not all oil price shocks are alike: a neoclassical ...econseminar/20131218paperoil... · 1...

Not All Oil Price Shocks Are Alike: A Neoclassical Perspective∗†

Vipin Arora‡

U.S. Energy Information Administration

Pedro Gomis-Porqueras§

DeakinUniversity

Junsang Lee¶

SungKyunKwan University

Abstract

This paper studies the consequences of endogenizing oil prices and quantities when accountingfor business cycles facts and crude oil dynamics. We first show that a model with endogenouscrude oil can better account for business cycle data than models with exogenous oil pricesor oil quantities. In particular, it can better account for the co-movements and first-orderautocorrelations of crude oil observables. Our results also highlight the fact that a model whichtakes the real oil price as exogenous cannot capture the interactions between this price andmacroeconomic aggregates in response to oil demand shocks. Similarly, a model that takes oilproduction as exogenous has difficulties when confronted with changes in oil supply. We alsoshow that responses to oil shocks depend crucially on how oil is modeled. The divergence inimpulse responses for consumption and hours across models lasts for more than twenty quartersimplying distinct welfare implications after the economy is hit by oil supply shocks.

JEL Classification: E37, F47, Q43.Keywords: Oil price, two regions, business cycle, endogenous.

∗The analysis and conclusions expressed here are those of the authors and not necessarily those of the U.S. EnergyInformation Administration.†We have benefitted greatly from the comments and suggestions of Dirk Krueger, Felix Klueber, Eric Leeper,

Bruce Preston, Rod Tyers, Bob Gregory, Tim Kam, Timo Henckel, Peter Robertson, E. Juerg Weber, Justin Wang,Scott McCracken, and Yiyong Cai. We also received very helpful comments in seminars at Australian NationalUniversity and University of Western Australia. Finally we would like to thank the participants at the 7th WMD atUniversity of Queensland as well as the Monash Macro Workshop for their valuable suggestions.‡U.S. Energy Information Administration, 1000 Independence Ave., S.W., Washington, D.C. 20585. E-mail:

[email protected]§Deakin University, School of Accounting, Economics and Finance, 70 Elgar Road, Burwood, VIC 3125, Australia.¶Department of Economics,College of Economics, SungKyunKwan University, Seoul, Korea

1

1 Introduction

There is a large body of work that explores the relationship between oil price changes and macroe-conomic performance.1 Much of the empirical literature has focused on the U.S. and assumed anexogenous oil price since the seminal contribution of [19]. A decade later, [30] incorporated anexogenously determined oil price in a real business cycle (RBC) framework.2 Subsequent papers inthe RBC literature have also assumed oil prices to be exogenous while including additional non-oilrelated features to better account for business cycle facts.3 [6] and [7] challenge this exogenous as-sumption, and [25] traces major real oil price increases since the 1970’s to global aggregate demandor demand specific to the oil market.4 In this view the real price of oil is ultimately determinedby market forces and subject to demand and supply shocks like any other good. The empiricalrelevance of such supply and demand forces in shaping crude oil dynamics motivates our work.

The objectives of this paper are to provide a framework for studying crude oil dynamics overthe business cycle, and to determine the quantitative importance of endogenizing both the realoil price and its demand when accounting for business cycle facts. We begin with a standard realbusiness cycle model where the real oil price is exogenous in the spirit of [30]. We then follow [4],[10], and [36] and assume that oil demand is exogenous while the oil price is endogenous. Ourthird framework contains both endogenous oil quantities and prices by including an oil exportingregion.5 This final environment allows for technology shocks in final goods production (whichgenerate a stochastic demand for oil), and technology shocks in oil production (which generate astochastic supply of oil). These shocks jointly determine the underlying dynamics of the economicenvironment. As a robustness check we also consider variable capacity utilization as in [18], ormarket power as in [41].6

Our paper is one of the few that explicitly models the crude oil market. Two other exceptionsare [37] and [38], who endogenize both oil prices and quantities while studying their impact onmacroeconomic aggregates. [37] show that oil played an important role in the Great Moderation,helping reduce the volatility of both inflation and GDP growth in the U.S. [38] study the monetarypolicy trade-offs when facing a dominant crude oil producer. Both of these papers report simulatedoil price volatilities, but not other summary statistics such as the co-movement of oil demand withoutput, thus not fully exploring the business cycle properties of an endogenous crude oil market.Similarly, [5] use a multi-region model with endogenous oil production and prices. They find thatchanges in the oil price are best understood as endogenous, and that oil price shocks have differentimpacts depending on their source. The authors do not report oil statistics over the business cycle,which makes it difficult to asses whether this framework is well suited to analyze the propagation

1See [12], [7], [22], [20], and [23] for overviews of this literature.2Their model can only account for a small portion of the variance of U.S. output growth. [41] introduce mark-up

pricing into an otherwise standard real business cycle model to improve these predictions, and are able to replicatesome of the observed movements in U.S. GDP and wages after an oil price shock. [18] obtains similar results usingvariable capacity utilization in lieu of mark-up pricing.

3See [3], [33], [14], [1], [34], [13], [17], [8], [32], [9], and [39] among others for papers that take the oil price to bean exogenous process.

4See also [24], [28], [29], and [21] for more on this issue.5We do not incorporate exhaustibility in the availability of oil or oil storage, as in the majority of papers in the

literature.6These two extensions are often used in conjunction with an exogenous oil price or production. See for example

[33], [14], [1], [34], [13], [44], [8], [32], and [9].

2

of oil shocks in the economy, or how relevant it is in accounting for business cycle facts.

What are the benefits of considering endogenous crude oil prices and quantities? Qualitatively,using such a framework accounts for the joint determination of oil prices and economic activity.There are quantitative benefits as well. Our model with an endogenous oil market is able to fit thedata better than the environments with either exogenous oil prices or exogenous oil quantities.7 Themodel with exogenous oil prices yields counterfactual co-movements between the real oil price andoutput. When oil production is exogenous, the magnitude of the correlation between non-U.S. oilproduction and output is vastly different from what is observed in the data. In contrast, when boththe oil price and its quantity are endogenous the model better accounts for oil-related observables.The predicted co-movement between the real price of oil and output is comparable to the modelwith oil production exogenous, but there is an improvement in matching the co-movement betweennon-U.S. oil production and output. Moreover, the predictions for the first-order autocorrelationof the real price of oil also improve.

The manner in which the oil market is modeled leads to differences in impulse responses to oilsupply shocks. Consumption responds most to the shock when the oil price is exogenous, and itresponds the least when both the price and the quantity of oil are endogenous. This is also trueof hours worked, while investment has the opposite response. The divergence in impulse responsesfor consumption and hours across models lasts for more than twenty quarters. These differentialpatterns based on how oil is modeled imply distinct welfare implications after the economy is hitby oil supply shocks. They also highlight a point made by [25], that if oil prices are assumed to beexogenous over the business cycle then the implied macroeconomic responses to oil price changespredicted by a dynamic stochastic general equilibrium model may be misleading.8

Discrepancies in the impulse responses of output, consumption, investment, and hours acrossmodels are also observed when the economy faces oil demand shocks. Finally, endogenizing oil isbetter able to reproduce the implied impulse responses generated by demand shocks when comparedto what is observed in the data through the lens of a reduced form VAR.9 A model with exogenousoil supply can be used to assess the impact of large, one-time shock, but is not suitable for studyingthe dynamics of sustained oil supply shocks. An advantage of using a framework where both theoil price and its demand are endogenous is that it is better equipped to deal with both supply anddemand shocks affecting the oil market.

The fact that endogenizing oil improves the predictions of business cycle models is not surprising,as such a model can capture important feedback mechanisms between oil prices, demand for oil,and macroeconomic observables. Our findings are consistent with the view put forth by [6], thatallowing endogenous determination of oil observables within a general equilibrium framework is keyin understanding how oil dynamics affect domestic macroeconomic aggregates.

7The endogenous oil framework has the lowest sum of squared errors when comparing model results to sampledata for the standard deviation, the relative standard deviation to GDP, the correlation with GDP, and the first-orderautocorrelations.

8The latter point has been elaborated and reaffirmed in a number of recent empirical and theoretical studiesincluding [26], [38], [11], and [27].

9This is a difficult exercise since it requires taking a stand on how oil shocks are identified in a VAR framework,and there are many debates in the oil and macroeconomy literature on how best to do this.

3

2 The Model

The basic building block is a real business cycle model that allows for variable capacity utilizationand monopolistic competition. As a benchmark we first consider either the oil price or oil productionto be exogenous. We then consider both of them to be endogenous. The economic environmenthas an oil producing and an oil consuming region, both with a representative consumer that ownsthe capital stock. The oil producing region has monopolistically competitive intermediate goodsproducers, and a final oil producer that exports oil to the consuming region, where it is used toproduce intermediate goods. These intermediate goods producers are monopolistically competitive,and each can vary the rate at which they use capital in production. Each intermediate goodsproducer sells their output to a perfectly competitive final goods producer. Notice that all oil ispurchased by the intermediate goods firms. This just reflects the fact that oil used in gasoline,plastics and energy must first be processed before households can consume these final goods.

As in the standard real business cycle model, the dynamics in the economy are driven bysupply shocks. In particular, we consider the standard real business cycle technology shock on finalproduction in the consuming region, and a technology shock on oil production. These processesinduce a stochastic event, st, in each period t. The history of events up to and including t is denotedby st = (so, s1, ..., st). The initial realization, so, is known. All equilibrium prices and allocationsare a function of these histories, but the dependence will be suppressed throughout the paper forsimplicity.

Domestic and foreign agents have access to complete asset markets. Thus the household ineach region has access to a contingent claims market where an array of Arrow securities, denotedby Bt+1(st+1|st) for the oil consuming region and B∗t+1(st+1|st) for the oil producing region, aretraded. These claims pay one unit of final consumption goods at t+ 1 if st+1 is realized given thehistory at t is st. The price of either security is denoted pb,t(st+1|st).

2.1 Representative Consumers

In the oil consuming region the representative household chooses consumption (Ct), labor (Nt),capital stock (Kt+1), holdings of Arrow securities (one for each possible realisation of st+1) and thecapacity utilization rate (Tt) as to maximize expected utility:

max{Ct,Nt,Kt+1,{Bt+1(st+1|st)}st+1 ,Tt}

∞t=0

Et

{ ∞∑t=0

βtC1−σct

1− σc+ ξ0

(1−Nt)1−ξ

1− ξ

}(1)

subject to the budget constraint and the capital accumulation equation:

Ct + It +

∫st+1

pb,t(st+1|st)Bt+1(st+1|st) = wtNt + rtTtKt +Bt + πt (2)

It = Kt+1 − (1− δt)Kt (3)

where It is investment, wt is the wage rate, rt is the return to capital, πt is firm’s profits, β isthe discount factor, δt the depreciation rate of capital, σc the coefficient of relative risk aversion

4

(CRRA), ξ is a parameter which determines the labor supply elasticity, and ξ0 is a parameter whichdetermines labor supply. Because of variable capacity utilization, the depreciation rate is a functionof the capital utilization rate so that:

δt = δT ηt (4)

with δ being a constant, and η (1 < η) a utilization parameter. Note that depreciation is convexin the utilization rate. Thus an increase in utilization raises depreciation, and successive increasesraise depreciation by a larger and larger increment. Consumers in the oil producing region solvean identical problem, except they do not choose a capacity utilization rate.

2.2 Firms

In the oil consuming region, there is a continuum of intermediate goods producing firms indexedby i ∈ [0, 1] that behave as imperfect competitors. The firms produce differentiated types ofintermediate goods [Yt(i)] by choosing oil [Qt(i)], capital, and labor to maximize profits:

maxQt(i),Kt(i),Nt(i)

py,t(i)Yt(i)− pq,tQt(i)− rtTtKt(i)− wtNt(i) (5)

where py,t(i) is the price of a firm’s good and pq,t denotes the price of oil. Capital services (Jt) area constant elasticity of substitution (CES) composite of the capital stock and oil given by:

Jt(i) = [γQt(i)τ + (1− γ)[Tt(i)Kt(i)]

τ ]1τ (6)

where γ is an oil share parameter, and τ =(σqk−1)σqk

, with σqk the elasticity of substitution between oil

and capital.10 The production technology of intermediate goods is Cobb-Douglas with ψ denotingthe oil share in production:

Yt(i) = ZtJt(i)ψNt(i)

1−ψ (7)

where Zt is exogenous (aggregate) total factor productivity (TFP) that evolves as follows:

lnZt = ρ lnZt−1 + εt (8)

and ρ captures the persistence of the shock. The innovation εt ∼ i.i.d N(0,σ2v), where σv denotes

the standard deviation.

The final goods producing firm behaves competitively and chooses these different intermediateinput types as to maximize per period profits which are given by:

max∫Yt(i)di

Yt −∫py,t(i)Yt(i)di (9)

10The assumption taken here is that oil and capital are weak substitutes, and this is standard in the currentframework as outlined in [30]. [2] provides some evidence in support of this assumption.

5

subject to:

Yt =

[∫Yt(i)

θdi

] 1θ

(10)

where 1θ is the markup.

From now on, variables specific to the oil producing region are denoted with (∗). In the oilproducing region, we assume there are a continuum of intermediate goods producing firms indexedby i∗ ∈ [0, 1] that behave as imperfect competitors. The firms produce differentiated types of oil[Qt(i

∗)] by choosing capital [K∗t (i∗)] and labor [N∗t (i∗)] to maximize profits:

maxK∗t (i∗),N∗t (i∗)

pq,t(i∗)Qt(i

∗)− r∗tK∗t (i∗)− w∗tN∗t (i∗) (11)

subject to a Cobb-Douglas production function with α denoting the capital share in production:

Qt(i∗) = Z∗tK

∗(α)t (i∗)N

∗(1−α)t (i∗) (12)

where α (0 < α < 1) is the capital share in production. Z∗t is exogenous (aggregate) total fac-tor productivity (TFP) that follows the same process as Zt, but may have a different first-orderautocorrelation coefficient and volatility. The final oil producing firm behaves competitively andchooses these different oil types as to maximize per period profits which are given by:

max∫Qt(i∗)di∗

Qt(i∗)−

∫pq,t(i

∗)Qt(i∗)di∗ (13)

subject to:

Qt(i∗) =

[∫Qt(i

∗)θ∗di∗] 1θ∗

(14)

where 1θ∗ is the markup. The optimality conditions and equilibrium concept are standard and

outlined in Appendix 1.

2.3 Data and Calibration

We consider quarterly U.S. data for the period 1974 to 2011. Our focus is on the U.S. to easecomparison with other papers in the literature. The observables that we use to calibrate and judgethe model are real GDP (Yt), real consumption (Ct), real investment (It), hours worked (Nt), thereal oil price (pq,t), and non-U.S. oil production (Qt). The sample period begins in 1974 becausethe data series we use for the oil price is available from this point forward.

The first four observables are taken from the Federal Reserve Economic Database (FRED),the real oil price is the deflated U.S. refiner acquisition cost of oil imports from the U.S. EnergyInformation Administration (EIA), and the non-U.S. production data comes from the EIA as well.Imported refiner acquisition costs are used because they are the costs paid by those who use oil as

6

an input to production, which is consistent with the model. Non-U.S. oil production is used insteadof global oil production because there is no oil produced by the oil consuming region in the model.This simplification is unlikely to be important as the U.S. share of global oil production is roughlyseven percent. Additional details regarding the data can be found in Appendix 2.

Following [42], all time series except the real oil price are HP filtered with a smoothing parameterof 1600. This HP filtering procedure is standard for macroeconomic aggregates such as GDP,consumption, investment and hours. Non-U.S. oil production is also filtered because its correlogramshows evidence of a non-stationary process. Although there is ongoing debate in the literature aboutthe order of integration of the real oil price, we filter the real oil price (pq,t) in what follows.11

The first four rows of Table 1 summarize standard business cycle statistics.12 Consumption isless volatile than GDP over this time horizon, and the correlation between the two is almost 87%.Investment has a stronger correlation with GDP at over 91%, and is also 4.9 times more volatilethan GDP. Hours worked are strongly procyclical at almost 89%, and are 1.25 times as volatile.Hours have a higher first-order autocorrelation than GDP, consumption, or investment.

Variables Description Corr(Xt, Yt) SD SDX/SDY Corr(Xt, Xt−1)

Yt Real GDP 1.00 0.016 1.00 0.859Ct Real Consumption 0.864 0.012 0.750 0.879It Real Investment 0.915 0.078 4.88 0.825Nt Hours 0.889 0.020 1.25 0.905pq,t Real Oil Price 0.152 0.185 11.56 0.730Qt Non-US Oil Production 0.336 0.040 2.50 0.295

Table 1: Quarterly Real U.S. and Oil Market Summary Statistics 1974-2011

The fifth row of Table 1 shows there has been a positive correlation, just over 15%, betweenthe real oil price and U.S. GDP. Unsurprisingly, the oil price is very volatile relative to U.S. GDPwith a relative standard deviation of roughly 11.5. The real oil price series also has a first-orderautocorrelation which is below the values for the macroeconomic aggregates. The final row showsthat non-U.S. oil production has a positive correlation with U.S. GDP, at over 33%. It has been2.5 times more volatile than U.S. GDP over the sample period, but is less autocorrelated than theother macroeconomic observables with a value of 0.295.

The model parameter values are calibrated to match stylized facts in the data; some are givenstandard values and others are obtained by the simulated method of moments. In particular, theCRRA parameters (σc and σc∗), discount factors (β and β∗), and capital shares (ψ and α) inboth regions take standard values for a quarterly model of 2, 0.99, and 0.36, respectively. Thedepreciation parameter in the oil producing region (δ∗) has also the standard value of 0.025. Thedepreciation rate in the oil consuming region (δ) is chosen so that the steady-state capital to outputratio is 12, consistent with the calibration in [17]. When variable capacity utilization is added tothe model, the steady state level of δt is set to 0.025, and η is chosen so that the steady-state capitalto output ratio is 12 in the oil consuming region. This capital to output ratio is consistent acrossall different versions considered in the paper.

The oil share parameter in capital services (γ) is chosen so that the share of oil in final goods

11See [16] for more on this debate.12SD stands for standard deviation.

7

output matches the average U.S. value of oil imports of 0.015, which is consistent with [1]. To allowfor unbalanced trade, we choose the size of the oil consuming region relative to the oil producingregion (µ) so that the ratio of U.S. imports from major oil producers to exports to major oilproducers over the sample is 1.4. The parameters ξ and ξ∗, are set at 0.5, which imply a standardFrisch elasticity of 2. The other labor parameters, ξ0 and ξ∗0 are chosen so that labor supply in eitherregion is 0.33 of available time. In the extension with monopolistic competition, θ is chosen to be0.9, as in [15]. We set θ∗=1, both because we lack a good estimate and changing this parameter doesnot substantially change our results. Each of the parameters outlined to this point are summarizedin panel (a) of Table 7 in Appendix 2.

The remainder of parameters in the model that describe the shock processes are determinedby the simulated method of moments as in [10]. The exact values are summarized in panel (b) ofTable 7 in Appendix 2. The parameter values are consistent across all variants used below andinclude the elasticity of substitution between oil and capital (σqk) in the consuming region, thefirst-order autocorrelations on each shock process (ρ, ρ∗, ρq, ρpo), and the volatilities of each shockprocess (σv, σ

∗v , σv,q, σv,po). Each model is calibrated by minimizing the square of the distance

between simulated model moments and those observed in the sample data. The relevant metric iscalculated using the standard deviations and first-order autocorrelations of U.S. GDP, consumption,investment, hours, the real oil price, and non-U.S. oil production. Each of the simulated values arenormalized by scaling by the size of the corresponding statistic in the data as in [10].

A key parameter in the model is the elasticity of substitution between oil and capital. Thecalibrated values for this parameter range from 0.21 in the exogenous production case to 0.31 inthe endogenous case. All of these values fall in the range both estimated and summarized in [35].The calibrated values of this parameter are below other estimates [0.4 as in [28]], but above others[0.09 as in [4]]. The calibrated first-order autocorrelations and volatilities on the oil consumingregion TFP processes are similar to standard values in the real business cycle literature. The TFPprocess in the oil consuming region has a relatively low value for the first-order autocorrelation(0.412), as do the processes for the oil price (0.240) and oil production (0.240) in the other twomodels. The respective volatilities on each of these shocks (0.076, 0.176, 0.034) are substantiallyhigher than that for consuming region TFP, mainly because the oil price is so volatile relative toGDP in the data.

A solution to the model is approximated using standard techniques. We first find the valuesfor each endogenous variable in the deterministic steady state. We then log-linearize the modelequations around these steady state values. Finally, this system of log-linear equations is solvedusing the method of undetermined coefficients, as in [43]. The reported statistics from all themodels considered in this paper are not HP filtered, as they are stationary by construction.

3 Quantitative Results

We first consider a situation where either the price or quantity of oil is exogenous. We then analyzethe case where both oil prices and quantities are endogenously determined. Given that introducingvariable capacity utilization as in [18] or market power as in [41] delivers similar results relative tothe competitive case, from now on we limit our reporting to the competitive case.

8

3.1 Exogenous Oil Prices

In order to have exogenous oil prices, we assume that the oil price follows an AR(1) process andthat oil production is exactly what the oil consuming region demands. This structure is standard inthe literature [see e.g. [33]]. The specific calibration for this model is given in Table 7 of Appendix2.

Note that equation (28), which is in the appendix 1, can be rearranged as follows:

Qt =

(pq,tJ

ρt

ψγYt

) 1ρ−1

.

We can clearly see from the previous expression that a rise in the oil price leads to a fall in demand(Qt). It follows that the demand for capital services (Jt) will decrease (capital and oil are onlyweak substitutes), so that output (Yt) will fall. Of course this negative correlation between the oilprice and final goods output may be off-set somewhat by general equilibrium effects. But these canonly work through Yt because pq,t is exogenous and Jt depends on oil, for which the price rises, andcapital, which is fixed in the current period. This highlights one important feedback mechanismwhich is missing in a model without an endogenous oil price. The quantitative implications ofhaving an exogenous oil price process are summarized in Table 2.

Ct It Nt pq,t QtData 0.864 0.915 0.889 0.152 0.336Model 0.875 0.921 -0.031 -0.060 0.403

(a) Correlations with Yt

Yt Ct It Nt pq,t Qt

Data 1.00 (0.016) 0.750 (0.012) 4.88 (0.078) 1.25 (0.020) 11.56 (0.185) 2.50 (0.040)Model 1.00 (0.020) 0.582 (0.011) 2.82 (0.055) 0.431 (0.008) 9.29 (0.181) 2.42 (0.047)

(b) Standard Deviations Relative to Yt, Absolute Standard Deviations in Parentheses

Yt Ct It Nt pq,t QtData 0.859 0.879 0.825 0.905 0.730 0.295Model 0.951 0.992 0.875 0.950 0.240 0.392

(c) First-Order Autocorrelation

Table 2: U.S. Business Cycle Predictions with Exogenous Oil Prices

The implied model co-movements of the standard real business cycle observables are similar tothose observed in [30]. In particular, the correlations of consumption and investment with respectto final goods output are both close to those observed in the data. However, the co-movementof hours worked is counterfactual. The relative volatilities of consumption and investment areboth lower than in the data. For hours worked, the model accounts for about 35% of the relativevolatility. The first-order autocorrelations of the macroeconomic aggregates are slightly higherthan the ones observed in the data with the exception of the real oil price, which is three timeslower. In general, the business cycle properties of the exogenous oil price model with respect tomacroeconomic observables are in line with standard real business cycle models [see [31]].

9

The main benefit of having a model with an exogenous oil price is that the relative volatility ofthe oil price can account for around 80% of the data. Somewhat surprisingly, the model’s predictionswith respect to oil production/demand perform also relatively well, accounting for about 97% of theobserved value. The major drawbacks of having an exogenous oil price are the implied correlationswith output. The co-movement of the oil price and output and the co-movement of hours andoutput are both counterfactual. The negative correlation between the oil price and final goodsoutput follows directly from the fact that the price is unable to adjust with the demand for oilas shown above. This lack of general equilibrium effects is also reflected in the implied first-order autocorrelation, which is far lower that what is observed. We conclude from the impliedco-movements that models with an exogenous oil price are not well suited to study the impact ofoil price changes on economic performance. Moreover, such models are unable to analyze variationsin oil demand which might be important to the economy.

3.2 Exogenous Oil Quantities

In this new environment oil demand (or non-U.S. production) is assumed to follow an AR(1)process. The specific calibration for the model is given in Table 7 of appendix 2. The oil price isendogenous here, and adjusts to the appropriate level given by the exogenously specified supply.The quantitative implications of having an exogenous oil price process are summarized in Table 3.

Ct It Nt pq,t QtData 0.864 0.915 0.889 0.152 0.336Model 0.800 0.934 0.456 0.356 0.037


Yt Ct It Nt pq,t Qt

Data 1.00 (0.016) 0.750 (0.012) 4.88 (0.078) 1.25 (0.020) 11.56 (0.185) 2.50 (0.040)Model 1.00 (0.024) 0.451 (0.011) 3.27 (0.080) 0.488 (0.012) 7.72 (0.188) 1.44 (0.035)




Table 3: U.S. Business Cycle Predictions with Exogenous Oil Production

The co-movements of macroeconomic aggregates are in line with the environment with exoge-nous oil prices, with the exception of the implied co-movement in hours and oil prices. Now thecorrelation between oil prices and output is no longer counterfactual. In fact, the implied co-movement between oil prices and output is now 2.3 times larger than what is observed in the data,while the co-movement of crude oil quantities and output is ten times smaller. In terms of therelative volatilities of consumption and investment, having an exogenous quantity of oil is betterable to account for the data than having an exogenous oil price. However, the model’s ability tomatch the relative volatilities of the oil price and oil production is reduced. It can now accountfor only 67% of the relative volatility of the oil price (compared with 80%), and for 57% of the

10

relative volatility of oil supply (compared with 97%). In terms of first-order autocorrelations, bothmodels perform similarly for non-oil related observables. With respect to the real oil price, theexogenous production model accounts for 61% of the autocorrelation, and it account for 81% of theautocorrelation in oil demand.

In this model environment there is positive co-movement between final goods output and theoil price. What is driving this result? Consider a rise in oil production (Qt). Equation (28), whichcan be found in Appendix 1, shows that, all else equal, the oil price must fall in order for the firmto increase demand in-line with this higher production. In particular, we have that:

pq,t =ψγQρ−1

t YtJρt

.

But the higher demand for oil leads to an increase in capital services (Jt), which leads to higherproduction of final goods (Yt). The equation above shows that both of these increases will createupward pressure on oil prices. There are offsetting effects on the oil price and the one whichperforms better will depend on the particular calibration of the model. Nevertheless, this model isan improvement relative to the exogenous oil price one because it allows the oil price to adjust sothat the exogenous production can be matched to endogenous demand. Where the model fails isin capturing the feedback between oil production and other observables. In particular, the model’simplied co-movement between oil production and final goods output is worse than those obtainedwhen the oil price is exogenous. In this new environment the correlation only accounts for about11% of the data, relative to almost 120% when the oil price is exogenous.

3.3 All Crude Oil Observables Endogenous

In this new environment the oil producing region is affected by the decisions of households andfirms in the oil consuming region. The structure of both regions is described in Section 2. Thespecific calibration for this model is given in Table 7 of Appendix 2. The quantitative implicationsof an endogenous crude oil market are summarized in Table 4.

The business cycle properties of macroeconomic aggregates in the endogenous model are noworse than those previously obtained when either the price or the quantity of oil are exogenous.In particular, the implied co-movements for consumption and investment are similar across allmodels. There are differences in hours, where the endogenous oil market model accounts for 25%of the data, which is less than the 51% accounted for by the exogenous quantity framework, but animprovement on the counterfactual results from the exogenous price model. The largest differencesare observed in the oil-related observables. As in the case where oil production is exogenous, thecorrelation between the oil price and output is no longer counterfactual. The model’s impliedcorrelation accounts for over 47% of the data, and also nearly accounts for all of the co-movementbetween the quantity of oil and output.

The implied relative volatilities for consumption are in line with the better of the two exogenousmodels, and similar results are obtained for the relative volatilities of investment and hours worked.The relative volatility of the oil price is lower than the other two models, accounting for 48% ofdata. This is not surprising, as the results in [4] indicate that it would be difficult for a modelwith only productivity shocks to generate sufficient volatility in the oil price. The relative volatility

11

Ct It Nt pq,t QtData 0.864 0.915 0.889 0.152 0.336Model 0.825 0.908 0.220 0.072 0.340


Yt Ct It Nt pq,t Qt

Data 1.00 (0.016) 0.750 (0.012) 4.88 (0.078) 1.25 (0.020) 11.56 (0.185) 2.50 (0.040)Model 1.00 (0.022) 0.525 (0.012) 3.24 (0.072) 0.488 (0.011) 5.45 (0.120) 1.93 (0.043)




Table 4: U.S. Business Cycle Predictions with Endogenous Oil Price and Oil Production

for the quantity of oil is improved, performing 20% better than the model with exogenous oil.Finally, regarding the first-order autocorrelations, the model with an endogenous crude oil markethas similar predictions as the other two models. The major departure among the three models isthe autocorrelation of the quantity of oil, where the prediction of the endogenous model is 13%closer to the data than the exogenous price model.

We conclude from Table 4 that the endogenous model improves the implied correlation betweenoil production/demand and GDP and the real oil price and GDP over the other two models whilepredicting similar business cycle properties for non oil-related observables.

3.4 Overall Fit

It is difficult to compare the overall goodness of fit across different models without specifying ametric. In this paper, we use the sum of squared differences between model moments and thesample data. The observables that we consider are the ones presented in previous sections: Yt,Ct, It, Nt, pq,t and Qt. The four different moments considered are the standard deviation (SD),the standard deviation relative to output (SDX/SDY ), the correlation with output [Corr(Xt, Yt)],and the first-order autocorrelation [Corr(Xt, Xt−1)]. When computing our goodness of fit measure,all observables and moments are weighted equally. Moreover, each model predicted moment isnormalized by the corresponding data counterpart. Table 5 reports the value of the sum of squareddifferences between model moments and the sample data for each model.

SD SDX/SDY Corr(Xt, Yt) Corr(Xt, Xt−1) Total Error

Exog Price 0.507 0.698 3.06 0.593 4.86Exog Prod 0.461 0.930 2.84 0.208 4.44All Endog 0.492 0.907 0.845 0.545 2.79

Table 5: Value of the Sum of Squared Deviations

12

Table 5 shows that the model with both the oil price and oil production endogenous best fitsthe data when taking into account these four moments. The total error is about half the size ofthe other two exogenous models. While this is true of the total error, differences in goodness of fitvary across the different moments. The model with exogenous oil production outperforms the othermodels with respect to the first-order autocorrelations, while the model with exogenous oil pricesfits the relative standard deviations the best. The largest difference observed among the differentmodels is when accounting for co-movements. The endogenous model outperforms the other twoby a factor of nearly three along this metric.

3.5 Variance Decomposition

In this section we follow [30] and use our model to quantify the importance of oil supply shocksin accounting for the variance of U.S. GDP. Our model has two shocks that affect the underlyingdynamics of the economy, an oil supply shock and an oil demand shock. Table 6 shows the per-centage of the variance for each observable that can be attributed to just oil supply shocks. Inthis case we have turned off the demand shock, recorded the respective standard deviation of eachobservable, and then reported the ratio of this value with respect to the standard deviation whenall shocks are turned on. The portion which is unexplained by oil supply shocks is then attributedto oil demand shocks.

Yt Ct It Nt pq,t QtExog Price 6.00 4.40 26.2 11.4 100 89.8Exog Prod 3.75 3.11 15.24 6.56 84.75 100.00All Endog 5.56 1.74 31.06 8.74 99.17 91.63

Table 6: Percent of Explained Variance Due to Oil Supply Shocks

It is clear from Table 6 that oil supply shocks are important in accounting for the variance ofthe real oil price and oil production in each model. These shocks are less important for investmentor hours, but still account for up to 11.4% of the variance in hours and 31.06% of the variance ininvestment in different model variants. Oil supply shocks have a much smaller impact on outputand consumption. In particular, the impact of the respective oil supply shocks on the variance ofGDP is lower than found in [30], but in line with the results of [10]. In [30] energy price shocksaccounts for 16% of output volatility in the CES case and this value is approximately 4% in [10].13

4 Impulse Responses

To complement the analysis in Section 3, we analyze the impulse responses of an oil demand shockand an oil supply shock. We first consider the impact of both supply and demand shocks on modelpredictions regarding GDP, consumption, investment and hours. We then examine the impact ofthese shocks on oil observables and GDP while comparing the implied model impulse responses tothose generated from two reduced form vector autoregression models.

13For the oil shock we use an AR(1) process rather than the ARMA process used by [30]. This difference in theexogenous process makes comparison with the paper of [30] more difficult.

13

Figure 1 shows the impact (in percent changes) of a positive one standard deviation TFP shockin the oil consuming region on various macroeconomic observables corresponding to the threedifferent models. Given that we study the TFP shock in the oil consuming region, we are thenanalyzing the impact to the economy when hit by stochastic demands for inputs. As we can see fromFigure 1, the qualitative responses to this oil demand shock for GDP, consumption, investment,and hours are similar across the three different models. These impulse responses are in line withthose reported in Figure 10 of [31] for the standard RBC model when the economy is hit by TFPshocks.

In terms of the relative magnitudes after impact, differences across models are more significant.For instance, the top left panel of Figure 1 shows that GDP responds most to the shock when oilproduction is exogenous, and it responds least when the oil price is exogenous. This difference isnot trivial, as it is approximately 0.35% of GDP, which is large compared to the size of the initialshock. Moreover, the implied time series for output after a demand shock exhibits a divergenceacross models that lasts approximately fifteen quarters. The difference between the instantaneousresponse of investment in these two models to an oil demand shock is around 1.5%. Similar patternsare observed for hours. In contrast, impulse responses for consumption are almost the same acrossmodels.14 Given the differences in the evolution of hours and similar time series behavior forconsumption after an oil demand shock, we find small welfare differences across models after theeconomy is hit by a TFP shock.

The implications of an oil supply shock on the economy are shown in Figure 2. An oil supplyshock in the model with exogenous oil prices is taken to be a positive one standard deviation shockto the oil price process. When oil production is exogenous, this supply shock is a negative onestandard deviation shock to the oil production process. And when both prices and quantities ofoil are endogenous, the oil supply shock is a negative one standard deviation shock to TFP in oilproduction. As we can see from Figure 2, the qualitative response to this oil supply shock for GDP,consumption and hours are similar across the different models. However, the endogenous crudeoil market model has a rather different investment impulse response relative to the other models.While the exogenous models predict a smooth transition to the steady state investment level, thefully endogenous model predicts an overshooting of around 0.5% of the steady state level.

In terms of the relative magnitudes after the impact of an oil supply shock, differences acrossthe three models are more significant. For instance, the top right panel of Figure 1 shows thatconsumption responds most to the shock when oil price is exogenous, and it responds least whenthe price and the quantity of oil is endogenous. This difference is approximately 0.15% of consump-tion. Moreover, the implied time series for consumption and hours after a supply shock exhibits adivergence across models that lasts for more than twenty quarters. The different consumption andhours time series patterns imply rather different welfare predictions that critically depends on howoil is modeled.

The different model implied impulse responses of macroeconomic aggregates show that the wayin which oil is modeled changes the magnitude of their responses and the underlying dynamics.Differences are less pronounced when analyzing shocks to oil demand. In contrast, when oil supplyshocks are analyzed the magnitude and dynamics across models show greater differences than thoseobserved when the economy is hit by oil demand shocks.

14This is likely the case because none of the models analyzed in this paper have oil in the consumption basket.

14

4.1 Impulses from VAR and RBCs

Having analyzed the impulse responses to oil shocks across the different RBC models, we nowcompare impulse responses for the oil price, oil production, and GDP relative to those generatedfrom two reduced form vector autoregression models (VARs). A general VAR process can beencapsulated by a mean-zero moving average representation (without a deterministic terms) givenby:

yt =∞∑j=0

BjGεt−j (15)

where yt is an N × 1 vector of observables, the Bj are N × N matrices of coefficients, and the

orthogonal innovations are εt = Gut, so that E(εt, ε′t) = GE(ut,u

′t)G

′= I, and u are reduced

form errors. In equation (15) the BjG summarize the impulse responses which we analyze below.

We use two different VAR models when calculating the impulse responses, both identified usingexclusion restrictions. The first matches our endogenous model exactly, in that it has an oil supplyshock and a demand shock. The second VAR model more closely follows the literature and has threeobservables. In particular, we follow [25] and [28] who have shown the importance of separatingout different demand shocks. The exclusion restrictions we use necessitate monthly data, and thisranges from 1974 to 2011.

We first examine the two-variable VAR model. The first variable is the change in non-U.S. oilproduction (∆pd), and the second is the change in the real oil price (∆po).15 Consistent with theprevious notation, we decompose the errors and identify the shocks in the model as follows:

ut ≡

(u∆pdt

u∆pot

)=

[g11 0g21 g22

](εoil supply shock

εdemand shock

). (16)

The first shock is an innovation to non-U.S. oil supply. We assume that such unexpected changes canimpact the real oil price in the current month. This ordering also implies that non-U.S. oil supplydoes not contemporaneously respond to the other shock. This reflects the costs and difficultiesof quickly changing oil production. The second shock summarizes any remaining demand shockswhich affect its price. These include changes both arising from demand due to economic activityand storage possibilities, an aspect not modeled in this paper.

In the three-variable model we follow the variable selection and ordering in [25]. The variablesinclude changes in non-U.S. oil production, changes in U.S. industrial production (∆ip), and changesin the real oil price. This three-variable version can be decomposed as follows:

ut ≡

u∆pdt

u∆ipt

u∆pot

=

g11 0 0g21 g22 0g31 g32 g33

εoil supply shock

εaggregate demand shock

εprecautionary demand shock

. (17)

15We use the natural logarithm of non-U.S. oil production and the real refiner acquisition cost of imported crudeoil, both from the EIA. First differences are used to make the VAR more comparable with our RBC models, each ofwhich uses stationary data.

15

Figure 3 shows the impulse responses to an aggregate demand shock for GDP, the real oil price,and non-U.S. oil production for each of the crude oil models and the three-variable VAR model.Here we assume that the TFP shock on final goods production is similar to an aggregate demandshock in the VAR. In the two-variable VAR this shock is the demand shock. The graph in the topleft panel of Figure 3 shows that the instantaneous responses of GDP to a demand shock in thethree models are qualitatively similar to those implied by the three-variable VAR. However, in theVAR the impact of the shock quickly dissipates while the model responses are more persistent. Interms of magnitudes, the initial responses for GDP are on the lower end in the VAR, closer to thosepredicted by the endogenous model or the model with an exogenous oil price.

In terms of oil observables, the top right panel of Figure 3 shows that the real oil price rises byalmost 0.5% in the three-variable VAR as a response to an aggregate demand shock, and by nearly6% in the two-variable VAR in response to a demand shock. The larger value in the two-variablecase reflects the fact that all demand is included in this shock, not just aggregate demand. Theinstantaneous impulse responses of the oil price in the three crude oil models are smoother andmore persistent. The endogenous model best fits the impulse response from the three-variable VARin this case. The bottom panel of Figure 3 shows that non-U.S. oil production has a jagged responseto the demand shocks in each VAR, which differ from the smooth responses of each model.

Having analyzed a demand shock we now compare the impulse responses to an oil supply shock.Figure 4 shows the responses of U.S. GDP, the real oil price, and non-U.S. oil production for eachof the three models and the VARs to an unexpected fall in oil production. The shape of eachmodel’s responses to this shock with respect to the GDP and oil production are similar to each ofthe VARs. One substantial difference is that all of the models imply a much larger instantaneousresponse in the oil price than shown by either VAR.

The simulated impulse responses from each model are similar in magnitude to those generatedfrom both two and three-variable VARs, but can have substantially different dynamics. In mostcases the model responses are more persistent than those obtained from the VARs. It is difficult todistinguish between the models using these impulse responses, except to make the point that onlythe endogenous model is able to be used for comparison for each variable considered. An importantadvantage of endogenizing both the real oil price and oil demand is that such a framework canbe used to analyze both oil supply and oil demand shocks. Historically, both of these shockshave contributed to oil price changes. Moreover, these oil price changes are believed to contributeto variations in U.S. GDP.16 This is not the case when either the oil price or oil demand areexogenous. Having both prices and quantities of oil endogenous allows us to capture importantfeedback mechanisms between oil prices, oil production, and macroeconomic aggregates which arecritical in determining how oil shocks propagate through the economy.

5 Conclusion

This paper studies the consequences of endogenizing oil prices and quantities when accountingfor business cycles facts and crude oil dynamics. We first consider a standard real business cyclemodel with either oil prices or oil quantities being exogenous. We then extend the benchmark realbusiness cycle model to include an oil exporting region so that both the oil price and its quantity

16See [25] and [29], among others, for more on this issue.

16

are endogenous.

We show that when oil prices are exogenous, the model delivers counterfactual business cyclefacts regarding the co-movement between the real oil price and U.S. GDP. Once both oil prices andquantities are endogenous, the model can account for most of the business cycle properties of oilwhile being consistent with the standard business cycle facts. To compare the overall goodness offit across different models we use the sum of squared differences between model moments and thesample data. We find that endogenizing oil improves the model’s fit to data relative to environmentswith exogenous oil prices or exogenous oil quantities.

To complement the business cycle analysis, we analyze the impulse responses of an oil demandshock and an oil supply shock on oil and non-oil observables. The implied impulse responses of anendogenous crude oil market are more in line when compared to a reduced form VAR. Assumingcrude oil to be exogenous in either prices or quantities is not innocuous as it may seem a priorias the implied time series for consumption and hours across models are quite different after oilshocks hit the economy. These different time series patterns imply distinct welfare which cruciallydepends how oil is modeled after oil shocks hit the economy. The findings of this paper suggest thatany framework intended to study the impact of oil shocks on the macroeconomy should endogenizeboth its price and quantity.

References

[1] Luis Aguiar-Conraria and Yi Wen. Understanding the large negative impact of oil shocks.Journal of Money, Credit and Banking, 39(4):925–944, 2007.

[2] Bobby E. Apostolakis. Energy-capital substitutibility/complementarity. Energy Economics,12(1):48–58, 1990.

[3] Andrew Atkeson and Patrick Kehoe. Models of energy use: Putty-putty versus putty-clay.The American Economic Review, 89(4):1028–1043, 1999.

[4] David K. Backus and Mario J. Crucini. Oil prices and the terms of trade. Journal of Interna-tional Economics, 50:185–213, 2000.

[5] Nathan S. Balke, Stephen P.A. Brown, and Mine K. Yucel. Oil price shocks and u.s. economicactivity: An international perspective. Working Paper 1003, Federal Reserve Bank of Dallas,2010.

[6] Robert B. Barsky and Lutz Kilian. Do we know that oil caused the great stagflation? amonetary alternative. In B. Bernanke and K. Rogoff, editors, NBER Macroeconomics Annual2001, pages 137–183. 2002.

[7] Robert B. Barsky and Lutz Kilian. Oil and the macroeconomy since the 1970s. Journal ofEconomic Perspectives, 18(4):115–134, 2004.

[8] Olivier J. Blanchard and Jordi Gali. The macroeconomic effects of oil price shocks: Why arethe 2000s so different from the 1970s? In Jordi Gali and Mark J. Gertler, editors, InternationalDimensions of Monetary Policy, chapter 7, pages 373–421. University of Chicago Press, 1stedition, 2010.

17

[9] Olivier J. Blanchard and Marianna Riggi. Why are the 2000s so different from the 1970s? astructural interpretation of changes in the macroeconomic effects of oil prices. Journal of theEuropean Economic Association, 2012. Forthcoming.

[10] Martin Bodenstein, Christopher J. Erceg, and Luca Guerrieri. Oil shocks and external adjust-ment. Journal of International Economics, 83(2):168–184, 2011.

[11] Martin Bodenstein and Luca Guerrieri. Oil effciency, demand, and prices: A tale of upsand downs. International Finance Discussion Paper 1031, Board of Governors of the FederalReserve System, 2011.

[12] Stephen P.A. Brown and Mine K. Yucel. Energy prices and aggregative economic activity: Aninterpretive survey. The Quarterly Review of Economics and Finance, 42:193–208, 2002.

[13] Alessia Campolmi. Oil price shocks, demand vs. supply in a two-country model. MNB WorkingPapers 2008/5, Magyar Nemzeti Bank, Budapest, 2008.

[14] Charles T. Carlstrom and Timothy S. Fuerst. Oil prices, monetary policy, and counterfactualexperiments. Journal of Money, Credit and Banking, 38(7):1945–1958, 2006.

[15] V.V. Chari, Patrick J. Kehoe, and Ellen R. McGrattan. Sticky price models of the businesscycle: Can the contract multiplier solve the persistence problem? Econometrica, 68(5):1151–1179, 2000.

[16] Juan Carlos Cuestas. Nonlinearities and the order of integration of oil prices. The EmpiricalEconomics Letters, 9(2):193–202, 2010.

[17] Rajeev Dhawan and Karsten Jeske. Energy price shocks and the macroeconomy: The role ofconsumer durables. Journal of Money, Credit and Banking, 40(7):1357–1377, 2008.

[18] Mary G. Finn. Perfect competition and the effects of energy price increases on economicactivity. Journal of Money, Credit and Banking, 32(3):400–416, 2000.

[19] James D. Hamilton. Oil and the macroeconomy since world war ii. Journal of PoliticalEconomy, 91:228–248, 1983.

[20] James D. Hamilton. Oil and the macroeconomy. In Steven N. Durlauf and Lawrence E. Blume,editors, The New Palgrave Dictionary of Economics. Palgrage Macmillan, 2nd edition, 2008.

[21] Bruce Hicks and Lutz Kilian. Did unexpectedly strong economic growth cause the oil priceshock of 2003-2008? Journal of Forecasting, Forthcoming.

[22] Donald W. Jones, Paul N. Leiby, and Inja K. Paik. Oil price shocks and the macroeconomy:What has been learned since 1996. Energy Journal, 25(2):1–32, 2004.

[23] Lutz Kilian. The economic effects of energy price shocks. Journal of Economic Literature,46(4):871–909, 2008.

[24] Lutz Kilian. Exogenous oil supply shocks: How big are they and how much do they matterfor the u.s. economy? Review of Economics and Statistics, 90(2):216–240, 2008.

18

[25] Lutz Kilian. Not all oil price shocks are alike: Disentangling demand and supply shocks in thecrude oil market. American Economic Review, 99(3):1053–1069, 2009.

[26] Lutz Kilian. Oil price shocks, monetary policy and stagflation. In R. Fry, C. Jones, andC. Kent, editors, Inflation in an Era of Relative Price Shocks, pages 60–84. Reserve Bank ofAustralia, 2010.

[27] Lutz Kilian and Logan T. Lewis. Does the fed respond to oil price shocks? The EconomicJournal, 121(555):1047–1072, 2011.

[28] Lutz Kilian and Dan Murphy. The role of inventories and speculative trading in the globalmarket for crude oil. Mimeo, 2012.

[29] Lutz Kilian and Dan Murphy. Why agnostic sign restrictions are not enough: Understandingthe dynamics of oil market VAR models. Journal of the European Economic Association,10(5):1166–1188, 2012.

[30] In-Moo Kim and Prakash Loungani. The role of energy in real business cycle models. Journalof Monetary Economics, 29:173–189, 1992.

[31] Robert G. King and Sergio T. Rebelo. Resusciting real business cycles. In J.B. Taylor andM. Woodford, editors, Handbook of Macroeconomics, volume 1, chapter 14, pages 927–1007.Elsevier, 1st edition, 1999.

[32] Anna Kormilitsina. Oil price shocks and the optimality of monetary policy. Review of EconomicDynamics, 14:199–223, 2011.

[33] Sylvain Leduc and Keith Sill. A quantitative analysis of oil-price shocks, systematic monetarypolicy, and economic downturns. Journal of Monetary Economics, 51:781–808, 2004.

[34] Sylvain Leduc and Keith Sill. Monetary policy, oil shocks, and TFP: Accounting for the declinein us volatility. Review of Economic Dynamics, 10:595–614, 2007.

[35] Kensuke Miyazawa. Estimation of the elasticity of substitution between oil and capital. Eco-nomics Bulletin, 29(2):655–660, 2009.

[36] Anton Nakov and Galo Nuno. A general equilibrium model of the oil market. Working Papers1125, Banco de Espana, 2011.

[37] Anton Nakov and Andrea Pescatori. Oil and the great moderation. The Economic Journal,120:131–156, 2009.

[38] Anton Nakov and Andrea Pescatori. Monetary policy trade-offs with a dominant oil producer.Journal of Money, Credit and Banking, 42(1):1–32, 2010.

[39] Jean-Marc Natal. Monetary policy response to oil price shocks. Journal of Money, Credit andBanking, Forthcoming.

[40] Maurice Obstfeld and Kenneth Rogoff. Foundations of International Macroeconomics. MITPress, Cambridge, MA, first edition, 1996.

19

[41] Julio J. Rotemberg and Michael Woodford. Imperfect competition and the effects of energyprice increases on economic activity. Journal of Money, Credit and Banking, 28(4):549–577,1996.

[42] James H. Stock and Mark W. Watson. Business cycle fluctuations in u.s. macroeconomic timeseries. In J.B. Taylor and M. Woodford, editors, Handbook of Macroeconomics, volume 1,chapter 1, pages 3–64. Elsevier, 1st edition, 1999.

[43] Harald Uhlig. A toolkit for analysing nonlinear dynamic stochastic models easily. In Ra-mon Marimon and Andrew Scott, editors, Computational Methods for the Study of DynamicEconomies, pages 30–61. OUP, 1999.

[44] Deren Unalmis, Ibrahim Unalmis, and D. Filiz Unsal. On the sources of oil price fluctuations.Working Paper WP/09/285, IMF, 2009.

20

Appendix 1: Optimality Conditions and Equilibrium

The consumer problem in both regions yield the following optimality conditions:

1

Ct= Et

{β

Ct+1[rt+1Tt+1 + (1− δt)]

}(18)

1

C∗t= Et

{β∗

C∗t+1

[r∗t+1 + (1− δ∗)]}, (19)

wt =ξ0Ct

(1−Nt)ξ, (20)

w∗t =ξ∗0C

∗t

(1−N∗t )ξ∗, (21)

rt = ηδT η−1t . (22)

pb,t(st+1|st) = βEt{CηctCηct+1

}(23)

pb,t(st+1|st) = β∗Et

{C∗(ηc∗ )t

C∗(ηc∗ )t+1

}(24)

These are for all t, and equations (23) and (24) are over all st+1. The first two state that anyreduction of consumption today, which is used for investment, must be equal to the discounted gainfrom the return on that investment. The third and fourth equations show that at an optimum thewage equals the marginal rate of substitution between labor and consumption. The fifth equatesthe benefit from utilizing an additional unit of capital (its rate of return) to the cost (a higherdepreciation rate). The final two conditions specify the price of Arrow securities in each regionmust be equal to the respective consumer’s marginal rate of substitution in consumption betweenperiods. These final two conditions can be combined to give:

βEt{CηctCηct+1

}= β∗Et

{C∗(ηc∗ )t

C∗(ηc∗ )t+1

}(25)

This expression holds at all dates and under all contingencies, meaning that the values on eitherside are proportional. Because of this, each countries’ share of total global output is the same overtime [see e.g. [40]], and the consumption of one country can be expressed as a constant share ofanother. The share is denoted µ here, which represents the size of the oil consuming region relativeto that of the oil producing region.

Intermediate oil producers demand the same capital and labor, charge the same price, andproduce the same level. This implies that Qt(i

∗)=Qt, K∗t (i∗)=K∗t , and N∗t (i∗)=N∗t , yielding two

optimality conditions:

21

r∗t =θ∗αpq,tQt

K∗t, (26)

w∗t =θ∗(1− α)pq,tQt

N∗t. (27)

Because of monopolistic competition, there is a markup ( 1θ∗ ) associated with the price of oil,

changing the marginal products of all factors relative to the perfectly competitive case (θ∗=1).A similar situation holds in the oil consuming region, where intermediate goods producers demandthe same oil, capital, and labor; charge the same price; and produce the same level. This impliesthat Yt(i)=Yt, Qt(i)=Qt, Kt(i)=Kt, and Nt(i)=Nt, yielding three optimality conditions:

pq,t =θψγQρ−1

t YtJρt

, (28)

rt =θψ(1− γ)(TtKt)

ρ−1YtJρt

, (29)

wt =θ(1− ψ)Yt

Nt. (30)

These equate factor payments to the value of their marginal products. Again, because of monop-olistic competition, there is a markup (1

θ ) associated with the price of final goods. The model isclosed with two market clearing conditions:

Yt = Ct + C∗t + It + I∗t (31)

Bt+1(st+1|st) +B∗t+1(st+1|st) = 0 (32)

The first is the global market clearing condition for final goods and the second states that bondsare in zero net supply.

In a symmetric equilibrium all intermediate goods and oil producers make identical decisions.Thus the equilibrium for this economy is a process of prices {py,t, pq,t, pb,t(st+1|st), rt, r∗t , wt, w∗t }∞t=0,a process of allocations {Ct, C∗t , Nt, N

∗t , It, I

∗t ,Kt,K

∗t , Bt+1(st+1|st), B∗t+1(st+1|st)Jt, Qt, Yt}∞t=0, a

process of utilization rates {Tt}∞t=0, and exogenous technology processes {Zt, Z∗t }∞t=0 such that (i)taking prices as given, consumers solve (1); (ii) taking all prices save their own as given, eachintermediate goods producer solves (5); (iii) taking all prices as given, the final goods producersolves (9); (iv) taking all prices save their own as given, each intermediate oil producer solves (11);(v) taking all prices as given the final oil producer solves (13); (vi) the oil, final goods, and labormarkets clear; and (vii) each consumer’s budget constraint is met.

22

Appendix 2: Data and Parameter Values

Data

Data on real U.S. GDP, real U.S. consumption, real U.S. investment, and U.S. hours are taken fromthe Federal Reserve Bank of St. Louis’s Federal Reserve Economic Data (FRED) database at aquarterly frequency. Each of the first three series are in billions of chained 2005 dollars, and basedon the corresponding series from the Bureau of Economic Analysis (BEA). Consumption data isreal personal consumption expenditures and investment data is real gross private investment. Hoursdata are available quarterly and are the hours of all persons from the non-farm business sector,based on the series from the Bureau of Labor Statistics (BLS). The logarithm of these series areHP filtered, with a smoothing parameter of 1600, to extract the cyclical components. The reportedstandard deviations and correlations are based on these cyclical series.

Oil price data is taken from the U.S. Energy Information Administration (EIA) imported refineracquisition costs at a monthly frequency. This nominal series is deflated by the U.S. ConsumerPrice Index (CPI) less energy, which is also taken from FRED. The monthly values are aggregatedto quarterly by taking an average, and the level of the oil price is taken to be the logarithm ofthese values. In the reported statistics these averages are HP filtered with a smoothing parameterof 1600, and the reported statistics are based on the cyclical series. Non-U.S. oil production datais taken from the EIA’s monthly energy review on crude oil production at a monthly frequency.These are aggregated to quarterly frequency. The logarithm of this series is HP filtered with asmoothing parameter of 1600, and the reported statistics are based on the cyclical series.

The reported ratio of U.S. imports to exports is with respect to U.S. trade with major U.S.suppliers of oil. The list of these major suppliers, as of 2011, is available from the EIA. Monthly Dataon the value of U.S. imports and exports with respect to these major suppliers are available from theU.S. Census Bureau for the period 1985-2011. This data can be used to construct monthly ratiosof imports to exports for each country in each year from 1985-2011. For each year these monthlyvalues are averaged, leaving an average annual ratio of imports to exports for each country for theperiod 1985-2011. Finally, the reported ratio is the median of these annual averages. The medianis used to remove the influence of a few outlying points.

Parameter Values

Table 7 summarizes parameter values for the full simulation.

23

Parameter Description Exog Price Exog Prod Endog

β Discount factor 0.99 0.99 0.99σc CRRA 2.0 2.0 2.0δ Depreciation 0.022 0.019 0.019δ∗ Depreciation - - 0.025ξ Labor supply parameter 0.50 0.50 0.50ξ∗ Labor supply parameter - - 0.50ξ0 Labor supply parameter 1.63 2.07 2.05ξ∗0 Labor supply parameter - - 382.2ψ Capital services share of final goods prod 0.36 0.36 0.36α Capital share of oil prod - - 0.36γ Oil share of final goods prod 1.0e-6 1.4e-6 6.0e-6

(a) Calibrated based on Stylized Facts

Parameter Description Exog Price Exog Prod Endog

σqk Elasticity of substitution, oil and capital 0.223 0.211 0.314ρ First-order autocorrelation of technology shock 0.950 0.925 0.943ρ∗ First-order autocorrelation of technology shock - - 0.412ρpo First-order autocorrelation of exogenous oil process 0.240 - -ρq First-order autocorrelation of exogenous oil prod - 0.240 -σv Volatility of technology shock 0.004 0.006 0.005σ∗v Volatility of technology shock - - 0.076σv,po Volatility of exogenous oil price shock 0.176 - -σv,q Volatility of exogenous oil production shock - 0.034 -

(b) Calibrated Using Simulated Method of Moments

Table 7: Model Parameter Values

Appendix 3: Figures

24

Figure 1: Impulse responses for select observables to a one standard deviation innovation in tech-nology on final goods production in the oil consuming region.

Figure 2: Impulse responses for select observables to a one standard deviation innovation in: (i)the oil price in the model with the oil price exogenous (positive shock); (ii) oil production in themodel with oil production exogenous (negative shock); and (iii) technology on oil production in themodel with both the oil price and oil production endogenous (negative shock).

25

Figure 3: Impulse responses for select observables to a one standard deviation innovation in tech-nology on final goods production in the oil consuming region. Also shown are the impulse responsesof a two and three-variable VAR to an aggregate demand shock.

Figure 4: Impulse responses for select observables to a one standard deviation innovation in: (i)the oil price in the model with the oil price exogenous (positive shock); (ii) oil production in themodel with oil production exogenous (negative shock); and (iii) technology on oil production in themodel with both the oil price and oil production endogenous (negative shock). Also shown are theimpulse responses of a two and three-variable VAR to an oil supply shock.

26

not all oil price shocks are alike: a neoclassical ...econseminar/20131218paperoil... · 1...

Documents