliergeneration of macromodels. DYNARE is a user-friendly front end for MATLAB written byMichel Juillard and his colleagues at CEPREMAP. It includes a state-of-the-art collection oftools designed for estimation and obtaining either perfect foresight solutions on nonlinearmodels or local approximations around a steady-state solution.

GETTING TO KNOW THE GLOBAL ECONOMY MODEL

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GEM to nontechnical readers and to provide an example that shows howDSGE models can provide useful insights that go well beyond reduced-formmacroeconometric models. Second, we provide a summary of the tool box weuse at the IMF to build and solve models. Third, we provide some viewsabout the weaknesses of these types of models and speculate how work on themodels will likely evolve over time. This first paper is followed by acompanion paper by Paolo Pesenti, which documents GEM’s equations andtheoretical structure. The remaining six papers provide examples ofapplications and extensions. In addition to the GEM applications andextensions presented in this volume, interested readers can find nontechnicalsummaries of GEM applications and the IMF’s other DSGE models inBayoumi and others (2004) and Botman and others (2007).

I. GEM and Exchange Rate Pass-through

GEM is a DSGE model that has rigorous behavioral foundations includinga wide-ranging assortment of real and nominal adjustment costs thatprovide plausible short-run and long-run properties. It is these sources ofinertia in adjustment within a clear theoretical framework that allow us toexplore issues that cannot be adequately addressed with reduced-formempirical models. This section provides an intuitive nontechnicalintroduction to GEM by looking at the specific issue of exchange ratepass-through. In particular, we show that both short-run and long-runexchange rate pass-through will depend critically on how monetary policyresponds to shocks and what type of shock is driving both the exchange rateand prices.

The model comprises firms that produce goods, households that consumeand provide labor and capital to firms, and a government that taxes andspends. Consumption and production are characterized by standard constantelasticity of substitution (CES) utility and production functions. Many smallfirms produce differentiated goods using labor, capital, and intermediategoods such as components or commodities. Goods are differentiated, and asa result firms possess market power and restrict output to create excessprofits—this setup allows a consideration of the effects of price markups.Capital and intermediate goods can be produced and traded while the laborforce in each country is fixed, with workers making a choice between workand leisure. Workers also have market power and hence restrict their laboreffort to raise their real wage.6 The workers own the firms in their country,and hence generate revenues in the form of wages and profits. Workers’income is subsequently spent on home and foreign goods based on a CESutility function.

6Bayoumi, Laxton, and Pesenti (2004) show that higher levels of competition in both thelabor market and goods market will permanently raise living standards and make the task ofmonetary policy easier to implement by increasing the sensitivity of inflation to marketconditions.

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Figure 2 illustrates a two-country version of GEM. Production is splitinto two stages. In the first stage, labor (L), capital (K), and (possibly) landare used to create intermediate goods that can be traded (T), such as oil orcomponents for manufacturing. These intermediate goods are then combinedwith additional labor and capital at home and abroad to produce final goods.A second feature, which is key for this paper, is the split of final goods intotraded and nontraded goods. Another important feature to note is thedistribution sector. There is strong evidence from microeconomic studies thatthe same goods are sold at different prices across countries. One way ofincorporating this observation is to include a distribution sector in themodel—see Corsetti and Pesenti (2005). All domestic and foreign goods needto go through this sector before they can be bought. As the distributionsector is assumed to consist of nontraded goods, this means that the finalprices of all goods include both the cost of producing these goods anddomestic distribution costs, so prices of imported tradable goods may notfully reflect changes in the exchange rate (even in the long run).7 Given the

Figure 2. GEM Flow Chart

K L L* K*

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7The largest version of GEM and the one used in the simulations below also distinguishesbetween imports of investment goods and consumption goods. Differences in importintensities can have important implications for the responses of the economy in response toshocks that change the real exchange rate. For countries that import a substantial amount ofcapital, an appreciation in the real exchange rate can raise living standards on a sustainablebasis by reducing the cost of capital.


217


preferences of consumers, firms, and governments, the goods are distributedacross countries.

GEM features a wide range of possible sources of inertia in both real andprice adjustment. In general, these mechanisms are modeled to reflectquadratic costs of adjustment. In each case, the resulting dynamic equation isfully embedded in optimizing behavior by economic agents. A fewparameters allow users to calibrate the relative strength of these costs indamping or delaying adjustment to shocks. For the basic model, theseparameters have been chosen using a variety of information, but always witha view to ensuring that the model has reasonable simulation properties.

Key Mechanisms for Understanding Exchange Rate Pass-through

Two mechanisms are highlighted in this paper. The model has costlyadjustment for both quantities and domestic prices of imported goods. Thus,when a relative price change occurs—the price of imported goods at the portof entry rises, say—there is gradual adjustment to this both in terms of thedomestic retail price of imported goods and in terms of the adjustment ofimport volumes to the new relative price. These two mechanisms, togetherwith the presence of a distribution sector, provide the hierarchy of sources ofinertia in pass-through that we study. In each case, we report the results ofthe shock with all these mechanisms turned off (the base-case model), andthen the results as we add them back in, starting with the distribution sector,then the price adjustment effect, and finally the quantity effect. With this laststep, we recover the full-model properties.

Exploring Exchange Rate Issues

We now consider a number of shocks to the model designed to illustrate thefeatures described above and how both the nature of the shocks and thesefeatures influence the results and their interpretation.8 As we noted above,both the nature of the shocks and the nature of adjustment dynamics areimportant in understanding exchange rates and pass-through.

The shocks are wide-ranging. We attempt to address the pass-throughquestion directly in studying the case where the shock is indeed to theexchange rate itself, implemented as a portfolio preference shock where thecountry risk premium changes. The discussion becomes more complex whenthe shock comes from another source and exchange rates, import prices, andconsumer prices are all responding to a shock arising elsewhere in the system.We begin this part of the discussion by considering a persistent increasein domestic demand in the Home economy and then show how pass-through

8The model used is our standard two-country training version of GEM, where the Homeeconomy has been calibrated to be a small open economy. The code for the model andexperiments is available in TROLL and can be obtained from the author’s website atwww.douglaslaxton.org. People interested in accessing the code can request a trial version ofTROLL from INTEX Solutions.

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www.douglaslaxton.org

and the long-run responses of all nominal variables depend on the speed atwhich monetary policy brings inflation back to target. We then exploit thesophisticated sectoral structure of GEM by considering permanent productivityshocks in the nontraded goods sector and the traded goods sector, consideredseparately.

Shock to the exchange rate (risk premium)

We begin with the closest we can get to the pure pass-through question byconsidering the shock to the country risk premium. The shock is temporary,but long-lasting and produces a long-lived nominal and real depreciation.The top panels of Figure 3 show the nominal exchange rate, the CPI, andtrade prices. In the top-left panel, where all the model’s adjustment featuresare turned off, we cannot see the trade prices because they follow the nominalexchange rate precisely. The import component of the CPI will be rising inline with the import weight in the CPI. In the end, pass-through is one to one,in the sense that the drift in the price level (about 5 percent after 40 quarters)reflects fully the nominal depreciation.

The charts on the bottom of Figure 3 show the paths of inflation(year over year) and real and nominal interest rates. In the left panel, nominalrates are increased sharply to resist the inflationary consequences of theshock.

As we add the sources of inertia in import price pass-through, we seethe scenario change dramatically, especially when we add import priceadjustment costs and import volume adjustment costs. The former,especially, delays and damps the response of import prices in the CPI,which reduces inflation and the monetary response. In the top-right panel, westill see one-to-one pass-through in the end, but the level drift is muchsmaller, about a fifth of the result with all the mechanisms shut off. In thebottom panel, we see that policy response is quite muted, embodying theimplications of the sluggishness in import price adjustment.

The charts in rows 2 and 3 show the real exchange rate and trade, andGDP and consumption and investment. Without adjustment costs, the effectof the real depreciation is stronger and faster. When we add these features,the initial trade response is muted. Without adjustment costs, the modelshows GDP rising initially, in response to the strong exports; this disappearswhen we add the adjustment costs.

This exercise demonstrates that even when the shock comes into domesticinflation through import prices, there are many things that can break the‘‘law of one price’’ at least at the CPI level. The presence of a distributionsector as well as both nominal and real rigidities all reduce both the short-runand long-run sensitivity of import prices and the CPI to changes in theexchange rate—see Figure 3. And the presence of these rigidities also meansthat the exchange rate must jump more in the short run to facilitateadjustments in the real economy.


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Shock to domestic aggregate demand

Figure 4 reports results for a positive shock to aggregate demand wherethere is a long-lasting increase in both consumption and investment in thedomestic economy. The real exchange rate appreciates through the firstpart of the shock to bring about the necessary reduction in exports. In the

Figure 3. Temporary Increase in the Country Risk Premium(In percent )

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case where all the adjustment mechanisms are cut off, the resultingnominal appreciation reduces import prices and inflation, and initially,monetary policy must ease. However, as we add the model’s sources ofinertia, we see the more normal picture emerging. CPI inflation rises inthe face of the higher demand and monetary policy raises nominal interest

Figure 4. Shock to Domestic Aggregate Demand(In percent )

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rates from the start. Note that additional rigidities increases the nominalappreciation, initially, and in the end there is more upward price level drift.Here, the addition of volume adjustment costs plays an important role,blunting and delaying the response of exports, so that the overall increase inGDP relative to control is larger and longer, despite the extra monetarytightening.

If we were looking at the pass-through question here, and did not knowthe shock, we would have some puzzles. The nominal exchange rateappreciates and import prices decline as CPI inflation increases. This isreadily understood, given the model and knowledge of the shock, but if oneattempted to treat the exchange rate movement as if it were at least part ofthe shock, it might appear that ‘‘the lags were longer’’ or something similar,and there might be a forecast of more disinflationary effects to come. Thiswould be unfortunate if it interfered with the tightening of policy in responseto the domestic shock.

Shock to domestic aggregate demand with different monetary policyresponses

Several commentators have argued that declining exchange rate pass-throughin reduced-form inflation equations simply reflects improved monetary policyframeworks that have anchored long-term inflation expectations and reducedthe amount of persistence in the inflation process—see Taylor (2000). Toillustrate this point in GEM Figure 5 shows what happens when we reducethe short-run interest rate response coefficient on inflation in the monetaryreaction function from its base-case value of 0.50 to 0.25. We report just thecomparison for the model with all the sources of inertia. The left panelsrepeat the full-model results reported in Figure 4 when the responsecoefficient on inflation is large enough that it stabilizes the increase in theprice level at a value that is less than 2 percent above baseline. In the shortrun the nominal exchange rate appreciates by about 1 percent reflecting theincrease in interest rates. However, since the shock disappears over time theexchange rate must eventually depreciate in line with the long-run increase inthe price level. As can be seen in the right panels, reducing the responsecoefficient on inflation increases the long-run response of both the price leveland the depreciation in the nominal exchange rate, showing that the responseof monetary policy can be a very important factor in determining the long-run responses of all nominal variables in response to aggregate demandshocks. Obviously, when demand shocks represent an important source ofvariation in the data it will appear that there will be very strong pass-throughfrom exchange rates into the price level when monetary policy is stronglyaccommodative.

Shock to productivity in the nontraded goods sector

Consider next a permanent real shock, an increase in productivity in theHome nontraded goods sector—see Figure 6. The higher productivity raises

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output in the nontraded goods sector, but there is insufficient domesticconsumption demand for this output, so resources must switch to tradedgoods. To sell the extra tradables output, the real exchange rate must

Figure 5. Shock to Domestic Aggregate Demand with Less AggressiveMonetary Policy

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depreciate. This also helps switch consumption demand to domestic goods,because the relative price of imported goods rises.

On the nominal side, the real depreciation is associated with a nominaldepreciation and imported consumption prices rise, as does the CPI, relativeto control. Here, however, since relative domestic nontraded goods prices are

Figure 6. Shock to Productivity in the Non-Traded Sector(In percent )

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lower, there is much less general CPI drift. Import prices are up sharply andremain so, but the overall CPI is less affected.

In this permanent real shock, the real relative price change dominates theresults in terms-of-trade prices and the nominal exchange rate. In Figure 6,we see that the path for these variables is not much affected by the inertiaterms. The inertia terms affect the domestic price results and the overall CPI.Note from the figure that when the full model operates, there is very littlemonetary response, whereas if the inertia terms are all turned off, the latentinflation pressures trigger a substantial initial tightening.

This is an interesting shock for the issue of pass-through. We see largeand permanent increases in the nominal exchange rate and import prices withlittle effect on CPI inflation. The decline in domestic nontraded goods pricescoming from the productivity increase largely offsets the effect of higherimport prices in the overall consumption bundle. If one were looking at thisas an exchange rate shock and trying to find pass-through effects like thosethat arise from a true exchange rate (risk-premium) shock, one would be verypuzzled.

Shock to productivity in the traded goods sector

Figure 7 reports the results for a permanent increase in productivity in theHome traded goods sector. Here adding the distribution sector (going fromcolumn 1 to column 2) reduces the magnitude of the shock on GDP and itssubcomponents as nontraded goods represent a larger share of value addedin the baseline. Interestingly, when all these mechanisms are turned off thereal exchange rate appreciates, but when these mechanisms are turned on thereal exchange rate depreciates over the first 40 quarters of the shock.Although not reported, the very long-run response of the real exchange rateis an appreciation, but the presence of these mechanisms reverse the sign overa 10-year horizon. These simulations require permanent changes in relativeprices, which imply a permanent wedge between the exchange rate and finalconsumption prices. Interestingly, adding the distribution sector tends tomute the response of inflation and interest rates, but then adding bothnominal and real adjustment costs in trade then requires more adjustment ininflation and interest rates.

II. Philosophy and Solution Procedures

The development of GEM and the Fund’s other DSGE models has benefittedenormously from a collection of tools and solution methods that have beendeveloped over the years to support macromodeling in both academia andpolicymaking institutions. Having access to powerful tools and systematicmethods for building, calibrating, and solving the models has made it mucheasier for new users in our modeling network to make progress quickly. Thissection starts by providing the basic philosophy that is used to build themodels and then provides a detailed roadmap for developing a steady-statecalibration, doing perfect-foresight solutions on the nonlinear dynamic


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versions of the models, or taking local approximations around an initialsteady-state solution.

Basic Philosophy

The basic philosophy behind GEM and the other DSGE models developed atthe IMF is much different than the first generation of large-scale econometric

Figure 7. Shock to Productivity in the Traded Sector(In percent )

Base Case Model Add Distribution Sector Add Import Price Adjustment Costs Add Import Volume Adjustment Costs

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models. These earlier large-scale econometric models focused more on fittingindividual equations by connecting variables and then assembling theequations on a computer. The dynamics and forecasts produced by theseequations were usually not considered to be very reliable so the modelerswould go back to their computers and fiddle with the equations andestimation routines until their models produced more plausible lookingresults.9 Following the abandonment of these models and their researchprogram in academia a new research program was developed that focusedmore attention on dynamic optimization theory and understanding theimportance of real and nominal rigidities for macrodynamics. At the sametime a similar research program was in place inside a few academic andpolicymaking institutions trying to build a second generation of forward-looking macromodels for forecasting and policy analysis.10 This researchprogram was also based on developing models with forward-lookingbehavior and although these models had a coherent theoretical structuremany of the dynamic equations were not derived explicitly from strongchoice-theoretic foundations. As the two research programs progressed itbecame natural to combine the best from both approaches. The end resulthas been a new generation of models that have stronger choice-thereoticfoundations, and with sufficient nominal and real rigidities that can produceplausible macrodynamics.

The development of GEM and the IMF’s other DSGE models benefitedenormously from work on the earlier models as well as the algorithms thatwere developed for solving these earlier models.11 The development ofmulticountry models involves considerably more complexity than smallopen-economy models because of a much larger set of variables andparameters. In addition, given that a major priority has been to developmodels that produce realistic dynamics that are comprehensible to a fairlywide audience it has been important to design the models in a way that makesit relatively easy to simplify them. In the design and teaching of GEM thisphilosophy is usually referred to as the seed and onion philosophy. The termseed is used to refer to computer programs that generate different versions ofGEM, which includes the full model depicted in Figure 2 as well as twosmaller versions where we reduce the number of goods in the models. Thisincludes a version that eliminates trade in primary goods as well as an evensimpler version that further eliminates nontradables from the model.

9For a more detailed explanation of why single-equation fitting was abandoned in favorof calibration methods, see Coletti and others (1996).

10For early examples of these models, see Masson, Symansky, and Meredith (1990);Bryant, Hooper, and Mann (1993); Taylor (1993); Black and others (1995); Coletti and others(1996); Brayton and Tinsley (1996); and Laxton and others (1998).

11For a discussion of the stacked-time algorithms developed at CEPREMAP, the Bank ofCanada and INTEX solutions, see Laffargue (1990); Boucekkine (1995); Juillard (1996);Armstrong and others (1998); and Juillard and others (1998). For a discussion of thealgorithms available in TROLL, see Hollinger (1996).


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Building models with this type of modular structure has been a very usefulapproach for making it easy to peel off layers of the onion to understand howextending a model changes its predictions. In addition, because GEM wasbuilt to encompass a large collection of modern DSGE models developed inacademia and other policymaking institutions, which tend to be muchsimpler in design, this approach has made it a great teaching device to go stepby step from extremely simple models to more complicated versions.

The seed and onion philosophy does not stop at simplifying GEM’s goodsstructure. It is also used extensively to get the initial steady-state calibration,which is used as a baseline for nonlinear perfect foresight solutions or to takelocal approximations around the initial stead-state solution. To do this theprogram that generates GEM also generates steady-state analogue modelsfor the three versions of the model, which simply involves replacing all theleads and lags in the models with the contemporaneous values of thevariables.12 Removing all the leads and lags of the model creates a set ofmodels that can be solved much easier than the larger dynamic versions,which have more complicated solutions because of the combination ofdynamics and additional nonlinearities that arise from adjustment costs.

The theoretical structure of the GEM is consistent with an underlyingsteady-state equilibrium where inflation and all real variables are constant.13

However, because of the presence of significant nonlinearities in the structureof the model, solving for this steady-state equilibrium for new calibrations ofthe model can be nontrivial. The next part of this section describes a Newton-based algorithm that has been designed to handle the specific features of largemodels like GEM, which feature several nontrivial nonlinearities that arisefrom its emphasis on microfoundations, imperfect competition, as well as theexistence of significant real and nominal rigidities.

Divide and conquer algorithms

The solution methods are referred to as divide-and-conquer (DAC)algorithms because they are based on a very simple idea in mathematicsthat it can be easier to solve a complex problem by breaking it down into aseries of less complicated problems that are much easier to solve. We havefound that in practice that this simple solution technique works very well formodels like the GEM, which contains several nontrivial nonlinearities.

Although the DAC solution techniques are reasonably robust, they dorequire a basic understanding of the structure of the model as well asNewton’s method for solving a nonlinear system of equations. The sectionprovides a simple introduction to what has to be known about the basic

12This approach was followed earlier in the development of the Bank of Canada’sQuarterly Projection Model and the IMF’s Mark 3 Version of MULTIMOD. See Black andothers (1995) and Laxton and others (1998).

13The model is consistent with a balanced growth path, but all real variables have beennormalized in a way that removes growth.

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algorithms that we use to obtain both steady-state and perfect foresightsolutions. To make the section accessible to a fairly wide audience we startwith some examples of very small models so that researchers can understandmore easily what is required to obtain solutions to GEM.14 We first start witha brief overview of the properties of Newton-based algorithms and then weuse this discussion to motivate a robust and efficient solution procedure forcomputing steady-state solutions of the model.

GEM’s nonstochastic steady state

Nonlinear rational expectations models like the GEM can be written as a setof n equations

EtðFðyt�r; . . . ; yt; . . . ; ytþs; xt�r; . . . ; xt; . . . ; xtþsÞÞ ¼ 0; (1Þ

where y is a vector of n endogenous variables and x is a vector of m exogenousvariables. Variables may appear with a maximum of r lags and s leads. A basicrequirement of this type of model is that the n equations must determine aunique solution for the current values of all the n endogenous variables, yt,given the values of the exogenous variables and of the lag and lead values ofthe endogenous variables. Because the GEM has been developed to be con-sistent with a steady state where inflation and all real variables are constant,the steady-state conditions can be imposed by simply transforming (1) byreplacing all the leads and lag variables in the model with their contempo-raneous values.15 The resulting system can be expressed as a nonlinear system,

FðY ; XÞ ¼ 0; (2Þ

where Y is a vector of n endogenous variables and X is a vector ofm exogenousvariables. Because of the existence of nonlinearities in the GEM it is notpossible to derive an analytical solution to Equation (1) and it is necessary toemploy numerical methods to solve for the vector of n endogenous variablesgiven the vector of m exogenous variables. Although there is no generalalgorithm that guarantees to find numerical solutions to this problem fromarbitrary initial guesses of the values for the endogenous variables, the

14Despite the extreme simplicity of these examples they can be used to explain a largenumber of the solution problems encountered in solving large models like the GEM. Someshort training programs have been written in TROLL so that users can gain some experiencesolving smaller models before moving on to much larger problems.

15In the base-case variant of GEM the monetary policy regime is assumed to be inflationtargeting. It is well known that in an inflation-targeting regime the price level will have a unitroot and will be subject to random drift. To remove the unit root from the model GEM hasbeen transformed by expressing all nominal variables as a ratio of the CPI. However, after adynamic solution of the model has been obtained it is then possible to construct the price levelby using the measure of inflation from the model to cumulate the CPI-based price level fromsome initial condition drawn from history. Likewise, after the CPI-based price level has beencreated it is then possible to create all other nominal prices using the measures of relativeprices from the model. The monetary policy reaction function in GEM is sufficiently generalthat it allows for targeting either the exchange rate or the price level.


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development of algorithms that can invert large sparse matrices has allowedresearchers to move beyond elementary first-order iterative methods such asGauss-Jacobi or Gauss-Seidel to more robust and efficient Newton-basedalgorithms.16

Brief review of Newton-based algorithms

The basic strategy of Newton’s method for solving (2) is to replace F with alinear approximation based on some initial guesses for the endogenousvariables and then solve this system to obtain a better linear approximationof the F function. This iterative process continues until convergence isdeclared by passing a stopping criterion.

In practice, if the guesses for the endogenous variables are in theneighborhood of the true solution, Newton-based algorithms will find thetrue solution extremely rapidly. However, if these initial guesses are not in theneighborhood of the true solution, Newton-based algorithms may fail toconverge.

The process of obtaining good starting guesses for Newton-basedmethods will obviously be more demanding in cases where models arebeing developed from scratch, or where researchers are actively investigatingnew structures for which they do not have any previous solutions andexperience to use as a basis for determining initial guesses. In suchcircumstances, it is critical for researchers to understand the properties oftheir solution algorithms in some detail so that they can distinguish betweenconvergence failures that arise from bad starting values, coding errors, orerrors in the model’s theoretical structure.17 To understand the basicproperties of Newton-based algorithms, it may be useful to start with somesimple examples that illuminate some of the properties of these algorithms.

Example of a simple linear system

Equations (3) and (4) provide a simple linear two-equation representation of(2) and for further simplicity we will assume that the value of the exogenousvariable x1 has been set equal to 2. As can be seen in Figure 8, the solution tothis problem is (y1, y2)¼ (1, 1).

� y1þy2 ¼ 0; (3Þ

y1 þ y2 � x1 ¼ 0: (4Þ

16See Armstrong and others (1998) and Juillard and others (1998) for a comparison ofelementary first-order iterative methods and Newton-based algorithms.

17Obviously, this debugging process will be extremely difficult in cases where researchersdo not have access to robust solution methods because it will be much more difficult todistinguish between different types of errors when several errors are present at the same time—see Armstrong and others (1998) for a discussion of the difficulties associated with using first-order methods to solve nonlinear macromodels with significant lags in the monetarytransmission mechanism.

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Solution of Equations (3) and (4) with Newton’s methods

Newton’s methods require four steps.Step #1: To solve (3) and (4) with Newton’s method it is necessary to

construct the Jacobian matrix of partial derivatives with respect to theendogenous variables. In this particular example F(Y,X) can be written as,

FðY ;XÞ ¼F1ðy1; y2; x1Þ

F2ðy1; y2; x1Þ

" #¼�y1 þ y2 þ 0

y1 þ y2 � 2

" #¼

0

0

" #; (5Þ

where the Jacobian of F(Y,X)¼ 0 is,

qFqY¼

qF1ðy1;y2Þqy1

qF1ðy1;y2Þqy2

qF2ðy1;y2Þqy1

qF2ðy1;y2Þqy2

24

35 ¼ �1 1

1 1

" #: (6Þ

Note that in this example the Jacobian does not depend on the values of y1and y2 because the model is linear.

Step #2: Starting from an initial guess for (y1, y2), the system F(Y,X)¼ 0can be evaluated to determine if all of the equations in the system hold.Define residuals (RES1 and RES2) for Equations (3) and (4) as the differencebetween the left-hand side (LHS) and right-hand-side (RHS) of eachequation. In the simple example above, if the initial values for (y1, y2) were(0, 0) the values of RES1 would be equal to 0 and RES2 would be equal to �2.Given the way the model has been written in the form F(Y,X)¼ 0, theseresiduals will simply be equal to the value of F(Y,X) evaluated at(y1, y2)¼ (0, 0). In this particular example the first equation passes throughthe coordinates (0, 0) and has a zero residual. However, the second equationcrosses the y2 axis at (0, 2) and is not consistent with the initial set of guessesfor y1 and y2. As will be shown below, the magnitude of these residuals andthe value of the Jacobian will determine how large the values of y1 and y2 willchange in each iteration.

Figure 8. Example of a Simple Linear Model

(0, 0)

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Step #3: Starting from an initial guess of Y, Y(0), we can then solve (fork¼ 0)

qFY ðkÞ

qY

" #DY ðkÞ ¼ �F ½Y ðkÞ�; (7Þ

to calculate a Newton step,

DY ðkÞ ¼ � qFY ðkÞ

qY

" #�1F ½Y ðkÞ�; (8Þ

and then perform a series of Newton iterations Ykþ 1¼YkþDYk. In thesimple example above, if the initial starting values for (y1, y2) is (0, 0) then (7)will be

�1 1

1 1

" #DY ð1Þ ¼

0

2

" #; (9Þ

and solving this for DY(1) results in the following Newton step.

DY ð1Þ ¼yð1Þ1

yð1Þ2

24

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ð0Þ1 þ Dyð0Þ1

yð0Þ2 þ Dyð0Þ2

24

35 ¼ 1

1

" #: (10Þ

Thus starting from (y1, y2)¼ (0, 0) Newton’s methods will raise both y1 and y2by one unit in the first iteration and directly reach the true solution of(y1, y2)¼ (1, 1) in one iteration. As can be seen in the example above, if wereplace the initial starting values for (y1, y2) to be equal to any real number(y1

(0), y2(0)) Newton’s method will continue to find the true solution in one

iteration. Thus, a very important property of Newton’s method is that it willfind the true solution in the first iteration starting from any arbitrary set ofstarting values for the endogenous variables. This is a very importantstrength of Newton’s methods over other methods. For example, using astandard linear approximation of the monetary transmission mechanism thatfeatures significant lags between the policy rate and inflation, Armstrong andothers (1998) show analytically that while Newton’s method is guaranteed tofind a solution in one iteration, first-order iterative solution techniques suchas Gauss-Seidel may take many iterations to converge, if indeed theyconverge at all. This lack of robustness with first-order methods is the onereason why many model builders have abandoned first-order methods infavor of Newton-based methods.18

18As can be seen in the example above, implementing a Newton-based method requiressoftware that can create and evaluate a Jacobian and then invert this matrix. For equationsystems that are small the matrix-inversion step is trivial. However, for large models thematrix-inversion step can become extremely inefficient unless this step exploits the sparsestructure of the Jacobian. Our experience thus far suggests that this will not result in asignificant problem for solving for the nonstochastic steady state of GEM using the standard

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Example of a simple nonlinear system

Equations (11)–(13) provide a simple nonlinear three-equation representationof F(Y,X).

� y1 þ y2 ¼ 0; (11Þ

y21 þ y22 � x1 ¼ 0; (12Þ

� logðy1Þ þ y3 ¼ 0: (13Þ

This example has been chosen because it can be used to illustrate several ofthe problems that model builders face when debugging models like the GEM,which represent a large collection of simultaneous linear and nonlinearequations as well as recursive blocks that may contain both. As can be seen inFigure 9, Equation (11) is a simple linear equation that passes through thecoordinates of (0, 0) for (y1, y2) and has a constant slope parameter equal toone. Equation (12) is a simple nonlinear equation that defines a circle centeredon the coordinates of (0, 0) for (y1, y2) with a radius equal to

ffiffiffi2p

, which isapproximated by the number 1.41 in Figure 9. As can be seen in Figure 9 thesolution to the system that includes only Equations (11) and (12) has multiplesolutions for (y1,y2) at (1, 1) and (�1,�1). Equation (13) is a simple nonlinearequation that rules out the second solution because y3 is equal to the log of y1, afunction whose domain is restricted to be strictly positive values for y1.Equation (13) also represents a recursive block of the complete system becausethe variable y3 depends on y1, but y1 and y2 do not depend on y3.

As indicated in the previous section, Newton’s approach to solving anonlinear system of equations, such as (11), (12), and (13), starts bylinearizing the system around some initial starting values for (y1, y2, y3),finding a solution of the linearized model, and then using this solution toupdate the guesses for (y1, y2, y3). This process continues until Newton’smethod either converges or fails to converge. In this simple example it isobvious that a negative value for the initial guess of y1 would be a poorchoice and may cause a Newton-based algorithm to fail.19

Solution of Equations (11)–(13) with Newton’s methods

Again Newton’s methods require four steps.

sparse-matrix code that is available in MATLAB or TROLL and we do not anticipate thatthis will be a problem for versions of the model that include many country blocks.

19Several Newton-based algorithms, which have been developed over the years, haveattempted to solve convergence failure problems automatically without the assistance of theuser and now are available in both TROLL and MATLAB. However, for researchersinterested in extending the GEM in nontrivial ways it is essential that they have someunderstanding of what the algorithms are doing. To facilitate this learning process we havedeveloped some very simple TROLL programs with small examples that allow researchers toexperiment with alternative starting values and solution techniques.


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Step #1: To solve the system defined by (11), (12), and (13) with Newton’smethod, it is necessary to construct the Jacobian matrix of partial derivativeswith respect to the endogenous variables. In this particular example theJacobian of F (Y,X)¼ 0 is the following matrix.

qFqY¼

�1 1 0

2y1 2y2 0

�y�11 0 1

2664

3775: (14Þ

Note that in this example the Jacobian depends on the values of y1 and y2because the model is nonlinear.

Step #2: Starting from an initial guess for (y1, y2, y3), the system F(Y,X)can then be evaluated to determine if all of the equations in the system areconsistent with these starting guesses. Define residuals (RES1, RES2, RES3)for Equations (11)–(13) as the difference between the LHS and RHS of eachequation. In the simple example above, if the initial values for (y1, y2, y3) wereall set equal to 0.1 the values for (RES1, RES2, RES3) would be (0, �1.9800,2.4026) and the numerical version of the Jacobian in this initial iterationwould be the following:

qFqY¼

�1 1 0

0:2 0:2 0

�10 0 1

2664

3775: (15Þ

Step #3: Starting from this initial guess of Y, Y(0), we can then solve

qFY ðkÞ

qY

" #DY ðkÞ ¼ �F ½Y ðkÞ�; (16Þ

Figure 9. Example of a Simple Nonlinear Model

(0, -1.41)

(1, 1)

(0, 1.41)

Y1

Y2

(1.41, 0)(-1.41, 0)

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to calculate a Newton step,

DY ðkÞ ¼ � qFY ðikÞ

qY

" #�1F ½Y ðkÞ�; (17Þ

and then perform a series of Newton iterations Ykþ 1¼YkþDYk. In thesimple example above, if the initial starting values for (y1, y2, y3) are(0.1, 0.1, 0.1), then (16) becomes

�1 1 0

0:2 0:2 0

�10 0 1

2664

3775DY ð1Þ ¼

0

�1:9800

2:4026

2664

3775; (18Þ

and solving this results in the following Newton step.

DY ð1Þ ¼

yð1Þ1

yð1Þ2

yð1Þ3

26664

37775 ¼

yð0Þ1 þ Dyð0Þ1

yð0Þ2 þ Dyð0Þ2

yð0Þ3 þ Dyð0Þ3

26664

37775 ¼

5:0500

5:0500

47:1971

264

375: (19Þ

As can be seen from (19), a linearization of the model initially around thepoints for (y1, y2, y3) equal to (0.1, 0.1, 0.1) results in a big Newton step thatsignificantly overshoots the true solutions for (y1, y2, y3). However as can beseen in Table 1, which reports the process of convergence after the firstiteration, an extremely accurate approximation of the true solution isachieved within six Newton iterations. This simple example illustrates anumber of points about some of the properties of Newton’s method.

1. Even in cases when the starting guesses are a long way from the truesolution, if Newton’s method does converge, in some cases it can performvery well. However, this is not a general result and will depend onthe types of nonlinearities in the model. If the initial guesses for theendogenous variables are a long way from the true solution there can beconvergence problems. This obviously poses a more serious problem forresearchers who are attempting to build models from scratch as they maynot have any previous experience picking starting values.

2. If the starting guesses are in the neighborhood of the true solution whereperturbations are well approximated by a linearized version of the model,then Newton’s method will find the true solution extremely quickly in afew iterations. Thus, once a solution has been obtained that can be usedas starting values in future computations it is very difficult to beatNewton-based methods with other methods.

3. The solution from Newton’s method is extremely accurate.4. Newton’s method is not foolproof and does require some knowledge of

the structure of the model to use it efficiently. In the nonlinear exampleabove, had the researcher used starting guesses that were negative instead


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of positive, Newton’s method would have attempted to converge to asolution where y1 and y2 was equal to �1. In these cases the convergenceprocess would have failed as the computer would have attempted to takethe log of a negative number. Furthermore, because the convergenceprocess depends on the analytical form of the Jacobian, which in turndepends on exactly how each of the equations has been coded, this canaffect the convergence process in significant ways.20

Solving the GEM with DAC algorithms

As we have tried to illustrate in the previous section, Newton-basedalgorithms in some cases can provide a very powerful tool for derivingthe steady-state solution of the model. This is particularly the case whenthe model has already been developed so that previous solutions andexperience working with the model can be drawn upon to developgood starting guesses for the endogenous variables. However, whenbuilding a model from scratch there are two approaches to solving forthe initial steady-state equilibrium. One approach is to code the modeland then fiddle with the initial values for the endogenous variables untilthe model builder finds a solution. This approach can be time consumingand difficult to replicate. The second approach is to employ a DACstrategy.

A DAC strategy involves breaking problems that are difficult tosolve into a series of problems that are easier to solve. The particular DACstrategy that is employed here exploits what is known about the two

Table 1. Newton’s Method Applied to the Simple Nonlinear Three-EquationExample

Iteration y1 y2 y3

0 0.1 0.1 0.1

1 5.0500 5.0500 47.1971

2 2.6240 2.6240 1.1390

3 1.5026 1.5026 0.5373

4 1.0840 1.0840 0.1286

5 1.0033 1.0033 0.0062

6 1.0000 1.0000 0.0000

20One of the example programs in TROLL is a three-equation model that consists ofEquations (11)–(13). To understand the importance of how the equations are coded weprovide a number of exercises including replacing the equation y1

2þ y22�x1¼ 0 with

y1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix1 � y22

qto show how strategies for choosing starting values depend on how the

equations are coded. Interestingly, aside from kinks caused by the zero interest rate floor mostof the nonlinearities in DSGE models can be well approximated by the training examples onthese extremely simple examples.

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most basic properties of Newton’s solution method for solving largesystems of nonlinear equations. First, as shown in one of the examplesabove if the model is linear, Newton’s method is guaranteed to find asolution in one iteration. Second, if the model does not contain largenonlinearities Newton’s method will find the solution extremely rapidly.These two properties suggest a very simple DAC strategy that involvesinitially finding the solutions of versions of a model that is easier to solve andthen using these solutions as starting values for solving more complicatedversions.

Very simple example of a DAC algorithm

The simplest example of a DAC strategy that is used to solve for the GEM’ssteady state is when we already have a solution for a steady state based onsome existing calibration of the model, but we would like to obtain anothercalibration of the model with nontrivial changes in either the structuralparameters or the exogenous variables. For example, after a model has beendeveloped and an initial steady-state solution to the model exists we will havea solution to (20),

FðY ð0Þ;X ð0Þ; yð0ÞÞ ¼ 0; (20Þwhere Y(0) is an initial vector of endogenous variables; X(0) is an initial vectorof exogenous; and y(0) is an initial vector of parameters. In this case if wewant to develop a new calibration of the model that is based on differentassumptions for the parameters y and exogenous variables X (say y(t) andX(t)) we may want to start with the existing values of Y(0), y(0), and X(0) andthen gradually eliminate the difference between (20) and what we would liketo compute which is (21).

FðY ðtÞ;X ðtÞ; yðtÞÞ ¼ 0: (21ÞThus, based on our knowledge of the fundamental property of Newton-basedalgorithm, which is that it will find the true solution extremely quickly whenthe starting values for Y are in the neighborhood of the true solution Y(t), wecan define a DAC step j so that each DAC step defined by (22)

FðY ðjÞ;X ðjÞ; yðjÞÞ ¼ 0; (22Þis always in the neighborhood of the last solution F(Y ( j�1)),X ( j�1), y( j�1)¼ 0.

Interestingly, the discussion above did not say anything about the choiceof the magnitude of the DAC steps, partly because it does not matter much inpractice given the efficiency of available sparse matrix code. Thus far,we have only experimented with two types of simple methods for determiningthe length of each DAC step, and we plan to leave it to others to experimentwith other procedures for determining the optimal length of each DACstep for the particular problem that they are interested in. We would liketo emphasize that this simple DAC approach is quite general and has alsobeen used to solve perfect foresight problems on the nonlinear versions of


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the models using the stacked-time algorithms available in TROLL’ssimulation toolbox.

Strategies for getting initial solutions for new or extended models

The discussion above suggests a very simple strategy for obtaining solutionsfor models where there are no previous solutions or for models that containsignificant nonlinearities. Recall, a basic property of this approach is that ifany solution can be found to a model it is relatively straight forward to findalternative solutions using previous solutions as starting points.

For two-country models like GEM depicted in Figure 2 this suggests avery simple robust and efficient strategy for obtaining steady-state calibra-tions of the models. For example, assuming countries have identical size,tastes, and production capabilities we will know in advance that relativeprices such as the real exchange rate will be equal to 1 in the initial steadystate. Thus, one strategy for obtaining a solution for a two-country model isto start off with assumptions for parameter and exogenous variables thatmake it easier to guess values for the endogenous variables and then usethese solutions as guesses for the desired calibration. In addition, models likeGEM will generally contain functions that include parameters values thatsimplify functions in ways that make it easier for model builders to knowmore about the solutions. For example, it is well known that CES functionsnest Cobb Douglas functions and for the case of the latter the exponents willrepresent share parameters, such as labor or capital’s income share in aproduction function. Thus, one strategy is to start off with elasticities ofsubstitution that are close to 1 and then once a solution has been foundto take a series of DAC steps to move these parameter values to theirdesired levels.

Strategies for getting steady-state calibrations quickly and reliably

In most cases researchers may want to obtain a calibration for the steadystate that is consistent with desired values for the model’s endogenousvariables. For example, the researcher may want to calibrate certain variablessuch as trade, consumption, or investment measured as a share of GDP to beconsistent with particular average values from the national accounts.Obviously, in a general equilibrium model the values for these variableswill depend on a significant number of parameter values that are related tothe underlying demand and supply functions in the model and it would be avery time-consuming process to change these parameters to obtain resultsthat are close to the desired calibration. To facilitate efficient and robustcalibrations of the models we have developed procedures that temporarilymake certain endogenous variables exogenous and then find the values ofsome truly exogenous variables or parameters that will support anequilibrium where these endogenous variables are tuned to their desiredvalues. For example, if we desire a particular value of the real exchangerate and the export-to-GDP ratio in a particular country we will typically

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back out a taste parameter in the utility function that will determine thedemand for imports in the two countries, which given an assumption forbalanced trade and export supply functions, will determine trade flowsand the equilibrium real exchange rate. In the programs that have beendeveloped to calibrate GEM this mapping includes a large number ofvariables and users are provided a list of variables that they will need targetvalues for to obtain a calibration relatively quickly. Again, this process offinding the desired calibration is both robust and efficient because of theDAC algorithms.

III. Model Development Priorities

There are two major areas for future development both inside and outside theFund. The first involves improving the IMF’s DSGE models’ structures toinclude better macrofinancial linkages and the second involves exploitingBayesian methods to take the models to the data. This section discusses a bitof the work that is already underway or is in the planning stage.

Significant effort has been underway for some time now in both academiaand policymaking institutions to create models with better macrofinanciallinkages. Having extended the basic analytical structure of modern DSGEmodels so that we can capture the effects of fiscal policy, the Modeling Unithas started to incorporate different types of financial accelerators into GIMFand smaller DSGE models that focus on specific issues.21 These features willallow us to better understand the implications of boom and bust cyclescaused by the interaction of bank credit and shocks that cause largemovements in asset prices. More importantly, unlike reduced-formeconometric models, which may be very useful for conjunctural analysis,these extended DSGE models will contain sufficient structure that shouldallow us to study the role of different types of policies for minimizing theeconomic costs associated with these boom and cycles.22

Over the last few years there have been enormous advances applyingBayesian methods to macromodels. Most of the work thus far has been oneither single country open-economy models or closed economy models.23

Applying these methods to multicountry versions of the models presentssome difficult challenges given the large number of structural parameters andstochastic processes that will need to be estimated. However, the potentialpayoff is enormous as Bayesian methods offer many advantages overclassical estimation procedures. First, at a general level they will be veryuseful in helping to bridge the enormous gap between econometric theory

21A similar project is underway at the Bank of Canada and European Commission toincorporate stronger macrofinancial linkages into GEM and QUEST and at some point wewill do a formal model comparison exercise that includes all three models.

22We also have a project underway to build a small-scale, reduced-form, multicountrymodel that can be used for forecasting and risk assessments.

23See Smets and Wouters (2004); Juillard and others (2005); Edge, Kiley, and Laforte(2006); Juillard and others (2007, 2008); and Adolfson and others (forthcoming).


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and how model builders parameterize models in practice. Second, byexplicitly accounting for and penalizing the use of priors in the model-building process they will allow us to do more meaningful statisticalinference. Third, in models where some parameters are weakly identified bythe data and classical procedures break down, the use of priors can helpprevent the model’s parameters from wondering off into implausible regions.This robustness property of Bayesian methods can be very helpful in themodel-building process as it provides solutions that can be analyzed. Fourth,in practice model builders can specify fairly flexible stochastic processes,which are necessary in many cases to generate sensible expectations andimpulse response functions for standard shocks. Fifth, the number ofstochastic shocks can be larger than the number of observable variables,allowing the model to interpret new data and to generate predictions that aremuch more flexible than by using classical procedures on models whereparameters are weakly identified. Sixth, the estimation strategy does not haveto involve prefiltering of data and in such circumstances there will be a bettermapping between the models in-sample fit and forecasting ability. Seventh,the model is estimated as a system, which in practice can be expected toperform better when there is important simultaneity, which is the basicnature of any DSGE model. Eighth, the presence of units roots does notcreate the enormous problems that are generated from classical econometrictheory. Ninth, economists and policymakers are interested as much inthe underlying uncertainty in the parameters estimates as they are in theunderlying point estimates. Forecasters and policymakers are keenlyinterested in how parameter uncertainty translates into measures offorecast confidence bands and how tail risks might influence their decisionsand the potential costs of making the wrong decisions. These are only someof the many practical benefits of Bayesian estimation procedures, and givenrecent advances in developing user-friendly routines to deploy theseprocedures to a much wider group of people it is very likely that morepeople will abandon their old ways of doing things and become interested inthem.

REFERENCESAdolfson, M., S. Laseen, and J. Lind, forthcoming, ‘‘Evaluating an Estimated

New Keynesian Small Open Economy Model,’’ Journal of Economic Dynamics andControl, (October), pp. 1–32.

Armstrong, J., R. Black, D. Laxton, and D. Rose, 1998, ‘‘A Robust Method forSimulating Forward-Looking Models,’’ Journal of Economic Dynamics and Control,Vol. 22, pp. 489–501.

Bayoumi, T., D. Laxton, and P. Pesenti, 2004, ‘‘Benefits and Spillovers of GreaterCompetition in Europe: A Macroeconomic Assessment,’’ ECB Working Paper No.341 (Frankfurt, European Central Bank).

_______, and others 2004, ‘‘GEM: A New International Macroeconomic Model,’’ IMOccasional Paper No. 239 (Washington, International Monetary Fund).

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Black, R., D. Laxton, D. Rose, and R. Tetlow, 1995, ‘‘The Bank of Canada’s NewQuarterly Projection Model: The Steady-State Model,’’ Technical Report No. 72(Ottawa, Bank of Canada), January.

Blanchard, O., 1985, ‘‘Debt, Deficits, and Finite Horizons,’’ Journal of Political Economy,Vol. 93, pp. 223–47.

Botman, D., D. Muir, D. Laxton, and A. Romanov, 2006, ‘‘A New-Open-Economy-Macro Model for Fiscal Policy Evaluation,’’ IMF Working Paper 06/045(Washington, International Monetary Fund).

_______, P. Karam, D. Laxton, and D. Rose, 2007, ‘‘DSGE Modeling at the Fund:Applications and Further Developments,’’ IMF Working Paper 07/200 (Washington,International Monetary Fund).

Boucekkine, R., 1995, ‘‘An Alternative Methodology for Solving Nonlinear Forward-Looking Models,’’ Journal of Economic Dynamics and Control, Vol. 19, No. 4,pp. 711–34.

Brayton, F., and P. Tinsley, 1996, ‘‘Guide to FRB/US: A Macroeconometric Model forthe United States,’’ Federal Reserve Board, FEDS Working Paper 1996-42.

Bryant, Ralph C., Peter Hooper, and Catherine L. Mann, 1993, Evaluating PolicyRegimes: New Research in Empirical Macroeconomics (Washington, BrookingsInstitution).

Coletti, D., B. Hunt, D. Rose, and R. Tetlow, 1996, ‘‘Bank of Canada’s New QuarterlyProjection Model. Part 3, The Dynamic Model: QPM,’’ Technical Report No. 75(Ottawa, Bank of Canada).

Corsetti, G., and P. Pesenti, 2005, ‘‘International Dimensions of Optimal MonetaryPolicy,’’ Journal of Monetary Economics, Vol. 52, No. 2, pp. 281–305.

Edge, R., M. Kiley, and J.P. Laforte, 2006, ‘‘A Comparison of Forecast PerformanceBetween Federal Reserve Forecasts, Simple Reduced-Form Models, and a DSGEModel,’’ (unpublished).

Erceg, C., L. Guerrieri, and C. Gust, 2005, ‘‘SIGMA: A New Open Economy Model forPolicy Analysis,’’ Working Paper, Federal Reserve Board.

Hollinger, P., 1996, ‘‘The Stacked-Time Simulator in TROLL: A Robust Algorithm forSolving Forward-Looking Models,’’ paper presented at the Second InternationalConference on Computing in Economics and Finance, Geneva, Switzerland,June 26–28, Needham, Massachusetts.

Juillard, M., 1996, ‘‘DYNARE: A Program for the Resolution and Simulation ofDynamic Models With Forward Variables Through the Use of a RelaxationAlgorithm,’’ CEPREMAP Working Paper No. 9602 (Paris, France, CEPREMAP).

Juillard, M., O. Kamenik, D. Laxton, and M. Kumhof, 2007, ‘‘Optimal Price Setting andInflation Inertia in a Rational Expectations Model,’’ Journal of Economic Dynamicsand Control, (October), pp. 1–38.

Juillard, M., P. Karam, D. Laxton, and P. Pesenti, 2005, ‘‘Welfare-Based MonetaryPolicy Rules in an Estimated DSGE Model of the US Economy,’’ Working Paper.

_______, 2007, ‘‘Measures of Potential Output from an Estimated DSGE Model of theUnited States,’’ paper presented at a workshop on ‘‘Issues in Measuring PotentialOutput,’’ Ankara, Turkey, January 16.

Juillard, M., D. Laxton, H. Pioro, and P. McAdam, 1998, ‘‘An Algorithm Competition:First-Order Techniques Versus Newton-Based Techniques,’’ Journal of EconomicDynamics and Control, Vol. 22, pp. 1291–18.


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Kumhof, M., and D. Laxton, 2007, ‘‘A Party Without a Hangover? On the Effects ofU.S. Fiscal Deficits,’’ IMF Working Paper 07/202 (Washington, InternationalMonetary Fund).

Laffargue, J.P., 1990, ‘‘Resolution d’un Modele Macroeconomique Avec AnticipationsRationnelles,’’ Annales d’Economie et Statistique, Vol. 17, pp. 97–119.

Laxton, D., and P. Pesenti, 2003, ‘‘Monetary Rules for Small, Open, EmergingEconomies,’’ Journal of Monetary Economics, Vol. 50, No. 5, pp. 1109–52.

_______, and others 1998, ‘‘MULTIMOD Mark III: The Core Dynamic andSteady-State Models,’’ IMF Occasional Paper No. 164 (Washington, InternationalMonetary Fund).

Masson, P., S. Symansky, and G. Meredith, 1990, ‘‘MULTIMOD MARK II: A Revisedand Extended Model,’’ IMF Occasional Paper No. 71 (Washington, InternationalMonetary Fund).

Murchison, S., and A. Rennison, 2006, ‘‘TOTEM: The Bank of Canada’s New QuarterlyProjection Model,’’ Bank of Canada Technical Report No. 97 (Ottawa, Bank ofCanada).

Obstfeld, M., and K. Rogoff, 1995, ‘‘Exchange Rate Dynamics Redux,’’ Journal ofPolitical Economy, Vol. 103, pp. 624–60.

_______, 1996, Foundations of International Macroeconomics (Cambridge, Massachusetts,MIT Press).

Sims, C, 2002, ‘‘The Role of Models and Probabilities in the Monetary Policy Process,’’Brookings Papers on Economic Activity, Vol. 2, pp. 1–40.

Smets, F., and R Wouters, 2004, ‘‘Shocks and Frictions in Business Cycles: A BayesianDSGE Approach,’’ ECB Working Paper (Frankfurt, European Central Bank and theNational Bank of Belgium).

Taylor, J., 1993,Macroeconomic Policy in a World Economy: From Econometric Design toPractical Operation (New York, W.W. Norton).

_______, 2000, ‘‘Low Inflation, Pass-Through and the Pricing Power of Firms,’’ EuropeanEconomic Review, Vol. 44, pp. 1389–408.

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The Global Economy Model: Theoretical Framework

PAOLO PESENTI�

This paper has two purposes. First, it provides a thorough exposition of thetheoretical framework underlying the Global Economy Model (GEM), as themodel stands in early 2008. Second, it discusses a number of variants andalternative features considered in the GEM-related literature since Laxton andPesenti (2003). For an updated survey of GEM and other dynamic, stochastic,general-equilibrium applications at the IMF, the reader is referred to Botmanand others (2007). Each section starts with a formal description of the relevantequations, and is followed by a presentation of modeling variants and options.When appropriate, the section provides a more detailed discussion of how thebuilding blocks of GEM relate to the literature. It is worth emphasizingfrom the very beginning that the paper is meant to be used as a technicalreference on GEM and related models, with apologies for the somewhatpedantic attention to details and formulas that stems directly from this premise.[JEL E27, E37, F37, F47]

IMF Staff Papers (2008) 55, 243–284. doi:10.1057/imfsp.2008.8

I. Peeking Inside the Box: Model Structure and Basic Notation

Building on recent theoretical developments in international finance andmonetary economics, especially the ‘‘new open-economy macroeconomics’’literature since the seminal contributions of Maurice Obstfeld and KennethRogoff (1995, 2000, 2002), the Global Economy Model (GEM) aims to

�Paolo Pesenti is an assistant vice-president with the Federal Reserve Bank of New Yorkand an associate of the Centre for Economic Policy Research and the National Bureau ofEconomic Research.



243


provide an optimizing intertemporal framework capable of addressing basicpolicy questions involving international transmission of policy and structuralshocks, while reproducing key elements of macroeconomic interdependenceamong countries and regional blocs.

Like other recent dynamic, stochastic, general-equilibrium (DSGE)models, the design of GEM combines the long-run properties of realbusiness cycle models with short-run ‘‘Keynesian’’ dynamics stemming fromnominal rigidities and inertia in the inflation process. Although obviouslyindebted to the classic Mundell-Fleming-Dornbusch tradition, GEM buildson explicit microfoundations allowing for a tightly integrated treatment ofpositive elements and welfare considerations.

A useful way to approaching GEM is by familiarizing oneself with itsbroad characteristics and notation with the help of a visual representation.Figure 1 illustrates the key macroeconomic variables in a representativecountry.

Consider first the households sector. Each household consumes a finalgood (C in Figure 1), and supplies labor ð‘Þ to all domestic firms. Somehouseholds do not have access to capital markets. They finance theirconsumption exclusively through disposable labor incomes. The remaininghouseholds own the portfolio of domestic firms and the domestic capitalstock (K), which they rent to domestic firms. They also buy and sell twobonds: a domestic bond denominated in domestic currency, and aninternational bond issued in zero net supply worldwide. When householdssell or purchase the international bond they pay a premium to financialintermediaries, whose size is a function of the aggregate net asset position ofthe country. Labor and physical capital are immobile internationally. The

Figure 1. The Structure of the Model

I

E

GI

GN

K

C Gc

A

N

T

Q MAbroad

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market for capital is competitive, and capital accumulation is subject toadjustment costs. In the labor market, wage contracts are subject to nominalrigidities.

On the production side, firms produce the final goods, an array ofdifferentiated intermediate goods, and provide intermediation services.

In each country there are two final goods—a consumption good (A) andan investment good (E )—produced by perfectly competitive firms. Theconsumption good is consumed either by domestic households or by thegovernment (GC). Similarly, demand for the investment good is split betweenprivate agents (I ) and the public sector (GI). Final goods are produced byusing all available intermediate goods as inputs.

There are many varieties of intermediate goods, each produced by a singlefirm under conditions of monopolistic competition. Each intermediate goodis produced by using domestic labor inputs and domestic capital.Intermediate goods are either nontraded (N ) or traded internationally (T ).The nontraded intermediate goods can be purchased by the government (GN)or used in the production of the final goods (NN). Domestic tradables used bydomestic firms are denoted Q, imports from all other country blocs aredenoted M. Imports are subject to short-term adjustment costs thattemporarily lower the response of demand to changes in relative prices.Prices of intermediate goods are subject to adjustment costs (nominal pricerigidities).

Finally, the government purchases the two national final goods, as well asnontradable services. As treasury, the government finances its expenditureswith net taxes on the domestic private sector. As central bank, thegovernment manages the national short-term nominal interest rate.Monetary policy is specified in terms of a credible commitment toguarantee price stability by managing the domestic nominal short-terminterest rate.

II. General Considerations

Country Size

The world economy consists of a set N of regional blocs (‘‘countries’’). Thesize of the world economy is normalized to one. The size of each country H isdenoted sH, with 0osHo1 and

PHs

H¼ 1 for H 2N. The country sizemeasures the world share of private agents who are resident in the country:both households and firms in country H are defined over a continuum ofmass sH.

Discussion

For applications focused on short- and medium-term analysis, the countrysize sH can be treated as a constant parameter. This specification isproblematic in simulation exercises in which one or more countries grow fora prolonged period of time below (or above) the common trend (the latter is

THE GLOBAL ECONOMY MODEL: THEORETICAL FRAMEWORK

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defined below). In these cases, maintaining the country size constant overtime leads to an upward (downward) bias of the long-term economicrelevance of these countries in a global context. Also, because the number ofproduct varieties and labor inputs in each country is normalized to sH,constant country sizes imply that the sectoral extensive margins (thenumber of firms and varieties in any given sector) remain constant overtime as well, and there is no labor immigration. For the time being, thecurrent version of GEM does not encompass endogenous firms’ entryand exit across sectors and countries. A possible way to deal with theseissues is to let sH be time varying and equal (for instance) to the size of GDP(or alternative measures of a country’s economy) in country H relativeto the world GDP. The model-based notion of GDP is discussed later, inSection IV.

Growth Trend

There is a common stochastic trend for the world economy (the variableTREND), whose gross rate of growth between time t and time t is denotedgt, t�TRENDt/TRENDt. All quantity variables in each country areexpressed in detrended terms, that is, as ratios of TREND. The exceptionis labor effort ‘, bounded by endowment. In the long run, gt, tþ 1 converges togSS and gt, t converges to gSS

t�t, where gSS is a constant.

Discussion

Each (detrended) real variable is stationary, that is, it converges to a well-defined steady-state level. This applies to all relative prices, including terms oftrade and real exchange rates. In the long term there is balanced growth (atthe rate g) across countries and sectors. The assumption is less restrictivethan it appears, as it is always possible to engineer persistent (albeit notpermanent) deviations from balanced growth for an arbitrarily long period oftime. Variants of the model could be considered to account for unit roots inrelative prices, but they are not discussed here.

Prices and Inflation Rates

As a convention throughout the model, nominal prices expressed in domesticcurrency are denoted with uppercase variables, but relative prices are denotedwith lowercase variables. Without loss of generality, in each country theconsumption good A is the numeraire of the economy and all nationalrelative prices are expressed in terms of domestic consumption units, that isrelative to the consumer price index (CPI). For instance, if PA denotes thenominal CPI and PE the nominal price of one unit of the E good, pE�PE/PA

denotes the price of one unit of E in terms of A. Of course, by definition wehave pA¼ 1.

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Also we denote the (gross) CPI inflation rate between time t and time twith pt, t�PA, t/PA, t. The inflation rate in sector E is therefore equal to

pEt;t �pE;t

pE;tpt;t: (1Þ

In steady state the inflation rate pt, tþ 1 converges to pSS and pt, t converges topSSt�t, where pSS is a constant equal to the inflation target of the government.

Discussion

GEM is coded up after transforming all prices in relative terms, so thatnominal prices do not appear in the model. Precisely for the same reason whyall quantities are defined in detrended terms, by normalizing all prices relativeto the domestic nominal trend PA we avoid dealing with unit roots, eithernominal or real, in quantitative simulations of the model over very long timehorizons. Because the inflation rate pt, t is part of the model solution, one canalways reconstruct the nominal path for the CPI level by arbitrarily settingthe value of PA at some initial time t¼ 0 and computing PA, t¼PA, 0p0, t. Inthe main text we typically adopt the notation with relative (lowercase) prices.We only switch to the notation with nominal (uppercase) variables whenappropriate in order to simplify the exposition.

As observed above, all relative prices p converge to well-defined steady-state levels. If two countries have different steady-state inflation rates,reflecting different policy preferences for the domestic nominal anchor, insteady state the nominal exchange rate between the two countries depreciatesat a rate equal to the difference between the two inflation rates but theCPI-based real exchange rate remains constant. We return to this point inSection III.

Usually inflation variables carry a double time index. In most appli-cations time t is measured in quarters, so that pt�1, t measures the quarterlyinflation rate at time t, (pt�1, t)

4 measures the annualized quarterly inflationrate at time t, and pt�4, t measures the year-over-year inflation rate at time t.When there is no risk of confusion, we adopt the notation pt as shorthand forquarterly inflation pt�1, t.

Notational Conventions and Other Formal Aspects

The convention throughout the model is that variables that are not explicitlyindexed (to firms or households) are expressed in domesticper-capita terms. For instance, At� (1/s)

Rs0At(x) dx and ‘t � ð1=sÞð

R s0 ‘tðnÞ

dnþR s0 ‘tðhÞdhÞ. Variables without time indices as well as variables with

subscript SS are used interchangeably to denote steady-state levels. Forinstance, gSS¼ g.

GEM allows for a rich menu of stochastic processes. As a generalconvention throughout the model, when we state that variable X follows an


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autoregressive process, we mean that the process for X is coded as

Xt ¼ ð1� lXÞXSS þ lXXt�1 þ eX;t; (2Þ

where 0olXo1, XSS is the steady-state value of Xt, and eX, t is an i.i.d.shock. If variable X is strictly positive, a logarithmic transformation isconsidered:

lnXt ¼ ð1� lXÞ lnXSS þ lX lnXt�1 þ eX ;t: (3Þ

Needless to say, the assumptions about the dynamic structure of therandom variables and the variance-covariance matrix play a crucial role involatility exercises. In general, alternative specifications of the stochasticprocesses can be introduced, depending on the specific nature of thesimulation project.

It is worth emphasizing that GEM has been developed and coded up innonlinear terms. This choice not only enhances the transparency of the modelcode relative to the theoretical apparatus but also allows for seamless higher-order extensions of the analysis beyond the traditional first-orderapproximations around the nonstochastic steady state. This flexibility isparticularly relevant for welfare analyses involving at least second-orderexpansions around the steady-state equilibrium. In one case below, however,we find it useful to focus the presentation on the linear approximations of theGEM equations, in order to facilitate the comparison between ourframework and similar analytical models.

III. The Domestic Macroeconomy in Partial Equilibrium

This section is devoted to the country-specific elements of the model that donot involve international interactions. Thus, in what follows we consider arepresentative country under the working assumption that trade-relatedvariables are exogenous and determined outside the equilibrium. For thisreason, country-specific indices play no role in this section. Generalequilibrium considerations and a fuller notation involving country indicesare introduced in Section IV.

Final Goods

In each country there is a continuum of symmetric firms producing two finalgoods, A (the consumption good) and E (the investment good). Both goodsare produced under perfect competition.

Consider first the consumption sector. Each firm is indexed by xA[0, s].Firm x’s output at time t is denoted At(x). The consumption good isproduced with the following nested constant elasticity of substitution

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248


(CES) technology:

AtðxÞ ¼(ð1� gAÞ

1eANA;tðxÞ1�

1eA þ g

1eAA

"n

1mAA QA;tðxÞ

1� 1mA

þð1� nAÞ1mAMA;tðxÞ

1� 1mA

# mAmA�1 1� 1

eA

� �) eAeA�1

ð4Þ

Three intermediate inputs are used in the production of the consumptiongood A: a basket NA of nontradable goods, a basket QA of domestic tradable(import-competing) goods, and a basket MA of imported goods. Theelasticity of substitution between tradables and nontradables is eA>0, andthe elasticity of substitution between domestic and imported tradables ismA>0. The weights of the three inputs are, respectively, 1�gA, gAnA andgA(1�nA) with 0ogA, nAo1.

Firm x takes as given the prices of the three inputs and minimizes its costspNNA(x)þ pQQA(x)þ pMAMA, t(x)subject to the technological constraint (4).Cost minimization implies that firm x’s demands for intermediate inputs are

NA;tðxÞ ¼ ð1� gAÞp�eAN;t AtðxÞ; (5Þ

QA;tðxÞ ¼ gAnAp�mAQ;t p

mA�eAXA;t AtðxÞ; (6Þ

MA;tðxÞ ¼ gAð1� nAÞp�mAMA;tpmA�eAXA;t AtðxÞ; (7Þ

where pN, pQ, and pMA are the relative prices of the inputs in terms of finalconsumption baskets, and pXA is the cost-minimizing price of the compositebasket of domestic and foreign tradables, or:

pXA;t � ½nAp1�mAQ;t þ ð1� nAÞp1�mAMA;t �1

1�mA : (8Þ

The production technologies in the consumption and investment sectors canbe quantitatively different but their formal characterization is similar, withself-explanatory changes in notation. For instance, a firm eA[0, s], thatproduces the investment good, demands nontradable goods according to

NE;tðeÞ ¼ ð1� gEÞðpN;t=pE;tÞ�eEEt: (9Þ

Discussion

Note that pMA and pME are sector-specific as they reflect the differentcomposition of imports in the two sectors, but pN and pQ are identical acrosssectors. In Section IV we discuss the role of import adjustment costs and theireffects on relative prices.


249


The weights gA, nA, gE, and nE can be modeled as constant parameters oras autoregressive processes. In the latter case, they can be interpreted aspreference shifters, reflecting shifts in households’ consumption demand fromtradables to nontradables, or from import-competing goods to foreignimports.

The CES specification is notationally cumbersome but widely adopted inDSGE models to allow for a flexible parametrization of elasticities. Ofcourse, when the elasticities are equal to one the equations collapse to thetraditional Cobb-Douglas specification. In most applications the elasticitiesof substitution between import-competing goods and imports, mA and mE, arelikely to be larger than the elasticities of substitution between nontradablesand tradables, eA and eE. Note however that there are no theoreticalrestrictions on the size of these elasticities.

Demand for Intermediate Goods

Intermediate inputs come in different varieties (brands) and are producedunder conditions of monopolistic competition. In each country there are twokinds of intermediate goods, tradables and nontradables. Each kind isdefined over a continuum of mass s. Without loss of generality, we assumethat each nontradable good is produced by a single domestic firm indexed bynA[0, s], and each tradable good is produced by a firm hA[0, s].

Focusing first on the basket NA, this is a CES index of all domesticvarieties of nontradables. Denoting as NA(n,x) the demand by firm x of anintermediate good produced by firm n, the basket NA(x) is

NA;tðxÞ ¼1

s

� � 1yNZ s

0

NA;tðn;xÞ1�1yNdn

24

35

yNyN�1

; (10Þ

where yN>1 denotes the elasticity of substitution among intermediatenontradables.

Firm x takes as given the prices of the nontradable goods p(n) andminimizes its costs

R0sp(n)NA, t(n,x) dn subject to (10), obtaining

NA;tðn;xÞ ¼1

s

ptðnÞpN;t

� ��yNNA;tðxÞ; (11Þ

where pN (the Lagrange multiplier) is the cost-minimizing price of one unit ofthe nontradable basket, or

pN;t ¼1

s

� �Z s

0

ptðnÞ1�yNdn� � 1

1�yN: (12Þ

The basket NE is similarly characterized. Aggregating across firms, andaccounting for public demand of nontradables—here assumed to have thesame composition as private demand—we obtain the total demand for

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250


good n asZ s

0

NA;tðn;xÞdxþZ s

0

NE;tðn; eÞdeþ GN;tðnÞ

¼ ptðnÞpN;t

� ��yNðNA;t þNE;t þ GN;tÞ ¼

ptðnÞpN;t

� ��yNNt; ð13Þ

where NA, t¼ (1/s)R0sNA, t(x) dx (and similar).

Following similar steps we can derive the domestic demand schedules forthe intermediate goods h:Z s

0

QA;tðh;xÞdxþZ s

0

QE;tðh; eÞde ¼ptðhÞpQ;t

� ��yTQt: (14Þ

Demand for imported intermediate goods will be characterized below.

Discussion

The elasticity of substitution y, either in the nontradables or the tradablessector, can be modeled as a constant parameter or as a time-varyingstationary process.

In Section IV we discuss how (13) changes when distribution services areconsidered.

Supply of Intermediate Goods

Each nontradable good n is produced with the following CES technology:

NtðnÞ ¼ ZN;t ð1� aNÞ1xN ‘tðnÞ

1� 1xN þ a

1xNN KtðnÞ

1� 1xN

" # xNxN�1

: (15Þ

Firm n uses labor ‘ðnÞ and capital K(n) to produce N(n) units of its variety.xN>0 is the elasticity of input substitution, and ZN is a stochastic process forproductivity, common to all producers of nontradables.

Following the notational convention regarding prices, we let mct, wt, andrt denote marginal costs, wages, and rental rates in consumption units. Firmn minimizes its costs wt‘tðnÞ þ rtKtðnÞ subject to (15). Cost minimizationyields the marginal cost in nontradables production as

mctðnÞ ¼1

ZN;tfð1� aNÞw1�xN

t þ aNr1�xNt g

11�xN ; (16Þ

and the capital-labor ratio is

KtðnÞ‘tðnÞ

¼ aN1� aN

rt

wt

� ��xN: (17Þ

In each country, labor inputs are differentiated and come in differentvarieties (skills). Each input is associated to one household, defined over a


251


continuum of mass equal to the country size and indexed by jA[0, s]. Eachfirm n uses a CES combination of all available labor inputs:

‘tðnÞ ¼1

s

� � 1cL

Z s

0

‘ðn; jÞ1�1cLdj

24

35

cL

cL�1

; (18Þ

where ‘ðn; jÞ is the demand of labor input of type j by the producer of good nand cL>1 is the elasticity of substitution among varieties of labor inputs.Cost minimization implies that ‘ðn; jÞ is a function of the relative wage:

‘tðn; jÞ ¼1

s

wtð jÞwt

� ��cL

‘tðnÞ; (19Þ

where w(j) is the wage paid to labor input j and the wage index w is defined as

wt ¼1

s

� �Z s

0

wtð jÞ1�cLdj

� � 11�cL

: (20Þ

Similar considerations hold for the production of tradables. We denote byT(h) the supply of each intermediate tradable h. Using self-explanatorynotation, we have:

TtðhÞ ¼ ZT ;t ð1� aTÞ1xT ‘tðhÞ

1� 1xT þ a

1xTT KtðhÞ

1� 1xT

" # xTxT�1

; (21Þ

where ZT is total factor productivity. Aggregating across firms, we obtain thetotal demand for labor input j as:Z s

0

‘tðn; jÞdnþZ s

0

‘tðh; jÞdh ¼ wtð jÞwt

� ��cL 1

s

Z s

0

‘tðnÞdnþZ s

0

‘tðhÞdh� �

¼ wtð jÞwt

� ��cL

‘t; ð22Þ

where ‘ is per capita total labor in the economy.

Discussion

Recall that all variables are defined in detrended terms. The implicitassumption is that in each country the effectiveness of labor effort ‘ grows atthe same rate as TREND, so that a shock Z (either in the tradables or in thenontradables sector) is defined as a total factor productivity deviation fromthe common world trend. The model allows for country-specific changes in Zthat do not affect the long-run balanced-growth properties of the model.Therefore, one can consider a scenario in which the level of Z changespermanently, or one in which Z grows or falls for some time, but not ascenario in which Z grows or falls permanently in steady state. Variants of

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the model allow for the possibility of transitory shocks to the effectiveness oflabor or capital in addition to total factor productivity.

A variant of the model considered in Juillard and others (2006)introduces adjustment frictions in the labor market. The adjustment termsreflect the fact that it takes time for labor inputs to be fully productivein production, so that from the viewpoint of national producers theireffective costs are higher in the short term than in steady state. RewriteEquation (15) as

NtðnÞ ¼ ZN;t ð1� aNÞ1xN ‘�t ðnÞ

1� 1xN þ a

1xNN KtðnÞ

1� 1xN

" # xNxN�1

; (23Þ

where ‘�ðnÞ is ‘‘effective’’ labor, defined as the product of two components:

‘�t ðnÞ ¼ ‘tðnÞð1� GN ½‘tðnÞ�Þ: (24ÞIn the expression above, ‘ðnÞ is the same CES basket of differentiated laborinputs as defined in (18). However, now we assume that changes in labor aresubject to firm-specific adjustment costs. These costs are specified relative tothe past observed level of labor effort in the sector and are zero in steadystate. Specifically, GN ½‘ðnÞ� can be modeled as a quadratic term:

GN ½‘tðnÞ� ¼fL

2

‘tðnÞ‘N;t�1

� 1

� �2

; (25Þ

where as usual ‘N;t�1 ¼ ð1=sÞs0‘t�1ðnÞdn. In this case, expression (17) isreplaced by

KtðnÞ‘�t ðnÞ

¼ aN1� aN

rt

wt=ð1� GN;tðnÞ � ‘tðnÞG0N;tðnÞÞ

!�xN;

and the marginal cost mc(n) is given by

mctðnÞ ¼1

ZN;tð1� aNÞ

wt

1� GN;tðnÞ � ‘tðnÞG0N;tðnÞ

!1�xN

þaNr1�xNt

0@

1A

11�xN

:

(26ÞThe adjustment terms in Equation (26) reflect the fact that, if ‘tðnÞ differsfrom ‘N;t�1, producers’ costs are temporarily higher to account for the lossesof efficiency associated with the change in labor inputs.

Another variant of GEM allows for heterogeneity in labor skills, tomodel situations in which differences between high- and low-skill workersmay be relevant. As we discuss below, there are two types of households,LC-type households and FL-type households (these indices will beexplained later). FL-type households represent a share (1�sLC) of domestichouseholds and are indexed by jA[0, s(1�sLC)]. LC-type householdsrepresent a share sLC of domestic households and are indexed by


253


jA(s(1�sLC), s]. Suppose each type of household supplies a different type oflabor input, and each type comes in many differentiated varieties. In thiscase, (18) is replaced with

‘tðnÞ ¼ s

1cL

LC‘LC;tðnÞ1� 1

cL þ ð1� sLCÞ1cL‘FL;tðnÞ

1� 1cL

" # cL

cL�1; (27Þ

where ‘LCðnÞ is a basket of LC-type labor inputs, ‘FLðnÞ a basket of FL-typeinputs, and cL the elasticity of substitution between the two types. The twobaskets are defined as

‘FL; tðnÞ ¼1

sð1� sLCÞ

� � 1cFL

Z sð1�sLCÞ

0

‘ðn; jÞ1�1

cFLdj

24

35

cFL

cFL�1

; (28Þ

‘LC;tðnÞ ¼1

s�sLC

� � 1cLC

Z s

sð1�sLCÞ‘ðn; jÞ1�

1cLCdj

24

35

cLC

cLC�1

; (29Þ

where ‘ðn; jÞ is the demand of labor input j by the producer of good n andcFL, cLC>1 are the elasticities of substitution among skills. Costminimization implies that ‘ðn; jÞ is a function of the relative wages

‘tðn; jÞ ¼1s

wtð jÞwFL;t

� ��cFL wFL;t

wt

� ��cL

‘tðnÞ forFL inputs

1s

wtð jÞwLC;t

� ��cLC wLC;t

wt

� ��cL

‘tðnÞ forLC inputs

8>><>>: ; (30Þ

where the wage indices wLC, wFL, and w are defined as

wFL;t ¼1

sð1� sLCÞ

� �Z sð1�sLCÞ

0

wtð jÞ1�cFL

dj

" # 11�cFL

; (31Þ

wLC;t ¼1

s�sLC

� �Z s

sð1�sLCÞwtð jÞ1�cLCdj

" # 11�cLC

; (32Þ

wt ¼ ½sLCw1�cL

LC;t þ ð1� sLCÞw1�cL

FL;t �1

1�cL : (33Þ

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254


Similar considerations hold for the tradables sector. Aggregating acrossfirms, we obtain the total demand for FL-type labor input j as

Z sð1�sLCÞ

0

‘tðn; jÞdnþZ sð1�sLCÞ

0

‘tðh; jÞdh

¼ wtð jÞwFL;t

� ��cFL wFL;t

wt

� ��cL

ð1� sLCÞ‘t; ð34Þ

where once again ‘ is per-capita total labor in the economy. Similarly, totaldemand for LC-type labor input j is

Z s

sð1�sLCÞ‘tðn; jÞdnþ

Z s

sð1�sLCÞ‘tðh; jÞdh

¼ wtð jÞwLC;t

� ��cLC wLC;t

wt

� ��cL

sLC‘t: ð35Þ

The elasticities cL, cFL, and cLC can be modeled as constants or as time-varying autoregressive processes.

Price Setting in the Nontradables Sector

Consider now profit maximization in the intermediate nontradables sector.The key element here is the presence of nominal rigidities. They are modeledas costs to nominal price adjustment measured in terms of total profitsforegone, building on Rotemberg (1982) and Ireland (2001). To illustrate asclearly as possible the role of nominal inertias, we find it useful to cast theanalysis first in terms of nominal prices, and later move back to our usualnotation involving relative prices.

Each firm n takes into account the demand (13) for its product and setsits nominal price Pt(n) to maximize the present discounted value of profits.The adjustment cost is denoted GPN, t [Pt(n),Pt�1(n)] and is a function of bothcurrent and lagged prices. The benchmark parameterization we adopt allowsthe model to reproduce realistic nominal dynamics:

GPN;tðnÞ �fPN

2

PtðnÞ=Pt�1ðnÞpN;t�1

� 1

� �2

: (36Þ

The adjustment cost is related to changes of the nominal price of nontradablen relative to the lagged inflation rate in the nontradables sector pN, t�1.Underlying this specification is the notion that firms should not be penalizedwhen their price hikes are indexed to some (publicly observable) measures ofaggregate or sectoral inflation.


255


The price-setting problem is then characterized as

maxPtðnÞ

TRENDt

PA;tEt

X1t¼t

Dt;tgt;t½PtðnÞ �MCtðnÞ�

PtðnÞPN;t

� ��yNNtð1� GPN;tðnÞÞ; ð37Þ

where Dt, t (with Dt, t¼ 1) is the appropriate nominal discount rate, to bedefined below in Equation (66). As real variables are detrended, Equation(37) includes the rate of growth of the global trend between t and t.

The first-order condition is

0 ¼ 1� yNPtðnÞ �MCtðnÞ

PtðnÞ

� �� PtðnÞPN;t

� ��yNð1� GPN;tðnÞÞ

� ½PtðnÞ �MCtðnÞ�PtðnÞPN;t

� ��yN qGPN;t

qPtðnÞ

� EtDt;tþ1gt;tþ1½Ptþ1ðnÞ �MCtþ1ðnÞ�

� Ptþ1ðnÞPN;tþ1

� ��yN Ntþ1Nt

qGPN;tþ1qPtðnÞ

; ð38Þ

where

qGPN;t

qPtðnÞ¼ fPN

PtðnÞ=Pt�1ðnÞpN;t�1

� 1

� �1

pN;t�1

1

Pt�1ðnÞ; (39Þ

qGPN;tþ1qPtðnÞ

¼ �fPN

Ptþ1ðnÞ=PtðnÞpN;t

� 1

� �Ptþ1ðnÞ=PtðnÞ

pN;t

1

PtðnÞ: (40Þ

Because marginal costs are symmetric across nontradables producers, sayMCt(n)¼MCNt, firms n charge the same equilibrium price P(n)¼PN. Thefirst-order condition can therefore be simplified as

0 ¼f½PNt 1� yNð Þ þ yNMCNt�ð1� GPN;tðnÞÞg

� ½PNt �MCNt�qGPN;t

qPtðnÞPNt

� �

� EtDt;tþ1gt;tþ1½PNtþ1 �MCNtþ1�Ntþ1Nt

qGPN;tþ1qPtðnÞ

PNt

� �: ð41Þ

The right-hand side of the previous equation consists of three expressions incurly brackets. When prices are fully flexible (GPN¼ 0), only the firstexpression matters and the optimization problem collapses to the standard

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256


markup rule:

PNt ¼yN

yN � 1MCNt; (42Þ

where the gross markup is a negative function of the elasticity of inputsubstitution. Deviations from markup pricing occur if firms are penalized formodifying their prices in the short term. The speed of adjustment in responseto shocks depends on the trade-off between current costs (second expressionin curly brackets) and future expected costs (third expression), making theprice-setting process forward looking.

We can now return to the standard notation in terms of relative prices:the optimization problem can be written as

maxptðnÞ

TRENDtEt

X1t¼t

Dt;tgt;tpt;t½ ptðnÞ �mctðnÞ�

ptðnÞpN;t

� ��yNNtð1� GPN;tðnÞÞ; ð43Þ

where the adjustment costs G are now expressed as a function of relativeprices:

GPN; tðnÞ �fPN

2ptptðnÞ=pt�1ðnÞ

pN;t�1� 1

� �2

: (44Þ

Note that GPN, t¼GPN, t, pt(n)qGPN, t/qpt(n)¼Pt(n)qGPN, t/qPt(n) andpt(n)qGPN, tþ 1/qpt(n)¼Pt(n)qGPN, tþ 1/qPt(n). The first-order condition isthen

0 ¼ð1� GPN;tðnÞÞ½ptðnÞð1� yNÞ þ yNmctðnÞ�

� ½ptðnÞ �mctðnÞ�qGPN;t

qptðnÞptðnÞ

� EtDt;tþ1pt;tþ1gt;tþ1½ptþ1ðnÞ �mctþ1ðnÞ�Ntþ1Nt

qGPN;tþ1qptðnÞ

ptðnÞ: ð45Þ

Discussion

Note that when y is very large, the first-order condition is approximatelysolved by pt(n)Emct(n) regardless of how sizable fPN is. This implies that in acompetitive economy (large yN) prices must move in tandem with the shocksaffecting marginal costs, even though such flexibility entails large adjustmentcosts. Instead, if price setters have strong monopoly power (yN is close to one,its minimum value), they can charge a high average markup over marginalcosts. In this case, when marginal costs increase owing to cyclical conditions,


257


firms find it optimal to maintain relatively stable prices and absorb thechange in production costs through a markup squeeze. In other words, whenyN is small, firms are able to keep their prices well above marginal costs andaccommodate changes in demand through supply adjustments, withoutcorresponding changes in prices. Other things being equal, an increase in yNreduces firms’ ability to use markup fluctuations as a shock absorber.

It can be useful to express the pricing equation above as a first-orderapproximation around the steady state where GPN, t¼ qGPN, t/qpt(n)¼qGPN, tþ 1/qpt(n)¼ 0, pNt¼ pNt�1¼ pNtþ 1¼ p, Dt, tþ 1pNtþ 1gt, tþ 1� 1/(1þ r)and p(n)¼ yN/(yN�1)mc(n). Also for simplicity consider the case in whichthere is zero growth in steady state or g¼ 1, so that 1/(1þ r)¼ b. DefiningyNt�mct(n)/pt(n), we can rewrite (45) as

0 ¼fð1� yN þ yNyNtÞð1� GPN;tðnÞÞg

� ð1� yNtÞqGPN; t

qptðnÞptðnÞ

� �

� EtDt;tþ1gt;tþ1pt;tþ1ð1� yNtþ1ÞNtþ1Nt

qGPN;tþ1qptðnÞ

ptðnÞ� �

: ð46Þ

Now linearize in the neighborhood of the steady state:

0 ¼yNdyNt �1

yNfPN

dpNt � dpNt�1p

� �

þ Etb1

yNfPN

dpNtþ1 � dpNt

p

� �: ð47Þ

Define cpNt ¼ dpNt=p and dyNt ¼ dyNt=yN . Obtain

ðyN � 1Þyt ¼1

yNfPNðcpNt � cpNt�1Þ

� 1

yNfPNEtbðcpNtþ1 � cpNtÞ; ð48Þ

which can be rewritten as a log-linear Phillips curve with full indexation, anexpression that relates changes in inflation to expected changes in inflationand real marginal costs:

DcpNt ¼ gcyNt þ bEtDcpNtþ1; g � ðyN � 1ÞyNfPN

: (49Þ

Similar considerations apply to the tradables sector.Notice that markup/monopoly power in our setup (y) directly affects the

slope of the Phillips curve g. The important implication is that a reduction ofmonopoly power in GEM (higher y) makes the Phillips curve steeper andreduces the sacrifice ratio faced by the economy. Similar considerations applyto an increase in price flexibility (lower fPN).

Paolo Pesenti

258


Variants of the model can exploit alternative assumptions about thedegree of indexation and inflation inertia in the model, simply by modifyingthe denominator of the term in brackets in (36) or (44). For instance, a modelin which

GPN;tðnÞ �fPN

2ptptðnÞ=pt�1ðnÞpaN;t�1p

1�at

� 1

!2

; (50Þ

implies weighted indexation with respect to past sectoral inflation and currenteconomy-wide inflation, and the resulting Phillips curve is characterized byasymmetries between forward- and backward-looking components of theinflation process:

cpNt ¼ acpNt�1 þ ð1� aÞpt þ gcyNt

þ bEtðcpNtþ1 � acpNt � ð1� aÞptþ1Þ; g � ðyN � 1ÞyNfPN

: ð51Þ

Price Setting in the Tradables Sector

In this section we only consider optimal price setting for domestic firmsselling in the domestic market, and we abstract from the role of thedistribution sector. Later we consider the price-setting problem faced byexporters and consider a variant of the model encompassing distributionservices.

The analysis is similar to the nontradables sector above. Adopting a self-explanatory notation, the price-setting problem of firm h at time t can becharacterized as follows:

maxptðhÞ

TRENDtEt

X1t¼t

Dt;tpt;tgt;t½ptðhÞ �mctðhÞ�

ptðhÞpQ;t

� ��yTQtð1� GPQ;tðhÞÞ; ð52Þ

and the first-order condition in a symmetric equilibrium with p(h)¼ pQ is

0 ¼ð1� GPQ;tðhÞÞ½ptðhÞð1� yTÞ þ yTmctðhÞ�

� ½ptðhÞ �mctðhÞ�qGPQ;t

qptðhÞptðhÞ

� EtDt;tþ1pt;tþ1gt;tþ1½ptþ1ðhÞ �mctþ1ðhÞ�Qtþ1Qt

qGPQ;tþ1qptðhÞ

ptðhÞ: ð53Þ


259


Consumer Preferences

In each country there is a continuum of households indexed by jA[0, s], thesame index of labor inputs. Some households have access to capital markets,some do not. The latter finance their consumption by relying exclusively ontheir labor incomes. We refer to the first type as ‘‘Ricardian’’ or ‘‘forward-looking’’ (FL). We refer to the second type as ‘‘non-Ricardian’’ or ‘‘liquidity-constrained’’ (LC ). The two types of households can also be heterogeneousin the labor market, as discussed above.

For each household j, we denote with Wtð jÞ the lifetime expected utilityand specify its preferences as

Wtð jÞ � TRENDtEt

X1t¼t

bt;tg1�st;t utðCtð jÞ; ‘tð jÞÞ; (54Þ

where the instantaneous felicity is a function of (detrended) consumption Cand labor effort ‘:

utðCtð jÞ; ‘tð jÞÞ ¼ZU

1� sCtð jÞ � bc

Cj;t�1gt�1;t

�

� ZV

1þ zð‘tð jÞ � b‘‘j;t�1Þ1þz

ð1� b‘Þz

#1�s: ð55Þ

In the expressions above, bt, t is the discount rate between time t and timet, possibly time-varying and different across countries. In steady state bt, tconverges to bSS

t�t where bSS is a constant.The term gt, t

1�s in (54) implies that the disutility of labor effort increaseswith the common trend, an assumption required to guarantee balancedgrowth. The implicit assumption is that technological progress associatedwith home production activities follows the same trend as the effectiveness oflabor in manufacturing production. The restriction limt-Nbt, tgt, t

1�so1 isimposed to ensure that utility is bounded.

The parameter s in (55), which affects the curvature of consumptionutility, is the reciprocal of the elasticity of intertemporal substitution. Theparameter z, which affects the curvature of labor disutility, is the reciprocalof the Frisch elasticity of labor supply.

There is habit persistence in consumption with coefficient 0obco1. Theterm Cj, t�1 in (55) is past per capita consumption of household j’s peers (thatis, either forward-looking or liquidity-constrained agents). Similarly, there ishabit persistence in leisure with coefficient 0ob‘o1. Households’ preferencesare therefore symmetric within their respective categories but, because ofdifferent reference groups in habit formation, they are not symmetric acrosscategories.

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The marginal utilities of consumption and leisure are

qutð jÞqCtð jÞ

¼ ZU Ctð jÞ � bcCj;t�1gt�1;t

� ZV


ð1� b‘Þz

" #�s; (56Þ

� qutð jÞq‘tð jÞ

¼ZU Ctð jÞ � bcCj;t�1gt�1;t

� ZV


ð1� b‘Þz

" #�s

�ZV‘tð jÞ � b‘‘j;t�1

1� b‘

� �z

ð57Þ

and the marginal rate of substitution is

MRStð jÞ ¼ �qutð jÞ=q‘tð jÞqutð jÞ=qCtð jÞ

¼ ZV‘tð jÞ � b‘‘j;t�1

1� b‘

� �z

(58Þ

Discussion

The specification of the utility function builds on Greenwood, Herkowitz,and Huffman (1988). The main reason underlying the choice of this para-meterization relatively to alternative options (such as additive separability orCobb-Douglas aggregators) is that it generates relatively high volatility inconsumption and countercyclical trade balances, consistent with empiricalstylized facts. This is because hours worked are determined exclusively by thereal wage (see (71) below after accounting for (58)), leading to a direct linkbetween fluctuations in labor effort and consumption growth.

The terms ZU and ZV can be modeled as positive parameters orautoregressive processes. Note that ZV is normalized so that in a steady statewith ‘tð jÞ ¼ ‘j;t�1, the marginal rate of substitution is independent of habitpersistence.

Budget Constraint (Forward-Looking Households)

The individual flow budget constraint for Ricardian agent jA[0, (1�sLC)s] is

Btð jÞ þ etB�t ð jÞpð1þ it�1ÞBt�1ð jÞ

pt�1;tgt�1;t

þ ð1þ i�t�1Þ½1� GB;t�1�etB�t�1ð jÞp�t�1;tgt�1;t

þ ð1� tKÞrtKtð jÞ þ ð1� tLÞwtð jÞ‘tð jÞð1� GW ;tð jÞÞ

� Ctð jÞ � pE;tItð jÞ þ ftð jÞ � TTtð jÞ: ð59Þ


261


Households hold two nominal bonds, one denominated in domesticcurrency and one denominated in an international currency. We will refer tothe country issuing the international currency as the ‘‘center.’’ In terms of ournotation, Bt�( j ) is holdings of the domestic bond by household j, expressedin terms of domestic consumption units, Bt( j) is holdings of the internationalbond, expressed in terms of center consumption units, and et is the CPI-basedreal exchange rate, expressed as the price of one center consumption basket interms of domestic consumption. If the domestic currency is also theinternational currency, e is equal to 1. Below, when we introduce explicitcountry indices, eH, J is the price of one consumption basket in country J interms of country H’s consumption baskets, and similarly eH,n is the bilateralreal exchange rate of country H relative to the center.

The short-term nominal rates it and itn are paid at the beginning of

period tþ 1 and are known at time t. The two rates are directly controlledby their respective national governments, so that i is the onshore ratein the center country. The spread between the onshore rate paid in thecenter country and the offshore rate received by domestic investors isdenoted GB. Only the center-currency bond is traded internationally and is inzero net supply worldwide. The domestic bond is in zero net supply at thedomestic level (although later we consider a model variant encompassingpublic debt).

Agents who take a position in the international bond market mustdeal with financial intermediaries who charge a transaction fee GB onsales/purchases of the international bond. The presence of the financialfriction GB guarantees that international net asset positions follow astationary process and the economies converge asymptotically to a well-defined steady state. This transaction cost is a function of the average netasset position of the whole economy. Specifically, we adopt the followingfunctional form:

1� GB;t ¼ 1� fB1

expðfB2½etB�t =GDPt � b�FDES�Þ � 1

expðfB2½etB�t =GDPt � b�FDES�Þ þ 1� ZB;t

� �b�t�1;tbt�1;t

; (60Þ

where 0rfB1r1, fB2>0, and etB� � ð1=sÞetR sð1�sLCÞ0 B�ð jÞdj represents the

per capita net asset position of the country in consumption units. The termbFDESn is the ‘‘desired’’ net asset position of the country expressed as a ratio ofGDP. This variable measures the degree of international exposure thatfinancial intermediaries consider appropriate for the economy, based on theirassessment of the global economic outlook.

To understand the role played by GB, suppose first that bFDESn ¼ZB¼ 0

and bn¼ b. In this case, when the net asset position of the country is equal toits ‘‘desired’’ level of zero, it must be the case that GB¼ 0 and the return onthe international bond is equal to 1þ i�. If the country is a net creditor,worldwide GB rises above zero, implying that the country’s households losean increasing fraction of their international bond returns to financialintermediaries. When holdings of the international bond go to infinity, the

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return on the international bond approaches (1þ in)(1�fB1). By the sametoken, if the country is a net debtor worldwide, GB falls from zero to �fB1,implying that households pay an increasing intermediation premium on theirinternational debt. When net borrowing goes to infinity, the cost ofborrowing approaches (1þ in)(1þfB1). In nonlinear applications of GEMthe parameter fB2 controls the flatness of the GB function: if fB2¼ 0 thenGB¼ 0 regardless of the net asset position; if fB2 tends to infinity then1�GB¼ (1�fB1) for any arbitrarily small net lending position, and 1�GB¼(1þfB1) for any arbitrarily small net borrowing position. An appropriateparameterization allows the model to generate realistic dynamics for net assetpositions and current account.

Consider now the other components of (60). The term bFDESn can be

positive or negative. The above considerations are still valid after reinter-preting the concepts of ‘‘net creditor’’ or ‘‘net borrower’’ in terms ofdeviations from the desired levels.

The variable ZB, t can be modeled as a stochastic process with zero meanin steady state, provided that fluctuations in ZB are not large enough to pushGB above 1. In our framework, uncertainty in international financialintermediation plays the same role that ‘‘uncovered interest parity shocks’’or risk-premium fluctuations play in similar open-economy models.

Finally, when rates of time preference diverge across countries andb�ab, the transaction cost is appropriately modified to account forasymmetries in real interest rates across countries, as in Faruqee andothers (2007).

Let us consider now the remaining components in the budget constraint.Households accumulate physical capital which they rent to domestic firmsat the after-tax rate r(1�tK). Gross investment before depreciation is denotedI. The law of motion of capital is

Ktþ1ð jÞgt;tþ1 ¼ ð1� dÞKtð jÞ þ GI ;tð jÞKtð jÞ; 0od � 1; (61Þ

where d is the country-specific depreciation rate of capital. Capitalaccumulation is subject to adjustment costs: GI (.) is an increasing, concave,and twice-continuously differentiable function of the investment/capital ratioIt( j)/Kt( j) with two properties entailing no adjustment costs in steady state:GI(dþ g�1)¼ dþ g�1 and G0I (dþ g�1)¼ 1. The specific functional form weadopt is quadratic and encompasses inertia in investment:

GI ;tð jÞ �Itð jÞKtð jÞ

ð1þ ZI ;tÞ �fI1

2

Itð jÞKtð jÞ

� ðdþ g� 1Þ� �2

� fI2

2

Itð jÞKtð jÞ

� It�1Kt�1

� �2

; ð62Þ


263


where fI1, fI2Z0, ZI, t is a transitory shock (modeled as a negativeadjustment cost) and g is the steady-state growth rate.

Labor incomes w‘ are taxed at the rate tL. Each FL-type household is themonopolistic supplier of a specific labor input and sets the nominal wage forits labor input j accounting for its demand ‘ð jÞ ¼ ðwð jÞ=wÞ�cL‘. There issluggish wage adjustment due to resource costs that are measured in terms ofthe total wage bill. The adjustment cost is denoted GWFL (for Wage Forward-Looking) and its specification is the analog of (44) above:

GWFL;tð jÞ �fWFL

2ptwtð jÞ=wt�1ð jÞ

pW ;t�1� 1

� �2

; (63Þ

where pW is the wage inflation rate.Ricardian households own all domestic firms and there is no

international trade in claims on firms’ profits. The variable F includes alldividends accruing to shareholders, plus all revenue from nominal and realadjustment rebated in a lump-sum way to all Ricardian households, plusrevenue from financial intermediation which is assumed to be provided bydomestic firms exclusively. A formal definition of F is given below inEquation (119).

Finally, agents pay lump-sum (nondistortionary) net taxes TTdenominated in consumption units.

Discussion

In GEM it is assumed that all intermediation firms are owned by thecountry’s residents, and that their revenue is rebated to domestic householdsin a lump-sum fashion. A simple variant of the model in whichintermediation firms are owned by foreign residents leaves the basic resultsvirtually unchanged. There are no intermediation costs for center residentsentering the international bond market, that is, there is no difference betweenonshore and offshore center interest rates. Note that the choice of currencydenomination of the international bond is arbitrary, and any availablecountry currency is viable.

Both desired (bFDESn ) and actual (eBn/GDP) net asset positions converge

over the long term to their steady-state value bF,SSn .

Consumer Optimization (Forward-Looking Households)

The representative Ricardian household chooses bond holdings, capital andconsumption paths, and sets wages to maximize its expected lifetime utility(54) subject to (59) and (61), taking into account (22) (or (34) if there aredifferent types of labor).

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For expositional convenience, it is worthwhile to write explicitly themaximization problem of agent jA[0, (1�sLC)s] in terms of the followingLagrangian:

maxCtð jÞ;Itð jÞ;Btð jÞ;B�t ð jÞ;Ktþ1ð jÞ;wtð jÞ

TRENDtEt

X1t¼t

bt;tg1�st;t fuðCtð jÞ;wtð jÞ�cLwcL

t ‘tÞ

þ mtð jÞð�Btð jÞ � etB�tð jÞ þð1þ it�1ÞBt�1ð jÞ

pt�1;tgt�1; t

þ ð1þ i�t�1Þð1� GB;t�1ÞetB�t�1ð jÞp�t�1;tgt�1;t

þ ð1� tLÞwtð jÞ1�cLwcLt ‘tð1� GW ;t½wtð jÞ;wt�1ð jÞ�Þ

þ ð1� tKÞrtKtð jÞ � Ctð jÞ � pE;tItð jÞ þ Ftð jÞ � TTtð jÞÞ

þ ltð jÞð�Ktþ1ð jÞgt;tþ1 þ ð1� dÞKtð jÞ

þ GI ;t½Itð jÞ=Ktð jÞ�Ktð jÞÞg; ð64Þ

where m and l are the multipliers associated with, respectively, the budgetconstraint and the capital accumulation process.

The first-order conditions with respect to Ct( j) and It( j) yield

mtð jÞ ¼ qutð jÞ=qCtð jÞ ¼ ltð jÞG0I;tð jÞ=pE;t: (65Þ

In a symmetric setup, qut( j)/qCt( j) is the same across Ricardian agents j.Their stochastic discount rate and pricing kernel is therefore the variable Dt, t,which is defined as

Dt;t � bt;tg1�st;t

mtmt

1

pt;t

1

gt;t: (66Þ

Accounting for the above expressions, the first-order conditions withrespect to Bt( j) and Bt( j) are, respectively,

1 ¼ ð1þ itÞEtDt;tþ1; (67Þ

1 ¼ ð1þ i�t Þð1� GB;tÞEtðDt;tþ1Dt;tþ1Þ; (68Þ


265


where D denotes the rate of nominal exchange rate depreciation against thecenter country, or

Dt;t ¼etet

pt;tp�t;t

: (69Þ

The first-order condition with respect to Ktþ 1( j) is

pE;t

G0I ;tð jÞEtgt;tþ1 ¼Et Dt;tþ1pt;tþ1gt;tþ1 ð1� tKÞrtþ1ð

þ pE;tþ1G0I ;tþ1ð jÞ

1� dþ GI ;tþ1ð jÞ

�G0I ;tþ1ð jÞItþ1ð jÞKtþ1ð jÞ

��: ð70Þ

Expression (70) links capital accumulation to the behavior of the after-taxprice of capital (1�tK)r. In a nonstochastic steady state 1þ (1�tK)r/pE isequal to the sum of the natural real rate gs/b and the rate of capitaldepreciation d.

Finally, taking the first-order condition with respect to w( j), theRicardian household’s wage rate is set according to

cLMRStð jÞ1

wtð jÞ¼ðcL � 1Þ½1� GWFL;tð jÞ�ð1� tLÞ

þ qGWFL;tð jÞqwtð jÞ

wtð jÞð1� tLÞ

þ EtDt;tþ1pt;tþ1gt;tþ1wtþ1ð jÞwtð jÞ

� ðwtþ1ð jÞ=wtþ1Þ�cL

ðwtð jÞ=wtÞ�cL

‘tþ1‘t

� qGWFL;tþ1ð jÞqwtð jÞ

wtð jÞð1� tLÞ; ð71Þ

where MRS has been defined in (58) above. The interpretation of (71)is similar to (112) above. In a nonstochastic steady state the real wagew( j) is equal to the marginal rate of substitution between consumptionand leisure, MRS ¼ �u‘=uc, augmented by the markup cL/(cL�1), whichreflects monopoly power in the labor market. For an analysis of wage

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rigidities in open-economy general equilibrium models, see Corsetti andPesenti (2001).

Discussion

In a nonstochastic steady state (67) implies (1þ iSS)/pSS¼ gSSs /bSS: recall that

pSS is the (gross steady-state quarterly) inflation rate, (1þ iSS)/pSS is theequilibrium real interest rate, gSS is the (gross steady-state quarterly) rate ofgrowth of the world economy, 1/bSS is the rate of time preference, and gSS

s /bSS is the steady-state ‘‘natural’’ real interest rate of the economy.International differences in natural rates can arise from asymmetric ratesof time preference. The financial friction GB in (60) is appropriately adjustedto take into account these asymmetries.

Expressions (67) and (68) yield the risk-adjusted uncovered interestparity, recalling that the return on international bond holdings is modified toaccount for the costs of intermediation GB. In steady state the interestdifferential (1þ iSS)/[(1þ iSS�)(1�GB,SS)] is equal to the steady-state nominaldepreciation rate of the currency vis-a-vis the United States, and relativepurchasing power parity holds.

Note that the expectation operator on the left-hand side of (70) is neededas shocks to the trend gt, tþ 1 are not part of the information set at time t. Thisis because variables are expressed as deviations from the current trend. Analternative specification which expresses variables as deviations from thelagged trend would make little difference.

When the two types of households also represent different typesof labor inputs with different elasticities, the first-order condition (71) isreplaced by

cFLMRStð jÞ1

wtð jÞ¼ðcFL � 1Þ½1� GWFL;tð jÞ�ð1� tLÞ

þ qGWFL;tð jÞqwtð jÞ

wtð jÞð1� tLÞ

þ EtDt;tþ1pt;tþ1gt;tþ1wtþ1ð jÞwtð jÞ

� ðwFL;tþ1=wtþ1Þ�cL

ðwFL;t=wtÞ�cL

‘FL;tþ1‘FL;t

� qGWFL;tþ1ð jÞqwtð jÞ

wtð jÞð1� tLÞ: ð72Þ

A variant of the model considers the role of money. Define as Mthe stock of real money balances held by household j. The budget


267


constraint (59) becomes

Mtð jÞ þ Btð jÞ þ etB�t ð jÞ �Mt�1ð jÞ þ ð1þ it�1ÞBt�1ð jÞ

pt�1;tgt�1;t

þ ð1þ i�t�1Þ½1� GB;t�1�etB�t�1ð jÞp�t�1;tgt�1;t

þ ð1� tKÞrtKtð jÞ

þ ð1� tLÞwtð jÞ‘tð jÞð1� GW ;tð jÞÞ

� Ctð jÞ½1þ GS;tð jÞ� � pE;tItð jÞ þ Ftð jÞ � TTtð jÞ: ð73ÞConsumption spending is subject to a proportional transaction cost GS

that depends on the household’s money velocity v, where

vtð jÞ �Ctð jÞMtð jÞ

: (74Þ

A suggested functional form for the transaction cost (implying a satiationpoint for the demand of real balances) is

GSðvtÞ ¼ fS1vt þfS2

vt� 2ðfS1fS2Þ1=2: (75Þ

Agents optimally choose their stock of real money holdings M so that atthe margin shopping costs measured in terms of foregone consumption areequal to the benefits from investing in yield-bearing assets. The first-ordercondition with respect to Mtð jÞ is

1� G0S;tð jÞv2t ð jÞ ¼ EtDt;tþ1; (76Þwhich defines real money balances M as a positive function of consumptionand a negative function of the nominal interest rate. Other equations of themodel need to be modified appropriately to account for the presence ofmoney. For instance, the asset pricing kernel is now equal to

Dt;t � bt;tg1�st;t

mtmt

1

pt;t

1

gt;t

1þ GS;tð jÞ þ G0S;tð jÞvtð jÞ1þ GS;tð jÞ þ G0S;tð jÞvtð jÞ

; (77Þ

and the government budget constraint is modified so that seigniorage revenueis rebated in a lump-sum fashion through net transfers.

Consumer Optimization (Liquidity-Constrained Households)

As liquidity-constrained households have no access to capital markets, theiroptimal choices are confined to labor supply. Similar to the Ricardianhouseholds, they can optimally set their wages to exploit their market power.Also similar to the Ricardian households, they face adjustment costs for theirwages. These costs are denoted GWLC, t (for wage liquidity constrained) andare similar to (63). Different from the Ricardian households, however, their

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optimal choices are purely static and do not entail forward-lookingcomponents.

The maximization problem of agent jA((1�sLC)s, s] can be written interms of the following static Lagrangian:

maxCtð jÞ;wtð jÞ

uðCtð jÞ;w�cLt ð jÞwcL

t ‘tÞ þ mtð jÞ½�Ctð jÞ � TTtð jÞ

þ 1� tLð Þwtð jÞ1�cLwcLt ‘tð1� GWLC;tð jÞ�: ð78Þ

It is assumed that redistributive policies TT rebate to LC-type householdsthe income losses associated with wage adjustment, so that their consumptionlevel is:

Ctð jÞ ¼ ð1� tLÞwtð jÞ‘tð jÞ: (79ÞThe first-order conditions with respect to C( j ) and w( j ) determines partialadjustment of wages:

cLMRStð jÞ1

wtð jÞ¼ ð1� tLÞ ðcL � 1Þð1� GWLC;tð jÞÞ

þ qGWLC;tð jÞqwtð jÞ

wtð jÞ�: ð80Þ

Denoting wFL the wage rate w( j ) that solves (71), and wLC the wage rate w( j )that solves (80), Equation (20) determines the wage rate for the wholeeconomy as

w1�cLt ¼ sLCw

1�cL

LC;t þ ð1� sLCÞw1�cL

FL;t : (81Þ

Discussion

When two types of labor inputs are considered, Equation (80) isreplaced by

cLCMRStð jÞ1

wtð jÞ¼ð1� tLÞ ðcLC � 1Þð1� GWLC;tð jÞÞ

þ qGWLC;tð jÞqwtð jÞ

wtð jÞ�: ð82Þ

Fiscal Policy

Public spending falls on nontradable goods, both final and intermediate. Inper-capita terms, GC is government consumption, GI is governmentinvestment, and GN denotes public purchases of intermediate nontradables.There are four sources of (net) tax revenue: taxes on capital income tK, taxes


269


on labor income tL, import tariffs tar, and lump-sum taxes net of transfers tohouseholds TT. In the benchmark version of GEM the government follows abalanced budget rule:

0 ¼ Gt � GREV ;t; (83Þwhere

Gt � GC;t þ pE;tGI ;t þ pN;tGN;t; (84Þand GREV is aggregate government revenue, to be defined below.

Discussion

Although GEM has not been designed to analyze fiscal policy issues in detail,variants of the model can be designed to provide a satisfactory quantitativeassessment of budgetary dynamics. In what follows we consider apossible extension in this direction, following Faruqee and others (2007,forthcoming).

The government finances the excess of public expenditure over net taxesby issuing debt denominated in nominal currency, denoted B in per-capitaterms. All national debt is held exclusively by domestic (Ricardian) agents.The budget constraint of the government is

Bt � ð1þ it�1ÞBt�1

pt�1;tgt�1;tþ Gt � GREV;t: (85Þ

Define now the average tax rate for the economy t as

tt � GREV;t=GDPt: (86ÞSimilarly, define the deficit-to-GDP ratio as

DEFt

GDPt¼ Bt �

Bt�1pt�1;tgt�1; t

� ��GDPt: (87Þ

From (85), in steady state we have

BSS

GDPSS¼ pSSgSSpSSgSS � ð1þ iSSÞ

GSS

GDPSS� tSS

� �

¼ pSSgSSpSSgSS � 1

DEFSS

GDPSS: ð88Þ

The previous equations define the relationships between the debt-to-GDP, average tax rate, and deficit-to-GDP ratio that are sustainable in thelong term. In what follows we treat the long-run debt-to-GDP ratio as apolicy parameter set by the government, and let tSS and DEFSS/GDPSS bedetermined by (88).

The government is assumed to control lump-sum taxes, trade policyparameters, t and tK directly, while tL is endogenously determined. A

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possible specification for the fiscal rule for t is

tt ¼ ðtt�1 þ tt þ Etttþ1Þ=3þ fTAX1

Bt

GDPt� fTAX2bTAR;t

�

�ð1� fTAX2ÞBt�1

GDPt�1

�þ fTAX3

DEFt

GDPt� DEFSS

GDPSS

� �

þ fTAX4

Gt

GDPt� GSS

GDPSS

� �; ð89Þ

where bTAR is the targeted debt-to-GDP ratio, a variable that converges toBSS/GDPSS in steady state. The tax rate is a smoothed function of past andexpected future rates, adjusted upward when the current debt-to-GDP ratiois above the average of its current target and its past observed level, whenthe current deficit-to-GDP ratio is above its sustainable steady-state level,and when current government spending as a share of GDP is above itslong-run level.

By construction, public debt is exclusively held by domestic agents, andthe net asset position of the country is independent of the extent of publicborrowing. This feature of the model is of course highly unrealistic. A way toenhance the realism of the simulations is by introducing a link between thedesired net asset position of country H and the debt-to-GDP ratios in theworld economy as follows:

b�HFDES;t ¼ b�HFNEUT � fHF1

BHt

GDPHt

þXJaH

fJ;HF2

BJt

GDPJt

: (90Þ

According to the previous expression, bFDESnH is equal to a country-specific

constant, bFNEUTnH , adjusted to account for changes in the debt-to-GDP ratios

in either the domestic economy (BH/GDPH) or in the other countries in theworld (B J/GDPJ).

This specification provides a plausible (albeit judgmental) link betweendebt imbalances and net asset positions. When the national debt-to-GDPratio increases, domestic agents reduce the share of foreign securities in theirportfolios by selling the international bond to foreigners. By the same token,if the debt-to-GDP ratio increases in the center country, internationalinvestors would require a higher return on center securities, leading to ahigher share of center assets in their portfolios or a reduction of netborrowing from the center.

Of course, our approach should be viewed only as a crude approximationto the actual determinants of cross-country spreads and interest ratepremiums in response to macroeconomic imbalances, whose endo-genization should be eventually incorporated in a self-contained model. Itremains unclear, however, whether the final benefits of such a frameworksignificantly outstrip the costs of incorporating the large amount ofcomplications from which we abstract here.


271


Quantitatively, one could take bFDES� as a free variable and estimate thefF1 and fF2 parameters on the basis of empirical evidence on the linkbetween net asset positions and debt levels. Alternatively, one could rely oncross-fertilization with respect to alternative theoretical models able to shedlight on the structural determinants of these parameters. In Faruqee andothers (2007), for instance, the calibration of (90) has relied on results basedon the Global Fiscal Model, an overlapping-generation multicountry modeldeveloped at the International Monetary Fund.

Monetary Policy

The government controls the short-term rate it. Monetary policy is specifiedin terms of annualized interest rate rules. The specification of the interest ruleis likely to change according to the nature of the simulation exercise. Abenchmark specification is

ð1þ itÞ4 ¼oið1þ it�1Þ4 þ ð1� oiÞð1þ ineutt Þ4

þ o1Etðpt�1;tþ3 �Pt�1;tþ3Þ: ð91Þ

The current interest rate it is an average of the lagged rate it�1 and the current‘‘neutral’’ rate it

neut, defined as

1þ ineutt �P0:25

t�4;tðgt�1;tÞs

bt�1;t; (92Þ

where Pt�t, t�tþ 4 is the year-over-year gross CPI inflation target (eitherexplicit or implicit) prevailing at time t for the four-quarter period betweent�t and t�tþ 4. This average is adjusted to account for the expectedinflation gap three quarters in the future. In a steady state when all constanttargets are reached it must be the case that the nominal interest rate is equalto the neutral level, equal to the product of the equilibrium ‘‘natural’’ realinterest rate gs/b times the inflation target:

1þ iSS ¼ 1þ ineutSS ¼P0:25

SS gsSSbSS

¼ pSSgsSSbSS

: (93Þ

Discussion

The rule (91) could be modified to include policy responses to a set of othervariables (such as measures of the output gap level or growth, the exchangerate, the current account, etc.) expressed as deviations from their targets. Foran extension to price-level path targeting, the reader is referred to Laxton,N’Diaye, and Pesenti (2006). For an introduction to optimal monetary policyin open economies, see Corsetti and Pesenti (2005).

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Market Clearing in the Domestic Economy

Maintaining international variables (including government revenue GREV,which depends on import tariffs) exogenous for the time being, the model isclosed by imposing the following resource constraints and market clearingconditions.

In each country, the domestic resource constraints for capital and laborare, respectivelyZ sð1�sLCÞ

0

Ktð jÞdj �Z s

0

KtðnÞdnþZ s

0

KtðhÞdh; (94Þ

and

‘tð jÞ �Z s

0

‘tðn; jÞdnþZ s

0

‘tðh; jÞdh: (95Þ

The resource constraint for the nontradable good nH is

NtðnÞ �Z s

0

NA;tðn;xÞdxþZ s

0

NE;tðn; eÞdeþ GN;tðnÞ; (96Þ

while the tradable h can be used by domestic firms or imported by foreignfirms (see below).

The final good A can be used for private or public consumption:Z s

0

AtðxÞdx �Z s

0

Ctð jÞdj þ sGC;t (97Þ

and similarly for the investment good E:Z s

0

EtðeÞde �Z ð1�sLCÞs0

Itð jÞdj þ sGI ;t: (98Þ

Market clearing in the domestic bond market requiresZ sð1�sLCÞ

0

Btð jÞdj ¼ sBt; (99Þ

where Bt¼ 0 in the benchmark model (see discussion above for the treatmentof public debt Bt>0).

IV. World Interdependencies in General Equilibrium

So far all trade-related variables have been taken as exogenous. Now we closethe model by considering a multicountry general-equilibrium setting. Thenotation becomes slightly more complicated, as explicit country indices mustbe introduced. We will refer to H as the ‘‘home’’ country and to JaH as oneof the remaining ‘‘foreign’’ countries. When a double country index isconsidered in the case of bilateral trade variables, the first index refers to theimporting (destination) country and the second index to the exporting


273


(source) country. Multicountry applications of GEM can be found inFaruqee and others (2007, forthcoming).

Demand for Imports

The derivation of the foreign demand schedule for good h is analyticallymore complex but, as we show in (108) at the end of this section, it shares thesame functional form as (13) and (14) above, and thus can be written as afunction of the relative price of good h (with elasticity yT) and total foreigndemand for imports.

We focus first on import demand in the consumption good sector ofcountry H. Denote the representative firm in the consumption sector asxHA[0, sH]. Its imports MA

H(xH) are a CES function of baskets of goodsimported from the other countries, or

MHA;tðxHÞ

1� 1rHA ¼

XJaH

ðbH;JA Þ1rHA ðMH;J

A;t ðxHÞð1� GH;JMA;tðxHÞÞÞ

1� 1rHA ; (100Þ

where

0 � bH;J � 1;XJaH

bH;J ¼ 1: (101Þ

In (100) above, rAH is country H’s elasticity of substitution across

exporters: the higher is rAH, the easier it is for firm xH to replace imports from

one country with imports from another. The parameters bAH, J determine the

composition of the import basket across countries. MAH, J(xH) denotes

imports from country J by firm xH located in country H.The response of import volumes to changes in demand as well as their

price elasticities is typically estimated to be smaller in the short term than inthe long run. To model realistic import dynamics, such as the delayed andsluggish adjustment to changes in relative prices typically referred to as the ‘‘Jcurve,’’ we assume that bilateral imports are subject to bilateral adjustmentcosts GMA

H, J. These costs are specified in terms of import shares relative to firmxH’s output. They are zero in steady state. Specifically, GEM adopts theparameterization

GH;JMA;t

MH;JA;t ðxHÞ

AHt ðxHÞ

,MH;J

A;t�1AH

t�1

" #

¼ fH;JMA

2

½ðMH;JA;t ðxHÞ=AH

t ðxHÞÞ=ðMH;JA;t�1=A

Ht�1Þ � 1�2

ð1þ ½ðMH;JA;t ðxHÞ=AH

t ðxHÞÞ=ðMH;JA;t�1=A

Ht�1Þ � 1�2Þ

; ð102Þ

with fMAH, J

Z0. The specification is such that GMAH, J[1]¼ 0, GMA

H, J[N]¼fMAH, J/2,

and GMAH, J[0]¼GMA

H, J[2]¼fMAH, J/4. Alternative parameterizations (for instance,

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274


quadratic) could be considered, although the suggested one has proven to beuseful in nonlinear simulation exercises with relatively large shocks.

Denoting pMH, J the price in country H of a basket of intermediate inputs

imported from J, firm xH minimizes its costsP

JaHpMH, JMA

H, J(xH) subject to(100). Cost minimization implies

MH;JA;t ðxHÞð1� GH;J

MA;tðxHÞÞ

ð1� GH;JMA;tðxHÞ �MH;J

A;t ðxHÞG0MA;tH; JðxHÞÞrHA

¼ bH;JA

pH;JM;t

pHMA;tðxHÞ

!�rHA

MHA;tðxHÞ; ð103Þ

where G0MAH, J(xH) is the first derivative of GMA

H, J(xH) with respect to MAH, J(xH)

and the cost-minimizing import price index pMAH (xH) is the Lagrangian

multiplier:

pHMA;tðxHÞ ¼XJaH

bH;JpH;JM;t

1� GH;JMA;tðxHÞ �MH;J

A;t ðxHÞG0MA;tH; JðxHÞ

!1�rHA

24

35

11�rH

A

: (104Þ

In principle, the import price pMAH (xH) is firm-specific, as it depends on firm

xH’s import shares. To the extent that all firms xH are symmetric within theconsumption sector, however, there will be a unique import price pMA

H . Itfollows that pMA

H MAH¼

PJaHpM

H, JMAH, J(1�GMA

H, J)/(1�GMAH, J�MA

H, JGMA0H, J).

Consider now the basket MAH, J(xH) in some detail. In analogy with (10)

above, it is a CES index of all varieties of tradable intermediate goodsproduced by firms hJ operating in country J and exported to country H.Denoting as MA

H, J(hJ,xH) the demand by firm xH of an intermediate goodproduced by firm hJ, the basket MA

H, J(xH) is

MH;JA;t ðxHÞ ¼

1

sJ

� � 1yJTZ sJ

0

MH;JA;t ðhJ ;xHÞ

1� 1yJT dhJ

24

35

yJTyJT�1

; (105Þ

where yTJ>1 is the elasticity of substitution among intermediate tradables,

the same elasticity entering (14) in country J.The cost-minimizing firm xH takes as given the prices of the imported

goods pH(hJ) and determines its demand of good hJ according to

MH;JA;t ðhJ ; xHÞ ¼

1

sJpHt ðhJÞpH;JM;t

!�yJTMH;J

A;t ðxHÞ; (106Þ


275


where MA, tH, J(xH) has been defined in (103) and pM

H, J is

pH;JM;t ¼1

sJ

� �Z sJ

0

pHt ðhJÞ1�yJT dhJ

" # 11�yJT

: (107Þ

The import demand schedules in the investment good sector can bederived in perfect analogy with the analysis above. As a last step, we canderive country J’s demand schedule for country H’s intermediate good hH,that is, the analog of (14). Aggregating across firms (and paying attention tothe order of the country indices) we obtainZ sJ

0

MJ;HA;t ðhH ; xJÞdxJ þ

Z sJ

0

MJ;HE;t ðhH ; eJÞdeJ

¼ sJ

sHpJt ðhHÞpJ;HM;t

!�yHTðMJ;H

A;t þMJ;HE;t Þ: ð108Þ

Discussion

Import adjustment costs GMAH, J and GME

H, J are treated in GEM as expendituresassociated with intermediation activities (transportation, distribution,training, etc.) Thus, they show up somewhere else in the economy asrevenue for the firms that provide these services, and as dividend incomes forthe households who own these firms. Below, we include these components inthe definition of F.

Variants of the model can include trade in commodities, parts, rawmaterials, and other ‘‘upstream’’ intermediate goods. The reader is referredto Laxton and Pesenti (2003) for a detailed algebraic treatment.

Price Setting in the Tradables Sector and Exchange Rate Pass-Through

In Section III we characterized the optimal price set by a firm producingtradable intermediate goods for the local market. We now reconsider theprice-setting problem in the tradables sector from the vantage point of thefirm hH located in country H and exporting to all other countries JaH. Wealso introduce the distinction between import prices at the national level andat the border level. National import prices pJ(hH) are paid by firms located incountry J to purchase one unit of the variety hH. These are the prices thatenter equations such as (103) above. Border import prices are indexed with abar (for example �pJ(hH)). These are the prices set by the exporting firm hH.The difference between the two prices stems from trade barriers such astariffs. Below we consider a more general specification of the model in whichthe gap between the two prices reflects distribution costs and retail margins.

Paolo Pesenti

276


In terms of our notation, we have

pJt ðhHÞ ¼ ð1þ tarJ;HÞ�pJt ðhHÞ; (109Þ

where tarJ,H is a proportional tariff duty imposed by country J over itsimports from country H.

To the extent that different country blocs represent segmented marketsin the global economy, each firm hH in country H has to set differentprices for the domestic market and all other export markets. Because thefirm faces the same marginal costs regardless of the scale of production ineach market, the different price-setting problems are independent of eachother.

Exports are invoiced (and prices are set) in the currency of the destinationmarket. Accounting for (108), the price-setting problems of firm h in countryH at time t can then be characterized as follows:

max�pJt ðhHÞ

TRENDtEt

X1t¼t

DHt;tp

Ht;tgt;t

�½eH; Jt pJt ðhHÞ �mcHt ðhHÞ�sJ

sHð1þ tarJ;HÞ�pJt ðhHÞ

pJ;HM;t

!�yHT

�ðMJ;HA;t þMJ;H

E;t Þð1� GJ;HPM;tðhÞÞ; ð110Þ

where pMJ,H is the price of the basket of country J’s imports from country

H, and MAJ,HþME

J,H is country J’s aggregate imports from country H.The term eH, J is the bilateral real exchange rate between country H andcountry J (an increase in eH, J represents a real depreciation of country H’scurrency against country J ). The term GPM

H, J(hH) denotes adjustment costsrelated to changes of the price of good hH in country J. These costs are theanalogs of (44) above:

GJ;HPM;tðhHÞ �

fJ;HPM

2pJt

�pJt ðhHÞ=�pJt�1ðhHÞ�pJ;HM;t�1

� 1

!2

; (111Þ

where �pM is the inflation rate for bilateral imports prices. Despite itsfastidiousness, the notation above is straightforward and the equations areself-explanatory.


277


Accounting for firms’ symmetry (�pJ(hH)¼MJ,H and (1þ tart

J,H)�pJ(hH)¼pMJ,H in equilibrium), profit maximization yields

0 ¼ð1� GJ;HPM;tðhHÞÞ½eH;Jt �pJt ðhHÞð1� yHT Þ þ yHT mcHt ðhHÞ�

� ½eH;Jt �pJt ðhHÞ �mcHt ðhHÞ�qGJ;H

PM;t

q�pJt ðhHÞ�pJt ðhHÞ

� Et DHt;tþ1p

Ht;tþ1gt;tþ1½e

H;Jtþ1 �pJtþ1ðhHÞ �mcHtþ1ðhHÞ�

n

�MJ;H

A;tþ1 þMJ;HE;tþ1

MJ;HA;t þMJ;H

E;t

!qGJ;H

PM;tþ1q�pJt ðhHÞ

�pJt ðhHÞ): ð112Þ

If adjustment costs in the export market are relatively large, the prices ofcountry H’s goods in the foreign markets are characterized by significantstickiness in local currency. In this case, the degree to which short-termexchange rate movements (and other shocks to marginal costs in country H)affect import prices in country J is rather small—as in Chari, Kehoe, andMcGrattan (2002). If instead the fPM

J,H coefficients are small, expression (112)collapses to a markup rule, and exchange rate pass-through is full:

eH;Jt �pJt ðhHÞ ¼ eH;Jt �pJ;hM;t ¼yHT

yHT � 1mcHt : (113Þ

If firm hH faces small adjustment costs in all sales markets, both domesticand foreign, the law of one price holds at the border level:

pHQ;t ¼ eH;Jt �pJ;HM;t ¼yHT

yHT � 1mcHt : (114Þ

Discussion

In the previous paragraph, low exchange rate pass-through is the result ofnominal price stickiness in export prices. There is no need, however, to limitour analysis of the determinants of pass-through to the role of nominalrigidities. As an example of an alternative approach, the variant of GEMstudied in Laxton and Pesenti (2003) and based on work by Corsetti andDedola (2005) considers the role of the distribution sector. In this section webriefly summarize this extension and its implications for export prices.

Suppose that firms producing the final goods A and E in country J do notimport intermediate tradables directly from the foreign producers. Instead,firms in the distribution sector purchase tradables abroad and distribute themto the firms producing the final good. The distribution technology is Leontief:to make one unit of an intermediate good available to downstreamproducers, firms in the distribution sector require ZZ0 units of the

Paolo Pesenti

278


nontradables basket N. Thus, total demand for nontradables (13) in country

J is appropriately modified as ðpJt ðnJÞ=pJN;tÞ�yJN ðNJ

A;t þNJE;t þ GJ

N;t þ ZJP

HaJ

ðMJ;HA;t þMJ;H

E;t Þ.Firms in the distribution sector are perfectly competitive. Because of

distribution costs, there is a wedge between producer (border) and consumer(retail) prices even in the absence of tariffs and trade barriers. It follows that

pJt ðhHÞ ¼ ð1þ tarJ;HÞ�pJt ðhHÞ þ ZJpJN;t: (115Þ

From the vantage point of firm hH exporting to country J, the price-settingequation (112) then becomes

0 ¼ð1� GJ;HPM;tðhHÞÞ eH;Jt �pJt ðhHÞð1� yHT Þ

þeH;Jt ZJpJN;t

1þ tarJ;Hþ yHT mcHt ðhHÞ

#

� ½eH;Jt �pJt ðhHÞ �mcHt ðhHÞ�qGJ;H

PM;t

q�pJt ðhHÞ�pJt ðhHÞ�

þZJpJN;t

1þ tarJ;H

!� Et DH

t;tþ1pHt;tþ1gt;tþ1

n

�½eH;Jtþ1 �pJtþ1ðhHÞ �mcHtþ1ðhHÞ�MJ;H

A;tþ1 þMJ;HE;tþ1

MJ;HA;t þMJ;H

E;t

!

�qGJ;H

PM;tþ1q�pJt ðhHÞ

�pJt ðhHÞ þZJpJN;t

1þ tarJ;H

!): ð116Þ

The key implication of the presence of a distribution sector is that, even in theabsence of adjustment costs, pass-through is no longer full. In fact, when thefPMJ,H coefficients are small, the above expression collapses to a double-

markup rule:

eH;Jt �pJt ðhHÞ ¼ eH;Jt �pJ;HM;t ¼yHT

yHT � 1mcHt þ

ZJ

yHT � 1

eH;Jt pJN;t1þ tarJ;H

; (117Þ

eH;Jt pJt ðhHÞ ¼ eH; Jt pJ;HM;t ¼yHT

yHT � 1mcHt ð1þ tarJ;HÞ

þ ZJ

yHT � 1eH;Jt pJN;t: ð118Þ


279


Market Clearing in the World Economy

All profits and intermediation revenue accrue to Ricardian households:Z sH ð1�sHLCÞ

0

FHt ð jHÞdjH

¼Z sH ð1�sH

LCÞ

0

ð1þ i�t�1ÞGHB;t�1

eH;�t B�Ht�1ð jHÞp�t�1;tgt�1;t

djH

þZ sH ð1�sH

LCÞ

0

GHWFL;tð jHÞð1� tHL;tÞwH

t ð jHÞdjH

þZ sH

sH ð1�sHLCÞGHWLC;tðjHÞð1� tHL;tÞwH

t ð jHÞdjH

þZ sH

0

½ pHt ðnHÞ �mcHt ðnHÞ�

�Z sH

0

NHA;tðnH ; xHÞdxH þ

Z sH

0

NHE;tðnH ; eHÞdeH þ GH

N;tðnHÞ !

dnH

þZ sH

0

½ pHt ðhHÞ �mcHt ðhHÞ�

�Z sH

0

QHA;tðhH ; xHÞdxH þ

Z sH

0

QHE;tðhH ; eHÞdeH

!dhH

þXJaH

Z sH

0

½eH;Jt pJt ðhHÞ �mcHt ðhHÞ�

�Z sJ

0

MJ;HA;t ðhH ; xJÞdxJ þ

Z sJ

0


!dhH

þXJaH

Z sH

0

MH;JA ðxHÞG0

H;JMA;tðxHÞ

1� GH;JMA;tðxHÞ �MH;J

A G0H;JMA;tðxHÞ

!pH;JM MH;J

A ðxHÞdxH

þXJaH

Z sH

0

MH;JE G0H;JME;tðeHÞ

1� GH;JME;tðeHÞ �MH;J

E G0H;JME;tðeHÞ

!pH;JM MH;J

E ðeHÞdeH ; ð119Þ

where eH, � is the bilateral real exchange rate between country H and thecenter country.

It may be helpful to go through the single elements on the right-handside. The first expression (integral) is revenue associated with financialintermediation in the bond market. The second and third expressions arerevenue associated with wage adjustment by either forward-looking orliquidity-constrained agents. Note that revenue associated with price

Paolo Pesenti

280


adjustment is not included here, as it is a cost for some firms and a revenuefor others. The fourth expression is monopoly profits in the nontradablessector (if ‘‘entry costs’’ were considered, they would appear here as negativeitems offsetting these profits). The fifth expression is domestic monopolyprofits in the tradables sector. The sixth expression is export profits.

The last two expressions in (119) are revenue associated with importadjustment, both in the consumption sector and in the investment sector. Thesum of these last components is referred to as IMPADJ (for importadjustment) in what follows.

The tradable good hH can be used by domestic firms or imported byforeign firms:

TtðhHÞ �Z sH

0

QA;tðhH ;xHÞdxH þZ sH

0

QE;tðhH ; eHÞdeH

þXJaH

Z sJ

0

MJ;HA;t ðhH ;xJÞdxJ þ

Z sJ

0


!: ð120Þ

Market clearing in the international bond market requires

XJ

Z sJ ð1�sJLCÞ

0

B�Jt ð jJÞdjJ ¼ 0: (121Þ

Finally, government revenue is given by

GHREV ;t �

1

sH

Z sH

0

TTHt ð jÞdj þ tHK r

Ht

Z sHð1�sHLCÞ

0

KHt ð jÞdj

þtHLZ sH

0

wHt ð jÞ‘Ht ð jÞdj

!

þ 1

sH

XJaH

tarH;Jt

Z sJ

0

�pHt ðhJÞðMH;JA;t ðhJÞ þMH;J

E;t ðhJÞÞdhJ : ð122Þ

Together with the appropriate transversality conditions, this concludes thedescription of the equilibrium.

Measuring Output and Trade Balance

GEM codes all quantity variables in per-capita terms. For the vast majorityof the equations above the aggregation is straightforward. In this section wefocus on the two most important macrovariables in the model, grossdomestic product and the current account.


281


Define first per capita net financial wealth in country H as

FHt �

1

sHð1þ i�t�1Þ½1� GB;t�1�

Z sHð1�sH

LCÞ

0

eH;�t B�Ht�1ð jHÞp�t�1;tgt�1;t

djH : (123Þ

Aggregating the budget constraints across private and public agents afterimposing the appropriate transversality conditions, the law of motion forfinancial wealth is

EtDHt;tþ1p

Ht;tþ1gt;tþ1F

Htþ1 ¼ FH

t þ GHB;t�1ð1þ i�t�1Þe

H;�t B�Ht�1

p�t�1;tgt�1;t

þ pHN;tNHt þ pHT ;tT

Ht

þXJaH

ðpHM;t � �pH;JM;tÞðMH;JA;t þMH;J

E;t Þ

þ IMPADJHt � CH

t � pHE;tIHt � GH

t ; ð124Þ

where the total value of tradables is defined as

pHT ;tTHt � pHQ;tðQH

A;t þQHE;tÞ þ

XJaH

sJ

sHeH;Jt �pJ;HM;tðM

J;HA;t þMJ;H

E;t Þ: (125Þ

Recall that the variable IMPADJ is the sum of the last two terms in (119).Expression (125) can be written as

CURBALHt ¼ eH;�t B�Ht �

B�Ht�1p�t�1;tgt�1;t

!¼ NFPH

t þ TBALHt : (126Þ

The left-hand side of (126) is country H’s current account in domesticconsumption units. The first term on the right-hand side is net factorpayments from the rest of the world to country H:

NFPHt ¼

i�t�1eH;�t B�Ht�1

p�t�1;tgt�1;t: (127Þ

TBAL is the trade balance or net exports:

TBALHt ¼ EXH

t � IMHt ; (128Þ

where total exports EX are evaluated at border prices:

EXHt ¼ pHT ;tT

Ht � pHQ;tðQH

A;t þQHE;tÞ; (129Þ

Paolo Pesenti

282


and, similarly, total imports IM are evaluated at border prices:

IMHt ¼

XJaH

�pH;JM;tðMH;JA;t þMH;J

E;t Þ: (130Þ

Using the definition above, the model-based gross domestic product (inconsumption units) is

GDPHt ¼ AH

t þ pHE;tEHt þ pHN;tG

HN;t þ TBALH

t

¼ pHN;tNHt þ pHT ;tT

Ht þ

XJaH

ðpHM;t � �pH;JM;tÞðMH;JA;t þMH;J

E;t Þ

þ IMPADJHt : ð131Þ

Note that there is a discrepancy between GDP measured according tonational accounting standards (goods output), and GDP measured asmanufacturing output. This discrepancy reflects the portion of the revenuefrom sales of goods associated with making imports available to downstreamusers, such as costs incurred with imports adjustment and wedges betweenborder- and market-prices of imported goods.

REFERENCESBotman, D., P. Karam, D. Laxton, and D. Rose, 2007, ‘‘DSGE Modeling at the Fund:

Applications and Further Developments,’’ IMF Working Paper 07/20 (Washington,International Monetary Fund).

Chari, V.V., P. Kehoe, and E. McGrattan, 2002, ‘‘Can Sticky Prices Generate Volatileand Persistent Real Exchange Rates?’’, Review of Economic Studies, Vol. 69, No. 3,pp. 533–63.

Corsetti, G., and L. Dedola, 2005, ‘‘Macroeconomics of International PriceDiscrimination,’’ Journal of International Economics, Vol. 67, pp. 129–56.

Corsetti, G., and P. Pesenti, 2001, ‘‘Welfare and Macroeconomic Interdependence,’’Quarterly Journal of Economics, Vol. 116, No. 2, pp. 421–46.

_______, 2005, ‘‘International Dimensions of Optimal Monetary Policy,’’ Journal ofMonetary Economics, Vol. 52, No. 2, pp. 281–305.

Faruqee, H., D. Laxton, D. Muir, and P. Pesenti, 2007, ‘‘Smooth Landing or Crash?Model-Based Scenarios of Global Current Account Rebalancing,’’ in G7 CurrentAccount Imbalances: Sustainability and Adjustment, ed. by R. Clarida (Chicago,University of Chicago Press).

_______, forthcoming, ‘‘Would Protectionism Defuse Global Imbalances and SpurEconomic Activity? A Scenario Analysis,’’ Journal of Economic Dynamics andControl.

Greenwood, J., Z. Herkowitz, and G. Huffman, 1988, ‘‘Investment, Capacity Utilizationand the Business Cycle,’’ American Economic Review, Vol. 78, pp. 402–17.

Ireland, P, 2001, ‘‘Sticky-Price Models of the Business Cycle: Specification and Stability,’’Journal of Monetary Economics, Vol. 47, No. 1, pp. 3–18.


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Juillard, M., P. Karam, D. Laxton, and P. Pesenti, 2006, ‘‘Welfare-Based MonetaryPolicy Rules in an Estimated DSGE Model of the U.S. Economy,’’ ECB WorkingPaper No. 613, April (Frankfurt, European Central Bank).

Laxton, D., P. N’Diaye, and P. Pesenti, 2006, ‘‘Deflationary Shocks and Monetary Rules:An Open-Economy Scenario Analysis,’’ Journal of the Japanese and InternationalEconomies, Vol. 20, No. 4, pp. 665–98.

Laxton, D., and P. Pesenti, 2003, ‘‘Monetary Rules for Small, Open, EmergingEconomies,’’ Journal of Monetary Economics, Vol. 50, No. 5, pp. 1109–46.

Obstfeld, M., and K. Rogoff, 1995, ‘‘Exchange Rate Dynamics Redux,’’ Journal ofPolitical Economy, Vol. 103, pp. 624–60.

_______, 2000, ‘‘New Directions for Stochastic Open Economy Models,’’ Journal ofInternational Economics, Vol. 50, No. 1, pp. 117–53.

_______, 2002, ‘‘Global Implications of Self-Oriented National Monetary Rules,’’Quarterly Journal of Economics, Vol. 117, pp. 503–36.

Rotemberg, J., 1982, ‘‘Sticky Prices in the United States,’’ Journal of Political Economy,Vol. 90, pp. 1187–211.

Paolo Pesenti

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The Impact on the United States of the Rise inEnergy Prices: Does the Source of the Energy Market

Imbalance Matter?

JARED BEBEE and BEN HUNT�

This paper uses a variant of the IMF’s Global Economy Model (GEM) toillustrate how the macroeconomic impact on the United States of the rise inenergy prices since the end of 2003 may vary depending on the source of theenergy market imbalance. If oil market supply-side factors are driving priceshigher, GDP will be permanently lower than it otherwise would be. However, ifhigher energy prices reflect primarily increased demand due to rising laborsupply or tradable sector productivity growth in emerging Asian economies, forexample, then GDP in the United States could actually rise in the long run. Thisoccurs because the United States receives some positive terms-of-trade effectscoming through nonenergy tradable goods prices that offset the negativeimplications for GDP of permanently higher energy prices. [JEL E3, E52]

IMF Staff Papers (2008) 55, 285–296. doi:10.1057/imfsp.2008.7;

published online 8 April 2008

The rise in energy prices since end-2003 has had an important impact onthe large industrial countries. Inflation, which had long been subdued,

even during the high-tech boom years of the late 1990s, has accelerated andGDP growth, although still healthy, has slowed relative to expectation. This

�Jared Bebee is a research assistant in the IMF’s European Department. Ben Hunt is thedeputy division chief of Division 3 in the IMF’s Asia and Pacific Department. The authorsthank the anonymous referee and seminar participants at the 2007 IMF Workshop on OpenEconomy Models for Policy Evaluation for helpful comments.



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paper outlines the extensions to the IMF’s Global Economy Model (GEM)that enable it to be used to examine the economic impact of rising energyprices. Simulation experiments are presented that estimate the macro-economic impact in the United States of the run-up in energy prices sinceend-2003. Further, the model is used to consider whether the source of energymarket imbalance has implications for the macroeconomic impact.

The model incorporates energy (oil and natural gas) as a finalconsumption good as well as a primary input in production. Becauseenergy enters the consumption basket directly, increases in energy pricesquickly affect households through their impact on the level of consumerprices and thus households’ real wages. With energy entering production,increases in energy costs affect overall aggregate supply capacity as firmsreduce output and factor utilization rates given the real increase in their costsstructures. Because there is a fully specified market for energy in the model,the analysis can consider how the source of the imbalance between energysupply and demand influences the macroeconomic consequences.

The analysis of the impact of higher energy prices focuses on three issues:the implications for the level of economic activity; the direct impact onheadline inflation; and how the source of the energy market imbalance affectsthe impact. The simulation results suggest that the increase in energy pricessince end-2003 increased U.S. headline consumer price index (CPI) inflationby roughly 1 percentage point. Although in the short run the impact onGDP is negative, the long-run implications will depend on the factorsunderlying higher energy prices. If higher energy prices are being drivenby nonenergy sector supply factors in emerging Asia, for example, thesimulation results suggest that the long-run impact on U.S. GDP could bepositive.

I. Energy in the GEM

GEM is a large multicountry macroeconomic model derived completely fromoptimizing foundations. The version used here characterizes the behavior oftwo countries, home (United States) and foreign (the rest of the world).Below, only a brief overview of GEM is presented and the interested readercan look to Hunt (2005) for a detailed description of the incorporation ofenergy into GEM as well as the calibration of the energy sector. Detaileddescriptions of the model’s general structure and properties can be found inLaxton and Pesenti (2003); and Hunt and Rebucci (2005).

Households

Households consume energy goods directly along with other tradable andnontradable goods. Households’ final consumption bundle is given by

A ¼ f ðN;Q;M;QE ;MEÞ; (1Þwhere A is the bundle of final goods consumed by households, N representsnontradable goods, Q represents domestically produced tradable goods, M

Jared Bebee and Ben Hunt

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represents imported tradable goods, QE represents domestically producedenergy goods, and ME represents imported energy goods. The function, f, is anested constant elasticity of substitution (CES) aggregator. Because energyenters the final good directly, energy price shocks will have an immediateimpact on headline inflation. However, because there is a distribution sectorin energy, which uses nontradables to market traded goods and representsthings like transportation and refining, the impact of changes in the producerprice of energy on the final consumption price is muted.

Firms

Firms produce three types of goods: nontradable goods, nonenergy tradablegoods, and a tradable energy good. Firms combine capital, labor, and energyto produce the tradable and nontradable goods. The production process isgiven by

Y ¼ f ðK;L;QE ;MEÞ; (2Þwhere Y denotes the output of tradable and nontradable goods (N,Q), K isthe capital input, L is the labor input, QE is the domestically produced energyinput, and ME is the imported energy input. The production technology, f,embodies CES; however, firms face adjustment costs in both capital andenergy that reduce the short-run elasticity of substitution below the long-runelasticity.

Energy producing firms combine capital, labor, and land to produce thetradable energy good. The production technology is given by

QE ¼ f ðK;L;LandÞ; (3Þ

where QE is domestically produced energy, K represents the capital input, Ldenotes the labor input, and Land is the known available reserve of energy(oil and natural gas). The production technology, f, embodies CES. It isassumed that there is monopolistic competition in energy productionenabling firms to charge a markup over the marginal cost of production.

Calibration

Energy is assumed to represent oil and natural gas given the historicalcorrelation in their prices. The shares in GDP of the consumption andproduction of energy valued at producer prices are calibrated to their levelsas of end-2003 (Table 1). In the rest of the world, it is assumed that roughlyone-third is consumed directly by households with the remaining two-thirdsused by intermediate goods producers.

The calibration of the production of energy assumes that land is theprimary input. The parameter that determines the share of land in productionis set to 0.96. Parameters determining capital’s and labor’s shares are setat 0.025 and 0.015, respectively. In the United States, it is assumed that inenergy production it is difficult to substitute among inputs, with the elasticityof substitution set at 0.2. In the rest of the world it is assumed that energy

THE IMPACT ON THE UNITED STATES OF THE RISE IN ENERGY PRICES

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production is Cobb Douglas. The production of intermediate goods is alsoassumed to be Cobb Douglas; however, because it is costly to adjust theamount of energy used in production, the short-run elasticity of substitutioncan be calibrated to be significantly below unity. The calibration ofadjustment costs is set to yield an evolution in energy’s share of GDP inUnited States similar to that witnessed after the oil price shock in 1973. In theabsence of costly adjustment of energy in households’ final consumption, it isassumed that the elasticity of substitution between energy and tradableintermediate goods is low, 0.175.

The elasticity of substitution between domestic and imported energy inintermediate goods production (100) and in final goods production (10) ischosen to ensure that given the calibration of the production of energy, therest-of-world and U.S. prices of energy move in parallel. Further, over thebusiness cycle, the relative price of energy is the most variable relative price,consistent with the data.

II. Simulation Experiments

The Rise in Oil Prices Since End-2003

Given the fully specified market for energy in GEM, the price of energy is theresult of the interaction of supply and demand factors. To implement anincrease in the price of energy in this section, factors on the supply side of theenergy market are altered, the markup or available reserve of energy (Land ).This implementation is consistent with the interpretation of the increases inenergy prices that occurred in the 1970s.

To examine the macroeconomic implications of rising energy prices, anenergy price increase that broadly matches that seen in oil prices over2004:Q1 to 2007:Q1 is simulated. One important feature of the recent energyprice increase has been the gradual evolution of expectations regarding itspersistence. To capture the impact of gradually evolving expectations, thesimulation in this section is built up, quarter by quarter, with an energy price

Table 1. U.S. Energy Intensity at End-2003 as a Share of Nominal GDP(Oil and natural gas valued at producer prices)

Production Imports Total Available Total Use Input Consumption Net Exports

United

States 1.50 1.26 2.76 2.72 1.23 1.49 �1.22

Sources: Organization for Economic Cooperation and Development (OECD);International Energy Agency; and IMF staff estimates.

Note: Data from OECD on indigenous production, imports, and exports. OECDconversion factor of 7.37 used for crude oil. Conversion: tons to barrels to dollar value using$30 per barrel. Natural gas conversion: cubic meters to dollar value using $162 per cubic meter.


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shock that matches that seen in the data both in terms of its magnitude andits expected persistence. The left-hand panel in Figure 1 presents the energyprice shock considered, with the dashed lines denoting the expectedpersistence of the shock in each quarter. The right-hand panel in Figure 1illustrates the actual increase in oil prices and the futures’ market path in eachquarter.

The simulations are run assuming that monetary policy follows aninflation-forecast-targeting rule, and the responses of the key macroeconomicvariables to the multiperiod energy price increase are presented in Figure 2.The peak effect on year-over-year CPI inflation is roughly 1 percentage point,reflecting the energy intensity of final consumption. The peaks occur in thefifth quarter. Beyond that horizon, the impact on inflation moderates.Assuming oil prices follow the futures market path as of end-March 2007, theimpact on year-over-year CPI inflation turns negative before returningtoward baseline. Because of the model’s structure, the direct impact of energyprice changes is reflected immediately in the CPI. In reality, this pass-throughis likely slower and, consequently, the precise quarterly dynamics should notbe interpreted too literally.1 The impact of the shock on GDP is negative andgrows over time as the supply side of the economy adjusts to the permanentlyhigher input cost.

One of the most striking features of this simulation is the very benigninflation outcome. This primarily reflects the fact that workers accept thedecline in their real consumption wage. In GEM, the real wage is

Figure 1. Energy Prices—Simulation and Data

0

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Oil Prices Spot and Futures (percent deviation from $29 per barrel)

Source: Bloomberg and GEM simulations.Note: Solid line represents actual path and expected path beyond quarter 13. Dashed line

represents expected path at each quarter prior to quarter 13.

1Because of the model’s complete choice theoretic framework, there is no scope formaking ad hoc changes to the dynamic adjustment properties to more closely match thepass-through properties in the data.


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Figure 2. An Energy Price Increase Matching Recent History(Percent deviation from baseline)

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fundamentally pinned down by the interaction of households’ preferencesand firms’ production technology. In the long run, the increase in the realfactor cost, energy, leads to a reduction in the capital stock, a decline in themarginal product of labor and, consequently, a reduction in the real producerwage. Although costly adjustment of nominal wages slows the decline in thereal wage, the real wage declines quickly. Households accept the decline inthe real consumption wage from both the rise in energy prices and the declinein the real producer wage. Consequently, the increase in firm’s energy costs isoffset by lower real wages and there are no second-round effects flowingthrough to nonenergy intermediate goods prices and on to CPI inflation. Asshown in Hunt, Isard, and Laxton (2002), if workers do not attempt to resistthis decline in their real wage, then energy price shocks will not result inpersistent inflation even if policymakers accommodate the direct impact ofthe shock on the price level. GEM simulations that consider alternativeresponses of both labor suppliers and monetary authorities that can leadto more persistent rises in inflation under these types of energy marketsupply-side price rises are presented in Hunt (2006).

The Implications of the Source of the Energy Market Imbalance

The energy price shock considered to this point is generated by alteringfactors on the supply side of the oil market (markup and Land ). This wouldbe an appropriate characterization of the shock if demand was growing asexpected, but the supply of energy was not. However, if demand for energy isgrowing faster than expected because of other factors in the nonenergysupply side of the economy, then the simulations will be ignoring animportant dimension. Specifically, it is often claimed that faster thanexpected growth in emerging Asia is driving energy prices higher. This rapidgrowth in Asia is thought to be contributing to declining prices for manymanufactured goods imported by industrial countries. Ignoring this effectwould overstate the negative impact of higher energy prices on industrialcountry GDP because of the positive terms-of-trade effect of fallingnonenergy import prices.

To consider how important this positive terms-of-trade effect might be,we compare three alternative energy price shocks of similar magnitude. Thefirst shock is generated the same way as those previously considered,changing energy sector supply-side factors. The second is generated byincreasing labor supply in the rest of the world. The third is generatedby temporarily increasing tradable sector productivity growth in the rest ofthe world. The magnitudes of the shocks are chosen to generate an increase inthe price of energy that rises over 10 years by a little over 50 percent withroughly half of that increase being permanent in the long run. The shocks arecalibrated to obtain as similar as possible dynamic paths for the price ofenergy, but they are not identical.

The results for some variables related to the output effect are presented inFigure 3. The solid line traces out the path when energy sector supply-side


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Figure 3. Alternative Drivers of Higher Energy Prices(Percent deviation from baseline)

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Note: Solid line denotes energy sector supply; dotted line denotes rest-of-world nonenergytradable sector productivity; dashed line denotes rest-of-world labor supply.


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Figure 4. Alternative Drivers of Higher Energy Prices(Percent deviation from baseline)

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Note: Solid line denotes energy sector supply; dotted line denotes rest-of-world nonenergytradable sector productivity; dashed line denotes rest-of-world labor supply.


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factors alone are generating the higher prices. The dashed line traces out theimpact when an increase in labor supply in the rest of the world is the sourceand the dotted line traces out the paths when the driver is an increase inproductivity in the nonenergy tradable sector in the rest of the world. Thefirst point to note is that in the short run, the impact on output is broadlysimilar. Initially GDP declines (as do investment and consumption) in allcases. However, the decline in GDP is temporary when nonenergy sectorsupply factors in the rest of the world are driving the shock and GDP risesabove baseline after roughly five years. A key factor driving this result isexport demand in the rest of the world. Quickly rising incomes fuel demandfor U.S. exports. In addition, the falling prices of imports from the rest of theworld increase the relative value of U.S. exports. Unlike under the pureenergy sector shock, production in the United States switches away fromtradables toward nontradables. In the pure energy sector supply shock,nonenergy tradables as a share of GDP in the United States rise becausenonenergy tradables must pay for the now more expensive imported energy.Whether the nonenergy sector shock arises from labor supply or tradableproductivity growth matters for the long-run value of the dollar. Under thelabor supply shock, the U.S. real exchange rate appreciates in the long run.The appreciation helps generate the declining relative price of rest-of-worldtradables sufficient to increase demand given greater supply capacity. Underthe tradable sector productivity shock, the Balassa-Samuelson effect leads toa depreciation in the U.S. real exchange rate.

The variables graphed in Figure 4 illustrate a very interesting point aboutU.S. CPI inflation. Under the two nonenergy sector shocks, the rise in CPIinflation exhibits considerable persistence. This reflects the impact of growingdemand in the rest of the world and the positive terms-of-trade componenton the real wage. Under the energy sector shock, the real wage declinespermanently. As noted previously, this reflects the fact that the permanentincrease in a factor cost leads to a reduction in the utilization of all inputs, alower marginal product of labor, and, consequently, a lower equilibrium realwage. Provided labor suppliers accept this reduction quickly, there is nopersistence in the inflationary impact of higher energy prices. However, withrising demand for exports and the wealth effect of the terms-of-tradeimprovement, the long-run capital stock rises (beyond horizon shown in thecharts) as does the real wage. The recovery in the real wage coupled withgreater demand pressures leads to persistence in the rise in inflation. In fact,interest rates must rise and remain above baseline for an extended periodunder the nonenergy sector shocks to contain the inflationary consequences.

There are several reasons why these simulation results should beinterpreted qualitatively rather than quantitatively. First, the magnitude ofthe positive long-run impact on U.S. GDP if nonenergy supply factors inemerging Asia are driving higher energy prices will depend on trade linkages.The stronger are the trade linkages between the United States and thoseemerging Asian countries driving the higher energy prices, the larger willbe the positive effects. Second, the short-run inflationary consequences


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will depend on the behavior of the exchange rate, with China managing itsexchange rate, the impact is likely to be different than in these simulationsthat assume a free floating exchange rate. Third, rising wealth in emergingAsia is probably also having an impact on the energy intensity of demand.This will have an impact identical to the pure energy sector supply shock,that is, driving up energy prices with no positive offsetting affects onindustrial country GDP. Fourth, faster than expected growth in emergingAsia is likely only one of the factors driving higher energy prices. The actualresults will depend on how important this is relative to energy sector supplyfactors. Finally, these shocks are done under certainty, although there is stillconsiderable uncertainty about what is in fact driving higher energy pricesand how persistent they are likely to be. Expectations will play an importantrole in shaping the dynamic adjustment paths, and future work shouldexplore the implications of this carefully.

III. Conclusions

The simulations results suggest that the impact of higher energy prices onU.S. GDP will depend on the underlying factors driving energy prices. Ifincreases in nonenergy sector supply factors in emerging Asia are animportant component, then there will be some offsetting effects to thenegative impact of a permanent increase in a factor cost. Headline inflationspikes up initially and persistent inflation effects can arise. Under the energysector supply shock, persistent above-target inflation does not emerge.However, when higher energy prices are being driven by nonenergy supplyfactors in the rest of the world, then persistent inflation effects arise becauseof additional demand pressures and a long-run increase in real wages.

Although the simulation results from the rise in energy prices seen sinceend-2003 suggest that, for the United States, the initial negative implicationsfor GDP are significant, there are reasons for optimism. If increases in othersupply factors in the nonenergy sector in emerging Asia are driving energyprices higher, then the United States will reap some benefit from fallingnonenergy import prices and rising demand for exports. In the long run,GDP could rise depending on the extent of trade linkages with emerging Asiaand the extent to which higher energy prices are resulting from faster thanexpected growth in emerging Asia. Unlike the price rises in the early 1970s,which evidence suggests were driven by energy market supply factors, thecurrent increase appears to be driven by increased demand for energy inemerging Asia (Kilian, 2006) owing to rapid productivity growth (Hunt, 2007).In addition, there has not appeared to be a significant increase in the energyintensity of demand in emerging Asia (Elekdag and others, 2007), raising theprobability that positive long-run benefits will materialize. However, oneinteresting aspect in the simulations is that monetary authorities might haveto be even more vigilant about the inflationary consequences if nonenergymarket supply factors in the rest of the world are important drivers of higherenergy prices.


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REFERENCESElekdag, S., R. Lalonde, D. Laxton, D. Muir, and P. Pesenti, 2007, ‘‘Oil Price

Movements and the Global Economy: A Model-Based Assessment,’’ IMF StaffPapers, Vol. 55, No. 2 (Washington, International Monetary Fund).

Hunt, B., 2005, ‘‘Oil Price Shocks: Can they Account for the Stagflation in the 1970s?’’IMF Working Paper 05/215 (Washington, International Monetary Fund).

_______, 2006, ‘‘Oil Price Shocks and the U.S. Stagflation of the 1970s: Some Insightsfrom GEM,’’ The Energy Journal, Vol. 27, No. 4, pp. 61–80.

_______, 2007, ‘‘UK Inflation and Relative Prices Over the Last Decade: How Importantwas Globalization?’’ IMF Working Paper 07/208 (Washington, InternationalMonetary Fund).

_______, and R. Rebucci, 2005, ‘‘The U.S. Dollar and Trade Deficit: What Accounts forthe Late 1990s?’’ International Finance, Vol. 8, No. 3, pp. 399–434.

_______, P. Isard, and D. Laxton, 2002, ‘‘The Macroeconomic Effect of Higher OilPrices,’’ National Institute Economic Review, No. 179 (January), pp. 87–103.

Kilian, L., 2006, ‘‘Not All Oil Price Shocks Are Alike: Disentangling Demand and SupplyShocks in the Crude Oil Market,’’ CEPR Discussion Paper No. 5994 (London,Centre for Economic Policy Research).

Laxton, D., and P. Pesenti, 2003, ‘‘Monetary Policy Rules for Small, Open, EmergingEconomies,’’ Journal of Monetary Economics, Vol. 50, No. 3, pp. 1109–46.


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Oil Price Movements and the Global Economy:A Model-Based Assessment

SELIM ELEKDAG, RENE LALONDE, DOUGLAS LAXTON, DIRK MUIR,and PAOLO PESENTI�

This paper develops a five-region version—Canada, a group of oil-exportingcountries, the United States, emerging Asia, and Japan plus the euro area—ofthe global economy model encompassing production and trade of crude oil. Inthe presence of real adjustment costs that reduce the short- and medium-termresponses of oil supply and demand, our simulations can account for largeendogenous variations of oil prices with large effects on the terms of tradeof oil-exporting versus oil-importing countries, and result in significant wealthtransfers between regions. This is especially true when we consider a sustainedincrease in productivity growth or a shift in production technology toward moreoil-intensive goods in regions such as emerging Asia. In addition, we study theimplications of higher taxes on gasoline, showing that such a policy couldincrease world productive capacity while being consistent with a reduction in oilconsumption. [JEL E66, F32, F47]


published online 25 March 2008

�Selim Elekdag is an economist with the IMF Research Department; Rene Lalonde isa model adviser with the Bank of Canada’s International Department; Douglas Laxton is anassistant to the director of the IMF’s Research Department; Dirk Muir is a principalresearcher with the Bank of Canada’s International Department; and Paolo Pesenti is anassistant vice-president from the Federal Reserve Bank of New York, and an associate of theCEPR and NBER. The authors thank Ryan Felushko, Laura Leon, Lei Lei Myaing, SusannaMursula, and Chris Tonetti for invaluable research assistance. This paper has benefited fromhelpful comments from Riccardo Cristadoro of the Banca d’Italia and participants of theBank of Canada Workshop on Commodity Price Issues, the IMF Workshop on OpenEconomy Models for Policy Evaluation and presentations at the Bank of Japan, the HongKong Monetary Authority, and the European Central Bank.



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Over the last few years, the persistent surge in oil prices in both the spotand futures markets has represented a challenge to the forecasting

abilities of private and public institutions worldwide. Even as the averagemonthly spot price of oil increased from $19 per barrel at end-2001 to $43 atend-2004, market participants expected prices to decline over time to ‘‘morereasonable levels.’’ However, since 2005, there have been striking upwardrevisions of near- and longer-term price expectations from the futuresmarkets, and the oil spot price in 2006 occasionally rose above $70 per barrel,and has stayed persistently above $50 per barrel.

This paper provides a preliminary assessment of these issues—and theirrelevance for the world macroeconomy—by developing an extended versionof the global economy model (GEM) that explicitly encompassesconsumption, production, and trade in oil. We address two key questionsabout the oil price run-up since 2003. First, what are the underlying causes ofthe oil price run-up? And given those causes, what are some potential policymeasures that could reduce oil prices with the least amount of (negative)impact on global welfare? Using the GEM allows us to study developmentsin the world economy that have significant effects on oil prices, theinternational transmission mechanism through terms-of-trade fluctuations,and the related wealth transfers between oil-importing and oil-exportingregions. We explore mainly the demand side—namely robust global growthsupported by the rapid (and continual) economic expansion in emerging Asia(particularly in China and India), which seems to have surprised marketparticipants (IMF, 2006).

I. Oil and the World Economy: Some Stylized Facts

There has been a persistent upward trend in oil prices over the last few years.Part of this is associated with repeated unanticipated increases in oil demandas GDP growth has been higher than expected, particularly in emerging Asia(IMF, 2005).

Although we will argue that oil price increases are being driven mainly bythe increase in oil demand, the magnitude of these increases is most likelyresulting from oil supply factors (which figure prominently in our calibrationof the oil sector). The most prominent of these is that OPEC spare capacity(including Iraq) has bottomed out. This fact is highlighted in Figure 1, whichshows quarterly figures for OPEC spare capacity as a percent of total supply,and the average petroleum spot price (APSP).1 Starting in mid-2003, there isa divergence between oil prices and spare capacity, which by June 2006, wasestimated at around 1.3 million to 1.8 million barrels per day (EnergyInformation Administration, 2007). At the same time, lagging investment ininfrastructure and refinery construction, as well as the aforementioned fact

1The APSP is the simple arithmetic average of the U.K. Brent, Dubai Fateh, and WestTexas Intermediate spot oil prices.

Selim Elekdag and others

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that it takes, on average, 11 years before an oil discovery is ready forproduction, have further compounded supply-side rigidities. Along withheightened geopolitical risks, oil supply has become markedly binding,making it excessively vulnerable to even minor disruptions.

II. New Features and the Calibration of the Model

For the complete description of the GEM, the reader is referred to Pesenti(2008). Here it suffices to discuss the regional composition, the addition ofthe oil and gasoline sectors, and the overall calibration of the model.2

The world economy consists of five country blocs (‘‘regions’’), dividedinto two groups. The oil-exporting regions consist of Canada and the groupof oil-exporting countries (GOEC) that includes OPEC, Mexico, Norway,and Russia. The oil-importing regions consist of the United States, emergingAsia, and the bloc of remaining countries that includes Japan and theEuropean Union.

There are extensive modifications to the model to allow the production ofrefined oil (‘‘oil’’ for short) as a traded upstream intermediate good, andgasoline (car fuel and retail heating fuel) as a nontraded downstreamintermediate good.

Figure 1. OPEC-11 Spare Capacity and World Oil Prices

2000 2001 2002 2003 2004 20050

5

10

15

20

25

30

10

20

30

40

50

60

70

OPEC-11 spare capacityAverage petroleum spot price (APSP)

Per

cent

of t

otal

cap

acity

U.S

. dol

lars

per

bar

rel

2A more complete description of the oil and gasoline sectors can be found in Lalonde andMuir (2007).

OIL PRICE MOVEMENTS AND THE GLOBAL ECONOMY

299


As with traded and nontraded goods, gasoline is produced with domesticlabor inputs, domestic capital, and oil. Oil can be imported or produceddomestically. Gasoline forms part of the final consumption good, and,therefore, enters the consumer price index (CPI) directly. This allows themonetary authority to pursue an inflation targeting regime, based on CPIexcluding energy (CPIX). Oil is the only traded upstream intermediate good.It is produced with capital, labor, and crude oil reserves.

As with other intermediate goods, both gasoline and oil producers havemarket power that can change over time. Oil prices are not subject tonominal rigidities, unlike intermediate goods prices or wages. However, thereare real adjustment costs on the use of capital and labor in the supply of bothoil and gasoline that result in very limited short-term responses of theirproduction to changes in demand. These are introduced in an attempt tocapture the effects of severe capacity constraints in the energy sector, as wellas the multiyear delay between oil discoveries and their commercialavailability. On the demand side, these real adjustment costs capture thefact that it takes years to change the fuel efficiency of the stock of motorvehicles or to replace the stock of technology that is used for heating andcooling. As a result, these real adjustment costs imply that both the demandand supply for crude oil will be extremely inelastic in the short run, requiringlarge movements in crude oil prices to clear the energy market.

There are several caveats about the model structure of the oil sector.First, oil is assumed not to be a storable commodity whose price is linked tothe rate of return on other assets, thereby implying that its price isdetermined entirely on its use value. Second, since the model does not includeoil inventories (which would offset the real adjustment costs in the case oftemporary oil demand shocks, for example), oil and gasoline prices mayrespond too strongly to temporary shocks. Overall, this implies that themodel is not meant to explain very short-run variations in oil prices due tomarket disruption: rather, it has been designed to explain the interaction ofoil prices and the world economy over the medium term.

The calibration of the entire model builds upon work already presentedin Faruqee and others (2007), but with extensive modifications for Canada,the United States, and the euro area based on Murchison and Rennison(2006); Gosselin and Lalonde (2005); and Coenen, McAdam, and Straub(2008), respectively, and more generally on Juillard and others (2006), foundin Table 1.

To calibrate the oil and gasoline sectors, we attempt to capture the broadfeatures of the world market (see the bottom of Tables 1 and 2). In the case ofoil production, some oil-exporting countries of the GOEC have the leastcapital-intensive technology (capital share of oil production is 12.9 percent),but Canada has a relatively capital-intensive technology (capital share ofoil production of 29.7 percent), meant to capture realistic features of the oilextraction process (such as the Athabasca tar sands). The elasticity ofsubstitution among factors used in oil production is 0.6, but it is 0.7 ingasoline production. The lower degree of elasticity in oil production reflects


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some of the long-term costs in switching production technology, whereas thehigher degree in gasoline production reflects the fact that there are severalmethods of varying efficiency (and hence capital and labor intensity) tomanufacture gasoline from oil. To significantly lower short-term oil priceelasticities of demand toward near-Leontieff levels, we impose strong short-run real adjustment costs on capital and labor, using the Rotemberg (1982)formulation, of around 300, with additional adjustment costs associated withchanges in the use of oil in the production of intermediate tradables,nontradables, and gasoline, and in the use of gasoline as a component of thefinal consumption bundle (also set to 300).

To allow for a world price for oil and a single global market, there arevery high elasticities of substitution between domestic and imported oil(at 10), although for imported oil there is less preference as to the regionof origin (at 3). Moreover, we have assumed almost no price markup inthe oil sector for any region, with the exception of the group of exportingcountries, which has a markup approaching 500 percent. It is estimatedthat the cost of oil production for OPEC countries is somewhere around$2 to $5 per barrel, while for a country like Canada it is closer to $25

Table 1. Steady-State National Accounts—Expenditure Side(In percent)

Ratio of GDP Canada

Oil-Exporting

Countries

United

States

Emerging

Asia

Remaining

Countries

Private consumption 56.5 64.3 65.8 50.1 58.8

Private investment 17.4 16.8 16.4 34.5 18.3

Government

expenditures

26.0 19.1 17.2 15.8 23.2

Trade balance 0.1 �0.2 0.5 �0.4 �0.2

Exports 37.1 23.8 14.2 26.1 8.8

Oil for producing

gasoline

1.2 2.0 0.1 0.2 0.2

Other oil 4.6 7.8 0.2 0.7 0.6

Imports 37.0 24.0 13.7 26.5 9.0

Oil for producing

gasoline

0.4 0.3 0.3 0.6 0.2

Other oil 1.8 1.4 1.4 2.3 1.0

Total oil demand 3.9 3.9 3.5 5.0 2.7

Gasoline demand 3.0 2.3 3.3 2.5 3.1

Net foreign assets �7.5 21.4 �50.0 35.0 23.0

Percent share of

world GDP

2.4 9.3 30.1 10.6 47.6


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(Energy Information Administration, 2007). Therefore for any given oil pricein the world market, the group of the oil-exporting countries has the largestmarkup to sustain the price of oil and guarantee production in the otherregions, where production costs are much higher. For gasoline, the markup isaround 16 percent for all regions. This excludes government taxes ongasoline, which we set for illustrative purposes at 30 percent in Canada andthe remaining countries bloc, and 15 percent elsewhere.

Bilateral world trade flows are calibrated to reflect the 2003 levels ofimports in the five regions, whereas the aggregate export-to-GDP ratios arethose necessary to support the net foreign asset-to-GDP ratios we havechosen (Table 1).3 The United States is a large net debtor (50 percent ofGDP), Canada is a small net debtor (7.5 percent of GDP), and the otherthree regions are all net creditors of varying degrees (with emerging Asiabeing the largest net creditor at 35 percent of GDP). The higher trade is, as apercent of GDP, the more likely an economy will be affected strongly byforeign shocks. Canada is very open (exports plus imports to GDP are 74.1percent), as is emerging Asia (52.6 percent) and the GOEC (48.0 percent),while the United States (27.9 percent), and the European Union and Japan(17.8 percent) are much more insulated from foreign disturbances. However,this is not necessarily the case in the oil market (Energy InformationAdministration, 2007). Here, not only does the degree of openness matter,but the direction of trade as well. The net exporters are Canada at 3.7 percent

Table 2. Steady-State National Accounts—Production Side(In percent)

Ratio of

GDP Canada

Oil-Exporting

Countries

United

States

Emerging

Asia

Remaining

Countries

Tradables 43.9 36.2 48.2 65.1 45.8

Nontradables 49.5 53.4 50.0 34.3 50.0

Gasoline 2.3 2.0 2.9 2.2 2.4

Oil production 7.5 11.9 3.1 2.3 2.1

Factor incomes (percent share of oil production)

Capital 29.7 12.9 20.7 24.0 26.5

Labor 10.8 8.1 8.3 16.2 9.9

Land 59.5 79.0 71.0 59.8 63.6

Note: Columns will not sum to 100, as gasoline and oil production overlap as a share ofGDP.

3The import data are based on a combination of the IMF’s Direction of Trade Statisticsand the UN’s COMTRADE database of commodity-based trade flows.


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of GDP and the GOEC at 8.1 percent of GDP, while the other regions are netimporters at 1.4 percent of GDP for the United States, 1.9 percent of GDPfor emerging Asia, and 0.4 percent of GDP for the remaining countries.Additionally, the group of oil-exporting countries has the largest amount ofits GDP coming from oil production (12 percent).

III. Why Oil Prices Have Increased: Some Illustrative Experiments

This section starts by presenting some simulation results that show that, inthe presence of real adjustment costs, an upward shift in productivity growthcan result in the combination of high oil prices and robust global growth. Asan extension of the productivity shock, we illustrate how the model can beused to assess major risks to the future demand for crude oil that are theresult of uncertainty about future levels of oil intensity and real incomes inemerging Asia. Taken in combination, these experiments can provide theexplanation for the increase in oil prices over the past several years.4

Higher Productivity Growth in Oil-Importing Regions

To investigate the effects of rising global demand for oil, we consider apositive shock in the oil-importing regions (the United States, emerging Asia,and the remaining countries bloc), which raises productivity growth in boththe tradables and nontradables sectors by 1 percentage point for 20 years(Figures 2 and 3). The oil-importing regions obviously benefit from higherlevels of productivity in their own region, but the increase in oil prices overtime also results in a favorable terms-of-trade shock for regions that are netexporters of oil (Canada and the GOEC), and a negative terms-of-tradeshock for the regions that are net importers of oil.

The price of oil trends upward in tandem with the increase in the demandfor oil, reflecting the assumption of diminishing returns in the production ofoil, because of a fixed factor (land). For example, for the group of oil-exporting countries, oil prices jump up on impact, decline over the first year,before rising steadily over time. Oil prices are substantially higher over themedium term, reflecting the sluggish response of the supply of crude oil,reaching a level that is about 80 percent higher after 15 years. Oil productionincreases by only 1.6 percent in the group of oil-producing countries. It isimportant to emphasize, in this simulation, that we are assuming that thereare no new discoveries of oil, and that production can only be increased byadding more capital and labor, based on existing reserves.

The rise in oil prices results in an improvement in the oil trade balance forCanada and the GOEC, and a deterioration in the regions that import oil.The rise in the price of oil results in an upward trend in the relative price of

4The results here abstract from any increases in the price of oil not related to thefundamentals of the market, such as the perceived political risks attached to regions such asthe Middle East or the sub-Saharan African countries. Quantification of such uncertainty hasno role in a structural model such as the GEM.


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gasoline. Although monetary policy is successful at keeping core inflationclose to the assumed target, headline inflation is systematically higher than inthe baseline.5

The dynamics for consumption, investment, and GDP are relativelystraightforward. In those regions that experience higher productivity growth,investment trends upward until the capital stock in these economies adjuststo its new higher level. In the medium term, high investment rates in theseregions crowd out investment in the oil-exporting countries, as their rates ofreturn on non-oil investment projects are significantly lower. However, theseeffects are eventually offset by higher rates of return in the oil sectors in theseeconomies, and aggregate investment rises above baseline. Consumption risesby more than GDP in the oil-exporting regions, and by less than GDP in theoil-importing regions, which simply reflects the wealth effect attributable toterms-of-trade improvement that the latter experiences.

There are two major forces that require the real effective exchange ratesfor the oil-importing regions to depreciate in the long run. The first is a result

Figure 2. Higher Productivity Growth in the Oil-Importing Regions—Part I(Deviation from control)

0

20

40

60

80

100

0

20

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100

0 10 20 30 40 50 60

WorldReal Oil Price

(Percent, U.S. dollars)

0

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80

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80

0 10 20 30 40 50 60

United StatesReal Gasoline Price


0

5

10

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25

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5

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25

0 10 20 30 40 50 60

GDP Consumption

United StatesNational Accounts

(Percent)

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0 10 20 30 40 50 60

Aggregate Oil

United StatesNominal Trade Balances

(Percent of GDP)

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60

United StatesReal Effective Exchange Rate

(Percent; +=depreciation)

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60

Headline Core

United States Inflation(Year-over-year

percentage points)

5While we do not have a neutral policy rate in the reaction function, the latter is specifiedin such a way that allows the real interest rate to depart from its long-run equilibrium valuewhen there are shocks that change the marginal product of capital over long periods of time.This, of course, is a necessary condition to keep core inflation close to the target.


304


of the improvement in the terms of trade in the oil-exporting regions, and thesecond reflects the assumption that higher growth in the oil-importingregions stems from higher levels of productivity in both the tradables andnontradables sector. In this case, equal-sized productivity shocks in both thenontradables and tradables sectors lead to a depreciation of the exchangerate in the long run, while the standard Balassa-Samuelson effect—whichpredicts a real exchange rate appreciation in the long run—relies onproductivity growth in the tradables sector exceeding that of thenontradables sector.

Perhaps surprisingly, for the United States, the real exchange rateappreciates in the short run. This reflects the fact that this region must absorbmost of the depreciation in emerging Asia and the remaining countries bloc,both blocs being characterized by strong trade linkages with the UnitedStates. The appreciation also explains the short-run fall in U.S. net foreignliabilities measured as a ratio of nominal GDP, even as the trade balanceworsens. In the very long run, the desired stock of U.S. net foreign liabilitiesis actually higher than in the baseline, a fact that contributes to generatepressure toward a long-run depreciation. The latter is needed to generate atrade surplus that finances the higher interest burden on the larger stock ofnet foreign liabilities.

Figure 3. Higher Productivity Growth in the Oil-Importing Regions—Part II(Deviation from control)

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60

Oil ExportersOil Production

(Percent)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

1.5

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2.5

3.0

0 10 20 30 40 50 60

Oil ExportersReal GDP(Percent)

0

2

4

6

8

10

12

0

2

4

6

8

10

12

0 10 20 30 40 50 60

Canada GOEC Canada GOEC Canada GOEC

Oil ExportersReal Consumption

(Percent)

-12

-10

-8

-6

-4

-2

0

2

-12

-10

-8

-6

-4

-2

0

2

0 10 20 30 40 50 60

Canada GOEC

Oil ExportersReal Effective Exchange Rate


-1

0

1

2

3

4

-1

0

1

2

3

4

0 10 20 30 40 50 60

Aggregate Oil

CanadaNominal Trade Balances

(Percent of GDP)

-0.05

0.00

0.05

0.10

0.15

0.20

-0.05

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60

Headline Core

Canada Inflation(Year-over-year percentage points)


305


Increase in the Demand for Oil in Emerging Asia

Long-term projections of the demand for oil depend critically onassumptions about the future of emerging Asia—its substantial population,the convergence of its real per capita income to the level of OECD countries,the use of motor vehicles, and the shift of production to goods requiring amore technologically advanced (and presumably energy-dependent) capitalstock. Studies that have focused on the implications of this uncertaintyhave usually taken energy prices as given and assumed that the supply ofoil will be sufficient to smoothly accommodate variations in its demand(IMF, 2005). Here, we introduce an endogenous response of energy prices.We assume that two factors drive the permanent shock to the futuredemand for oil in emerging Asia: a taste shift that raises consumers’demand for gasoline, and a technology shift that increases the amount ofoil needed to produce tradable and nontradable goods. The shock is phasedin, so that the real level of oil consumption rises by roughly 2.5 percent ofGDP after 15 years. We introduce these factors in tandem with higherproductivity growth in emerging Asia (of the magnitude found in theprevious section).

In Figure 4, crude oil prices worldwide rise by an additional 10 percenton impact, decline during the first year and then trend upward overtime reaching a peak that is more than twice as large as only the productivityshock. It should be understood that if we considered this intensity-in-useshock in isolation, the increase in oil prices would not be as large. Theeffects of the intensity-in-use shock are amplified by the increase inproductivity, and vice versa—the outcome from the two shocks occurringsimultaneously is closer to being multiplicative, rather than additive. Theintensity-in-use shock also magnifies the shift of the terms of trade againstemerging Asia. This extends more generally to a shift in the terms oftrade in favor of the oil-exporting regions and against the oil-importingregions. As a result, consumption increases in the regions that arenet exporters of oil and eventually declines in the regions that are netimporters.

Again, the profile for oil prices reflects very low short-run elasticities ofsupply and demand for crude oil, which means that oil prices have to bear theentire burden of adjustment in the short run. The effects on oil trade balancesare much larger in the short run for the GOEC and Canada relative to thebaseline (equal to 8.1 and 3.6 percent of GDP, respectively). The negativeeffects on the oil trade balance in emerging Asia build up over time and reachabout 5 percentage points of GDP after about 15 years above that of the pureproductivity shock.

In sum, by considering extra shocks related to the usage of oil inemerging Asia, we can greatly amplify the effects on oil prices. Themagnitude of the effect is greater than that of the shock by itself, because ofthe interplay between the shift in production and consumption preferenceswith the increase in productivity in emerging Asia.


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IV. A Global Increase in Gasoline Tax Rates

Given the long-run nature (that is, usually a minimum of 15 years) of thescenarios offered above, it is appropriate to provide some normativesuggestions as to how policymakers (particularly the regions’ governments)can help reduce dependence on oil and reduce the negative impacts thatstill-increasing and high oil prices will have on future world output growth.We focus on one concrete policy measure, not regulatory measures or legalrestrictions on fuel usage in the automobile sector or industry, as these can behard to quantify in a model-consistent fashion. We demonstrate a global hikein tax rates of 25 percentage points on gasoline, in tandem with an offsettingreduction in taxes on labor income to achieve a notable reduction in oil pricesand use of oil, but hold government tax revenues neutral. As a result,productive capacity increases, with positive effects on aggregate employmentand investment. The results are reported in Figures 5 and 6.

The tax hike on gasoline eventually results in a substitution away fromconsumption of energy, but this is a very long and slow process given the lowshort-run elasticities of demand for oil. Oil prices decline by almost 5 percent.This decline in prices results in a reduction in the oil trade balance in theGOEC, that is about twice the effect for Canada, reflecting differences intheir initial oil trade balances. The reduction in labor tax rates raises the

Figure 4. Higher Growth and Oil Intensity in Emerging Asia(Deviation from control)

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Real Price of Oil(Percent, U.S. dollars)

-8

-6

-4

-2

0

2

-8

-6

-4

-2

0

2

0 10 20 30 40 50 60

Oil Trade Balance(Percent of GDP)

-0.15

-0.10

-0.05

0.00

0.05

0.10

-0.15

-0.10

-0.05

0.00

0.05

0.10

0 10 20 30 40 50 60

Core Inflation(Year-over-year percentage points)

0

20

40

60

80

0

20

40

60

80

0 10 20 30 40 50 60

Real GDP(Percent)

-10

0

10

20

30

-10

0

10

20

30

0 10 20 30 40 50 60

Real Consumption(Percent)

0

20

40

60

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100

120

0

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120

0 10 20 30 40 50 60

Real Investment(Percent)

Note: Solid line=productivity only; dashed line=combined shocks.


307


aggregate real wage, and results in higher investment and GDP in the oil-importing countries, but this effect is also quite significant in Canada, wherethe expansion in employment in the non-oil sector outweighs the decline inemployment in the oil sector.

Consumption in the oil-importing (oil-exporting) regions increases(decreases) because lower oil prices represent a positive terms-of-tradeshock and a wealth transfer from oil-exporting regions to oil-importingregions. In Canada, this negative terms-of-trade shock results in a decline inconsumption in the short run, but, over time, the expansion in productivecapacity and real income results in higher levels of consumption. Realexchange rates depreciate in the oil-exporting regions and appreciate in theoil-consuming regions.

The long-run welfare implications, expressed in terms of the consumptionequivalent, are fairly small, as shown in Table 3.6 The steady-stateimplications of the global gasoline tax among the regions are at most �0.4percent of consumption. Not surprisingly, the biggest loser is the group ofoil-exporting countries. Canada loses the consumption equivalent of 0.29

Figure 5. A Global Increase in Gasoline Tax Rates by 25 Percentage Points—Part I(Deviation from control)

-8

-6

-4

-2

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2

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-6

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2

0 10 20 30 40 50 60

WorldReal Oil Price


0

5

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0 10 20 30 40 50 60

United StatesReal Gasoline Price


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60

GDP Consumption

United StatesNational Accounts

(Percent)

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 10 20 30 40 50 60

Aggregate Oil

United StatesNominal Trade Balances

(Percent of GDP)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 10 20 30 40 50 60

United StatesReal Effective Exchange Rate


-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 10 20 30 40 50 60

Headline Core

United StatesInflation

(Year-over-year percentage points)

6Welfare is measured in terms of consumption equivalents, defined as the amount ofconsumption required to achieve a certain level of utility, holding labor supply (leisure) at itspre-shock steady-state level.


308


percent in the long run—less than the other oil exporters because of its morediversified economy. In contrast, oil importers experience minimal welfarelosses (less than 0.1 percent of consumption equivalent), as they do notface the direct wealth effect that the oil exporters experience from loweroil revenues. In general, liquidity-constrained consumers benefit, as their taxburden falls significantly relative to forward-looking consumers, who bearmore of the burden of the gasoline tax (and are owners of the oil wealth

Figure 6. A Global Increase in Gasoline Tax Rates by 25 Percentage Points—Part II(Deviation from control)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0 10 20 30 40 50 60

Oil ExportersOil Production

(Percent)

-0.05

0.00

0.05

0.10

0.15

0.20

-0.05

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60

Oil ExportersReal GDP(Percent)

0.0

-0.8

-0.6

-0.4

-0.2

0.2

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0 10 20 30 40 50 60

Canada GOEC Canada GOEC Canada GOEC

Oil ExportersReal Consumption

(Percent)

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60

Canada GOEC

Oil ExportersReal Effective Exchange Rate


-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 10 20 30 40 50 60

Aggregate Oil

CanadaNominal Trade Balances

(Percent of GDP)

-0.01

0.00

0.01

0.02

0.03

0.04

-0.01

0.00

0.01

0.02

0.03

0.04

0 10 20 30 40 50 60

Headline Core

CanadaInflation

(Year-over-year percentage points)

Table 3. Steady-State Welfare Implications of a Global Increase in Gasoline TaxRates of 25 Percentage Points

Welfare (consumption

equivalent) Canada

Oil-Exporting

Countries

United

States

Emerging

Asia

Remaining

Countries

All consumers �0.29 �0.40 �0.02 �0.04 �0.09Forward looking

consumers

�0.30 �0.42 �0.03 �0.07 �0.10

Liquidity-constrained

consumers

1.02 0.66 0.56 1.01 0.70


309


which decreases). Therefore welfare declines in all regions, as the majority ofconsumers are forward looking.

V. Conclusions

In this paper, we developed a five-region model of the global economy andcarried out scenario analyses to study the implications of different shocksdriving oil prices worldwide. The model introduces significant realadjustment costs in the energy sector, making both the demand and supplyfor crude oil extremely inelastic in the short run, thus requiring largemovements in crude oil prices to clear the energy market.

To answer the first question about the underlying causes of the oil pricerun-up since 2001, the model properties offer a story based on strongerproductivity growth in oil-importing regions, coupled with shifts in oilintensity in production (emerging Asia). Oil price shocks stemming fromhigher growth in the oil-importing regions are accompanied by wealthtransfers through terms-of-trade movements, leading consumption to growslower than output in the oil-importing regions. In the medium term, highinvestment rates in the high-growth regions crowd out investment in theoil-exporting regions. Moreover, the positive effects of higher oil prices onconsumption need not translate into reduced current account surpluses in theoil-exporting regions, to the extent that they are accompanied by an upwardshift in the desired net foreign asset positions. The conclusions about the roleof increased productivity in the oil-importing regions can be reinforced byconsidering emerging Asia in particular, with its increased intensive use of oilin the production of tradable goods.

Our second question, about whether policy can be used to amelioratemany of the negative impacts of increasing and higher oil prices, is answeredby exploring the implications of a global tax hike on gasoline. Such ameasure reduces oil prices by almost 5 percent, and results in a positiveterms-of-trade shock for the oil-importing regions, as well as a wealthtransfer from oil-exporting regions to oil-importing regions. This leads to anincrease in consumption in the oil-importing regions and decreaseseverywhere else. Furthermore, the reduction in labor tax rates raises theaggregate real wage and results in higher investment and GDP. On net, theworld suffers a small welfare loss, but this masks regional variations, wherethe effects are negligible in the oil-importing regions but notable in the oil-exporting regions.

REFERENCESCoenen, Gunter, Peter McAdam, and Roland Straub, forthcoming, ‘‘Tax Reform and

Labor-Market Performance in the Euro Area: A Simulation-Based Analysis Usingthe New Area-Wide Model,’’ Journal of Economic Dynamics and Control.

Energy Information Administration, 2007, ‘‘Short-Term Energy Outlook—October2007,’’ Available via the Internet: www.eia.doe.gov/emeu/steo/pub.


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www.eia.doe.gov/emeu/steo/pub

Faruqee, Hamid, Douglas Laxton, Dirk Muir, and Paolo Pesenti, 2007, ‘‘SmoothLanding or Crash? Model-based Scenarios of Global Current Account Rebalancing,’’in G7 Current Account Imbalances: Sustainability and Adjustment, ed. by RichardClarida (Chicago, University of Chicago Press).

Gosselin, Marc-Andre, and Rene Lalonde, 2005, ‘‘MUSE: The Bank of Canada’s NewProjection Model of the U.S. Economy,’’ Bank of Canada Technical Report No. 96.

International Monetary Fund (IMF), 2005, World Economic Outlook, September. WorldEconomic and Financial Surveys (Washington, September).

_______, 2006, World Economic Outlook, April. World Economic and Financial Surveys(Washington, April).

Juillard, Michel, Philippe Karam, Douglas Laxton, and Paolo Pesenti, 2006, ‘‘Welfare-based Monetary Policy Rules in an Estimated DSGE Model of the US Economy,’’ECB Working Paper 613, European Central Bank.

Lalonde, Rene, and Dirk Muir, 2007, ‘‘The Bank of Canada’s Version of the GlobalEconomy Model (BoC-GEM),’’ Bank of Canada Technical Report No. 98.

Murchison, Stephen, and Andrew Rennison, 2006, ‘‘ToTEM: The Bank of Canada’sNew Projection and Policy Analysis Model,’’ Bank of Canada Technical ReportNo. 97.

Pesenti, Paolo, 2008, ‘‘The Global Economy Model (GEM): Theoretical Framework,’’IMF Staff Papers, Vol. 55, No. 2.

Rotemberg, Julio, 1982, ‘‘Sticky Prices in the United States,’’ Journal of PoliticalEconomy, Vol. 90, No. 6, pp. 1187–211.


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Productivity and Global Imbalances: The Roleof Nontradable Total Factor Productivity

in Advanced Economies

PIETRO COVA, MASSIMILIANO PISANI, NICOLETTA BATINI,and ALESSANDRO REBUCCI�

This paper investigates the role played by total factor productivity (TFP) in thetradable and nontradable sectors of the United States, the euro area, and Japan inthe emergence and evolution of today’s global trade imbalances. Simulationresults based on a dynamic general equilibrium model of the world economy, andusing the new EU KLEMS database, indicate that TFP developments in theseeconomies can account for a significant fraction of the deterioration in the U.S.trade balance since 1998, as well as for some of the surpluses in the euro area andJapan. Differences in TFP developments across sectors can also partially explainthe evolution of the real effective value of the U.S. dollar during this period. Theseresults highlight the importance of focusing on productivity developments in thenontradable sector of these large, relatively closed economies to understand theevolution of their trade balance and real exchange rate. [JEL E0, F3, F4, G1]



�Pietro Cova and Massimiliano Pisani are economists in the Banca d’Italia ResearchDepartment; Nicoletta Batini is a senior economist in the IMF Western HemisphereDepartment; and Alessandro Rebucci is a senior economist in the IMF Research Department.The authors would like to thank the editors (Bob Flood and Doug Laxton), an anonymousreferee, Susanto Basu, Francesco Giavazzi, Luca Guerrieri, Ben Hunt, Ellen McGrattan,Enrique Mendoza, Gian Maria Milesi-Ferretti, Sergio Rebelo, and seminar and conferenceparticipants from the Central Banks of Chile and Peru, the University of Surrey, the 2007 IMFGlobal Economy Modeling Conference, and the 11th CEPR/ESI Annual Conference on‘‘Global Imbalances, Competitiveness and Emerging Markets’’ for helpful discussions andsuggestions on earlier drafts of this paper.

IMF Staff PapersVol. 55, No. 2& 2008 International Monetary Fund

312


During the 1990s, large trade imbalances developed in different regionsof the world, with the United States running persistent deficits, and

Japan and the euro area first, and later emerging Asia and oil-exportingcountries, running surpluses (Figure 1). Today, the United States absorbsthree-quarters of the world’s current account surpluses, and net U.S.liabilities are at record-high, representing over one-fifth of U.S. GDP.

The debate about the sources and hence possible resolutions of theseexternal imbalances is polarized. Some argue that global imbalances should notbe resisted. This is because they largely manifest an equilibrium phenomenon,generated by the interaction of growth and financial development differentialsamong countries, that will resolve themselves slowly over time.1 Many,however, trust that these imbalances originate in economic distortions, and thatthey should be resolved primarily through policy adjustment, includingsignificant changes in effective exchange rates and fiscal policies or both.2

One issue that, by contrast, is relatively undisputed is that differences inrelative productivity across world regions have likely played a nonnegligible rolein the emergence and evolution of today’s trade imbalances. This generalperception is supported by empirical evidence. Glick and Rogoff (1995), forexample, estimate that a 1 percent increase in country-specific productivitydecreases the current account balance by 0.15 percent of GDP. Estimates byBems, Dedola, and Smets (2007); Edwards (2007); and Corsetti, Dedola, andLeduc (2006) detect even larger elasticities between shocks to productivityand imbalances. A few recent studies also examined the potential role of totalfactor productivity (TFP) differences across countries in explaining the globalimbalances, based on multicountry dynamic general equilibrium (DGE) modelswith calibrated TFP processes. Erceg, Guerrieri, and Gust (2002) and Huntand Rebucci (2005), for instance, find that a permanent shock to the level ofTFP in the United States, combined with uncertainty or learning about itspersistence, can explain at least in part the behavior of the U.S. trade deficit in thelate 1990s.

As Obstfeld and Rogoff (2007) note, however, productivity could onlyhelp to reduce the large U.S. trade deficit if it were concentrated either in thetradable sector of the United States (as foreign goods become less attractiveto both U.S. and non-U.S. residents) or in the nontradable sector in the euroarea and Japan (as this boosts their wage and capital income and hence theirdemand for U.S. goods).3 Reasoning along these lines, they infer that much

1See, for example, Engel and Rogers (2006); Blanchard (2007); Caballero, Fahri, andGourinchas (2006); Mendoza, Rios-Rull, and Quadrini (2007); Fogli and Perri (2006); andMcGrattan and Prescott (2007).

2See, for example, IMF (2005 and 2006a); Blanchard, Giavazzi, and Sa (2005); Mussa(2004); Obstfeld and Rogoff (2007); Roubini and Setser (2004); and Yoshitomi (2007).

3Guerrieri, Henderson, and Kim (2005) also point out that the transmission of a TFPshock in the tradable sector may differ significantly from that of a shock in the nontradablesector of the U.S. economy, in terms of the responses of the exchange rate and the tradebalance.

PRODUCTIVITY AND GLOBAL IMBALANCES

313


of the widening of the U.S. trade deficit over the past 10 years or so musthave originated from the boom in relative productivity in the U.S.nontradable sector.

This paper investigates the role played by TFP in the tradable andnontradable sectors of the United States, the euro area, and Japan in theemergence and evolution of today’s global trade imbalances. Specifically, wefeed sector-specific TFP data from 1995 to 2004 for these countries, froma new and homogenous data set, to a flexible-price version of the (DGE)model of the world economy developed by Cova and Pisani (2007) at theBank of Italy.

This model is a five-region DGE. It comprises an emerging Asia anda rest-of-the-world bloc, in addition to the United States, the euro area,and Japan, and shares many features with the IMF’s Global EconomyModel (GEM).4 The model does not treat oil-exporting economiesseparately. It does not incorporate realistic financial frictions, possiblyinducing precautionary demands for official reserves or constraining thesupply of marketable financial assets, as well as other policy distortions, suchas sustained sterilized foreign exchange intervention.5

Subject to the caveat that the analysis in this paper focuses only on oneamong several factors likely to drive the current constellation of global

Figure 1. Global Merchandise Trade Balances(In percent of GDP)

-7

-5

-3

-1

1

3

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 20050

5

10

15

20

25

Euro area (left scale)

United States (left scale)

Japan (left scale)

Emerging Asia (left scale)

Fuel exporters (right scale)

4See Laxton and Pesenti (2003); Hunt and Rebucci (2005); Batini, N’Diaye, and Rebucci(2005); and Faruqee, Muir, and Pesenti (2007).

5See IMF (2006b and 2007) on the role of oil prices and exchange rate changes for globalimbalances.

Pietro Cova, Massimiliano Pisani, Nicoletta Batini, and Alessandro Rebucci

314


imbalances, we find that TFP developments in advanced economies, andespecially in the nontradable sector of the United States, can account for asignificant fraction of the deterioration in the U.S. trade balance after 1998,as well as for some of the surplus periods in the euro area and Japan. Sector-specific productivity differentials in the United States also do well atcapturing the direction, persistence, and turning point of the U.S. dollareffective exchange rate since the mid-1990s, although the volatility of thesimulated exchange rate path is much smaller, and the turning point earlier,than in the data.

I. Methodology

We feed to our model historically realized TFP paths for the United States,the euro area, and Japan. We then compare actual and simulated paths forthe trade balance, as well as the real effective exchange rate and the nationalaccounts. This section briefly describes the model, its calibration andsolution, and the data that we use in the analysis.

Model, Calibration, and Solution

The analysis uses a flexible price version of the model of the world economydeveloped by Cova and Pisani (2007) at the Bank of Italy.6 This is afive-region and two-sector (tradable and nontradable) DGE model withincomplete international asset markets, home bias in consumption andinvestment, international price discrimination (due to the presence of adistribution sector), capital accumulation, and nonzero net foreign assetpositions in steady state. The five regions are the United States, Japan, euroarea, emerging Asia, and the rest of the world. The calibration of the modeldraws on previous GEM work at the IMF and on the international realbusiness cycle and trade literature. The model is coded in DYNARE and issolved using the deterministic (perfect foresight) simulation command‘‘simul’’ with a simulation length of 500 periods or quarters.7

We run perfect foresight simulations recursively to allow for a revision ofthe agents’ expectations about the future evolution of TFP.8 Specifically, werun a sequence of perfect foresight simulations based on a sequence ofcountry- and sector-specific TFP forecasts. At each period, as a newrealization of the historical TFP path is added, agents update their forecastfor the remaining part of the TFP path. These forecasts are based oncountry- and sector-specific AR(1) processes for the rate of growth of TFP,

6Specific features of the model, and the details of its calibration, are reported anddiscussed in the working paper version of this paper.

7The ‘‘simul’’ instruction uses a Newton method to solve simultaneously all the equationsfor every period (see Julliard, 1996). Simulations with up to 6,000 periods give similar results.

8For more details, see the working paper version of the paper, which also reports resultswithout recursive evolution of expectations. We thank the editors, Bob Flood and DougLaxton, for the suggestion to solve the model in this more realistic manner.


315


estimated on the first difference of the historical TFP paths (detrended asdescribed below).9 Departing from a perfect foresight simulation in thismanner introduces time-varying expectations about future TFP evolutionthat slows the response of the economy to actual TFP changes.10

In the simulations, we assume the world economy is in steady state in1994:Q4 and that, after 2004:Q4, historical TFP paths for the United States,the euro area, and Japan revert to trend at the rate of 0.001 per quarter (thatis, with an autoregressive coefficient of 0.999). The TFP paths of emergingAsia and the rest of the world are assumed to remain in steady statethroughout the simulation period. Given that the spillover from othercountries’ TFP evolution to the United States are very small (see below), westart the simulations in 1995. Thus, the simulations attach no weight to the1990–95 productivity slowdown in Japan and the euro area.

TFP Paths

We construct the historical path for TFP in the United States (US), the euroarea (EA, defined here as EU-15), and Japan (JA), for the tradable andnontradable sector, from the new EU KLEMS database ‘‘Growth andProductivity Accounts’’ (euklems.net).

We identify the tradable sector with ‘‘Manufacturing’’ and the nontrad-able with the weighted average of ‘‘Wholesale and retail trade,’’ ‘‘Electricity,gas and water supply,’’ and ‘‘Transportation, storage, and communication,’’with weights given by the relative value added within the sector. We includeonly a subset of all the sectors available because these are the most accuratelymeasured (Basu and Fernald, 2006). The results reported in the next section,however, are robust to using a narrower definition of the nontradable sectoror a broader definition of the tradable sector.

The data are in line with the conventional wisdom about the evolution ofproductivity growth in these areas.11 Table 1 reports five-year averages ofannual TFP growth, together with their average over the whole sampleperiod available, and from 1981 to 2004 for ease of comparison acrosscountries. U.S. tradable TFP growth accelerated temporarily in late 1990s,while nontradable TFP growth lagged behind for most of the 1990s,

9We find similar results (not reported but available on request from the authors)estimating these processes on the detrended level of the historical TFP paths, imposingautoregressive coefficients of 0.99 in the cases in which the estimated process has a unit root orit is explosive (like for instance in the case of the U.S. nontradable TFP path).

10Running perfect foresight simulations recursively as we described here is akin topositing a simple learning process on the evolution of TFP. Erceg, Guerrieri, and Gust (2002);and Hunt and Rebucci (2005), for instance, calibrate a learning process about future TFPgrowth to the time evolution of actual medium-term growth forecasts for the United Statesand show this can help improve the model’s ability to match the data, especially consumptionand the exchange rate. Introducing ‘‘news shocks,’’ along the line of Jaimovich and Rebelo(2007), is an alternative way to address the same issue.

11See, for example, Jorgenson (2003); Jorgenson and Motohashi (2005); Gordon (2004);and Oliner, Sichel, and Stiroh (2007).


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accelerating sharply only in the last five-year period. In Japan, tradable TFPgrowth was below average during the 1990s, falling sharply in the first half ofthe 1990s. The fall in TFP growth in the nontradable sector lagged by aboutfive years, but was deeper and more persistent than that experienced in thetradable sector. In the euro area, tradable and nontradable TFP growthslowed down markedly in the 1990s. In the first half of the 2000s, tradableproductivity recovered partially, while nontradable productivity continued todecline.12

Interestingly, although the differences in TFP growth across sectors andcountries are large and persistent over the past 15 years or so, longer-termaverages are remarkably similar. The TFP growth acceleration in thetradable sector of the United States, in particular, appears to be temporary,consistent with the estimates of Ireland and Schuh (2007) for the degree ofpersistence of investment-specific technological progress.

Detrended historical TFP paths are computed taking country- andsector-specific gross percent deviations from linear trends. The country- andsector-specific linear trends are calculated as time averages from 1980 up tothe beginning of the shock periods. The beginning of the shock periods, in

Table 1. Annual Average Total Factor Productivity Growth by Sector and Country(Percent per year)

United States Japan EU-15

Tradables Nontradables Tradables Nontradables Tradables Nontradables

1971–74 3.3 2.8 NA NA NA NA

1975–79 1.3 1.9 7.6 2.0 NA NA

1980–84 0.2 �0.1 1.3 4.3 2.1 0.9

1985–89 3.3 0.8 4.0 3.3 2.0 2.0

1990–94 1.7 1.1 �0.8 3.7 1.7 1.3

1995–99 4.0 0.2 1.3 0.2 0.7 1.9

2000–04 1.7 3.9 2.5 0.4 1.3 1.1

Average full

sample

2.2 1.5 2.8 2.4 1.5 1.5

Average

1981–2004

2.4 1.3 1.8 1.7 1.5 1.5

Source: EU KLEMS.Note: Tradable sector identified with ‘‘Manufacturing.’’ Nontradable sector identified

with the weighted average of ‘‘Wholesale and retail trade,’’ ‘‘Electricity, gas and water supply,’’and ‘‘Transportation, storage, and communication,’’ with weights given by the relative valueadded within the sector. NA=not available.

12We also looked at the TFP evolution in emerging Asia, with data from Jaumotte andSpatafora (2006). These data point to a possible deceleration of TFP growth in the region,consistent with the notion of a catch up and convergence with more advanced economies. Thisslowdown, however, is modest and it is thus unclear to what extent it may have had impact onthis region’s large trade surplus after the mid-1990s crisis.


317


turn, is identified maximizing the model-based simulation’s ability to fit theU.S. trade balance path. The identified beginning of the shock periods are1995 and 2000 for the U.S. tradable and nontradable sector, respectively; and1990 and 1995 for the euro area and Japan tradable and nontradable sector,respectively. The resulting historical TFP paths, from 1995 to 2004, areplotted in Figure 2.

II. Results

The results compare actual and simulated paths. We simulated the modelunder four different scenarios: (1) U.S. nontradable TFP only; (2) U.S.tradable TFP only; (3) both U.S. tradable and nontradable TFP; and (4)tradable and nontradable TFP in all three economies. Figure 3 plots the U.S.trade balance of goods and services as a share of GDP, in deviation from themodel steady state, normalized so that the steady state is equal to the data in1994:Q4 in all four scenarios. Figure 4 compares actual and simulated pathsfor the trade balance of the United States, Japan, the euro area, and emergingAsia, in the fourth scenario (measured as in Figure 3). Figure 5 plots the U.S.real effective exchange rate in the fourth scenario (in deviation from themodel steady state, normalized so that the steady state is equal to the datavalue in 1994:Q4).

The simulation with only U.S. nontradable TFP tracks the U.S. tradebalance evolution reasonably well (Figure 3). U.S. nontradable TFP declinesmildly between 1995 and 1999, with a sharper fall in 1999, and then increasesstrongly through 2004 (Figure 2). The associated trade balance dynamicsresults from the net effect of three different forces.13 First, there is a‘‘composition’’ effect associated with the complementarity between tradablesand nontradables and the strong substitutability among tradables. Driven byTFP changes, the relative price of nontradable goods first rises and then falls(not reported). Correspondingly, U.S. demand of nontradables first decreasesand then increases. Because of the complementarity between tradables andnontradables, U.S. consumption of tradable goods also decreases first andthen increases. The U.S. terms of trade first deteriorates and then improves,and, with high substitutability, foreign demand of U.S. tradables (U.S.imports of foreign tradables) first increases and then decreases (first decreaseand then increase). Therefore, these composition effects tend to push the U.S.trade balance into surplus initially, and then into deficit. Second, there isconsumption smoothing. Households initially decrease and then increaseconsumption, but less than the labor and capital income changes associatedwith actual TFP changes. This second force tends to offset the compositioneffect, initially increasing and then reducing the trade balance deficit. Third,firms postpone investment, which is relatively intensive in tradables and lessbiased toward U.S. goods than the consumption basket, toward relatively more

13More details on the transmission mechanism are discussed in the forthcoming IMFWorking Paper version of this article.


318


productive times.14 This third force pushes the trade balance in the samedirection as the composition effect, initially into surplus and then into deficit.

The simulation with only U.S. tradable TFP results in a persistent andcounterfactual trade balance improvement in the United States between 1998

Figure 2. Total Factor Productivity Paths(Percent deviation from trend)

-25

-20

-15

-10

-5

0

5

10

15

2019

94Q

4

1995

Q4

1996

Q4

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

U.S. nontradable

U.S. tradable

Euro area nontradable

Euro area tradable

Japan nontradable

Japan tradable

Figure 3. Actual and Simulated U.S. Trade Balance

Actual

U.S. tradable and nontradableproductivity

All TFP paths

-7

-6

-5

-4

-3

-2

-1

0

1

1994

Q4

1995

Q4

1996

Q4

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

U.S. tradable productivity

U.S. nontradableproductivity

Note: Actual trade balance in percent of GDP; simulated trade balance in percentage points ofGDP deviation from steady state. TFP¼ total factor productivity.

14The share of tradable goods in aggregate investment and consumption is 0.75 and 0.35,respectively. The bias toward domestic goods in the traded good basket of both the investmentand consumption composite goods is 0.87.


319


Figure 4. Actual vs. Simulated Trade Balances1

(Percentage points of GDP deviation from steady state)

Japan

Actual

Simulated

-2

-1

0

1

2

3

4

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Euro Area

Actual

Simulated

0

0.5

1

1.5

2

2.5

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Asia

Actual

Simulated

-2

-1

0

1

2

3

4

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

United States

Actual

Simulated

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

1All total factor productivity paths.

Pietro

Co

va,

Ma

ssimilia

no

Pisan

i,N

ico

letta

Batin

i,a

nd

Ale

ssan

dro

Re

bu

cc

i

320


and 2002 (Figure 3). U.S. tradable TFP declines slightly in 1995 and thenincreases sharply until 2001, when it starts to revert toward its trend. Thetransmission mechanism is similar to the one for nontradable TFP.Consumption and investment gradually rise over time as labor and capitalincome increase. However, the composition effect depresses the U.S. terms oftrade sharply and persistently, in this case, after a short-lived improvement.15

World demand, therefore, shifts strongly in favor of U.S. tradable goodsafter 1996, driving the trade balance into persistent surplus. Not surprisingly,the simulation with both tradable and nontradable U.S. TFP tracks theevolution of the U.S. trade balance less well than in the case of onlynontradable TFP, with the deficit deteriorating persistently only after 2003 inthe latter case.

The simulation with tradable and nontradable TFP in all three economiestracks the trade balance of the euro area and Japan relatively well. In the caseof emerging Asia, however, the model cannot account for the very large tradebalance reversal associated with the crisis in 1997 and 1998 (Figure 4). Forthe euro area, the model fit is better in the first part of the simulation period,while for Japan the fit is better in the second part.16 Note, however, that therelatively large TFP swings that we feed to the model have small spillovereffects to other countries. For instance, adding the TFP evolution of the euroarea and Japan to the model (as in the fourth scenario reported) hasessentially no impact on the U.S. trade balance evolution (Figure 3).

Figure 5. Actual and Simulated U.S. Real Effective Exchange Rate(Increase=Appreciation; 1994 Q4=100)

Actual

Simulated

85

90

95

100

105

110

115

120

125

13019

94Q

4

1995

Q4

1996

Q4

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

15The relative price of nontradable goods initially falls, but by less than the increase in thetradable good price (because of the complementarity between tradables and nontradables),and then increases over time.

16We do not report model-based results for the rest of the world because we do not have adata benchmark for this aggregate owing to the well-known global trade discrepancy.


321


The simulation with tradable and nontradable TFP in all three economiesalso tracks the evolution of the U.S. real effective exchange rate relativelywell. The simulation tracks well the direction, persistence, and turning pointof the exchange rate response, although the volatility is less, and the turningpoint is earlier, than in the data (Figure 5). For example, the dollar stopsappreciating in 1998:Q4, when nontradable productivity starts to increase,and starts to fall in 2000:Q4. However, in the data, the dollar reversal in 1999is followed by a renewed sustained appreciation through end-2001. As for thetransmission mechanism, the simulated exchange rate dynamics is driven by aHarrod-Balassa-Samuelson effect. The relative price of nontradable goodsfirst raises and then declines sharply, in the simulation, dominating move-ments in the terms of trade. This is because of both the timing differences inTFP changes across tradable and nontradable sectors and the large share ofthe nontradable sector in the U.S. consumption basket.

These results are robust to the assumptions on the elasticity ofsubstitution between home and foreign tradable goods and betweenimports from different countries (see the working paper version of thisarticle for more details on the latter). The results, however, are sensitive totwo other model features. First, reducing the value of the financial interme-diation cost that determine model stationarity alters agents’ intertemporalconsumption smoothing possibilities, strengthening the consumptionresponse, and hence resulting in larger trade deficits, at the beginning ofthe simulation period.17 Second, as we mentioned in the previous section, theresults are also sensitive to the implicit assumptions on agent’s expectationsabout future productivity, which would effectively alter actual TFP paths fedto the model.

Our results are partly consistent with the existing empirical literature. Wefind that a 1 percent increase in U.S. productivity in the nontradable sectordecreases the U.S. trade account by 0.16 percent of GDP,18 a value at thelower end of the 0.15–0.5 range of elasticities in the empirical work of Glickand Rogoff (1995); Bems, Dedola, and Smets (2007); and Edwards (2007).On the other hand, given our calibration of the model, the U.S. trade balancemoves into surplus, and the U.S. terms of trade depreciate, in response to a 1percent increase in tradable TFP,19 which runs counter the recent empiricalevidence of Corsetti, Dedola, and Leduc (2006).

III. Conclusions

This paper examined the role of TFP differences in the tradable andnontradable sector of the United States, the euro area, and Japan on the

17In our simulations it would be possible to eliminate the adjustment costs on net foreignasset, provided we specify the end value of the net foreign asset position, and solve the modelwith a two-point boundary algorithm (for example, Mendoza and Tesar, 1998).

18See Figure A2 in the working paper version of this article.19See Figure A2 in the working paper version of this article.


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emergence and evolution of today’s constellation of global trade imbalances.Feeding these differences to a global, flexible price DGE model yieldsdynamics that are partially consistent with those observed in the data. Thesimulations can explain a significant fraction of the overall deterioration inthe U.S. trade balance since 1998, some of the surpluses in Japan and theeuro area, and the persistent U.S. exchange rate swings observed in the data.The basic mechanisms at work in the model, however, result in an exchangerate that is too little volatile compared with the data.

One important implication of the analysis is that, as past TFPaccelerations seem persistent but ultimately temporary, and spillovers fromTFP changes in individual countries appear small, rebalancing of the U.S.,and hence global, trade imbalance should happen, at least in part, naturally,as the acceleration in U.S. nontradable TFP slowly unwinds. More generally,the analysis highlights the importance of focusing on productivity develop-ments in the nontradable sector to understand the evolution of the tradebalance and the exchange rate of large, relatively closed economies such asthe United States, the euro area, and Japan.

We see the analysis of TFP differences across sectors and countries in thepresence of financial frictions and policy distortions (such as for instancesustained sterilized foreign exchange intervention) as a natural complementof the work reported in this paper and a promising area of future research.

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_______ , F. Giavazzi, and F. Sa, 2005, ‘‘The U.S. Current Account and the Dollar,’’NBER Working Paper No. 11137 (Cambridge, Massachusetts, National Bureau ofEconomic Research).

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Engel, C., and J.H. Rogers, 2006, ‘‘The U.S. Current Account Deficit and the ExpectedShare of World Output,’’ Journal of Monetary Economics, Vol. 53, No. 5, pp. 1063–93.

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Faruqee, H., D. Laxton, D. Muir, and P. Pesenti, 2007, ‘‘Smooth Landing or Crash?Model-Based Scenarios of Global Current Account Rebalancing,’’ NBER WorkingPapers 11583 (Cambridge, Massachusetts, National Bureau of EconomicResearch).

Fogli, A., and F. Perri, 2006, ‘‘The ‘Great Moderation’ and the US External Imbalance,’’NBER Working Paper W12708 (Cambridge, Massachusetts, National Bureau ofEconomic Research).

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Gordon, R., 2004, ‘‘Five Puzzles in the Behavior of Productivity, Investment, andInnovation,’’ NBER Working Paper 10662 (Cambridge, Massachusetts, NationalBureau of Economic Research).

Guerrieri, L., D. Henderson, and K. Jinill, 2005, ‘‘Investment-Specific and MultifactorProductivity in Multi-Sector Open Economies: Data and Analysis,’’ InternationalFinance Discussion Papers No. 828 (Washington, Board of Governors of the FederalReserve System).

Hunt, B., and A. Rebucci, 2005, ‘‘The US Dollar and the Trade Deficit: What Accountsfor the Late 1990s?’’ International Finance, Vol. 8, No. 3, pp. 399–434.

International Monetary Fund (IMF), 2005, ‘‘Appendix 1.2. How Will Global ImbalancesAdjust?’’ World Economic Outlook (Washington, April).

_______ , 2006a, ‘‘Box 1.3. How Will Global Imbalances Adjust?’’ World EconomicOutlook (Washington, April).

_______ , 2006b, ‘‘Chapter 2: Oil and Global Imbalances,’’ World Economic Outlook(Washington, April).

_______, 2007, ‘‘Chapter 3: Exchange Rates and External Imbalances,’’ World EconomicOutlook (Washington, April).

Ireland, P.N., and S. Schuh, 2007, ‘‘Productivity and U.S. Macroeconomic Performance:Interpreting the Past and Predicting the Future with a Two-Sector Real BusinessCycle Model,’’ NBER Working Paper 13532 (Cambridge, Massachusetts, NationalBureau of Economic Research).

Jaimovich, N., and S.T. Rebelo, 2007, ‘‘News and Business Cycles in Open Economies,’’NBER Working Paper W13444 (Cambridge, Massachusetts, National Bureau ofEconomic Research).

Jaumotte, F., and N. Spatafora, 2006, ‘‘Asia Rising: A Sectoral Perspective, IMF WP07/130,’’ (Washington, International Monetary Fund, September).

Jorgenson, D., 2003, ‘‘Information Technology and the G7 Economies,’’ WorldEconomics, Vol. 4, No. 4, pp. 139–69; updated and reprinted in Revista di PoliticaEconomica, Vol. 95, Nos. 1–2, January–February 2005, pp. 25–56.


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Laxton, Douglas, and Paulo Pesenti, 2003, ‘‘Monetary Rules for Small, Open, EmergingEconomies,’’ Journal of Monetary Economics, Vol. 50, No. 5, pp. 1109–46.

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_______, J.-V. Rios-Rull, and V. Quadrini, 2007, ‘‘Financial Integration, FinancialDeepness and Global Imbalances,’’ NBER Working Paper 12909 (Cambridge,Massachusetts, National Bureau of Economic Research).

Mussa, M., 2004, ‘‘Exchange Rate Adjustments Needed to Reduce Global PaymentsImbalances,’’ in Dollar Adjustment: How Far? Against What? ed. by C. Fred Bergstenand John Williamson (Washington, Institute for International Economics).

Obstfeld, M., and K. Rogoff, 2007, ‘‘The Unsustainable U.S. Current Account PositionRevisited,’’ in G7 Current Account Imbalances, ed. by R. Clarida (Chicago, ChicagoUniversity Press).

Oliner, S.D., D.E. Sichel, and K.J. Stiroh, 2007, ‘‘Explaining a Productive Decade,’’Brookings Papers on Economic Activity, No. 1 (Washington, Brookings Institution).

Roubini, N., and B. Setser, 2004, ‘‘The U.S. as a Net Debtor: The Sustainability of theU.S. External Imbalances’’ (unpublished; Stern School of Business, New YorkUniversity).

Yoshitomi, M., 2007, ‘‘Global Imbalances and East Asian Monetary Cooperation,’’ inToward an East Asian Exchange Rate Regime, ed. by Duck-Koo Chung and BarryEichengreen (Washington, Brookings Institution Press).


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Inflation Targeting and Price-Level-Path Targeting in theGlobal Economy Model: Some Open Economy

Considerations

DONALD COLETTI, RENE LALONDE, and DIRK MUIR�

This paper compares the capability of simple inflation targeting (IT) and price-level-path targeting (PLPT) rules to minimize inflation and output gapvariability in a two-country, two-sector version of the Global Economy Modelcalibrated for Canada and the United States. We find that simple PLPT rulesare slightly better than simple IT rules at macroeconomic stabilization and thatthe presence of terms-of-trade shocks tends to bolster the case for PLPT.Lastly, we demonstrate that the choice of monetary policy framework in theUnited States does not affect the relative merits of IT vs. PLPT in Canada.[JEL C51, C52, E17, E31, E52]



One way of implementing a strong nominal anchor for the economythat has become particularly popular in recent years is the adoption

�Donald Coletti is a research adviser, Rene Lalonde is a model adviser, and Dirk Muir isa principal researcher with the Bank of Canada’s International Department. We would like tothank Carlos DeResende, Wei Dong, Ippei Fujiwara, Robert Lafrance, Douglas Laxton,Warwick McKibbin, Rhys Mendes, Paolo Pesenti, Nooman Rebei, Lawrence Schembri, YangZhang, an anonymous referee, and participants at the Reserve Bank of New Zealandworkshop on ‘‘The Interface Between Monetary Policy and Macro Modelling’’ held in March2006; the IMF ‘‘Workshop on Open Economy Models for Policy Evaluation’’ held in April2007; and the Reserve Bank of Australia workshop ‘‘Monetary Policy in Open Economies’’held in December 2007. We owe special thanks to Stephen Murchison for his invaluableinsights. We also thank Susanna Mursula, Hope Pioro, and Andre Poudrier for excellentresearch assistance.


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of formal inflation targets. The basic principles of inflation targeting (IT) arestraightforward. In the advent of a shock that pushes inflation away fromtarget, the central bank adjusts policy interest rates to affect both the level ofspending in the economy and inflation expectations, thereby pulling inflationback to target.

IT in Canada and in many other countries has proved to be quitesuccessful, as inflation expectations have become better anchored leading to areduction in inflation volatility and persistence, with no increase in outputvolatility (Mishkin and Schmidt-Hebbel, 2001). Despite these notableachievements, it is also clear that IT may have some important limitations.In particular, owing primarily to the fear of hitting the lower zero bound onnominal interest rates, inflation targets worldwide typically remain at about 2percent, despite a consensus in the economics community that there would bebenefits associated with moving to a lower target. In addition, price-levelmovements are not completely reversed under IT, leading to price-level driftand leaving uncertainty about future price levels higher than it needs to be.This is problematic for agents who are risk averse and who enter into long-term, nominal contracts (for example, home mortgages).

An alternative way to achieve a strong nominal anchor for the economythat may help alleviate these problems is price-level-path targeting (PLPT).PLPT differs from IT because, under PLPT, a shock that pushes the pricelevel above its target path would require the monetary authority to fullyreverse the initial positive shock, by creating a period in which prices mustrise by less than the growth rate of the target path. With price-level-pathtargets, there is good reason to believe that they could serve to anchorinflation expectations, even when there is significant downward pressure onnominal interest rates, thus reducing the likelihood of encountering the zerobound on nominal interest rates (Eggertsson and Woodford, 2003; andLaxton, N’Diaye, and Pesenti, 2006). If this is true, everything else beingequal, the relative benefits of PLPT vs. IT rise, as the underlying trendincrease in prices falls. PLPT also caps the variance of expected futureprices, thus leading to a fall in price-level uncertainty. PLPT, however, maynot offer a panacea. Many authors have argued that PLPT has thepotential to increase the volatility of inflation and/or output relative to IT(see, for example, Lebow, Roberts, and Stockton, 1992; and Fillion andTetlow, 1994).

This paper focuses on the argument that PLPT generates increasedmacroeconomic instability relative to IT. We compare the capability ofsimple IT and PLPT interest rate feedback rules to minimize inflation andoutput gap variability in a simplified, two-country, two-sector (tradable andnontradable goods) version of the global economy model (GEM), calibratedfor Canada and the United States.1

1For a description of the full GEM, see Pesenti (2008). For the purposes of our work, therisk-adjusted uncovered interest rate parity (UIRP) condition in the GEM was modified to

INFLATION TARGETING AND PRICE-LEVEL-PATH TARGETING

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Our results suggest that simple PLPT rules perform slightly betterthan simple IT rules, and that this finding is reinforced by the presence ofterms-of-trade shocks. In addition, we demonstrate that our results aresensitive to the interaction between how forward-looking price formation isand the incidence of different types of shocks. Lastly, we demonstrate thatthe relative merits of PLPT and IT are independent of the monetary policyframework followed in the United States.

I. Calibration and Model Properties

Calibration Methodology

The calibration of the model reflects our desire to broadly match a number ofselected unconditional moments in the historical data (temporal cross-correlations, autocorrelations, and relative variances), as well as impulseresponses to specific domestic shocks (for example, technology, demand,monetary policy) from the Bank of Canada’s model of Canada, the terms-of-trade economic model (ToTEM) (see Murchison and Rennison, 2006),and to the Bank of Canada’s model of the U.S. economy, the Model of theUnited States Economy (MUSE) (see Gosselin and Lalonde, 2005).2 Theparameterization process involves selecting a set of candidate modelparameters and then using the historical data to ‘‘back out’’ a historicalpath for the model’s shock terms that allows us to exactly replicate history.3

Using the variance of the historical shocks, we then conduct stochasticsimulations, calculate key moments, and compare them to those from thehistorical data.4

Impulse responses from the model are also simulated and comparedwith those from ToTEM and MUSE. The simulation process is repeateduntil the model is able to broadly match both the unconditional momentsin the historical data and the impulse responses suggested by the othermodels.

The model has 23 behavioral shocks. We group the shocks into fivecategories. Domestic demand shocks (consumption, investment, imports,

address the forward premium puzzle, as in Adolfson and others (2005). For a nontechnicaldescription of the version of the GEM used in this analysis, see Coletti, Lalonde, and Muir(forthcoming).

2An alternative approach is to use Bayesian techniques to estimate the model. Bayesiantechniques allow modelers to incorporate priors on the structural parameters. However, weagree with the views expressed in Murchison and Rennison (2006) that the priors (especiallythose of policymakers) are actually more closely related to the behavior of the model ratherthan the structural parameters themselves. As a result, we pay attention to matching our priorson the impulse responses (gleaned from the other models) rather than the values of thestructural parameters.

3Over history monetary policy is characterized by simple Taylor-type rules. See Coletti,Lalonde, and Muir (2008) for more details.

4Each shock, z, is modeled as a first-order autoregressive stochastic process with standarderror of the random disturbance, se, and persistence, l: zt ¼ lzt�1 þ et.

Donald Coletti, Rene Lalonde, and Dirk Muir

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government spending, and interest rates) share the common feature thatthey occur in the home country and generate a positive covariance betweendomestic output (as well as the domestic output gap) and inflation.5 Thesecond broad class of shocks consists of domestic supply shocks, whereoutput and inflation covary negatively. Domestic supply shocks are furtherdisaggregated, depending on the behavior of the domestic output gap. Morespecifically, in domestic productivity shocks (technology shocks to theproduction of tradable and nontradable goods), the domestic output gapcovaries positively with inflation, while in the remaining supply shocks—thethree domestic mark-up shocks (prices in the tradable goods sector; pricesin nontradable goods sector; and the real wage) and a domestic laborsupply shock—there is a negative covariance between domestic inflation andthe output gap. The final two shocks—those originating in the foreign countryand the exchange rate shock—have a stronger open economy flavor. Thesetypes of shocks lead to a positive correlation in Canadian inflation andthe output gap.

To identify the shocks empirically we use 21 historical data series and anassumption regarding the disaggregation of wage shocks and labor supply shocksin both countries based on previous empirical work (Juillard and others, 2006).6

The historical series that we use are real consumption, real investment, realgovernment spending, real imports, the price of consumption goods (coreCPI for Canada and core personal consumption expenditure, or PCE, for theUnited States), the price of nontradable consumption goods, wages, totalemployment in the nontradable-goods sector, total employment in the tradable-goods sector, the real Canadian-U.S. exchange rate (deflated by the prices ofconsumption goods), and the 90-day commercial paper rate.7 Real data aredetrended using a Hodrick-Prescott filter with a stiffness parameter of 10,000. AllCanadian nominal variables are detrended using the inflation target, post-1991,and an implied inflation target over the 1983 to 1990 period (Amano andMurchison, 2005), while all U.S. nominal variables are detrended using anestimated inflation target (Lalonde, 2006). The historical sample studied covers1983:Q1 to 2004:Q2.

5The output gap is defined as the difference between the economy’s actual output and itspotential output. We use a measure of potential output that is consistent with the conventionalmeasure usually used at central banks. This measure is calculated based on a productionfunction approach where output is evaluated with actual total factor productivity, actualcapital stock, and steady-state labor supply.

6Our results are robust to alternative decompositions of the labor supply and wage mark-up shocks.

7For Canada, consumer price data is the consumer price index excluding eight volatilecomponents and the effects of indirect taxes (CPIX). Nontradable goods prices are proxied bythe prices of services excluding financial services in the core Canadian CPI. Similar price seriesare used for the United States based on the U.S. PCE deflator. Total employment in thenontradable goods sector is set equal to employment in services excluding financial servicesfrom the Canadian Labor Force Surveys. Similar data for the United States are provided bythe U.S. Bureau of Economic Activity.


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Matching Unconditional Moments

In this section, we demonstrate the ability of the Canadian-U.S. version ofthe GEM to reproduce some key unconditional moments from history.8

Table 1 shows the decomposition of the long-run variance of consumer priceinflation, the output gap, the short-term nominal interest rate, exports,imports, the real exchange rate, and the terms of trade. Foreign shocks areextremely important for explaining economic developments in Canada,accounting for about 60 percent of the variance in the output gap, and about35 percent of the variation in consumer price inflation. Domestic demandshocks, on the other hand, are less important, explaining about 20 percent ofthe variability in the output gap and about 10 percent of inflation variability.Mark-up and labor supply shocks account for little of the variation in theoutput gap (about 10 percent), but explain a significant proportion (40percent) of the variation in consumer price inflation in Canada.9

Our calibration of the GEM also does a good job at replicating thepersistence of GDP growth and year-over-year core inflation in Canada, as

Table 1. Variance Decomposition Using Model-Generated Data(In percent)

Standard

Deviation Demand Productivity

Mark-up and

Labor

Exchange

Rate

Foreign

Shocks

Canada

CPI inflation 0.7 9.9 2.8 39.2 12.7 35.4

Output gap 2.1 22.3 7.0 7.9 4.7 58.1

Interest rate

(change)

0.4 36.9 2.0 32.8 4.7 23.6

Exports 3.0 3.9 1.8 12.9 6.9 74.5

Imports 3.1 43.7 4.0 11.1 13.6 27.6

Real exchange

rate

2.9 8.7 2.5 17.7 19.6 48.6

Terms of trade 1.7 8.6 2.4 22.3 21.5 45.2

United States

CPI inflation 0.6 38.9 17.5 42.9 0.1 0.6

Output gap 1.2 39.8 35.0 15.1 0.1 1.0

Interest rate

(change)

0.7 50.1 30.4 18.8 0.0 0.7

Note: CPI=consumer price index.

8See Coletti, Lalonde, and Muir (2008) for further evidence.9The model structure assumes that the shocks are independent. However, we find that

one in five covariances are statistically significant at conventional levels, although most arerelatively small. Almost all of the covariances are limited to shocks that are withinthe same major grouping. Our main results, at least qualitatively, are not sensitive to allowingfor these covariances.


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shown in Figure 1.10 The persistence of price and wage inflation in bothcountries is matched by calibrating the adjustment cost technology, so thatthe weight on lagged inflation in the linearized Phillips curves is equal toabout 0.41, and the weight on forward-looking expectations of inflation inthe next period is 0.58. Furthermore, from Figure 1, we can see that themodel captures the broad pattern of the correlations between the real interest

Figure 1. Auto- and Cross-Correlation Functions: The Global Economy Model (GEM)Against Historical Data

-0.4

-0.2

0.0

0.2

0.4

0.6

-0.4

-0.2

0.0

0.2

0.4

0.6Change in Real GDP

-1 -2 -3 -4-0.5

0.0

0.5

1.0

-0.5

0.0

0.5

1.0Year-on-Year Inflation

-1 -2 -3 -4

-2

-1

0

1

-2

-1

0

1

Change in Real Consumptionand the Real Interest Rate

-6 0 +6-0.4

-0.2

0.0

0.2

0.4

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-0.2

0.0

0.2

0.4

Change in the Real Exchange Rateand Change in Real Imports

-6 0 +6

-0.5

0.0

0.5

1.0

-0.5

0.0

0.5

1.0

Change in Real GDPand Change in U.S. Real GDP

-6 0 +6-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

Year-on-Year Inflationand the Output Gap

-6 0 +6

Note: Grey line is the stochastic simulation of the GEM; black solid line is the historical data;dashed lines are the historical 95 percent confidence intervals

10The solid grey lines represent the average correlations based on the GEM data, the solidblack lines are the historical correlations and the dashed lines represent the 95 percentconfidence intervals around the historical correlations.


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rate and consumption growth, the growth in real imports, and the change inthe real exchange rate, and Canadian and U.S. GDP growth.11 On thedownside, our version of the GEM tends to introduce a four-quarter phaseshift in the peak positive correlation in lags of the output gap and inflation,relative to the historical data. Although the model tends to overpredict thedegree of volatility in most of the key macro series, we find that whennormalized for the volatility in the output gap, the model generates relativevariability that is much closer to the empirical estimates for inflation,nominal interest rates, and the real exchange rate (see Table 2).12

II. Inflation Targeting vs. Price-Level-Path Targeting

Methodology

In order to assess the relative merits of the alternative monetary policy frameworks,we assume that the central bank seeks to minimize the quadratic loss function:

L ¼ lps2p þ lys2

y þ lis2Di; (1Þ

where sp2, sy

2, and sDi2 are the unconditional variances of the deviations of year-

over-year inflation from its targeted level, the output gap, and the firstdifference of the nominal interest rate. lp, ly, and li are the respective weightson the deviations. We feel that this characterization of central bank objectiveshas the benefit of being quite transparent and consistent with central banks’often stated desire to control inflation, while stabilizing the business cycle.13

Table 2. Relative Standard Deviations

History Global Economic Model

VariableCanada United States Canada United States

5th–95th percentile 5th–95th percentile

Inflation 0.2–0.4 0.2–0.4 0.3 0.5

Interest rate 0.6–1.0 0.6–1.2 0.6 1.4

Real exchange rate 1.1–3.7 — 1.4 —

11Each figure plots the correlation between the first variable identified in the figure title onthe vertical axis and the six lags and leads of the second variable identified on the horizontalaxis. So the number �6 along the horizontal axis represents a lag of six periods for the secondvariable.

12To better replicate the absolute variability of the key macro variables, we scale thevariance of the shocks used in the stochastic simulations by a common factor.

13One weakness of using an ad hoc loss function to evaluate the relative merits of IT andPLPT is that relative weights on the output gap and inflation are also arbitrary in nature. Analternative approach is to assess policies in terms of their relative abilities to maximize thewelfare of the model’s representative agent.


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In our baseline, we assume that the central bank cares equally about bothinflation and output gap volatility, so we set lp¼ ly¼ 1. Also, a small weight(li¼ 0.1) is placed on the change in the nominal interest rate, in order topenalize policy rules in which the nominal short-term interest rate hits thezero lower bound more than 5 percent of the time.14

We limit our analysis to simple monetary policy rules. Simple rules differfrom fully optimal rules in that they only consider a subset of the variablesthat are included in the fully optimal rules. Our choice to focus on simplerules is motivated by the belief that they are more likely to be robust acrossplausible models, than are fully optimal rules (Levin, Wieland, and Williams,2003), and because central banks find them easier to communicate to thepublic. We use the following generic form from Batini and Yates (2003):

it ¼ oiit�1 þ ð1� oiÞi�

þ opðEtptþk � ZEtptþk�1 � pTARtþk þ ZpTARtþk�1Þ þ oyyt; ð2Þ

where i is the nominal interest rate, i� is the equilibrium nominal interest rate,E denotes the expectations operator, p is the logarithmic level of consumerprices, and TAR denotes a targeted value. The central bank attempts tominimize the loss function (1), by choosing the degree of interest ratesmoothing, oi; the short-run elasticity of the nominal interest rates toexpected deviations of prices (inflation) from target, op; the short-runelasticity of the nominal interest rates to expected deviations of real GDPfrom potential output, oy; and the feedback horizon over which policy isconducted, k. For IT, Z is assumed to be unity; for PLPT, it is zero.

We minimize the central bank loss function by searching over all of thecoefficients and the feedback horizon, using stochastic simulations conductedwith numerical perturbation methods. As we are searching over four differentparameters, the process is extremely computationally intensive.

Results

Macroeconomic stabilization

The first question that we focus on is the relative ability of IT and PLPT tominimize the variability in inflation and the output gap. Table 3 reports thevalue of the loss function and the standard deviations of key macroeconomicvariables in Canada and the United States under the optimized IT and PLPTrules. For the United States, there are only two rules: IT and PLPT. ForCanada, there are four rules: IT and PLPT conditional upon the UnitedStates following either IT or PLPT.

The first part of our discussion concentrates on the case of Canada,assuming that the United States chooses IT. From Table 3 we see that PLPT

14This calculation is based on a real interest rate of 3 percent and an inflation target of 2percent (or, alternatively, a price-level-path target that grows by 2 percent per year).


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is preferred to IT in terms of the loss function. The overall gain is, however,quite small, as the incremental benefit of moving from the optimized IT ruleto the optimized PLPT rule is only 0.5 percent of the gain of moving from thehistorical Taylor rule to the optimized IT rule. It is interesting to note that,under PLPT, lower inflation and nominal interest rate variability come at theexpense of higher output gap variability. We conclude that PLPT rules candeliver a reduction in price-level uncertainty, while simultaneously reducinginflation and interest rate variability. This could all be achieved at the cost ofa small increase in output gap variability.

Table 4 shows that the simple PLPT rule is more forward looking thanthe simple IT rule. The PLPT rule has a target feedback horizon of threequarters, longer than two quarters in the case of the IT rule. Central bankschoose a longer horizon for PLPT relative to IT because it allows them totrade off less output gap volatility for higher inflation variability (Smets,2003). Note the very high value for the interest rate smoothing term(oi¼ 0.97) in the IT rule. Everything else being equal, as oi-1, the degree ofprice-level drift under IT falls, and IT looks to be increasing like PLPT.Optimal IT in the model implies a much higher degree of interest ratesmoothing than is suggested by estimates of historical policy rules.

To assess the robustness of our results, we conduct a number ofsensitivity analyses. First, we confirm results previously seen in the literature,which suggest that increasing the degree to which price and wage determi-nation is forward looking tends to enhance the merits of PLPT relative to IT.Second, we vary the relative weights on inflation and output gap variability inthe loss function. Increasing the relative weight on inflation variability tendsto reinforce the attractiveness of PLPT. However, as PLPT does notdominate IT in terms of both output gap and inflation stabilization, it ispossible to choose a large enough weight on output gap variability thatresults in IT being preferred to PLPT.

Our most interesting finding concerns the robustness of our results to thedistribution of the shocks. To address this issue, we recalculate optimizedPLPT and IT rules for each of the major categories of domestic shocks inCanada—first under the baseline calibration, and then under the alternative

Table 3. Standard Deviations of Key Variables under the Optimized Rules

United States Canada (U.S. IT) Canada (U.S. PLPT)

IT PLPT IT PLPT IT PLPT

Loss function 0.962 0.903 2.148 2.134 2.167 2.154

CPI inflation 0.350 0.363 0.499 0.407 0.498 0.405

Output gap 0.800 0.750 1.335 1.366 1.343 1.373

Interest rate (change) 1.410 1.440 1.087 1.020 1.079 1.017

Note: IT=inflation targeting; PLPT=price-level-path targeting; CPI=consumer price index.


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assumption that price and wage determination are completely forwardlooking. Under the baseline model calibration, we find that IT is preferred inthe mark-up and labor supply shocks, but that PLPT is favored in all othershocks. Alternatively, in the model with perfectly forward-looking price andwage determination, PLPT is preferred in all shocks, including the mark-upand labor supply shocks. These simulations lead us to conclude that therelative merits of IT and PLPT are sensitive to an important interactionbetween the degree to which price and wage determination is forwardlooking, and the importance of mark-up and labor supply shocks relative todemand and productivity shocks.

Why is it that the source of the shock matters when inflation is partiallyindexed to lagged inflation? To gain some insight, we first consider a pricemark-up shock in the model with fully forward-looking inflation. PLPToffers disadvantages and advantages relative to IT. On the downside, thesimple idea of having to return the price level to its target path, everythingelse being equal, means that the variance of inflation under PLPT must belarger than under IT. On the plus side, PLPT offers a powerful expectationschannel. The commitment to a lower future inflation rate under PLPT thanwhat would be implied under IT means that current period inflation will belower under PLPT than under IT. To generate this result, the central bankmust create more cumulative excess supply under PLPT (that is, as long asthe price level is above the target, PLPT requires excess supply). Everythingelse being equal, a PLPT central bank will find it optimal to create less initialexcess supply that lasts longer. Taken together, this means that although thecumulative output gap is larger under PLPT, the PLPT output gap has asmaller variance than that generated under IT.

Now consider a positive demand shock. As in the case of the price mark-up shock, the commitment of the central bank to the price-level-path targetimplies that future inflation rates must be lower under PLPT than under IT.This leads to inflation that is initially lower than under IT. To support thisoutcome, the central bank needs to create excess supply at some time inthe future under PLPT, but not under IT. In addition, the initial jump in theoutput gap, under PLPT, is smaller than under IT. As a result, both the

Table 4. Results for Simple Optimized Rules

United States Canada (U.S. IT) Canada (U.S. PLPT)

IT PLPT IT PLPT IT PLPT

k 1.00 2.00 2.00 3.00 2.00 3.00

oi 0.86 0.88 0.97 0.85 0.98 0.86

op 2.95 2.20 2.44 3.74 2.45 3.84

oy 1.22 1.83 0.70 0.85 0.70 0.85

Note: IT=inflation targeting; PLPT=price-level-path targeting.


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cumulative output gap and the variance of the output gap, under PLPT,are smaller than under IT.

We can conclude, in the perfectly forward-looking model, that therelative benefits from PLPT vs. IT are larger in demand shocks than inmark-up shocks. If we gradually increase the weight on lagged inflation in thePhillips curve, the monetary control problem becomes more difficult, andthe relative advantage of PLPT begins to disappear. Our calibration of themodel lies in the zone for which PLPT is still favored in demand shocks, butthe degree of indexation in inflation is high enough to tilt the results towardIT in mark-up shocks.

Does the presence of terms-of-trade shocks matter?

In the second part of our analysis, we focus on the role played by terms-of-trade shocks. Our interest in this question is motivated, in part, by argumentsthat suggest that stabilizing the aggregate price level in face of relative priceshocks could introduce increased variability in output, that would outweighthe benefits associated with reduced price-level uncertainty (Bank of Canada,2006).

The first question that we consider is the definition of a terms-of-tradeshock. Based on the long-run historical variance decomposition suggested bythe model, we conclude that the shocks that have had the most importantinfluence on Canada’s terms of trade are (1) the U.S. consumption shock, (2)the U.S. import demand shock, (3) the exchange rate shock, and (4) theCanadian tradable price mark-up shock, as they account for 60 percent of thetotal variation in the terms of trade. Then, we re-optimize the simple PLPTand IT rules for this basket of shocks only, and find that PLPT is favoredover IT. This result comes about because Canadian terms-of-trademovements have been principally associated with shocks that generate apositive covariance between the output gap and inflation (for example,variations in the demand for Canadian goods).

Does the choice of monetary policy framework in the United Statesmatter for Canada?

Finally, we consider another open economy element of our analysis. Srour(2001) suggests that if alternative monetary policy regimes in the large foreigncountry lead to significantly different behavior of real variables in the foreigneconomy, then it is possible that exchange rate adjustment will notcompletely insulate the small home country from the consequences of theforeign regime choice.

Table 4 shows, however, that the choice of PLPT or IT in the UnitedStates has no influence on the relative merits of IT and PLPT in Canada. Thisresult comes through because the choice of PLPT or IT in the United Stateshas little influence on the real factors important for Canada, such as U.S.demand variability, or the variability of U.S. interest rates (see Table 3).Moreover, we find that the choice of IT vs. PLPT in the United States has


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negligible implications for the parameterization of the monetary policy rulein Canada.

III. Conclusions and Future Extensions

We find that simple PLPT rules are slightly better than simple IT rules, interms of minimizing inflation and output-gap variability. Our analysishighlights the important interaction between the degree to which pricedetermination is forward looking and the distribution of the shocks to theeconomy.

Also, our work addresses two important open economy considerations.First, we isolate the contribution of terms-of-trade shocks on the relativemerits of PLPT and IT. We find that most shocks that have importantimplications for explaining the Canadian terms of trade over history alsoimply a positive covariance between inflation and the output gap in Canada.Consequently, our analysis suggests that macroeconomic stabilization is bestachieved by following a simple PLPT rule. Lastly, we find that the choice ofmonetary policy framework in the United States does not affect the relativemerits of IT vs. PLPT in Canada.

There are many possible extensions to our work. In particular, given theimportance of fluctuations in commodity prices to the terms of trade forCanada and the United States, we think that it would be prudent toincorporate commodities into the model, as in Lalonde and Muir (2007).Second, we would like to add a distribution sector to the model, tobetter address the issue of exchange rate pass-through from measuredborder prices to consumer prices. Third, we would like to consider othermodel modifications that would help us better match the unconditionalmoments of the historical data. Finally, we are interested in extending theanalysis by performing a full welfare analysis of the two monetary policyframeworks.

REFERENCESAdolfson, Malin, Stefan Laseen, Jesper Lind, and Matthias Villani, 2005, ‘‘Evaluating an

Estimated New Keynesian Small Open Economy Model,’’ paper presented at theIRFMP-IMF conference ‘‘DSGE Modeling at Policymaking Institutions: Progressand Prospects,’’ Washington, December 2–3.

Amano, Robert, and Stephen Murchison, 2005, ‘‘Factor-Market Structure, ShiftingInflation Targets and the New Keynesian Phillips Curve,’’ Issues in InflationTargeting, Bank of Canada, proceedings of a conference held by the Bank ofCanada, Ottawa (April).

Bank of Canada, 2006, Renewal of the Inflation-Control Target: Background Information(Ottawa, Bank of Canada).

Batini, Nicoletta, and Anthony Yates, 2003, ‘‘Hybrid Inflation and Price-LevelTargeting,’’ Journal of Money, Credit and Banking, Vol. 35, No. 3, pp. 283–300.


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Coletti, Donald, Rene Lalonde, and Dirk Muir, 2008, ‘‘Inflation Targeting and Price-Level-Path Targeting in the GEM: Some Open Economy Considerations,’’ Bank ofCanada Working Paper 2008-6 (Ottawa).

Eggertsson, Gauti, and Michael Woodford, 2003, ‘‘The Zero Bound on Interest Rates andOptimal Monetary Policy,’’ Brooking Papers on Economic Activity: 1, pp. 139–233.

Fillion, Jean-Francois, and Robert Tetlow, 1994, ‘‘Zero-Inflation or Price-LevelTargeting? Some Answers from Stochastic Simulations on a Small Open-EconomyMacro Model,’’ in Economic Behaviour and Policy Choice Under Price Stability,proceedings of a conference held by the Bank of Canada, Ottawa (October).

Gosselin, Marc-Andre, and Rene Lalonde, 2005, ‘‘MUSE: The Bank of Canada’s NewProjection Model of the U.S. Economy,’’ Bank of Canada Technical Report No. 96.

Juillard, Michel, Philippe Karam, Douglas Laxton, and Paolo Pesenti, 2006, ‘‘Welfare-based Monetary Policy Rules in an Estimated DSGE Model of the US Economy,’’ECB Working Paper 613 (European Central Bank).

Lalonde, Rene, 2006, ‘‘Endogenous Central Bank Credibility in a Small Forward-Looking Model of the U.S. Economy,’’ Bank of Canada Working Paper 2005-16.

_______, and Dirk Muir, 2007, ‘‘The Bank of Canada’s Version of the Global EconomyModel (BoC-GEM),’’ Bank of Canada Technical Report No. 98.

Laxton, Douglas, Papa N’Diaye, and Paolo Pesenti, 2006, ‘‘Deflationary shocks andMonetary Rules: An Open Economy Scenario Analysis,’’ Journal of the Japanese andInternational Economies, Vol. 20, pp. 665–98.

Lebow, David, John Roberts, and David Stockton, 1992, ‘‘Economic PerformanceUnder Price Stability,’’ Finance and Economics Discussion Series 1992–15, Board ofGovernors of the Federal Reserve System.

Levin, Andrew, Volker Wieland, and John C. Williams, 2003, ‘‘The Performance ofForecast-Based Monetary Policy Rules Under Model Uncertainty,’’ AmericanEconomic Review, Vol. 93, No. 3, pp. 622–45.

Mishkin, Frederic S., and Klaus Schmidt-Hebbel, 2001, ‘‘One Decade of InflationTargeting in the World: What Do We Know and What Do We Need to Know?’’ inInflation Targeting: Design, Performance, Challenges, ed. by Norman Loayza andRaimundo Soto (Santiago, Central Bank of Chile).

Murchison, Stephen, and Andrew Rennison, 2006, ‘‘ToTEM: The Bank of Canada’sNew Quarterly Projection Model,’’ Bank of Canada Technical Report No. 97.

Pesenti, Paolo, 2008, ‘‘The Global Economy Model (GEM): Theoretical Framework,’’IMF Staff Papers, Vol. 55, No. 2.

Smets, Frank, 2003, ‘‘Monetary Price Stability: How Long is the Medium Term?’’Journal of Monetary Economics, Vol. 50, No. 6, pp. 1293–309.

Srour, Gabriel, 2001, ‘‘Price-Level Targeting Versus Inflation Targeting in a Small OpenEconomy,’’ Bank of Canada Working Paper 2001-24 (Ottawa).


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The Macroeconomic Costs and Benefits of Adoptingthe Euro

PHILIPPE KARAM, DOUGLAS LAXTON, DAVID ROSE and NATALIA TAMIRISA�

This paper uses a two-country version of the global economy model toinvestigate some costs and benefits of a small, emerging economy’s abandoninga flexible exchange rate regime in favor of adopting the currency of its maintrading partner. The topic is particularly relevant for countries in central andeastern Europe, which recently joined the European Union and are nowpreparing to adopt the euro. We begin by evaluating macroeconomicperformance in an inflation-targeting regime under various monetary policyrules. The results are then compared with the case where the small economygives up its flexible exchange rate and joins the monetary union, under a numberof alternative assumptions about the magnitude of shocks and structuralrigidities. The analysis shows that although the monetary union has the benefitof eliminating exchange rate shocks, the loss of the buffering role of theexchange rate leads to greater volatility in domestic output and inflation. Thesecosts are likely to decline over time, as markets become more competitive,flexible, and integrated in the monetary union. [JEL C51, E31, E52]



�Philippe Karam is a senior economist with the IMF Institute; Douglas Laxton isassistant to the director of the IMF Research Department; David Rose is an IMF consultant;and Natalia Tamirisa is the deputy chief of the IMF Research Department’s World EconomicStudies Division. The authors thank Gian Maria Milesi-Ferretti for providing comments onan earlier version of this paper. We gratefully acknowledge the invaluable support of MichelJuillard, Heesun Kiem, and Susanna Mursula in developing the procedures used in the modelsimulations. Finally, we thank Yasmina Zinbi for her help in formatting the paper.



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This paper uses a two-country version of the Global Economy Model(GEM) to examine the costs and benefits of a small emerging market

economy’s abandoning an inflation-targeting and adopting the currency ofits main trading partner, a large advanced economy. This topic is particularlyrelevant for transition economies in central and eastern Europe, such as theCzech Republic, Hungary, Poland, and the Slovak Republic, which recentlyjoined the European Union (EU) and are now preparing to adopt the euro.

The literature has concentrated on the long-run welfare benefitsassociated with membership in a monetary union. Rose (2000, 2002) andFrankel and Rose (2002) showed that common currency boosts trade—thefinding that has spawned extensive investigations about the likely magnitudeof trade creation, for example, by Bayoumi and others (2004a) and Faruqee(2004).1 Besides the gains from trade, savings from lower transaction costsand dynamic gains from larger foreign direct investment are likely to raisepotential growth and improve the long-run welfare of a small open economyin a monetary union.

However, these long-run benefits are not the focus of this paper. Instead,we highlight an issue that has received less attention in the euro adoptionliterature—the benefits and costs relating to macroeconomic volatility underalternative exchange rate regimes.

A stylized feature of emerging market economies is higher volatility inexchange rates than that in advanced economies (Clark, Laxton, and Rose,2001). An emerging market economy can gain from the elimination of theexchange rate shocks vis-a-vis the common currency of the monetary union.However, this benefit needs to be weighed against the cost of losing theexchange rate as a mechanism for absorbing shocks. The magnitude ofexchange rate shocks is thus an important factor determining whether joiningthe monetary union would be beneficial or not for a small open economy. Butit is not the only factor. The ability of the economy to adjust to shocksthrough other mechanisms, depending on the flexibility of its product, labor,and financial markets, is also relevant. The degree of similarity in theeconomic structures of the small open economy and its trading partners alsomatters, as it determines the degree of synchronization in their economicactivity and similarity in the transmission of shocks—considerations, theimportance of which has been highlighted in the long-standing optimalcurrency area literature.

GEM is well suited for the analysis of euro adoption issues. The modelhas strong theoretical microfoundations, which make it more immune thanempirical models to the Lucas critique that agents’ behavior may changeunder an alternative policy regime. GEM provides a multicountry general

1See Micco, Stein, and Ordonez (2003). For a recent survey of the literature on how theeuro has boosted trade, see Baldwin (2006). According to Baldwin, detailed theoreticalhypothesis as to how the euro affects trade needs to be emphasized and less so the ‘‘howmuch’’ did the euro boost trade.

Philippe Karam, Douglas Laxton, David Rose, and Natalia Tamirisa

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equilibrium perspective, which is essential for examining the costs andbenefits of a monetary union. It has a complete multisector structure, with adetailed representation of traded and nontraded goods sectors. This allows usto consider the details of trade between the small economy and its largetrading partner as well as sector-specific productivity shocks. The model alsohas a new-Keynesian macroeconomic structure, with sticky nominaladjustment that provides a framework for considering the output-inflationvariability trade-offs under different policy regimes and differentassumptions about shock distributions. Another strength of the model,which we exploit here, is that it has sufficient structure to consider the effectson nominal dynamics of structural reforms that enhance market efficiency.

The GEM version we use is an updated calibration of a two-countrymodel developed in Laxton and Pesenti (2003). We treat the smalleconomy as a representative new EU member state (NM) with a flexibleexchange rate, and the large economy as its main trading partner—the euroarea (EA). The starting point for the calibration and the initial distributionof shocks is the stylized features and historical data for the Czech Republic—a typical NM economy. These country-specific data are supplementedwith selected regional data for NMs, particularly recent information on thedegree of competition in labor and product markets. After obtainingresults with the base-case calibration, we undertake extensive sensitivityanalyses. The primary motivation for these analyses is to identify the keyfactors determining the macroeconomic costs and benefits of euro adoption.Yet the tests also have another benefit—ascertaining the implicationsof cross-country differences in NMs’ characteristics and mitigating againstparameter uncertainty inherent in calibration-based modeling. Togetherwith an eclectic calibration of the model, which draws on both country-specific and regional information, the sensitivity tests help ensure that thequalitative conclusions of the paper apply to all NMs, even thoughthe quantitative findings may not be relevant for any particular country orNMs as a group.

The focus of the paper is on comparing the trade-off between output andinflation volatility under alternative exchange rate regimes. Under the firstpolicy regime, both EA and the NM pursue inflation targeting, and thecurrencies are linked by a flexible exchange rate. The analysis of the output-inflation trade-offs under the calibration assumptions renders base-caseefficiency frontiers for the foreign economy—the original euro area—and theNM economy. Next, we remove the flexible exchange rate and consider amonetary union, where a combined monetary policy target is a weightedaverage measure of inflation and the output gap in EA and NM. NM (andEA) tend to do worse in terms of output-inflation variability under themonetary union, because they can no longer buffer the effects of otherrigidities through the exchange rate. In the sensitivity analyses we begin withexperiments designed to investigate the importance of structural flexibilityand efficiency and then turn to experiments focusing on the implications ofthe underlying distribution of shocks. Major advances in simulation

THE MACROECONOMIC COSTS AND BENEFITS OF ADOPTING THE EURO

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technology permit the gamut of alternative assumptions and shockdistributions to be considered fairly easily.

The analysis of monetary policy under inflation targeting is based onTaylor rules (TAY) and inflation-forecast-based (IFB) monetary reactionfunctions. In IFB monetary rules, the central bank changes interest rates inresponse to the forecast profile of deviations of inflation from the target level,conditioned on the state of the economy as represented by the output gap,normally with some smoothing of the adjustment. TAY rules use current,rather than future deviations of inflation from the target rate.2 These rulescan be derived by minimizing a loss function that penalizes a weighted sum ofmeasures of the variability of inflation, output, and interest rates. An‘‘optimal’’ form of the reaction function will have coefficients that depend onthe relative weights in the loss function and the nature of the jointdistribution of shocks. By changing the weights in the loss function we canderive a trade-off efficiency frontier that shows the best availablecombinations of variability in output and inflation, given the model andthe assumptions about shock distributions. An efficiency frontier willgenerally have the convex shape typical of trade-offs. More stable inflationwill typically be available only at the cost of higher volatility in output, withthe slope of the trade-off reflecting diminishing returns at the margin.

I. Model and Calibration

The model is taken directly from Laxton and Pesenti (2003).3 This was thefirst version of GEM, which was calibrated to the Czech Republic and theeuro area.4 The model includes firms that produce goods, households thatconsume and provide labor and capital to firms, and a public sector thattaxes and spends. Production is split into two stages. In the first stage, labor,capital, and land are used to create intermediate goods that can be traded,such as components for manufacturing. These intermediate goods are thencombined with additional labor and capital at home and abroad to producefinal goods.5 Goods are differentiated, and as a result firms possess marketpower and restrict output to create excess profits. A second feature is a splitof intermediate goods into traded and nontraded goods, which is central to a

2For a discussion of IFB and Taylor rules, see Clark, Laxton, and Rose (2001); Batini andNelson (2001); and Laxton and Pesenti (2003).

3See Laxton and Pesenti (2003) for the complete set of equations.4For the purpose of this paper we will refer to the model for the Czech Republic as a

representative NM. There are two reasons for this. First, while many aspects of the modelapply to other new member states we do not want readers to focus excessively on the exactquantitative magnitudes. Second, some of the sensitivity analysis we perform is motivated bycharacteristics of other NMs.

5The addition of intermediate goods allows the model to examine issues that areimportant for developing countries. This includes policy challenges in economies that supplylow value-added components to industrial countries, or assemble higher-technologycomponents from such countries into final products, or are commodity producers andexporters.


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number of issues in international macroeconomics. It is necessary to explainfeatures in transition countries such as the higher investment in the tradablegoods sector, as well as the effects of structural reforms and a productionshift toward the desired higher quality goods supplied by more advancedeconomies. Rapid productivity increases in traded goods relative tonontraded goods also help explain why real exchange rates tend toappreciate in countries that are growing rapidly. Workers make a choicebetween work and leisure. They have market power and hence restrict theirlabor to raise their real wage. The model also features adjustment costs onreal and nominal variables to ensure that it exhibits meaningful dynamics.

The model is closed with a monetary policy reaction function. Over thelast decade, the literature on the performance of interest rate rules inmacroeconomic models has mainly focused on two types of rules, both ofwhich have been extensively used in research and policy analysis in centralbanks. The first one has come to be known universally as the TAY, followingthe seminal contribution by Taylor (1993) showing that a simple interest ratereaction function, which depended on contemporaneous values for inflationand the output gap, could provide both policymakers and researchers auseful organizational device for thinking about monetary policy issues. Thesecond type of monetary policy rule has come to be known as an IFB rule,but IFB rules are simply more ‘‘forward-looking’’ versions of a TAY, as theshort-term policy rate is assumed to respond to a forecast of future inflationrather than the contemporaneous level of inflation. IFB rules have been usedextensively in the types of macro models that inflation-targeting centralbanks use to create forecasts and risk assessments.

Structural change and short data sets in the transition economies makeformal estimation unreliable and so it is necessary to use calibration methods.Our approach to calibration is very pragmatic.6 For parameters that definemedium- and long-term responses of firms and consumers we often useestimates from microeconomic studies when they are available. Otherparameters are selected to mimic key characteristics of the economicenvironment, such as the relative size of the countries, their levels of trade,and their capital-output ratios. Adjustment costs on real and nominalvariables are chosen to generate realistic dynamic responses—elongating theresponses to shocks and ensuring that consumption, investment, andproduction do not immediately jump to a new long-term equilibrium inresponse to new information. Foremost, the model’s parameters have beencalibrated to mimic the monetary transmission mechanism that is representedby the core production models that are used at the Czech National Bank andthe European Central Bank.

6See the IMF Working Paper upon which this article is based for a discussion of theassumptions behind the parameters’ choice and the calibration of key steady-state ratios thatare consistent with national accounts data (Karam and others, forthcoming). See Box 2.1 ofBayoumi and others (2004b) for a high-level description of how parameters have beencalibrated in GEM.


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The calibration of the model largely follows Laxton and Pesenti’s originalGEM version (2003), with one notable exception. Markups in product andlabor markets, which were set as equal for NM and EA in Laxton and Pesenti(2003), were recalibrated in this paper in light of new cross-country studies onmeasures of regulatory and institutional rigidities in product and labormarkets. Conceptually, such rigidities are the primary reason for noncom-petitive, markup pricing. In product markets, regulations and barriers tocompetition render market power to firms, allowing them to charge consumersa markup over costs. Likewise, labor market regulation (for example, minimumwages and employment protection) and other institutional arrangements (forexample, rent regulations creating barriers to geographical mobility) preventcompetitive forces from operating fully.

The calibration of markups in product and labor markets is importantfor the analysis of the costs and benefits associated with euro adoption.Bayoumi, Laxton, and Pesenti (2004) show that reforms that raise com-petition and reduce markups in labor and product markets strengthen themonetary transmission mechanism, making the task of monetary policyeasier. An advantage of inflation targeting—that the exchange rate can playthe role of a shock absorber, facilitating adjustments in the economy withnominal rigidities and imperfect competition—would be reduced if priceswere flexible and markets were highly competitive, because in this case theburden of adjustment would fall on prices rather than the exchange rate.(Indeed, in a pure competitive equilibrium, where firms and workers do nothave any market power, there will be little difference between inflationtargeting and a monetary union.)

There are no empirical estimates of markups for the NM states, toour knowledge. However, recent studies provide useful cross-country com-parisons of various regulatory and institutional measures of rigidities inproduct and labor markets. These studies allow one to gauge how the degreeof market competition in the NM states compares to that in the euro areaand other advanced economies. On balance, institutional measures suggestthat the degree of labor market flexibility is higher in the NM states than inthe euro area, and the opposite is true for product markets—for a descriptionof the markups that were chosen, see Karam and others (2008) and thereferences therein.

The specific forms of the Taylor and IFB rules considered in this papercan be nested into a general rule of the form:

ð1þ itÞ4 ¼ oi½ð1þ it�1Þ4 � 1� þ oyyt

þ ð1� oiÞXtj¼0

ojEtPtþjPt�4þj

" #ð1þ �rtÞ4 � 1

" #

þ op

Xtj¼ 0

ojEtPtþjPt�4þj

�Ptþj

� �; ð1Þ


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where it is the policy rate, r�t the equilibrium real interest rate, yt the outputgap and ptþ j/pt�4þ j a measure of the year-over-year change in the price levelj quarters ahead, P is the inflation target and

PjtojEt( ptþ j/pt�4þ j) is a

weighted measure of inflation forecasts that has weights summing to one(P

jtoj¼ 1). In our simulations, the output gap is defined as the deviation of

real GDP from the model’s stationary equilibrium. Note that, when t and oi

are set to zero and when op, oy¼ 0.5, and oj¼ 1.0 for j¼ 0 and 0 for all otherj, expression (1) becomes the original Taylor (1993) rule. By contrast, whent>0, we refer to the rule as an IFB rule, because the interest rate in this casewill depend on weighted forecasts of the year-over-year inflation rate up to tquarters into the future. In the analysis below we consider a general casewhere the IFB rule is based on inflation forecasts up to four quarters in thefuture (referred to as IFB(0–4)) as well as simpler IFB rules that only dependon one measure of inflation j periods ahead.7 For example, we will refer to anIFB ( j) rule as a special case of expression (1) where we eliminate all but oneinflation measure j periods ahead and an IFB (j and k) rule where we consideronly two measures of inflation j and k periods ahead. For example, an IFB(4)rule reduces to

ð1þ itÞ4� 1 ¼ oi½ð1þ it�1Þ4 � 1� þ oyyt

þ ð1� oiÞPtþ4Ptð1þ �rtÞ4 � 1

� �

þ opEtPtþ4Pt�Ptþ4

� �: ð2Þ

To compare macroeconomic performance under alternative rules, we findthe parameters in the rules that plot out the trade-off between inflation andoutput variability subject to a constraint that the standard deviation of thefirst difference in the policy rate be no larger than 80 basis points. As inLaxton and Pesenti (2003), the constraint on interest rate variability isnecessary to rule out extremely aggressive rules that result in implausiblylarge and volatile changes in the policy rate.8

The list and structural characteristics of the shocks in the model and thecalibration of the stochastic processes to reflect the historical variability of

7For simplicity it has been quite common for central bank models to rely upon thesesimpler IFB rules. For example, the Czech National Bank’s model has an IFB rule thatdepends on the forecast of inflation four quarters in the future.

8The constrained efficiency frontiers (EF) are constructed with an extended version of theOptimal Simple Rule (OSR) routine in DYNARE (Dynamic Rational Expectations Program,by Adjemian and others, 2007) that allows for constrained optimization. The earlier Laxtonand Pesenti (2003) results, which compared EFs for simple IFB rules and simple TAY rules,were constructed with a numerical grid search and took a significant amount of time andcomputer simulations to construct. The new OSR routine was programmed by Michel Juillardand produces EFs for this model in under 30min, which is very impressive considering themodel has 13 stochastic shocks and 88 state variables.


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key macroeconomic variables—discussed in details in Laxton and Pesenti(2003)—are reported in Karam and others (2008).

II. The Case of Independent Monetary Policies

In the first policy regime, both EA and the NM pursue inflation targeting,and the currencies are linked by a flexible exchange rate. Figure 1 shows fourefficiency frontiers. The inner pair of curves shows the trade-offs facing theEA economy, but the outer pair of curves shows the equivalent curves for theNM under inflation targeting with a flexible exchange rate. The two frontiersin each case reflect the results under the two particular alternative policyrules, TAY and IFB with a four-quarter lead in the inflation term (that is, thecentral bank responds to the forecast of the difference between inflation andthe target rate, four quarters ahead).

The first point that emerges is that the EA economy experiences far lessvolatile outcomes. The EA curves lie southwest of the NM curves because theNM faces much more volatile shocks generally, and important risk-premium,productivity, and import preference shocks in particular.9

The second point is that the form of the monetary rule makes virtually nodifference in the much larger, more closed EA economy. The IFB(4) rule does atiny bit better, but the difference is miniscule. A TAY works well when currentmeasures capture virtually all the information about the future dynamics ofoutput and inflation. This tends to be the case for large, closed economies. Thisresult echoes previous findings with a variety of models on the U.S. economy.

The same is not true for the small emerging economy. Figure 1 showsthat there are significant macroeconomic performance gains available forsuch economies from the use of the more forward-looking IFB rule. Theshocks hitting such economies are larger and, owing to the more open natureof these economies, the resulting movements in the exchange rate areimportant. These effects are essentially irrelevant in the larger economy.Moreover, the more open nature of small economies amplifies the importanceof international transmission mechanisms. In short, the dynamic propertiesin such economies are more volatile and current measures of the inflation gapdo not capture all the essential information. The important role of theexchange rate in the nominal adjustment process for such economies is partof the reason. In any case, our results indicate that for such economies aflexible exchange rate can provide policymakers with significant scope tolimit volatility in output and inflation.

Figure 1 presents a version of the IFB results with the lead on theinflation forecast term at four quarters, as was chosen for the first core modelused for IT in the Czech Republic. Under an IFB rule, the policy response isto some forecast of the deviation of inflation from target. But what should

9By import preference shocks we mean shocks to the relative preference for foreign goodsover domestic goods. Such shocks contribute to volatility in trade and exchange rates, which isan important issue here.


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the lead be? The general answer is that no one lead produces optimal results.We need a linear combination of leads in the reaction function. Figure 2shows the IFB results for the NM economy under a number of individualleads. Note that there is no general dominance. If the desired choice is lowinflation variability, then shorter leads produce better results. As the choicemoves to lower output variability, with consequent higher inflation variability,the optimal lead rises. At lead four quarters, we see a dominance result. As thelead is extended further, the results deteriorate. The frontiers for leads eightand nine are dominated by the TAY, at least over some regions.

The lesson is that the TAY and any simple IFB rule may or may notprovide points on the general efficiency frontier, which is an envelope curveencompassing all options for horizon. In Figure 2 we also show the result for

Figure 1. Comparison of IFB (4) and the Taylor Rule (IFB(0)) for the Euro Area and NewEuropean Union Member Economies

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

NM IFB(0)=Taylor

EA IFB(0)=Taylor

NM IFB(4)

EA IFB(4) (dotted line)

Stan

dard

dev

iatio

n of

CPI

infl

atio

n

Standard deviation of output

Note: IFB¼ inflation-forecast-based monetary reaction functions; EA¼ euro area; NM¼ newmember of the European Union; CPI¼ consumer price index.


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a simple combination of a lead four IFB formulation (a common choice incentral bank models) and a lead zero Taylor formulation. The resultdominates both simple alternatives in the bottom-right region. Also shown isthe solution that allows weights to be placed on all leads up to four quarters.It dominates the other solution, again especially in the bottom-right region oflow inflation variability and high output variability. In all results to follow,we use this generalized formulation of the reaction function.

III. Comparison of Monetary Union and Independent Monetary Policies

We focus on the NM economy in the discussion from here on, because thecomparative results for the EA economy are little influenced by any of thefactors that we consider. The solid lines in Figure 3 compare the results for

Figure 2. Comparison of Alternative IFB Rules for the NM Economy

1.25 1.50 1.75 2.00 2.251.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

IFB(0)=TaylorIFB(1)

IFB(3)

IFB(4)IFB(5)

IFB(8)

IFB(0 and 4)IFB(0-4)

Stan

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Note: IFB¼ inflation-forecast-based monetary reaction functions; NM¼ new member of theEuropean Union; CPI¼ consumer price index.


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the IFB rule and monetary union. The line labeled ‘‘EMU base case’’ tracesout combinations of standard deviation pairs for the NM economy undermonetary union. To generate these, we eliminate the risk premium shocksand force a common interest rate on the two regions that depends on aweighted sum of inflation and the output gap in the two regions, where theweights are equal to relative population size. We then trace out the points forthe NM economy as we move along the combined European Economic andMonetary Union (EMU) efficiency frontier—not reported in the figures.Because the size of the shocks to the exchange rate play a large role indetermining overall volatility in the NM economy we also consider analternative case in Figure 3 where we increase the standard deviation of therisk premium shocks by 75 percent.

Figure 3. NM Inflation and Output Variability Under an IFB Rule and Monetary Union(includes cases with greater nominal rigidities and larger risk premium shocks)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

IFB(0-4) with Larger Risk Premium Shocks

IFB(0-4) Base Case

EMU Base Case

EMU Greater Rigidities

Stan

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Note: IFB¼ inflation-forecast-based monetary reaction functions; EMU¼European MonetaryUnion; NM¼ new member of the European Union; CPI¼ consumer price index.


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The curve ‘‘EMU base case’’ comes from combinations generated underthe EMU base-case assumptions. All combinations lie above and to the rightof the frontier for the IT-flexible exchange rate regime, which is labeled as‘‘IFB(0–4) base case’’ in Figure 3. This means that there is a clear loss to theNM economy under monetary union. This loss reflects the suboptimalmonetary policy that is forced on the NM economy under monetary unionunder the base-case assumptions. In the base case, the variation in theexchange rate has a buffering effect that reduces overall macroeconomicvariability. Under monetary union, this buffering role is not available and theadjustment must be transferred to other domestic variables, principallyinflation. What used to come as a change in the real exchange rate from anominal exchange rate change with sticky domestic costs and prices mustnow come from those domestic nominal variables. The result is deteriorationin the overall variability results.

This conclusion is subject to possible qualification, depending on the sizeof the risk-premium (exchange rate) shocks that are eliminated undermonetary union. The union locus is not everywhere outside the efficiencyfrontier for the flexible exchange-rate locus under the higher shockdispersion. Thus, if the eliminated risk-premium shocks are large enough,there could be a gain from monetary union. Whether there would be stilldepends on choices made in overall EMU policy, but improvement for theNM economy becomes possible, in principle, if the initial conditions includelarge exchange rate shocks.

The final locus on Figure 3 shows the combinations available undermonetary union when we increase the degree of rigidity in nominaladjustment processes in the NM economy to be equal to that in the EAeconomy. With the greater rigidities, the cost for the NM economy of losingthe contribution of the flexible exchange rate is significantly higher.

Consider next the results in Figure 4. In this experiment, we increase thecompetitiveness of the NM markets, halving the monopolistic markup inprices (37–18.5 percent) and wages (23–11.5 percent). There is a shift tothe left of the locus under a common currency. One could conclude that thecosts of monetary union associated with the loss of exchange rate flexibilitycan be moderated if the common currency is associated with less protectionfor home markets, either through reforms at home or simply a morecomplete integration of markets. If we also assume increased competitivenessin the EU economy after the union through a halving of markups, this effectgets considerably stronger (Figure 5). In other words, lower markups in theEU economy lead to less volatility in both economies, and with significantextra gains in the NM economy (Figure 5 shows a much larger shift thanFigure 4).

Figure 6 shows a striking result when we lower the volatility of shocks topreferences for imported goods in both the EA and NM economies. For NMeconomies, volatility in trade tends to be high, more so than can be explainedby the degree of openness and the volatility of demand, and this is animportant part of overall cycle properties. In GEM, we capture this through


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a shock to the relative preference for foreign goods vs. domestic goods. Herewe reduce the volatility of these preference shocks. The result is a dramaticreduction in the volatility of the economy under IT and flexible exchangerates, and this has a big effect on the costs of monetary union. When importdemand shocks are less important, the overall volatility of the economy isreduced, and, because there is less need for exchange rate response, there isless volatility in inflation coming from import prices. This reduces the costs ofcurrency union; note that the locus of pairs under monetary union shifts ineven more strongly. Indeed, there are points available where the home, NMeconomy is less volatile after a monetary union than it was with a flexibleexchange rate. This is an important result, as it might be expected that goods

Figure 4. NM Inflation and Output Variability Under an IFB Rule and Monetary Union(includes cases of smaller NM markups under monetary union)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

IFB(0-4) Base Case

EMU Base Case

EMU Smaller Home Markups

Stan

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Note: IFB¼ inflation-forecast-based monetary reaction functions; EMU¼European MonetaryUnion; NM¼ new member of the European Union; CPI¼ consumer price index.


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would become more homogeneous and preferences would become lessvariable over time within an economic union.

We considered a number of other possible influences on the impact ofmonetary union, including changing the size of fiscal shocks, investmentshocks, and labor market shocks. Only the latter revealed anythinginteresting. If home labor markets become less volatile, as might beexpected to happen over time in a monetary union, there could be a smallreduction in the costs of the union. However, the lower labor shock case doesnot change the basic results. The trade-off available with a flexible exchangerate shifts to the left, as does the postunion locus. There is no sense in which

Figure 5. NM Inflation and Output Variability Under an IFB Rule and Monetary Union(includes cases of smaller NM and EA markups under monetary union)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

IFB(0-4) Base Case

EMU Base Case

EMU Smaller Home and Foreign Markups

Stan

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Note: IFB¼ inflation-forecast-based monetary reaction functions; EA¼ euro area; EMU¼European Monetary Union; NM¼ new member of the European Union; CPI¼ consumer priceindex.


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this creates a case for gains from a monetary union. But, one can see aslightly larger shift of the postunion locus, meaning that the costs of theunion are offset a bit, if labor markets become less volatile.

IV. Conclusions

In this paper, we investigate using GEM, the costs and benefits in terms ofthe volatility of output and inflation when a small, emerging economy adoptsthe currency of its main trading partner. We establish as a point of departurethat the high relative openness of such economies combined with therelatively high volatility in the shocks they face leads to a systematically

Figure 6. NM Inflation and Output Variability Under and IFB Rule and Monetary Union(includes cases of smaller import demand shocks in NM and EA economies)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

IFB(0-4) Smaller Import Demand Shocks

IFB(0-4) Base Case

EMU Base Case

EMU Smaller Import Demand Shocks

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Note: IFB¼ inflation-forecast-based monetary reaction functions; EA¼ euro area; EMU¼European Monetary Union; NM¼ new member of the European Union; CPI¼ consumer priceindex.


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worse policy efficiency frontier compared with that of the larger tradingpartner. Small, open economies are inherently more volatile than large,relatively closed economies, in part because of their greater exposure tovolatility in trade.

We show that one consequence is that TAY, which use contemporaneousmeasures of the deviation of inflation from target in the monetary policy rule,tend to work reasonably well for larger, more closed economies, whereasbetter performance is available for small, open economies in responding to aforecast for inflation. We show, further, that for policymakers who wish toput a high weight on minimizing inflation volatility, a short lead isappropriate, whereas if the preference for minimizing output volatility isgiven more weight, the optimal lead for the inflation forecast rises. For thismodel, there is no case for going beyond a lead of four quarters, becauseresults systematically deteriorate for longer leads.

We find that a flexible exchange rate plays an important buffering rolethat facilitates macroeconomic adjustment to shocks in small, emergingeconomies, which allows the central bank to achieve better outcomes in termsof domestic volatility. In general, the results show that there is a cost to asmall, emerging economy in joining a common currency area when thisflexibility is lost. The essential reason is that there are rigidities in domesticadjustment, and when the burden of macroeconomic adjustment is forcedonto domestic nominal variables under the common currency,macroeconomic volatility generally increases.

This conclusion must be tempered, however, by the results of thesensitivity analysis. In general, if the volatility of shocks were to decline inmonetary union, some of these costs would be at least mitigated. Indeed, weshow that there are some assumptions that can open the possibility of betterperformance within a monetary union. In terms of mitigating costs, there is ageneral result that the more competitive and flexible are markets, the lessrigid are adjustment processes and the less important will be the loss of thebuffering role of the exchange rate. Looking at the results as indicators ofwhat might happen over time as emerging economies adopt world technologyand as markets become more competitive and more integrated, we wouldconclude that any macroeconomic costs of a monetary union are likely to fallover time. Finally, our experiments show dramatic improvement in thevolatility frontier, and consequent reduction in the costs of joining amonetary union, when the volatility of preferences for foreign vs. domesticgoods is reduced.

REFERENCESAdjemian, S., M. Juillard, M. Ferhat, and S. Villemot, 2007, ‘‘DYNARE: A Program for

Simulating and Estimating DSGE Models,’’ Available via the Internet:www.cepremap.cnrs.fr/dynare.

Baldwin, R., 2006, ‘‘The Euro’s Trade Effect,’’ Working Paper No. 594 (Frankfurt,European Central Bank).


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www.cepremap.cnrs.fr/dynare

Batini, N., and E. Nelson, 2001, ‘‘Optimal Horizons for Inflation Targeting,’’ Journal ofEconomic Dynamics and Control, Vol. 25, pp. 891–910.

Bayoumi, T., M. Kumhof, D. Laxton, and K. Naknoi, 2004a, ‘‘Exchange Rate Regimes,International Linkages and the Macroeconomic Performance of the New MemberStates,’’ policy version prepared for a conference at the European Central Bank(October); an extended version was prepared for the IMF Annual ResearchConference (November).

_______, D. Laxton, H. Faruqee, B. Hunt, P. Karam, J. Lee, A. Rebucci, and I.Tchakarov, 2004b, ‘‘GEM: A New International Macroeconomic Model,’’ IMFOccasional Paper No. 239 (Washington, International Monetary Fund).

_______, and P. Pesenti, 2004, ‘‘Benefits and Spillovers of Greater Competition in Europe:A Macroeconomic Assessment,’’ Working Paper No. 341 (Frankfurt, EuropeanCentral Bank).

Clark, P., D. Laxton, and D. Rose, 2001, ‘‘An Evaluation of Alternative Monetary PolicyRules in a Model with Capacity Constraints,’’ Journal of Money Credit and Banking,Vol. 33, No. 1, pp. 42–64.

Faruqee, H., 2004, ‘‘Measuring the Trade Effects of EMU,’’ IMF Working Paper 04/154(Washington, International Monetary Fund).

Frankel, J.A., and A. Rose, 2002, ‘‘An Estimate of the Effect of Common Currencies onTrade and Income,’’ Quarterly Journal of Economics, Vol. 117 (May), pp. 437–66.

Karam, P., D. Laxton, D. Rose, and N. Tamirisa, 2008, ‘‘The Macroeconomic Costs andBenefits of Adopting the Euro,’’ IMF Working Paper (Washington, InternationalMonetary Fund).

Laxton, D., and P. Pesenti, 2003, ‘‘Monetary Policy Rules for Small, Open, EmergingEconomies,’’ Journal of Monetary Economics, Vol. 50, pp. 1109–46.

Micco, A., E. Stein, and G. Ordonez, 2003, ‘‘The Currency Union Effect on Trade: EarlyEvidence from EMU,’’ Economic Policy, Vol. 18, pp. 317–56.

Rose, A.K., 2000, ‘‘One Money, One Market? The Effect of Common Currencies onInternational Trade,’’ Economic Policy, Vol. 30, pp. 7–45.

_______, 2002, ‘‘The Effect of Common Currencies on International Trade: Where Do WeStand?,’’ Occasional Paper 22 (Berkeley, University of California).

Taylor, J., 1993, ‘‘Discretion Versus Policy Rules in Practice,’’ Carnegie-RochesterConference Series on Public Policy, Vol. 39, pp. 195–14.


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Why It Pays to Synchronize Structural Reforms in the EuroArea Across Markets and Countries

LUC EVERAERT and WERNER SCHULE�

Simulations with the IMF’s Global Economy Model, calibrated to the EuropeanUnion, suggest that there are sizable long-term gains in output and employmentfrom boosting competition in product and labor markets. Coordinating reformsacross these markets in a given country is found to be beneficial: it reducestransition costs in the short run and generates synergies in the long run.However, to prevent a temporary fall in euro area consumption, synchronizationacross countries is needed if they are to benefit from a monetary policy reaction.[JEL C53, E52, F47]



Europe has been struggling to raise trend-growth as a result of the lack offlexibility in its product and labor markets. The remedy to brighten the

prospects for higher growth—structural reforms—has been well established.Diminishing regulations and barriers to competition in product marketswould force firms to reduce the markup they charge customers and leadto lower prices for consumers, raising real wages and lowering resistance tolabor market reforms (Blanchard and Giavazzi, 2003).

The focus of this study, setting it apart from previous applications ofthe IMF’s Global EconomyModel (GEM), is on the transition dynamics andthe potential gains from synchronizing structural reforms across markets and

�Luc Everaert is a division chief and Werner Schule a senior economist with the IMF’sEuropean Department.


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across countries within a monetary union, the euro area. Traded goodmarket reforms alone have immediate positive effects on output, wages, andwelfare, while stand-alone labor market reforms lead to output gains andreduce real wages. Stand-alone reforms in the nontraded sector, whererigidities are the highest, would push consumption and output significantlybelow baseline in the near term. Synchronizing the timing of product andlabor market reforms mitigates downward pressures on real wages, but maynot suffice to avoid a transitory decline of output, and especially ofconsumption below baseline. Coordinating reforms among euro areaeconomies brings into play monetary policy, which will ease as reformsreduce inflation in the entire euro area. Monetary accommodation is sufficientto prevent a temporary fall in consumption. Long-run (steady-state) effects areconsistent with earlier studies (Bayoumi, Laxton, and Pesenti, 2004).

In the version of GEM used here, the world is confined to the 2005-European Union (EU) and split into four blocs: a reforming economy(France or Belgium, respectively); the rest of the euro area (RE); a group ofthree non-euro-area EU members (Denmark, Sweden, and the UnitedKingdom); and a group of 10 new member states (NMS). Trade (in percentof GDP) covers intra-EU flows only. Therefore, the four blocs appear lessopen than they are in reality, and the spillover effects are limited to those thatbenefit EU members.

Behavioral parameters were taken from the relevant literature, some ofwhich are invariant across countries, but others were modified using country-specific information. Differences across blocs and countries, which aregeographically and culturally very close, were kept to the minimumnecessary. Hence, all key elasticities of substitution, the discount factor, andhabit persistence have been set at the same value. Based on a recentmetaregression (Evers, de Mooij, and van Vuuren, 2005), the elasticity of laborsupply with respect to wages is set at 0.33. This elasticity is key for the responseof the model to labor market reforms. All agents have perfect foresight. EUeconomies are characterized by relatively strong real rigidities, relatively highadjustment costs in the investment equations, and strong habit persistence inconsumption and labor supply, combined with a high intertemporal elasticityof substitution. Real rigidities and adjustment costs in price and wageequations are calibrated to reproduce realistic sacrifice ratios. Together,nominal and real rigidities generate typical VAR-type responses to shocks.

Monetary policy authorities are assumed to target 2 percent inflationthree quarters ahead, while smoothing fluctuations in the interest rate, whichis used as a policy instrument. The European Central Bank (ECB) setsmonetary policy on the basis of area-wide indicators. Nominal interest ratesin France and Belgium are determined by the ECB, which takes into accountthese countries’ inflation rates, weighted by their respective shares in area-wide GDP. With the euro as its currency, changes in relative prices betweentraded and nontraded goods, or the real effective exchange rate, take theform of inflation differentials and result in important cross-countryvariations in the real interest rate after shocks.

WHY IT PAYS TO SYNCHRONIZE STRUCTURAL REFORMS

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Fiscal policy is essentially passive; a fiscal rule ensures debt sustainabilityin the long run, with labor tax rates adjusting such that, after a shock, publicdebt returns to a target level. However, fiscal policy is not neutral; ifstructural reforms improve the tax base, the tax rate on labor declines withpositive feedback effects on labor supply.

I. Markups in Labor and Product Markets

Markups reflect imperfect competition in product and labor markets. Theelasticity of substitution between diverse products determines the firm’smarket power, which sets prices subject to the risk of losing marking sharesso as to maximize profits: ignoring adjustment costs, pt¼ y/(y�1)mct, where yis the elasticity of substitution. The setup for diverse labor inputs is similar.Competition-enhancing structural reforms will be simulated through areduction in the markups in labor, traded, and nontraded product markets.The simplicity of modeling markups makes the analysis tractable, but comesat the expense of having to be agnostic about specific reasons for imperfectcompetition.

Empirical estimates show significant markups in product and labormarkets for most countries, though estimates vary in size. Recent jointestimates of product market markups and workers’ bargaining powerindicate much higher product market markups than traditional estimates,which omitted the part of the firm’s rent captured by workers.1 The modelwas calibrated with product markups from such joint estimates (Table 1). Asestimates of markups are not available for all countries in the EU and allmarkets, the following additional assumptions were made. The euro area wasapproximated by Germany and Italy (and France or Belgium, respectively),but the RE area bloc was calibrated with estimates for the United Kingdom.For product market markups in the NMS, their relative position on theOrganization for Economic Cooperation and Development measure of thedegree of product market restrictedness was used to guide their calibration(Conway, Janod, and Nicoletti, 2005). Services markups were defined relativeto goods markups on the basis of direct rather than joint estimates becauseunion power is difficult to measure in the service sector. Lacking empiricalestimates on the NMS, it was assumed that wage markups lie in the middlebetween the euro area and the RE bloc.

II. Scenarios

The definition of the four blocs provides a natural design for the simulationexercise. The group of Denmark, Sweden, and the United Kingdom (RE) ison average further advanced in labor and product market reforms than the

1See Oliveira Martins and Scarpetta (1999); and Jean and Nicoletti (2002) for productmarkets; Saint-Paul (2004); Crepon, Desplatz, and Mairesse (2002); Dobbelaere (2004); andKonings, Van Cayseele, and Warzynski (2001) for joint labor-product market estimates; andDumont, Rayp, and Willeme (2006) for estimates of union bargaining power.

Luc Everaert and Werner Schule

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other parts of the European Union. Hence, simulations quantifying the effectof increasing competition in product and labor markets to the average levelof this bloc are a meaningful benchmark. Because some markup may bejustified as an incentive for innovation and as the result of efficiency-wagetype contracts, zero markups are not necessarily ideal. The determination ofoptimal levels of markups, however, is beyond the scope of this paper.

Reform in each of the markets—labor, goods (or traded products), andservices (or nontraded products)—is simulated separately. Because GEMdoes not contain explicit interactions between markups in various markets,the steady-state effects as well as the transition dynamics of the reforms arelargely additive. Even so, because of nonlinearities, when a given market ismore efficient, reforms in another market have a slightly greater impact.Reforms are also considered, whether they are implemented in stand-alonefashion by France or Belgium, or synchronized with the rest of the euro area.These sets of simulations permit an assessment of the merits of synchronizingreforms across markets and across countries.

Reforms are implemented through a gradual reduction in markups inlabor and product markets to the level of the RE bloc. Markups in labor andgoods markets are reduced over a period of 5 years, but in the services sector,deregulation is assumed to progress slower, taking 10 years. In the model,agents have perfect foresight, thus eliminating any uncertainty about thenature and path of these reforms.

III. Long-Run Effects of Structural Reforms

The simulated overall gains from more competition in labor and productmarkets are substantial in terms of GDP, employment, and consumption.Once the adjustment to reform in all markets is complete, real GDP would be17.9 percent above the baseline in France and about 11.9 percent in Belgium.The difference between these two outcomes is due to the different startingpoint, with France somewhat further away from the benchmark, particularlyin the labor market. The capital stock would rise very substantially and hoursworked would also rise, but by less. The increase in consumption is smallerthan the gain in GDP, because resources need to be diverted to investment tomaintain a higher capital stock (Table 2).

Table 1. Markups in Labor and Product Markets

Labor Tradables Nontradables

Belgium 1.29 1.19 1.39

France 1.35 1.21 1.41

Euro area 1.35 1.21 1.40

Denmark, Sweden, United Kingdom 1.13 1.14 1.24

New member states 1.23 1.29 1.45


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Complementarities between labor market reform and goods and servicesmarket reforms are important. When implemented in isolation, labor marketreform raises output and consumption by broadly the same amount, buthours worked go up more than proportionally and the capital stock less thanproportionally. Moreover, real wages remain permanently below baselinebecause goods and services prices do not decline in proportion with wages, asfirms increase rents and limit the expansion of output. On the other hand,product market reforms raise the capital stock sharply, triggering higher realwages as labor becomes relatively scarce. Consequently, output rises by morethan hours worked.

Although the long-run increase in output as a result of joint reforms doesnot go beyond the combined long-run impact of reforms in each countryseparately, welfare gains from joint reforms are important.2 Reformselsewhere ultimately reverse the terms-of-trade loss that a country sufferswhen attempting to sell additional output abroad. Consequently, joint

Table 2. Synchronized Euro Area-Wide Structural Reform: Long-Run Impact(Deviations from baseline in percent)

Real

GDP Consumption

Hours

Worked

Real

Wage

Capital

Stock

Welfare

CV1

France2

Labor market 7.4 7.4 7.5 -0.2 7.4 2.5

Services 7.0 4.9 5.6 10.2 9.3 5.0

Goods 2.6 2.2 1.8 3.3 6.8 1.1

All markets 17.9 15.0 15.4 13.8 25.0 8.4

Of which: Spillover from

euro area 1.8 1.9 0.4 1.3 2.3 1.5

Belgium2

Labor market 4.9 4.9 5.1 -0.2 4.8 1.1

Services 5.0 3.5 3.9 8.6 7.0 2.8

Goods 1.5 1.3 1.0 2.2 4.2 0.4

All markets 11.9 10.1 10.3 10.9 16.9 4.1

Of which: Spillover from

euro area 1.6 1.6 0.4 1.1 1.6 1.4

1CV=Compensating variation; 3 percent annual discount rate.2Markups were reduced in France by 22 percentage points in labor markets, 17 percentage

points in nontradables, and 7 percentage points in tradables. Reductions in Belgium were 16,15, and 5 percentage points, and in the euro area were 22, 16, and 7 percentage points.

2Welfare gains are measured in present-value consumption units that would be needed toachieve the post-reform utility level, holding hours worked at baseline (compensatingvariation). Transitory declines in consumption matter for the present value (3 percent annualdiscount rate). However, with the focus on the long run, welfare effects of volatility inconsumption as such are ignored (see Leigh, 2008).


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reform leads to higher consumption and lower hours worked and thus morewelfare than stand-alone reforms. For a smaller country, the welfare gainsare more modest as the initial terms-of-trade loss is smaller.

International spillover and feedback effects of reform are limited. Reformacross the euro area and France yields additional output for France of about1.8 percent over stand-alone reforms in France (16.1 percent). In the case ofBelgium, it yields a 1.6 percent increase over stand-alone reforms (10.3percent). Practically all additional GDP gains are direct spillovers fromreforms abroad. The limited size of spillovers in the long run stems from thefact that the reforms drive up supply and income in the reforming countryproportionally, ultimately leading to a similar demand response. Changes interms of trade, which would alter this outcome, are relatively small.

The simulation results are sensitive to alternative values of keyparameters, though without altering the qualitative conclusions. The lesslabor supply reacts to changes in the wage, the lower the impact of reforms,predictably more so for labor market reforms than for product marketreforms. A lower share of liquidity-constrained consumption raises thebeneficial impact of labor market reforms as more of the rewards to work,and thus consumption, can be intertemporally allocated. Finally, if tradeelasticities are lower (domestic and foreign traded goods are poorersubstitutes), the impact of reform diminishes substantially, with a largereffect in the smaller, more open country.3

IV. Transition Dynamics

The dynamic adjustment paths of real variables differ significantly betweenreforms (Figure 1). In response to labor market reforms, output andemployment rise gradually, but consumption falls below baseline for abouttwo years. The real wage declines, the real exchange rate depreciates, andinflation is below baseline for some time. Reforms in the traded goods sectorimmediately lift all real variables and push inflation and real wages abovebaseline, and the real effective exchange rate appreciates. Conversely, reformsin the services sector have an initial negative effect on output, consumption,and employment, though inflation falls significantly, allowing real wages torise. In all cases of reform, investment rises above baseline immediately inanticipation of the positive output effects of the reform. In the case of labormarket reforms, the rise in investment is moderate initially because therelative price of labor to capital falls, but the investment response is verystrong after service market reforms, as the real price of labor moves in theopposite direction.

All reforms lower equilibrium prices and raise equilibrium output. Due toadjustment costs, however, prices and quantities adjust slowly, and inflationfalls temporarily below baseline. With reforms in the traded goods sector,these effects are relatively small and short lived, because these goods are

3For a sensitivity analysis, see Everaert and Schule (2006).


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easily sold abroad. With labor market reforms, the real wage falls, furtherdampening consumer demand and creating slack, though rising employmentalmost offsets the negative effect from the decline in wages. With servicesector reforms, equilibrium prices fall the most, largely because initialmarkups have been larger than in other markets, and there is limited

Figure 1. Structural Reform in France (Labor, Services, and Goods Markets)(Deviation from control, in percent)

-5

0

5

10

-5

0

5

10Real Income (GDP)

-10

-5

0

5

10

-10

-5

0

5

10Consumption

0

5

10

15

0

5

10

15Investment

-1

0

1

2

-1

0

1

2Trade Balance/GDP

-5

0

5

10

-5

0

5

10Hours Worked

-5

0

5

10

15

-5

0

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10

15Aggregate Capital Stock

-3

-2

-1

0

1

-3

-2

-1

0

1CPI Inflation (y-o-y)

-5

0

5

10

15

-5

0

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10

15Real Wage

-5

0

5

10

-5

0

5

10Net Foreign Assets/GDP

-5

0

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10

15

-5

0

5

10

15Real Effective Exchange Rate (+ = depreciation)

-0.4

-0.2

0.0

0.2

-0.4

-0.2

0.0

0.2Nominal Interest Rate

-2

0

2

4

-2

0

2

4Real Interest Rate

0 12 18 24 30 36 42 48 54 606 0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

Note: Solid lines¼ labor; dashed lines¼ goods; dotted lines¼ services; x axis in quarters.


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flexibility to shift resources between the tradables and nontradables sectors.Synchronizing reforms across markets in a given country averts a decline inreal wages and reduces transition costs in terms of foregone consumption.

Inflation plays a key role in short-term aggregate dynamics. As nominalinterest rates are determined by euro area aggregates, the behavior of pricesstrongly affects real interest rates in the reforming countries. The decline ineuro area inflation, as a result of reforms covering all markets in eitherFrance or Belgium, is relatively small. In the case of stand-alone reforms inFrance, the monetary policy rule produces a maximum decline in the nominalinterest rate by only 0.3 percent below baseline, but inflation falls by up to 2.7percent. In the case of Belgium the effect on the euro-area-wide nominalinterest rate is negligible. As a result, real interest rates in France or Belgiumrise almost proportionally with the decline in national inflation after thereforms, motivating forward-looking consumers to postpone consumption.In the case of service sector reforms, the increase in real interest rates is verypronounced and the main cause of the temporary decline in consumptionand output. Once the price-level adjustment is complete, inflation and thereal interest rate return to baseline, consumption rises, and investmentaccelerates.

With domestic inflation differing from inflation in trade partnercountries, the real exchange rate adjusts. Increasing competition in thetraded goods sectors makes domestic firms internationally more competitiveas well. Because they are partly price-takers, they can afford to pay somewhathigher wages, which quickly leads to an expansion of demand, a realappreciation, and a current account temporarily below baseline.4 For theother reforms, domestic prices fall, the real exchange rate depreciates(nontradables become cheaper relative to tradables), and net exports rise.However, the improvement in the trade balance is insufficient to fullycompensate for the temporary shortfall of domestic demand relative to supply.Once the price-level adjustment is complete, the trade surplus evaporates.

V. Coordination of Reforms in the Euro Area

Although monetary policy is neutral in the long run, the adjustment pathdepends strongly on the stance of monetary policy during the transition.When markups are reduced only in the reforming country, area-widenominal interest rates fall very little, as monetary policy reacts only to euro-area-wide indicators. Similarly, the euro depreciates very little in nominalterms. As a result, monetary conditions in the reforming country tighten,exerting additional deflationary pressure. The depreciation of the realeffective exchange rate, needed to balance supply and demand, mustcome about through temporary lower inflation, further depressing prices,and raising the real interest rate. In the presence of nominal rigidities,

4Alternatively, more competition in the tradables sector lowers tradables prices vis-a-visnontradables prices and therefore represents a real appreciation of the home currency.


363


insufficient monetary accommodation slows the response of investment andconsumption.

Coordination of the timing of structural reforms in the euro area resultsin faster adjustment and prevents a temporary fall in consumption (Figure 2).When markups are reduced in the entire euro area, nominal interest rates fall

Figure 2. Structural Reform in All Markets (Euro-Area-Wide)(Deviation from control, in percent)

0

5

10

15

20

0

5

10

15

20Real Income (GDP)

0

5

10

15

0

5

10

15Consumption

-20

0

20

40

-20

0

20

40Investment

-0.5

0.0

0.5

1.0

-0.5

0.0

0.5

1.0Trade Balance/GDP

0

5

10

15

20

0

5

10

15

20Hours Worked

-10

0

10

20

30

-10

0

10

20

30Aggregate Capital Stock

-3

-2

-1

0

1

-3

-2

-1

0

1CPI Inflation (y-o-y)

-5

0

5

10

15

-5

0

5

10

15Real Wage

-1

0

1

2

3

-1

0

1

2

3Net Foreign Assets/GDP

0

1

2

3

0

1

2

3Real Effective Exchange Rate (+ = depreciation)

-4

-2

0

2

-4

-2

0

2Nominal Interest Rate

-2

-1

0

1

-2

-1

0

1Real Interest Rate

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

0 12 18 24 30 36 42 48 54 606

Note: Solid lines¼France; dashed lines¼Belgium; x axis in quarters.


364


sufficiently to mitigate transitory deflation. In the first year, the nominalinterest rate declines by 2 percentage points, leaving the real interest rate littlechanged. This makes a large difference to demand: with stand-alone reforms,consumption in France would be 2.7 percent below baseline in the first yearand investment 3 percent above. With synchronized reforms, consumptionwould be 5 percent above baseline and investment, almost 8 percent.

In reality, other factors not considered in the model are likely to influencetransition dynamics and the monetary policy reaction. Reforms might raiseuncertainty about income and employment, delaying agents’ positiveresponse to the long-run benefits of reform. Uncertainty typically leads tocaution, including on the side of monetary policymakers. As a result,monetary policies may not be fully accommodative, even in the case ofsynchronized euro-area-wide reform.

VI. Conclusion

In the European Union, reform in the nontraded (services) sector is likely toyield the largest gains because the degree of competition in this sector iscomparatively the lowest. Labor market reforms come a close second, butreforms in the traded (goods) sector produce fewer, though still significant,benefits because markups are already lower in this sector. Benefits are moreevenly distributed when market forces are strengthened in all marketssimultaneously. In particular, combining product and labor market reformscan avoid the decline in real wages associated with the latter. Reforms arealso mutually reinforcing across markets.

Steady-state spillovers of coordinated reforms in the euro area are limitedbecause the resulting increase in supply leads to an equivalent increase indemand in the long run. However, synchronization of reforms would preventa temporary fall in consumption. In the short run, stand-alone reforms causeinflation to fall and real interest rates to increase in the reforming country,slowing the investment response and deferring consumption. Area-widereforms in a monetary union would allow monetary policy to ease sufficientlyto bring forward final demand and prevent a transitory decline in GDP andconsumption.

These model-based results are subject to a number of caveats, though thequalitative conclusions are robust. The magnitude of the reform benefitsis sensitive to key parameters. In addition, interactions between laborand product market reforms are only implicitly reflected in the model, andproductivity remains exogenous, which likely results in an underestimation ofthe benefits of reform. Furthermore, full policy credibility, perfect foresight,and complete knowledge of the structure of the economy are strongassumptions. In reality, reforms may not be credible initially, and there isuncertainty about how the economy will react. Monetary authoritiesmay exert caution rather than mechanically follow a simple rule, whichwould limit monetary accommodation and prevent the full elimination oftransition costs.


365


REFERENCESBayoumi, T., D. Laxton, and P. Pesenti, 2004, ‘‘Benefits and Spillovers of Greater

Competition in Europe: A Macroeconomic Assessment,’’ ECB Working Paper 341(Frankfurt, European Central Bank).

Blanchard, O., and F. Giavazzi, 2003, ‘‘Macroeconomic Effects of Regulation andDeregulation in Goods and Labor Markets,’’ Quarterly Journal of Economics, Vol.118, No. 3 (August), pp. 879–907.

Conway, P., V. Janod, and G. Nicoletti, 2005, ‘‘Product Market Regulation in OECDCountries: 1998 to 2003,’’ OECD Economics Department Working Paper 419 (Paris,Organization for Economic Cooperation and Development).

Crepon, B., R. Desplatz, and J. Mairesse, 2002, ‘‘Price-Cost Margins and Rent Sharing:Evidence from a Panel of French Manufacturing Firms’’ (unpublished; CREST-ENSAE, France).

Dobbelaere, S., 2004, ‘‘Estimation of Price-Cost Margins and Union Bargaining Powerfor Belgian Manufacturing,’’ International Journal of Industrial Organization, Vol. 22,No. 10 (December), pp. 1381–98.

Dumont, M., G. Rayp, and P. Willeme, 2006, ‘‘Does Internationalization Affect UnionBargaining Power? An Empirical Study for 5 European Countries,’’ Oxford EconomicPapers, Vol. 58, No. 1, pp. 77–102.

Everaert, L., and W. Schule, 2006, ‘‘Structural Reforms in the Euro Area: EconomicImpact and Role of Synchronization Across Markets and Countries,’’ IMF WorkingPaper 06/137 (Washington, International Monetary Fund).

Evers, M., R.A. de Mooij, and D.J. van Vuuren, 2005, ‘‘What Explains the Variation inEstimates of Labor Supply Elasticities?’’ CESifo Working Paper 1633 (Munich,CESifo Group Munich).

Jean, S., and G. Nicoletti, 2002, ‘‘Product Market Regulation and Wage Premia InEurope and North America: An Empirical Investigation,’’ OECD EconomicsDepartment Working Paper 419 (Paris, Organization for Economic Cooperationand Development).

Konings, J., J.P. Van Cayseele, and F. Warzynski, 2001, ‘‘The Dynamics of IndustrialMarkups in Two Small Open Economies: Does National Competition PolicyMatter?’’ International Journal of Industrial Organization, Vol. 19, No. 5 (April), pp.841–59.

Leigh, D., 2008, ‘‘To Starve or Not to Starve the Beast?’’ IMF Working Paper(Washington, International Monetary Fund).

Oliveira Martins, J., and S. Scarpetta, 1999, ‘‘The Levels and Cyclical Behaviour ofMarkups Across Countries and Market Structures,’’ OECD Economics DepartmentWorking Paper 213 (Paris, Organization for Economic Cooperation andDevelopment).

Saint-Paul, G., 2004, ‘‘Did European Labour Markets Become More Competitive in the1990s? Evidence From Estimated Worker Rents,’’ CEPR Discussion Paper 4327(London, Centre for Economic Policy Research).


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