productivity analysis in global manufacturing...

Productivity Analysis inGlobal Manufacturing Production∗

Markus Eberhardta,b† Francis Tealb,c

a St Catherine’s College, Oxford OX1 3UJ, Englandb Centre for the Study of African Economies,

Department of Economics, University of Oxford,Manor Road, Oxford OX1 3UQ, Englandc Institute for the Study of Labor (IZA),

Schaumburg-Lippe-Str. 5-9, 53113 Bonn, Germany

This version: 30th June 2010

Abstract:

Despite the widely recognised importance of the manufacturing industry for successful de-velopment relatively few studies empirically investigate this sector in cross-country analysis.In this paper we attempt to fill this gap in the literature by investigating manufacturing pro-duction across a large number of developing and developed countries using an unbalancedpanel of UNIDO data (1970-2002). Our empirical framework allows us not only a greatdeal of flexibility with regard to the production technology, but also enables us to modelthe complex network of endogeneities, the web of interdependencies not merely within butalso across economies, which previously has been largely ignored in cross-country empir-ics. We apply a novel two-stage estimator which can account for these matters and checkthe robustness of our results against a range of alternative methods from the recent paneltime series literature. Our results imply that differences in production technology, not justdifferences in TFP, are of crucial importance for understanding cross-country differencesin labour productivity and their underlying causes. They furthermore imply that conven-tional interpretation of regression intercepts as TFP level estimates is no longer valid andwe therefore provide an alternative methodology.

Keywords: Global Manufacturing Production; Parameter Heterogeneity; Productivity lev-els; Nonstationary Panel Econometrics; Common Factor ModelJEL classification: C23, O14, O47

∗We are grateful to Michael Binder, Stephen Bond, Steven Durlauf, David Hendry, John Muellbauer,Hashem Pesaran, Ron Smith and Jonathan Temple for helpful comments and suggestions. We bene-fited from comments during presentations at the 2nd Advanced Summer School at the Department ofEconomics of the University of Crete, the Gorman Student Research Workshop and the ProductivityWorkshop, University of Oxford, the Nordic Conference for Development Economics in Stockholm, theEconomic & Social Research Council (ESRC) Development Economics conference in Brighton and at theInternational Conference for Factor Structures for Panel and Multivariate Time Series Data in Maas-tricht. All remaining errors are our own. The first author gratefully acknowledges financial support fromthe ESRC [grant numbers PTA-031-2004-00345 and PTA-026-27-2048].†Corresponding author: Centre for the Study of African Economies (CSAE), Department of Eco-

nomics, Manor Road Building, Oxford OX1 3UQ, UK; Email: [email protected];phone: +44-(0)1865 271084; fax: +44-(0)1865 281447.

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1 Introduction

The central importance of the manufacturing sector for successful development has be-come a widely recognised ‘stylised fact’ in development economics. However, in contrastto the literature on cross-country growth regressions using aggregate economy data (seesurvey by Durlauf, Johnson, & Temple, 2005), there is limited empirical work dedicatedto the analysis of the manufacturing sector in a large cross-section of countries (a notableexception is Martin & Mitra, 2002). Cross-country empirical analysis at the sectorallevel is typically based on Total Factor Productivity (TFP) accounting and/or limited toOECD countries (Bernard & Jones, 1996a; Harrigan, 1999; Malley, Muscatelli, & Woitek,2003; Hultberg, Nadiri, & Sickles, 2004).

In this paper we attempt to fill this gap in the literature by estimating cross-country pro-duction functions for the manufacturing sector in 48 developing and developed countriesusing annual data from 1970 to 2002 (UNIDO, 2004). Building on earlier work on growthempirics (Eberhardt & Teal, 2010) we show that technology differences are of crucialimportance for understanding cross-country differences in labour productivity and theircauses (Durlauf, Kourtellos, & Minkin, 2001). Note that we refer to heterogeneity in‘technology parameters’ to indicate differential production function parameters on ob-servable and unobservable inputs across countries. This aside our study emphasises theimportance of time-series properties of factor inputs and TFP (Nelson & Plosser, 1982;Bernard & Jones, 1996b; Funk & Strauss, 2003; Bond, Leblebicioglu, & Schiantarelli,2007) as well as of accounting for cross-section correlation in the panel (Westerlund &Edgerton, 2008; Moscone & Tosetti, 2009; Sarafidis & Wansbeek, 2010).1 We adopt acommon factor modelling framework (Bai & Ng, 2004; Pesaran, 2006; Kapetanios, Pe-saran, & Yamagata, 2009; Bai, 2009) and introduce a novel estimation approach that canaccommodate all of the above matters. The Augmented Mean Group (AMG) estimatorfurther provides insights into the evolution of global manufacturing TFP and we carryout a number of robustness checks to confirm the validity of our empirical results.

Our findings have important implications for productivity analysis both at the sectoraland the aggregate economy level: first, like firms in different industries, different countriesare characterised by different production technologies. Our study shows that attempts atestimating cross-country production functions in pooled models, where by constructionthe same technology applies in all countries, are fundamentally misspecified and yield bi-ased estimates for the technology parameters and thus any TFP estimates derived fromthem. Second, merely allowing for technology heterogeneity is also insufficient to capturethe complex production process at the country-level: in a globalising world economiesinteract through trade, cultural, political and other ties and at the same time are affecteddifferentially by global phenomena such as the recent financial crisis or the emergence ofChina as a major economic player. This creates a web of interdependencies within andacross economies, leading to the breakdown of standard panel estimators employed inthe existing cross-country studies. Our empirical strategy accommodates this interplayof heterogeneity and commonality to provide evidence for the fundamental forces driv-ing manufacturing development across the globe. Third, the conventional interpretationof regression intercepts as TFP level estimates breaks down once production technol-ogy is allowed to differ across countries. We introduce an alternative methodology forTFP level determination which is robust to this feature and provide an analysis for themanufacturing case.

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The remainder of the paper is structured as follows: in the first part of the paper inSections 2 to 4 we concern ourselves with the conceptual motivation, set out the empiricalmodel and discuss empirical implementation. In the second part in Section 5 to 7 wepresent our regression results, formally investigate parameter heterogeneity and provideevidence that our results are robust to reverse causality. The third part in Section 8 coversthe implications of these findings for conventional TFP determination in the parametricliterature, providing a simple alternative methodology. Section 9 concludes.

2 Conceptual development

In this section we motivate the concerns with which we approach the estimation of cross-country production functions. Technology heterogeneity as well as the time-series andcross-section correlation properties of macro panel data have not been considered in greatdetail in the empirical growth literature (Durlauf & Quah, 1999; Temple, 1999; Durlaufet al., 2005), but have solid foundations in the theoretical literatures on growth andeconometrics. We discuss each of these issues in some more details in the following.

A theoretical justification for heterogeneous technology parameters can be found in the‘new growth’ literature. This strand of the theoretical growth literature argues thatproduction functions differ across countries and seeks to determine the sources of thisheterogeneity (Durlauf et al., 2001). Intuitively, the heterogeneity in production tech-nology could be taken to mean that countries can choose an ‘appropriate’ productiontechnology from a menu of feasible options. The model by Azariadis and Drazen (1990)can be seen as the ‘grandfather’ for many of the theoretical attempts to allow countriesto possess different technologies from each other. Their model incorporates a qualita-tive change in the production function, whereby upon reaching a critical ‘threshold’ ofhuman capital, economies will jump to a higher steady-state equilibrium growth pathrepresented by a different production function. Further theoretical work leads to mul-tiple equilibria interpretable as differential production technology across countries (e.g.Murphy, Shleifer, & Vishny, 1989; Durlauf, 1993; Banerjee & Newman, 1993). A simplerjustification for heterogeneous production functions is offered by Durlauf et al. (2001),namely that the Solow model was never intended to be valid in a homogeneous specifi-cation for all countries, but may still be a good way to investigate each country, i.e. ifwe allow for parameter differences across countries.2

In our general empirical model we emphasise a view of TFP as a ‘measure of ignorance’(Abramowitz, 1956), incorporating a wider set of factors that can shift the productionpossibility frontier (“resource endowments, climate, institutions, and so on”, Mankiw,Romer, & Weil, 1992, p.410/1). This is in contrast to the notion of TFP as a definitiveefficiency index, as commonly adopted in the microeconometric literature on produc-tion analysis. Furthermore, we allow for the possibility that TFP is in part commonto all countries, e.g. representing the global dissemination of non-rival scientific knowl-edge or global shocks, such as the recent financial crisis or the 1970s oil crises. Finally,we do not impose restrictions on the individual evolution paths of these unobservables.These considerations lead to the adoption of a TFP structure that allows for commonand/or country-specific evolution, which we implement using the common factor modelapproach.

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In the long-run, variable series such as value-added or capital stock often display highlevels of persistence, such that it is not unreasonable to suggest for these series to be‘nonstationary’ processes in some countries (Nelson & Plosser, 1982; Granger, 1997;Lee, Pesaran, & Smith, 1997; Rapach, 2002; Bai & Ng, 2004; Pedroni, 2007; Canning& Pedroni, 2008). Although economic time-series in practice are usually not preciselyintegrated of any given order, it is for our purposes sufficient to assume that nominaland real value series typically behave as I(2) and I(1) respectively (Hendry, 1995; Jones,1995). Further, Pedroni has suggested that variable (non)stationarity should not be seenas a ‘global’ property, valid for all times, but as a “feature which describes local behaviourof the series within sample” (Pedroni, 2007, p.432). The issue of nonstationarity is alsoprevalent with regard to TFP. A number of empirical papers report that their measuresof TFP display nonstationarity, whether analysed at the economy level (Coe & Helpman,1995; Coe, Helpman, & Hoffmaister, 1997; Kao, Chiang, & Chen, 1999; Engelbrecht,2002; Bond et al., 2007) or at the sectoral level (Bernard & Jones, 1996b; Funk &Strauss, 2003). Further, Coakley, Fuertes, and Smith (2006) state explicitly with referenceto cross-country production function estimation that technology shocks are plausiblynonstationary.

Taking these insights about heterogeneity, cross-section dependence and nonstationarityat face value one may then suggest that the macro production process is representativeof a cointegrating relationship between output and ‘some set of inputs’, likely includ-ing TFP (Pedroni, 2007; Canning & Pedroni, 2008). This relationship could apply to allcountries in the world in the same way, implying that all countries had the same long-runequilibrium trajectory (homogeneous cointegration). Alternatively, each country couldfollow a different long-run trajectory (heterogeneous cointegration). Existing empiricalwork however has primarily concerned itself with the potential endogeneity of regres-sors in the empirical framework, an issue that is given considerably more attention inthe literature than the data properties or the potential misspecification of the empiricalregression model.

3 Empirical framework

We adopt a common factor representation for a standard log-linearised Cobb-Douglasproduction function model: for i = 1, . . . , N , t = 1, . . . , T and m = 1, . . . , k let

yit = β′i xit + uit uit = αi + λ′i ft + εit (1)

xmit = πmi + δ′mi gmt + ρ1mi f1mt + . . .+ ρnmi fnmt + vmit (2)

ft = %′ft−1 + εt and gt = κ′gt−1 + εt (3)

where f ·mt ⊂ ft. yit represents value-added and xit is a vector of observable factor-inputs including labour and capital stock (all in logarithms).3 For unobserved TFP weemploy the combination of a country-specific TFP level αi and a set of common factorsft with country-specific factor loadings λi — TFP is thus in the spirit of a ‘measureof our ignorance’ (Abramowitz, 1956) and operationalised via an unobserved commonfactor representation. In equation (2) we provide an empirical representation of thek observable input variables, which are modeled as linear functions of the unobservedcommon factors ft and gt, with country-specific factor loadings respectively. The model

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setup thus introduces cross-section dependence in the observables and unobservables.As can be seen, some of the unobserved common factors driving the variation in yit inequation (1) also drive the regressors in (2). This setup leads to endogeneity wherebythe regressors are correlated with the unobservables of the production function equation(uit), making it difficult to identify βi separately from λi and ρi (Kapetanios et al.,2009). Technology parameters βi can differ across countries but are assumed constantover time.4 Equation (3) specifies the evolution of the unobserved factors, which includesthe potential for nonstationary factors (% = 1, κ) and thus nonstationary factor inputsand output. Note that the common factor framework is sufficiently general to allow forcommon and heterogeneous business cycles which are commonly seen to distort empiricalanalysis using annual data.5

The three most important features of the above setup are the potential nonstationarityof observables and unobservables (yit, xit, ft, gmt), the potential heterogeneity in theimpact of observables and unobservables on output across countries (αi, βi, λi) as wellas the endogeneity of observable input variables created by the common factor structure.These properties have important bearings on estimation and inference in macro paneldata which are at the heart of this paper.

4 Empirical implementation

The matters of parameter heterogeneity, data time-series properties and cross-sectiondependence in empirical analysis using macro panel data are developed at great lengthelsewhere (Eberhardt & Teal, 2010). In this section we therefore restrict ourselves tothe discussion of the identification problem highlighted above, before we introduce ournovel estimation approach which allows for heterogeneity in the impact of observablesand unobservables.

If we assume factors ft (and gmt) in our general model above are stationary, the consis-tency of standard panel methods such as a pooled Fixed Effects or a Pesaran and Smith(1995) Mean Group estimator rests on the factor loadings of the unobserved common fac-tors contained in both the y and x-equations (λi, ρi): if their averages are jointly non-zeroa regression of y on x and N intercepts will be subject to the omitted variable problemand hence misspecified, since regression error terms will be correlated with the regressor,leading to biased estimates and incorrect inference (Coakley et al., 2006; Pesaran, 2006).In the case of nonstationary factors the consistency issues are altogether more complexand will depend on the exact specification of the model. However, regardless of theirorder of integration, standard estimation approaches neglecting common factors will notyield an estimate of β or the mean of βi, but of βi + λiρ

−1i , as shown by Kapetanios

et al. (2009): βi is unidentified. Under the specification described, a standard pooledFixed Effects or Pesaran and Smith (1995) Mean Group estimator will therefore likelyyield an inconsistent estimator (due to residual nonstationarity) of a parameter we arenot interested in (due to the identification problem).

Our empirical approach emphasises the importance of parameter and factor loading het-erogeneity across countries. The following 2 × 2 matrix indicates how the various esti-mators implemented below account for these matters.6 We abstract from discussing theexisting panel estimators here and refer to the overview article by Coakley et al. (2006),

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as well as the articles by Pedroni (2000, 2001) and Pesaran (2006) for more details.

Factor loadings:homogeneous heterogeneous

Technology parameters: homogeneous POLS, FE, FD-OLS CCEPheterogeneous MG, RCM, GM-FMOLS AMG, ARCM, CMG

Essentially, in our model setup all estimators neglecting the heterogeneity in unobserv-ables (left column) suffer from the identification problem described above. In addition,the time-series properties of both observable and unobservable processes create furtherdifficulties for estimation and inference in these empirical approaches as errors may benonstationary. Inference is problematic in this case since conventional standard errorswill be invalid (Kao, 1999). Among these estimators the Pedroni (2000) GM-FMOLS isthe only one avoiding this issue by adopting a nonstationary panel econometric approachrelying on cointegrated variables.

The estimators allowing for heterogeneity in factor loadings adopted here (right column)operate through augmenting the regression equation(s) with ‘proxies’ or estimates for theunobserved common factors. This augmentation avoids the identification problem and isalso an appropriate strategy to account for other cross-section dependence, e.g. spatialcorrelation, in the presence of nonstationary variables (Kapetanios et al., 2009). It is inthis context that we suggest the Augmented Mean Group (AMG) estimator.

The Augmented Mean Group (AMG) estimator accounts for cross-section dependenceby inclusion of a ‘common dynamic process’ in the country regression. This process isextracted from the year dummy coefficients of a pooled regression in first differences (FD-OLS) and represents the levels-equivalent mean evolution of unobserved common factorsacross all countries. Provided the unobserved common factors form part of the country-specific cointegrating relation (Pedroni, 2007), the augmented country regression modelencompasses the cointegrating relationship, which is allowed to differ across i.

Stage (i) ∆yit = b′∆xit +T∑t=2

ct∆Dt + eit ⇒ ct ≡ µ•t (4)

Stage (ii) yit = ai + b′ixit + cit+ diµ•t + eit bAMG = N−1

∑i

bi (5)

Stage (i) represents a standard FD-OLS regression with T−1 year dummies in first differ-ences, from which we collect the year dummy coefficients (relabelled as µ•t ). This processis extracted from the pooled regression in first differences since nonstationary variablesand unobservables are believed to bias the estimates in the pooled levels regressions.7 Instage (ii) µ•t is included in each of the N standard country regressions which also includelinear trend terms to capture omitted idiosyncratic processes evolving in a linear fashionover time. Alternatively we can subtract µ•t from the dependent variable, which impliesthe common process is imposed on each country with unit coefficient. In either case theAMG estimates are derived as averages of the individual country estimates, following thePesaran and Smith (1995) MG approach. Based on the results of Monte Carlo simulations(Bond & Eberhardt, 2009) we posit that the inclusion of µ•t allows for the separate iden-tification of βi or E[βi] and the unobserved common factors driving output and inputs,like in the Pesaran (2006) CCE approach. In analogy, we can use ∆µ•t in the country

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equations in first differences and can augment the Swamy (1970) RCM estimator in asimilar fashion to yield the Augmented Random Coefficient Model (ARCM) estimatorsin levels and first differences — results for these were very similar to those in the AMGand in the interest of space are therefore omitted in the empirical section.

The focus of the CCE estimators is the estimation of consistent b and not the natureof the unobserved common factors or their factor loadings: we cannot obtain an explicitestimate for the unobserved factors ft or the factor loadings λi, since the average impactof the factors (λ) is unknown. Our augmented estimators use an explicit rather thanimplicit estimate for ft from the pooled first stage regression. Compared with the CCEapproach we can obtain an economically meaningful construct from the AMG setup: thecommon dynamic process µ•t = h(λft) represents common TFP evolution over time,whereby common is defined either in the literal sense, or as the sample mean of country-specific TFP evolution. The country-specific coefficient on the common dynamic process,di from equation (5), represents the implicit factor loading on common TFP.

Immediate concerns about this estimator relate to the issue of second stage ‘regressionswith generated regressors’ (Pagan, 1984). However, our simulation results (Bond & Eber-hardt, 2009) suggest that the average standard error of the AMG estimates is of similarmagnitude to the empirical standard deviation. A theoretical explanation is provided inBai and Ng (2008), who show that second stage standard errors need not be adjusted forfirst stage estimation uncertainty if

√T/N → 0, as is arguably the case in our empir-

ics.

5 Data and main empirical results

5.1 Data

For our empirical analysis we employ aggregate sectoral data for manufacturing fromdeveloped and developing countries for the period 1970 to 2002 (UNIDO, 2004). Oursample represents an unbalanced panel of 48 countries with an average of 24 time-seriesobservations (min: 11, max: 33). A detailed discussion of the data and descriptivestatistics can be found in the Appendix. All of the results presented are strikingly robustto the use of a reduced sample constructed with application of a set of rigid ‘cleaning’rules. Furthermore, we carried out all regressions below in a gross-output model withmaterials as additional input — VA-equivalent results are virtually identical to thesepresented (detailed results available on request).

5.2 Time-series properties of the data

We carried out a range of stationarity and nonstationarity tests for individual countrytime-series as well as the panel as a whole (see Technical Appendix).8 The tests conductedinclude country-specific unit root tests and panel unit root tests of the first (Im, Pesaran,& Shin, 1997; Maddala & Wu, 1999) and second generation (Pesaran, 2007). In case ofthe present data dimensions and characteristics, and given all the problems and caveats

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of individual country unit root tests as well as panel unit root tests, we can suggest mostconservatively that nonstationarity cannot be ruled out in this dataset.

5.3 Pooled regressions

We estimate pooled models with variables in levels or first differences, including T − 1year dummies or country-specific period-averages a la Pesaran (2006). By construction,the slope coefficients on the factor-inputs in these models are restricted to be the sameacross all countries. Our results are presented in Table 1, with unrestricted models andmodels with CRS imposed in the upper and lower panel respectively.

[Table 1 about here]

Estimates for the factor input parameters in the regressions without any restrictions onthe returns to scale are statistically significant at the 5% level or 1% level. The POLS re-sults in [1] suggest that failure to account for time-invariant heterogeneity across countries(fixed effects) yields biased results: at around .8 the capital coefficient is considerablyinflated. Inclusion of country intercepts in [2] reduces these coefficient estimates some-what. The same parameter in the CCEP results in [3] is yet lower still, around .6. In boththe FE and CCEP estimators the fixed effects are highly significant (F -tests reported intable footnote). For all three estimators in levels the regression diagnostics suggest serialcorrelation in the error terms, while constant returns to scale are rejected at the 1%level of significance except for POLS. Note that for the FE estimator the data rejectsCRS in favour of increasing returns — an unusual finding. The OLS regressions in firstdifferences in [4] yield somewhat different technology estimates: the capital coefficientis now around .3 in both specifications. CRS cannot be rejected, the AR(1) tests showserial correlation for this model, which is to be expected given that errors are now in firstdifferences. There is however evidence of some higher order autocorrelation.9

Under intercept and technology parameter heterogeneity, given nonstationarity in (someof) the country variable series the pooled FE estimates in column [2] asypmtoticallyconverge to the ‘long-run average’ relation at speed

√N (Phillips & Moon, 1999) provided

T/N → 0 (joint asymptotics) and cross-section independence. In the present sample,however, nonstationary error terms and unobserved common factors seem to influence theresults considerably: a capital coefficient of around .7 is more than twice the magnitudeof the macro data on factor shares in income (Mankiw et al., 1992; Gomme & Rupert,2004), a common finding in the literature (Islam, 2003; Pedroni, 2007). Further recallthat t-ratios are invalid for the estimations in levels if error terms are nonstationary(Kao, 1999; Coakley, Fuertes, & Smith, 2001). The CCEP estimator accounts for cross-section dependence and yields, as the residual analysis suggests, stationary errors terms.The difference estimator in [4] converges to the common cointegrating vector β or themean of the individual country cointegrating relations, E[βi], at speed

√TN (Smith &

Fuertes, 2007). Further investigation regarding alternative specification with parameterheterogeneity as well as residual diagnostics will be necessary to judge the bias of theCCEP results.

Our pooled regression analysis suggests that time-series properties of the data play animportant role in estimation: we suggest that the bias in the levels models is the resultof nonstationary errors, which are introduced into the pooled OLS and FE equations by

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the imposition of parameter homogeneity — we investigate both matters in more detailbelow. In contrast, the FD-OLS regressions where variables are stationary yield moresensible capital parameters. This pattern of results fits the case of I(1) level-series inat least some of the countries in our sample. The results for the CCEP are somewhatsurprising and we would speculate that these are driven by outliers.

5.4 Common TFP

Following our argument above, the FD-OLS regression represents the only pooled re-gression model which estimates a cross-country average relationship safe from difficultiesintroduced by nonstationarity. We therefore make use of the year dummy coefficientsderived from our preferred pooled model to obtain an estimate of the common dynamicprocess µ•t , which represents an estimate of the common TFP evolution. Figure 1 illus-trates the evolution path of this common dynamic process for the unrestricted and CRSmodels.

[Figure 1 about here]

The graphs show severe slumps following the two oil shocks in the 1970s, while the 1980sand 1990s indicate considerable upward movement.10 If we follow the ‘measure of igno-rance’ interpretation of TFP (Abramowitz, 1956), then a decline in global manufacturingTFP as evidenced in the 1970s should not be interpreted as a decline in knowledge, buta worsening global manufacturing environment.11

5.5 Country regressions

In the following we relax the assumption implicit in the pooled regressions that all coun-tries possess the same production technology. At the same time, we maintain that com-mon shocks and/or cross-sectional dependence have to be accounted for in some fashion.We consider: [1] the standard Pesaran and Smith (1995) Mean Group (MG) estimator;the Augmented Mean Group (AMG) estimator either [2] with the common dynamic pro-cess (µ•t ) imposed with unit coefficient, or [3] included as additional regressor. The MeanGroup version of the Common Correlated Effects estimator (CMG) is estimated in twoalternative specifications, namely [4] as defined by Pesaran (2006), and [5] augmentedwith a country-specific linear trend term.12

Unweighted averages of country parameter estimates are presented for regressions in levelsand first differences in the upper and lower panels of Table 2 respectively. In all cases wehave imposed constant returns to scale on the country regression equation, in line withthe findings from our preferred pooled model in first differences — this decision and itsimplications are discussed in more detail below.

The t-statistics for the country-regression averages reported in all tables are measuresof dispersion for the sample of country-specific estimates, following Pesaran and Smith(1995).13 We further provide the Pedroni (1999) ‘panel t-statistic’ (1/

√N)∑

i ti, con-structed from the country-specific t-statistics (ti) of the parameter estimates, which in-dicates the precision of the individual country estimates. We can see that the individual

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country estimates for the levels specification are on average more precisely estimated thanthose in the specifications in first differences.


Our first observation regarding the levels results in Table 2 is that across all specificationsthe means of the capital coefficients are considerably lower than in the pooled levelsmodels: between .2 and .5 rather than between .6 and .9 in the pooled levels models.Comparing results for the levels specification with those for the specification in firstdifferences reveals that estimates from these two sets of heterogeneous models followvery similar patterns.14 In all cases the technology parameters are estimated reasonablyprecisely and a considerable number of country trends/drifts are significant at the 10%level, although much more so for the levels than for the first difference specifications.15

Coefficients on the common dynamic process µ•t in model [3] for both specifications areuniformly high and close to their theoretical value of unity.

Closer inspection of the capital coefficients suggests the following patterns: firstly, esti-mation approaches that do not account for unobserved common factors have parameterestimates around .2. Secondly, for the ‘augmented’ estimators which account for a com-mon dynamic process in the estimation equation the averaged coefficients are around .3.Thirdly, the results for the CMG with and without additional country trend differ con-siderably, with the former close to all other augmented regression results and the latterslightly larger, around .45.

5.6 Diagnostic testing

We first investigated the density estimates for country-specific technology parametersestimated in the levels regressions using standard kernel methods with automatic band-width selection. The plots indicate that the distribution of these parameter estimates issymmetric around their respective means and roughly Gaussian, such that no significantoutliers drive our results (see Technical Appendix).

We further carried out a number of standard residual diagnostic tests including analysisof stationarity (see Technical Appendix). A cautious conclusion from these procedureswould be that we are more confident about the country regression residuals possessing de-sirable properties (stationarity, normality, homoskedasticity) than we are for their pooledcounterparts.

Cointegration tests are commonly carried out as a pre-estimation testing procedure, how-ever we have delayed these until after estimation since we hypothesise that unobservableTFP forms part of the cointegrating vector. Employing our first stage estimate µ•,vat wecarry out a cointegration testing procedure based on the error correction model represen-tation, first introduced by Westerlund (2007) and refined by Gengenbach, Urbain, andWesterlund (2009). We estimate the following equation for each country i

∆yit = αiyi,t−1 + γ1iki,t−1 + γ2iµ•,vat−1 (6)

+

pi∑s=1

π1is∆yi,t−s +

pi∑s=0

π2is∆ki,t−s +

pi∑s=0

π3is∆µ•,vai,t−s + εit

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where y and k represent value-added per worker and capital stock per worker respectively(both in logs) and µ• is the ‘common dynamic process’. The three sums represent laggeddifferences of these processes with lag-length pi. Table 3 presents results for the caseswhere the cointegration equation includes no deterministic terms, an intercept, or anintercept and a trend respectively. For each case the test statistic τ ∗ is a simple averageof the t-ratios for αi from the country ECM regressions, where extreme values for ti havebeen replaced using a truncation rule — see Gengenbach et al. (2009) for more details.Similarly for the averaged Wald statistic ω∗, which is based on country-specific tests ofαi = γ1i = γ2i = 0. Since the individual t-ratios and F -distributions for these testsas well as their averages under the null have non-standard distributions we provide therespective critical values. We employ the Akaike Information Criterion (AIC) or theSchwarz Information Criterion (BIC) to establish the appropriate lag-length pi in eachcountry equation and report the average for each model and case.


This analysis suggests there are good grounds to suggest that value-added per worker,capital per worker and our estimate for TFP are cointegrated.

5.7 The importance of constant returns to scale

Further investigation reveals that the imposition of constant returns to scale, justifiedby the CRS test for the pooled regression with variables in first differences, plays animportant role in our story. We repeat the country regressions with all variables in‘raw levels’ rather than in per worker terms (for results see Technical Appendix). Thefailure to impose constant returns to scale leads to a loss of precision in the capitalestimates in virtually all specifications. The labour coefficients are however around .7 inall cases and only one out of 16 models estimated rejects a parameter test for constantreturns to scale. This pattern is confirmed in the models in first difference. Despite thesereaffirming diagnostics, the sharp difference between the impact of imposing CRS in thecountry regressions (considerable loss of precision) and the pooled regressions (limitedchange) is somewhat puzzling and merits further investigation in the future.

5.8 Discussion of the main empirical results

We investigated the changing parameter estimates across a number of empirical speci-fications and estimators. Our pooled estimators in levels are suggested to be severelybiased, given the diagnostic tests and the fact that their capital coefficients range from.6 to .8, far in excess of the macro evidence of around 1/3. This bias may arise from themisspecification of homogeneity or the failure to account for unobserved common factorsappropriately. The fact that CCEP yields very similar results to POLS and FE suggeststhat interplay of parameter heterogeneity and variable stationarity plays an importantrole. The first difference estimator (FD-OLS) in contrast has sound diagnostics and yieldssensible parameter coefficients.

The heterogeneous parameter estimators yield uniformly lower capital coefficients, morein line with the aggregate economy factor income share data. Across levels and first differ-ence, gross-output and value-added specifications there seems to be a consistent pattern

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whereby the standard heterogeneous MG estimator obtains qualitatively different resultsfrom the augmented ones (AMG, CMG). Diagnostic tests cannot differentiate betweenthese two groups of estimators, however we can argue that the MG estimator is likelyto be biased: firstly, it uses an overly simplistic representation for TFP evolution (lineartrend) which requires stationarity; secondly, it is argued to suffer from the identificationproblem introduced above.

Turning to the augmented estimators, we suggest that the combination of a common dy-namic process and a linear country trend is confirmed by the data: a considerable numberof country trends are statistically significant, while the cross-country average coefficientfor µ•t is close to unity in the model where it is included as additional regressor. TheCMG estimator provides results broadly in line with those for the AMG, with the latteron the whole more consistent across specifications. The comparison between the countryregression results presented above and the results for ‘demeaned’ variables (see TechnicalAppendix) indicate that the unobserved common factors exert differential impact acrosscountries, thus meriting the adoption of approaches which allow for heterogeneous factorloadings (and thus TFP).16

6 Testing technology heterogeneity

The country coefficients emerging from the regressions in the previous section imply con-siderable parameter heterogeneity across countries. This apparent heterogeneity mayhowever be due to sampling variation and the relatively limited number of time-seriesobservations in each country (Pedroni, 2007). We therefore carried out a number of for-mal heterogeneity tests for the results from the AMG and CMG estimations (levels andfirst differences): firstly, we constructed predicted values based on the mean parameterestimates of our heterogeneous parameter models, and regressed these on input variables,a common trend and country intercepts in a pooled regression. The rationale of this testis that if parameter estimates were truly homogeneous we would not expect significantcoefficients on any input variable. Secondly, we obtained Swamy (1970) S statistics forlevels and first difference specifications. Thirdly, we constructed Wald statistics follow-ing Canning and Pedroni (2008), and fourthly, we produced F -statistics for standardand augmented MG estimators following Pedroni (2007).17 Taken together the resultsfor these various tests (see Technical Appendix) give a strong indication that parameterhomogeneity is rejected in this dataset. Systematic differences in the test statistics forlevels and first difference specifications indicate that nonstationarity may drive some ofthese results. Nevertheless, even if heterogeneity were not very significant in qualitativeterms, our contrasting of pooled and country regression results has shown that it nev-ertheless matters greatly for correct empirical analysis in the presence of nonstationaryvariables.

7 Reverse causality

In the analysis of empirical production functions the issue of variable endogeneity istypically of great concern, requiring means and ways to instrument for factor inputs.

12

A popular approach to address this problem is to convert macro-panel data into a shortpanel of typically 5-year averages and to employ empirical estimators originally developedfor large N , small T micro-panels (Arellano & Bond, 1991; Blundell & Bond, 1998).18

When model parameters differ across countries the instrumentation strategy in theseGMM-type estimators (and any other IV strategies for pooled regressions) breaks downsince informative instruments are invalid by construction (Pesaran & Smith, 1995). In thefollowing we therefore adopt the empirical approach by Pedroni (2000, 2007) and estimatecountry regressions by Fully-Modified OLS, whereupon parameter estimates are averagedacross countries (Group-Mean FMOLS). Provided the variables are nonstationary andcointegrated the individual FMOLS estimates are super-consistent and robust to theinfluence of variable endogeneity (Pedroni, 2007).


In the upper panel of Table 4 we present averaged parameter estimates for the full sampleFMOLS regressions, where column [1] represents the standard Group-Mean FMOLS, andcolumns [2] and [3] augment the country FMOLS equation with the common dynamicprocess µ•,vat . Columns [4] and [5] apply FMOLS to a country regression with the CCE-augmentation. In the lower panel of the same table our sample only includes 26 countrieswhich ‘pass’ two nonstationarity test (KPSS, ADF) for value-added per worker and capitalstock per worker respectively.

The standard Pedroni (2000) approach yields insignificant capital estimates, whereasaugmentation with the common dynamic process yields statistically significant estimatesvery close to those arising from our previous AMG regressions. Once we include µ•,vat wethus obtain the same empirical results in the Group-Mean Fully-Modified OLS and MeanGroup OLS approaches. Similar to the results in Table 2 the CCE-augmented averageestimate is somewhat larger at .55, although inclusion of a linear country-trend yieldsan average estimate for capital of around .3. These results are robust to a restrictionof the sample to countries for which value-added and capital stock per worker ‘pass’the two nonstationarity tests. We take these results as a vindication of our previousfindings.

8 TFP in a heterogeneous parameter world

For many applications the estimation of production functions is just the first step in anempirical analysis that concentrates on the magnitudes and determinants of TFP — attimes TFP is almost treated like an observable variable. In our analysis we have thus farfocused on the factor parameter estimates and their magnitudes and robustness acrossspecifications. We now want to provide some estimates for TFP and its evolution. Fromthe country regressions we can obtain estimates for the intercept, technology parameters,idiosyncratic and common trend coefficients or the parameters on the cross-section av-erages for AMG and CMG specification respectively. One may be tempted to view thecoefficients on the intercepts as TFP level estimates, just like in the pooled fixed effectscase. However, once we allow for heterogeneity in the slope coefficients, the interpreta-tion of the intercept as an estimate for base-year TFP level is no longer valid. In orderto illustrate our case, we employ a simple linear relationship between value-added andcapital where the contribution of TFP growth has already been accounted for.

13

[Figure 2 about here]

In Figure 2 we provide scatter plots for ‘adjusted’ log value-added per worker (y-axis)against log capital per worker (x-axis) as well as a fitted regression line for these ob-servations in each of the following four countries: in the left panel France (circles) andBelgium (triangles), in the right panel South Korea (circles) and Malaysia (triangles).The ‘adjustment’ is based on the country-specific estimates from the AMG regression(CRS value-added specification):19 we compute

yadjit = yit − cit− diµ•t (7)

where ci and di are the country-specific estimates for the linear trend term and thecommon dynamic process respectively. We then plot this variable against log capital perworker for each country separately. The left panel of Figure 2 shows two countries (France,Belgium) with virtually identical capital coefficient estimates (slopes). The in-samplefitted regression line is plotted as a solid line, the out-of-sample extrapolation toward they-axis is plotted in dashes. The country-estimates for the intercepts can be interpreted asTFP levels, since these countries have very similar capital coefficient estimates (bi ≈ bj).

In this case, the graph represents the linear model yadjit = ai + b log(K/L)it, where aipossesses the ceteris paribus property. In contrast, the right panel shows two countries(Malaysia, South Korea) which exhibit very different capital coefficient estimates. Inthis case ai cannot be interpreted as possessing the ceteris paribus quality since bi 6= b:ceteris non paribus ! In the graph we can see that Malaysia has a considerably higherintercept term than South Korea, even though the latter’s observations lie above those ofthe former at any given point in time. This illustrates that once technology parametersin the production function differ across countries the regression intercept can no longerbe interpreted as a TFP-level estimate.

We can suggest an alternative measure for TFP-level which is robust to parameter het-erogeneity. Referring back to the scatter plots in Figure 2, we marked the base-year levelof log capital per worker by vertical lines for each of the four countries. We suggest touse the locus where the solid (in-sample) regression line hits the vertical base-year capitalstock level as an indicator of TFP-level in the base year. In the value-added specificationthese adjusted base-year and final-year TFP-levels are thus

ai + bi log(K/L)0,i and ai + bi log(K/L)0,i + ciτ + diµ•τ (8)

respectively, where log(K/L)0,i is the country-specific base-year value for capital perworker (in logs), τ is the total period for which country i is in the sample and µ•τ is theaccumulated common TFP growth for this period τ with the country-specific parameterdi — it is easy to see that the intercept-problem discussed above only has bearings onTFP-level estimates. A similar formula applies for the CMG estimator.

Focusing exclusively on the TFP-levels in the base-year, Table 5 presents the rank (bymagnitude) for adjusted TFP levels derived from the AMG and CMG estimators. Wefurther show the country ranking based on a pooled fixed effects estimation, such as thatpresented in Table 2, column [2]. As can be seen in the right half of the table, the rankingsdiffer considerably between the AMG or CMG results on the one hand and standard fixedeffects results on the other (median absolute rank difference (MARD): 10, respectively),but not between the results for AMG and CMG (MARD: 1).

14

We present adjusted TFP base-year and final-year levels for these AMG and CMG modelsin Figure 3.20 The countries in both charts are arranged in order of magnitude of theirfinal-year adjusted TFP levels in the AMG(ii) model, for which results are shown in theleft bar-chart. With exception of a small number of countries (e.g. MLT — Malta, SGP— Singapore) the general ordering of countries by final-year TFP levels is very similar inthe two specifications: countries such as Finland, Canada, the United States or Irelandcan be found toward the top of the ranking, with Bangladesh, India, Sri Lanka and Polandcloser to the bottom.

9 Concluding remarks

In this paper we investigated how technology differences in manufacturing across countriescan be empirically modelled. We employed an encompassing framework which allows forthe possibility that the impact of observable and unobservable inputs on output differsacross countries, as well as for nonstationary evolution of these processes. We introducedour novel Augmented Mean Group estimator, which is conceptually close to the MeanGroup version of the Pesaran (2006) Common Correlated Effects estimator. Both of thesemethods allow for a globally common, unobserved factor (or factors) interpreted either ascommon TFP or an average of country-specific TFP evolution. While in the CMG thiscommon dynamic process is only implicit, the AMG approach uses an explicit estimatefor this process in the augmentation of country-regressions.

Our empirical framework allowed us to model a number of characteristics which are likelyto be prevalent in manufacturing data from a diverse sample of countries: Firstly, we al-lowed for technology heterogeneity across countries. Empirical results are confirmed byformal testing procedures to suggest that technology parameters in manufacturing pro-duction indeed differ across countries. This result supports earlier findings by Durlauf(2001) and Pedroni (2007) using aggregate economy data: if production technology differsin cross-country manufacturing, aggregate economy technology is unlikely to be homoge-neous. The result of production technology heterogeneity across countries has immediateimplications for standard TFP analysis: it leads to the breakdown of the interpretation ofregression intercepts as TFP-level estimates. We therefore introduced a new procedure tocompute ‘adjusted’ TFP-level estimates, which is robust to parameter heterogeneity andcan thus be compared across countries and between pooled and heterogeneous parame-ter models.21 Further analysis highlighted the significant differences between ‘adjusted’TFP-level estimates derived from our preferred heterogeneous parameter estimators onthe one hand and the standard pooled fixed effects estimator on the other. The findingof cross-country technology heterogeneity thus questions the validity of standard growthand development accounting practices to impose common coefficients on capital stock toextract country-specific measures of TFP.

Secondly, we allowed for unobserved common factors to drive output, but with differentialimpact across countries, thus inducing cross-section dependence. These common factorsare visualised by our common dynamic process, which follows patterns over the 1970-2002sample period that match historical events. The interpretation of this common dynamicprocess µ•t would be that for the manufacturing sector similar factors drive production inall countries, albeit to a different extent. This is equivalent to suggesting that the ‘global

15

tide’ of innovation can ‘lift all boats’, and that technology transfer from developed todeveloping countries is possible but dependent on the country’s production technologyand absorptive capacity, among other things.

Thirdly, our empirical setup allows for a type of endogeneity which is arguably very intu-itive, namely that some of the unobservables driving output are also driving the evolutionof inputs. This leads to an identification problem, whereby standard panel estimatorscannot identify the parameters on the observable inputs as distinct from the impact ofunobservables. Additional Monte Carlo simulations (Bond & Eberhardt, 2009) have high-lighted the ability of the Pesaran (2006) CCE estimators and our own AMG approachto deal with this problem successfully. Furthermore, our additional analysis in Section 7confirms that the empirical results are robust to the use of a panel time-series economet-ric approach. The Pedroni (2000) Group-Mean FMOLS approach suggests that failureto account for unobserved common factors when analysing cross-country manufactur-ing production leads to the breakdown of the empirical estimates, whereas the inclusionof the common dynamic process yields results very close to those from the AMG andCMG. Standard practices to deal with endogeneity (instrumentation with third vari-ables or ‘own-instrumentation’ with lagged values) are only appropriate in a stationaryframework. This aside many researchers have expressed concerns over instrument va-lidity in macro panel data (e.g. Clemens & Bazzi, 2009). Adopting a nonstationarypanel econometric approach that accounts for cross-section dependence in our view is asound empirical alternative to address both these concerns and should be applied morewidely to cross-country productivity-analysis (Bai, 2009; Chudik, Pesaran, & Tosetti,2010; Eberhardt & Teal, 2010).

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Notes

1Empirical productivity analysis which allows for cross-section dependence is still rel-atively limited, e.g. production functions for Italian regions (Costantini & Destefanis,2009) or Chinese provinces (Fleisher, Li, & Zhao, 2009).

2In line with the cross-country growth empirics literature (Durlauf et al., 2005) oursetup assumes parameter constancy over time.

3Parameter estimates and interpretation will differ between a value-added based andgross-output based empirical specification, but if we assume constancy of the material-output ratio we can transform results to make them directly comparable: βKi,va = βKi /(1−βMi ) where βK and βM are capital and materials coefficients respectively (Soderbom &Teal, 2004). Similarly for the labour coefficient.

4The latter assumption is clearly restrictive, but given the focus on cross-countrytechnology heterogeneity against the background of data restrictions in the time-seriesdimension we cannot relax this assumption for the heterogeneous regression models. Forthe pooled models we ran separate regressions using pre- and post-1985 subsamples forthe value-added models. Estimates for POLS, CCEP and FD-OLS are virtually identicalfor the two sub-periods. Period estimates for the FE estimator differ somewhat but the

20

95% confidence intervals still show considerable overlap.

5For details see Eberhardt and Teal (2010, Section 4).

6Abbreviations: POLS — Pooled OLS, FE — Fixed Effects, FD-OLS — OLS withvariables in first differences, MG — Pesaran and Smith (1995) Mean Group, RCM —Swamy (1970) Random Coefficient Model, GM-FMOLS — Pedroni (2000) Group-MeanFully Modified OLS, CCEP/CMG — Pesaran (2006) Common Correlated Effects esti-mators, and AMG/ARCM — Augmented MG and RCM, described in detail below. Notethat our FE estimator (like the OLS and FD-OLS) is augmented with T−1 year dummiessuch that it is in effect a ‘Two-Way Fixed Effects’ (2FE) estimator.

7We also applied an alternative estimator where the first stage allows for heterogeneousslopes across countries. Results for the AMG second stage are next to identical to thosepresented in Table 2.

8Empirical analysis in this paper is carried out using Stata 9 and 10, GAUSS 9 andWinRATS 6.2.

9Note that we obtain identical results for models in [1], [2] and [4] if we use data indeviation from the cross-sectional mean (results not presented) instead of using a set ofyear dummies. Replacing year dummies with cross-sectionally demeaned data is onlyvalid if parameters are homogeneous across countries (Pedroni, 1999, 2000).

10These graphs are ‘data-specific’: for years where data coverage is good, this can beinterpreted as ‘global’, whereas in later years (10 countries have data for 2001, only 2 for2002, omitted from the graph) this interpretation collapses. In the graph we omit thedata-point for 2002 for which there are only two observations.

11An alternative explanation may be that our variable deflation does not adequatelycapture all the price changes in general, and material input price changes vis-a-vis outputprices in particular, occurring in the post-oil shock periods.

12We do not use ‘demeaned’ data here, since cross-sectional demeaning is only validif all model parameters are homogeneous across countries, but creates bias in case ofparameter heterogeneity (Pedroni, 2000; Smith & Fuertes, 2007). If we apply ‘demeaned’data results are in line with our argument of heterogeneous factor loadings (see TechnicalAppendix).

13In case of the MG-type estimators these are computed from the standard errorsse(βMG) = [

∑i(βi− βMG)2]−1/2. For the Swamy estimators, see the footnote of the table

for details.

14Results presented are robust to alternative specifications for the country-level deter-ministics (additional squared trend in the levels models, additional trend in the modelsin first difference; results not reported).

15The statistically insignificant mean in all of the ‘augmented’ regressions (AMG,ARCM) is easily explained: these country-specific trends have positive and negativemagnitudes for different countries.

16As a further robustness test we also carried out pooled and country regressions adopt-ing a dynamic empirical specification — results do not change considerably in comparison

21

to the static analysis presented here, albeit with considerably reduced precision (see Tech-nical Appendix).

17Further tests for parameter heterogeneity (Phillips & Sul, 2003; Pesaran & Yamagata,2008) were considered but not pursued due to their low power in the present paneldimensions.

18For the analysis of other macroeconomic relationships it is also not uncommon to seethese estimators applied to annual data where T becomes moderate to large, despite thedifficulties arising from ‘overfitting’ (Bowsher, 2002; Roodman, 2009).

19The results applied are those presented in the lower panel of Table 2, column [4].

20Note that in our sample base- and final-year differ across countries (see Table A-IIin the Appendix).

21Issues of estimate precision could be addressed using bootstrapping to constructstandard errors.

22

Tables and Figures for main text

Table 1: Static pooled regressions

Panel (A): Unrestricted Returns to Scale

[1] [2] [3] [4]estimator POLS FE CCEP FD

dependent variable lY lY lY ∆lY

log labour 0.2100 0.4402 0.6009[12.08]∗∗ [17.43]∗∗ [19.48]∗∗

∆log labour 0.6849[7.43]∗∗

log capital 0.7896 0.7174 0.6144[67.34]∗∗ [32.17]∗∗ [22.76]∗∗

∆log capital 0.3463[3.40]∗∗

intercept 1.1510 -0.0470 -0.5160[7.99]∗∗ [0.13] [0.98]

CRS: F .96 .00 .00 .72FE: F .00 .00AR(1) .00 .00 .00 .00AR(2) .00 .00 .00 .01I(1) 1.00 1.00 .00 .00RMSE .462 .130 .102 .103

Panel (B): CRS imposed

[1] [2] [3] [4]estimator POLS FE CCEP FD

dependent variable ly ly ly ∆ly

log capital pw 0.7895 0.6752 0.5823[72.97]∗∗ [29.89]∗∗ [23.38]∗∗

∆log capital pw 0.3195[3.61]∗∗

intercept 1.1474 2.3786 0.2489[8.47]∗∗ [9.98]∗∗ [0.63]

FE: F .00 .00AR(1) .00 .00 .00 .00AR(2) .00 .00 .00 .01I(1) 1.00 .78 .00 .00RMSE .462 .135 .113 .103

Notes: Values in brackets are absolute t-statistics, based on White heteroskedasticity-consistent standarderrors. We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively. Regressions are forN = 48 countries, n = 1, 194 (n = 1, 128) observations in the levels (first difference) regressions. Dependentvariables: lY (ly) — log value-added (per worker), ∆lY(∆ly) — growth rate of value-added (per worker). Forthe CCEP estimator we include sets of cross-section period averages of value-added, labour, and capital stock(in the CRS equations the respective variables in per worker terms), all in logs (estimates not reported) — seePesaran (2006) for details. All other models include T − 1 year dummies in levels or FD (estimates notreported). For all diagnostic tests (except RMSE) we report p-values: (i) The null hypothesis for the Wald testsis constant returns. (ii) The F -tests in the FE and CCEP regressions reject the null that fixed effects do notdiffer across countries. (iii) The Arellano and Bond (1991) AR test on the residuals has the null of no serialcorrelation. (iv) ‘I(1)’ reports results for a Pesaran (2007) CIPS test with 2 lags, null of nonstationarity (fullresults: Technical Appendix, Table TA-5). (v) RMSE is the root mean squared error.

23

Table 2: Country regression averages (CRS imposed)

Panel (A): Models in Levels

[1] [2] [3] [4] [5]estimator MG AMG AMG CMG CMG

dependent variable ly ly-µva •t ly ly ly

log capital pw 0.1789 0.2896 0.2982 0.4663 0.3125[2.25]∗ [3.95]∗∗ [3.70]∗∗ [6.76]∗∗ [3.72]∗∗

common trend 0.8787[4.39]∗∗

country trend 0.0174 0.0001 0.0023 0.0108[5.95]∗∗ [0.04] [0.56] [3.09]∗∗

intercept 7.6528 6.3823 6.2431 0.8961 4.7860[9.05]∗∗ [8.42]∗∗ [7.40]∗∗ [0.89] [3.66]∗∗

Panel t-statistics, trends†capital pw 12.42 16.55 17.43 31.86 16.15country trend 27.65 20.40 12.12 16.08# of sign. trends (at 10%) 39 28 19 24DiagnosticsI(1) .00 .00 .00 .00 .00RMSE .100 .097 .091 .100 .088

Panel (B): Models in First Differences

[1] [2] [3] [4] [5]estimator ∆MG ∆AMG ∆AMG ∆CMG ∆CMGdep. var. ∆ly ∆ly-∆µva •t ∆ly ∆ly ∆ly

∆log capital pw 0.1642 0.2734 0.2834 0.3837 0.2577[1.91] [3.48]∗∗ [3.77]∗∗ [5.62]∗∗ [3.48]∗∗

common drift 1.0497- - [5.71]∗∗

country drift 0.0161 -0.0011 -0.0020 0.0123[5.54]∗∗ [0.44] [0.50] [3.76]∗∗

Panel t-statistics, trends†capital pw 4.81 8.30 7.66 12.00 7.18country trends 9.53 5.77 7.46 7.68# of sign. trends (at 10%) 14 6 10 11DiagnosticsI(1) .00 .00 .00 .02 .06RMSE .097 .094 .090 .090 .088

Notes: All variables are in logs. Dependent variable: ly — log value-added per worker. ∆ly — growth rate ofvalue-added (per worker). µva •t is derived from the year dummy coefficients of a pooled regression (CRSimposed) in first differences (FD-OLS) as described in the main text. Regressions are for N = 48 countries,n = 1, 194 (n = 1, 128) observations in the levels (first difference) regressions. We omit reporting the parameterson the cross-section averages for the CMG estimators (columns [4] and [5]) to save space. Values in brackets areabsolute t-statistics following Kapetanios et al. (2009). These were obtained by regressing the N countryestimates on an intercept term. We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗

respectively. ‘I(1)’ reports p-values for a Pesaran (2007) CIPS test with 2 lags, null of nonstationarity (fullresults: Technical Appendix, Table TA-6). RMSE is the root mean square error. † We report the Pedroni

(2000) panel-t statistics (1/√N)

∑i ti where ti is the country-specific t-statistic of the parameter estimate.

24

Table 3: Gengenbach, Urbain & Westerlund (2009) cointegration tests

ECM-based Cointegration Test

no intercept AIC BIC 10% 5% 1%τ ∗ (truncated) -2.58 ∗ -2.75 ∗∗ -2.48 -2.55 -2.67ω∗ (truncated) 25.66 ∗∗ 25.61 ∗∗ 12.10 12.43 13.07avg. lag length 2.0 1.7

intercept AIC BIC 10% 5% 1%τ ∗ (truncated) -2.63 -2.78 -2.86 -2.92 -3.03ω∗ (truncated) 17.04 ∗∗ 17.12 ∗∗ 14.08 14.42 15.04avg. lag length 2.3 1.7

intercept, trend AIC BIC 10% 5% 1%τ ∗ (truncated) -2.44 -2.61 -3.227 -3.282 -3.395ω∗ (truncated) 12.54 13.13 16.23 16.59 17.31avg. lag length 2.1 1.8

Notes: The τ∗ and ω∗ statistics are averages of the N t-ratios and F -statistics from the country ECMregressions, where extreme t-ratios/F -statistics have been replaced by bounds (truncated; we used ε = .000001)following the strategy devised in Gengenbach et al. (2009). This paper also provides simulated critical values wepresent here (N = 50). Both test statistics are one-sided: for the τ∗ large negative values lead to rejection ofthe null, whereas for the ω∗ it is large positive values which lead to rejection. H0 in all cases: no errorcorrection, i.e. no cointegration; lag-length pi determined using AIC or BIC as indicated.

25

Table 4: Country regressions using FMOLS

Panel A: Full Sample (N=48)

[1] [2] [3] [4] [5]estimator : FMOLS- MG AMG AMG CMG CMG

dependent variable ly ly-µ•,vat ly ly lylog capital pw 0.1663 0.2659 0.2937 0.5544 0.3042

[1.99] [3.32]∗∗ [3.18]∗∗ [8.05]∗∗ [3.33]∗∗

common process 0.8977[3.49]∗∗

country trends 0.0171 0.0004 0.0014 0.0108[5.50]∗∗ [0.12] [0.29] [2.95]∗∗

intercept -4.6095 6.5985 7.1405 5.6737 -1.6007[1.63] [2.69]∗∗ [1.52] [5.57]∗∗ [0.57]

Panel-t statistics, diagnosticscapital pw 18.29 14.73 15.36 40.59 15.88trends 24.94 18.93 12.71 20.70# of sign. trends (at 10%) 37 25 23 28RMSE .099 .096 .090 .103 .088

Panel B: I(1) Sample (N=26)

[1] [2] [3] [4] [5]estimator : FMOLS- MG AMG AMG CMG CMG

dependent variable ly ly-µ•,vat ly ly lylog capital pw 0.0816 0.2675 0.2784 0.5528 0.2485

[1.27] [4.11]∗∗ [3.08]∗∗ [7.38]∗∗ [3.13]∗∗

common process 0.8034[4.61]∗∗

country trends 0.0179 -0.0012 0.0019 0.0108[5.64]∗∗ [0.40] [0.41] [2.56]∗

intercept -4.9092 6.1012 5.2980 5.3936 -2.3070[1.59] [2.63]∗ [1.50] [4.60]∗∗ [0.76]

Panel-t statistics, diagnosticscapital pw 11.45 10.37 9.97 34.96 10.16trends 23.28 14.63 10.56 17.10# of sign. trends (at 10%) 23 15 15 16RMSE .071 .068 .065 .080 .062

Notes: The results in [1] are for the Pedroni (2000) Group-Mean FMOLS estimator; the results in theremaining columns allow for cross-section dependence using either µ•,vat or cross-section averages in the FMOLScountry regressions. In all cases the estimates presented are the unweighted means of the FMOLS countryestimates. Panel B uses observations from only those countries for which variables were determined to benonstationary (via ADF and KPSS testing).

26

Table 5: Country rankings by TFP-level

Comparison of Country Ranking across Estimators

Country Rank Absolute Rank Difference[1] [2] [3] abs([2]-[1]) abs([3]-[1]) abs([3]-[2])

Country FE AMG† CCE‡ AMG-FE CCE-FE CCE-AMG

AUS 12 14 13 2 1 1AUT 22 10 10 12 12 0BEL 24 12 12 12 12 0BGD 34 45 45 11 11 0BOL 4 29 23 25 19 6BRB 33 32 32 1 1 0CAN 6 5 4 1 2 1CHL 3 21 19 18 16 2COL 11 31 31 20 20 0CYP 20 28 29 8 9 1ECU 41 34 36 7 5 2EGY 48 44 44 4 4 0ESP 5 15 16 10 11 1FIN 14 7 6 7 8 1FJI 43 35 34 8 9 1FRA 18 8 7 10 11 1GBR 19 13 14 6 5 1GTM 17 30 30 13 13 0HUN 45 41 42 4 3 1IDN 44 47 48 3 4 1IND 46 48 47 2 1 1IRL 2 17 20 15 18 3IRN 23 23 24 0 1 1ISR 21 2 9 19 12 7ITA 15 4 3 11 12 1KOR 13 25 27 12 14 2LKA 31 46 46 15 15 0LUX 39 6 5 33 34 1MAR 32 42 39 10 7 3MEX 9 19 17 10 8 2MLT 8 38 38 30 30 0MYS 35 39 40 4 5 1NLD 27 9 8 18 19 1NOR 25 11 11 14 14 0NZL 29 16 15 13 14 1PAN 37 22 22 15 15 0PHL 30 37 35 7 5 2POL 47 40 41 7 6 1PRT 36 24 26 12 10 2SEN 38 27 28 11 10 1SGP 10 26 25 16 15 1SWE 16 3 2 13 14 1SWZ 40 43 43 3 3 0TUN 42 36 37 6 5 1TUR 7 18 18 11 11 0USA 1 1 1 0 0 0VEN 28 20 21 8 7 1ZWE 26 33 33 7 7 0

Median 10.3 10.1 1.0

Notes: The table provides the respective TFP level ranking (by magnitude) for each country derived from thethree regression models, as well as the absolute rank differences between them. † AMG refers to the AugmentedMean Group estimator, Table 2, upper panel, column [3]. ‡ CCE refers to the Pesaran (2006) CMG estimator,ibid. column [4]. The TFP-level adjustment in for both sets of estimates is detailed in Section 8.

27

Figure 1: Evolution of the ‘common dynamic process’ µ•t

0

.1

.2

.3

.4

.5

1970 1975 1980 1985 1990 1995 2000year

CRS imposed unrestricted

1973:Oil crisis

1979: Iranian Revolution

Late 1980s: Global Recession Sample size

drops

Notes: derived from results in column [4], Panels (A) and (B) of Table 1.

Figure 2: Regression intercepts and TFP level estimates

Korea's log(K/L) in 1970Malaysia'slog(K/L)in 1970

Malaysia

South Korea

8.5

9

9.5

10

10.5

11

9 10 11 12Capital stock per worker (in logs)

Belgium

Belgium'slog(K/L) in 1970

France

France's log(K/L) in 197010.2

10.4

10.6

10.8

11.4 11.8 12.2 12.6Capital stock per worker (in logs)

28

Figure 3: TFP levels — adjusted from AMG and CMG estimates∗

AMG(ii) CCE(i)

7.0 8.0 9.0 10.0 11.0 12.0

BGD

IND

LKA

POL

TUN

HUN

IDN

FJI

EGY

MAR

PHL

SWZ

GTM

ZWE

SEN

PAN

ECU

BOL

COL

MYS

PRT

CYP

KOR

CHL

MEX

IRN

VEN

TUR

NZL

ESP

BRB

SGP

ISR

NLD

AUS

AUT

GBR

NOR

SWE

BEL

LUX

ITA

FRA

IRL

CAN

USA

FIN

MLT

Final year TFP level (adjusted) Base-year TFP level (adjusted)

7.0 8.0 9.0 10.0 11.0 12.0

BGD

IND

LKA

POL

TUN

HUN

IDN

FJI

EGY

MAR

PHL

SWZ

GTM

ZWE

SEN

PAN

ECU

BOL

COL

MYS

PRT

CYP

KOR

CHL

MEX

IRN

VEN

TUR

NZL

ESP

BRB

SGP

ISR

NLD

AUS

AUT

GBR

NOR

SWE

BEL

LUX

ITA

FRA

IRL

CAN

USA

FIN

MLT

Final year TFP level (adjusted) Base-year TFP level (adjusted)

Notes: Models with CRS imposed. ∗AMG(ii) has µ•t included as additional regressor, CCE(i) refers to thestandard CMG estimator (see Table 2, columns [3] and [4]). Countries are ranked by AMG(ii) final periodTFP-level. Levels adjustment as described in the main text.

29

Appendix: Data construction and descriptives

Data for output, value-added, material inputs and investment in manufacturing, all incurrent local currency units (LCU), are taken from the UNIDO Industrial Statistics 2004(UNIDO, 2004), where material inputs were derived as the difference between output andvalue-added. The labour data series is taken from the same source, which covers 1963-2002. The capital stocks are calculated from investment data which has been transformedinto constant US$ (see below) following the ‘perpetual inventory’ method discussed inKlenow and Rodriguez-Clare (1997).

In order to make data in monetary values internationally comparable, it is necessary totransform all values into a common unit of analysis. We follow the transformations sug-gested by Martin and Mitra (2002) and derive all values in 1990 US$,22 using current LCUand exchange rate data from UNIDO, and GDP deflators from the UN Common Statis-tics database (UN, 2005), for which data are available from 1970-2003. Since our modelis for a small open economy, we prefer using a single market exchange rates (LCU-US$exchange rate for 1990) to purchasing-power-parity (PPP) adjusted exchange rates, sincethe latter are more appropriate when non-traded services need to be accounted.

The resulting panel is unbalanced and has gaps within individual country time-series. Wehave a total of n = 1, 194 observations (n = 1, 162 for the gross-output specification) fromN = 48 countries, which have a time-series dimension between T = 11 and T = 33, withaverage T = 24. Table A-I provides the descriptive statistics for the raw variables andvariables in logs used in our regressions, further country-specific information is containedin Table A-II.

As a robustness check we also produced a ‘cleaned’ dataset where we applied mechan-ical ‘cleaning rules’ in order to address the most serious issues of measurement error,23

which created a sample of n = 872 observations for N = 38 countries. The empiricalresults for this sample are surprisingly close to those from the larger sample (available onrequest).

30

Table A-I: Descriptive statistics

Variables in Level Terms

Variable obs mean median std. dev. min. max.levelsvalue-added 1,194 5.47E+10 9.04E+09 1.78E+11 1.76E+07 1.50E+12labour 1,194 1,469,186 502,214 2,924,524 5,552 1.97E+07capital 1,194 1.32E+11 2.61E+10 3.12E+11 5.78E+07 2.27E+12logsvalue-added 1,194 22.70 22.93 2.15 16.68 28.04labour 1,194 12.92 13.13 1.79 8.62 16.79capital 1,194 23.72 23.98 2.22 17.87 28.45annual growth ratevalue-added 1,128 3.9% 3.5% 12.3% -78.3% 92.7%labour 1,128 1.7% 0.7% 8.1% -38.8% 78.1%capital 1,128 4.1% 3.1% 4.4% -2.4% 47.8%

Variables in per worker terms

Variable obs mean median std. dev. min. max.levelsvalue-added 1,194 76,932 45,865 72,843 2,007 346,064capital 1,194 25,305 17,867 19,385 1,660 91,011logsvalue-added 1,194 9.78 9.79 0.92 7.41 11.42capital 1,194 10.80 10.73 1.00 7.60 12.75annual growth ratevalue-added 1,128 2.2% 2.5% 10.8% -90.3% 74.4%capital 1,128 2.5% 2.5% 7.9% -68.0% 45.4%

Notes: We report the descriptive statistics for value-added, labour and capital stock for N = 48 countries andn = 1, 194 (n = 1, 128) observations in the levels (growth) specification. Monetary values are in real US$ (baseyear 1990). Labour is in number of workers.

31

Table A-II: Sample of countries and number of observations

Sample

Country Code levels FD t = 1 t = T I(1)∗

Australia AUS 20 17 1970 1993 XAustria AUT 30 28 1970 2000 XBelgium BEL 28 27 1970 1997 XBangladesh BGD 14 12 1970 1992 XBolivia BOL 11 10 1987 1997Barbados BRB 26 25 1970 1995Canada CAN 21 20 1970 1990 XChile CHL 25 24 1974 1998 XColombia COL 30 29 1970 1999 XCyprus CYP 33 32 1970 2002 XEcuador ECU 30 29 1970 1999Egypt EGY 26 25 1970 1995Spain ESP 26 25 1970 1995Finland FIN 28 26 1970 2000 XFiji FJI 25 24 1970 1994 XFrance FRA 26 25 1970 1995United Kingdom GBR 23 22 1970 1992 XGuatemala GTM 16 15 1973 1988 XHungary HUN 26 25 1970 1995Indonesia IDN 26 25 1970 1995 XIndia IND 32 31 1970 2001Ireland IRL 22 21 1970 1991Iran IRN 24 22 1970 2001Israel ISR 13 12 1989 2001Italy ITA 31 30 1970 2000Korea KOR 32 31 1970 2001Sri Lanka LKA 20 17 1970 2000 XLuxembourg LUX 23 22 1970 1992 XMorocco MAR 17 16 1985 2001 XMexico MEX 16 14 1984 2000 XMalta MLT 32 31 1970 2001 XMalaysia MYS 28 25 1970 2001Netherlands NLD 24 23 1970 1993 XNorway NOR 32 31 1970 2001 XNew Zealand NZL 21 20 1970 1990Panama PAN 30 28 1970 2000Philippines PHL 26 25 1970 1995Poland POL 31 30 1970 2000 XPortugal PRT 31 30 1970 2000 XSenegal SEN 17 14 1970 1990Singapore SGP 33 32 1970 2002 XSweden SWE 18 17 1970 1987 XSwaziland SWZ 24 22 1970 1995Tunisia TUN 21 19 1970 1997Turkey TUR 27 25 1970 1997United States USA 26 25 1970 1995 XVenezuela VEN 26 24 1970 1998 XZimbabwe ZWE 27 26 1970 1996Obs 1,194 1,128 644

Notes: ∗This refers to the sample used in Section 7.

32

Technical Appendix — Not intended for publication

Time-series properties of the data

Since the time dimension of the panel is sizeable (T = [11, 33], average T = 24), wecarry out Augmented Dickey and Fuller (1979) (ADF), Phillips and Perron (1988) (PP)and Kwiatkowski, Phillips, Schmidt, and Shin (1992) (KPSS) tests for the variable serieswithin each individual country.24 The results are shown in Table TA-1: we report theshare of countries (in %) for which the null hypothesis (stationarity or nonstationarityas indicated) is rejected. For the majority of countries the ADF and PP tests cannotreject nonstationarity, whereas the majority of country KPSS tests reject the null of levelstationarity — these results are stronger for variables in per worker terms than for thosein levels. The overall pattern of test results is reversed when we run ADF and KPSStests on variables in first-difference, indicating ‘difference-stationarity’.

Our dataset is an unbalanced panel with missing observations — properties that mayaffect the unit root tests. We carried out ADF tests for the altered dataset (levels, firstdifferences) where we replace gaps with the last known observation. Simulations by Ryanand Giles (1998) suggest that this procedure yields more powerful unit root tests in com-parison with those where gaps were ignored (regular Dickey-Fuller critical values remainvalid). We obtaine very similar patterns of rejection as when testing original data withgaps (not reported).

Given the well-known low power of single unit-root tests, we next apply panel tests tothe data. Note here that rejection of the unit root null hypothesis does not imply thatthe panel is stationary, but rather that the variable series does not follow a unit rootprocess in all countries. We first present the results for a test by Im et al. (1997) andthe Maddala and Wu (1999) panel unit root test, both of which do not account for cross-sectional dependence in the variables. Results in Table TA-2 show that for the variableseries in ‘levels’ these tests cannot agree on the level of integration prevalent in the data.For the per worker variable series, however, neither test can reject the null hypothesisthat all countries have I(1) series.

Over the past decade panel unit root tests which explicitly allow for cross-sectional de-pendence in the variable series have been developed. Here we implement the Pesaran(2007) CIPS test which in analogy to the CCE estimators augments the ADF equationwith cross-section averages. In most cases these testing procedures cannot reject the nullof nonstationarity once we account for serial correlation in the data. If we apply theCIPS test to data in first differences, we reject nonstationarity throughout if we augmentwith up to two lags (or none); for more lags the p-value for most variable tests jumps tounity (not reported).

i

Table TA-1: Time-series unit root tests — rejection frequency

Unit root testsshare of country tests which reject H0 (stationarity or nonstationarity as indicated);

no adjustment for cross-sectional dependence

Testing for levels-stationarity

Test H0 H1 variable output value-added labour capital materialsvariables in levels

ADF without trend nonstationary levels-stationary 17% 21% 21% 10% 19%PP without trend nonstationary levels-stationary 19% 10% 17% 17% 17%KPSS without trend levels-stationary nonstationary 85% 81% 73% 98% 79%

variables in levels (in per worker terms)ADF without trend nonstationary levels-stationary 4% 8% 6% 2%PP without trend nonstationary levels-stationary 8% 17% 8% 10%KPSS without trend levels-stationary nonstationary 77% 69% 71% 77%

Testing for trend-stationarity

Test H0 H1 variable output value-added labour capital materialsvariables in levels

ADF with trend nonstationary trend-stationary 21% 29% 19% 31% 25%PP with trend nonstationary trend-stationary 15% 10% 10% 4% 10%KPSS with trend trend-stationary nonstationary 31% 25% 42% 46% 31%

variables in levels (in per worker terms)ADF with trend nonstationary trend-stationary 23% 25% 31% 25%PP with trend nonstationary trend-stationary 27% 13% 6% 15%KPSS with trend trend-stationary nonstationary 31% 23% 31% 27%

Testing for difference-stationarity

Test H0 H1 variable output value-added labour capital materialsvariables in first differences

ADF with drift nonstationary stationary 94% 85% 90% 83% 88%PP with drift nonstationary stationary 90% 94% 71% 29% 90%KPSS with drift stationary nonstationary 4% 0% 4% 10% 2%

variables in first differences (in per worker terms)ADF with drift nonstationary stationary 94% 90% 83% 83%PP with drift nonstationary stationary 96% 94% 75% 94%KPSS with drift stationary nonstationary 2% 2% 2% 4%

Notes: All variables are in logs. We report the share of countries (out of N = 48) for which the respective unit root test is rejected atthe 5% level of significance. All unit root tests for variables in levels contain an intercept term in the estimating equation. ADF refers tothe augmented Dickey-Fuller test, which has the null of nonstationarity. PP refers to the Phillips and Perron (1988) unit root test, whichhas the null of nonstationarity. KPSS refers to the Kwiatkowski et al. (1992) unit root test, which has the null of (trend-)stationarity.Lag-augmentation or bandwidth selection in these tests to account for serial correlation in the variables is allowed to vary by country.For the ADF test we determined ‘ideal’ lag-augmentation using the Akaike Information Criterion (AIC). The PP test uses

int(4(T/100)2/9) lags throughout, for the KPSS tests an automated bandwidth selection following Hobijn et al. (1998) is used. For thelatter we use the kpss command in Stata written by Kit Baum.

ii

Table TA-2: First generation panel unit root tests

Im, Pesaran & Shin (1997) panel unit root tests — IPS]

H0: unit root process (reject reported); augmentation with country-specific lag length (average reported)

output value-added labour capital materialslags [t-bar] lags [t-bar] lags [t-bar] lags [t-bar] lags [t-bar]1.42 -1.57 1.96 -1.54 1.48 -1.78 reject 1.50 -1.92 reject 1.65 -1.67

output/worker VA/worker capital/worker materials/workerlags [t-bar] lags [t-bar] lags [t-bar] lags [t-bar]1.44 -0.92 1.65 -1.03 1.71 -0.97 1.83 -1.05

Maddala and Wu (1999) panel unit root tests — MW]

H0: unit root process; augmentation with lags as indicated;

output value-added labour capital materialslags pλ (p) lags pλ (p) lags pλ (p) lags pλ (p) lags pλ (p)0 129.37 (.01) 0 125.69 (.02) 0 142.42 (.00) 0 274.01 (.00) 0 126.47 (.02)1 126.57 (.02) 1 109.99 (.16) 1 141.35 (.00) 1 67.05 (.99) 1 133.62 (.01)1.42 69.12 (.98) 1.96 85.44 (.77) 1.48 114.54 (.10) 1.50 55.16 (1.00) 1.65 66.65 (.99)2 114.75 (.09) 2 124.13 (.03) 2 105.34 (.24) 2 80.86 (.87) 2 134.85 (.01)3 74.36 (.95) 3 56.97 (1.00) 3 88.76 (.69) 3 87.84 (.71) 3 108.31 (.18)

output/worker VA/worker capital/worker materials/workerlags pλ (p) lags pλ (p) lags pλ (p) lags pλ (p)0 107.76 (.19) 0 102.23 (.31) 0 54.16 (1.00) 0 102.35 (.31)1 70.70 (.98) 1 84.92 (.78) 1 60.09 (1.00) 1 77.74 (.91)1.44 30.08 (1.00) 1.65 63.13 (1.00) 1.71 32.32 (1.00) 1.83 32.45 (1.00)2 75.85 (.94) 2 65.26 (.99) 2 34.04 (1.00) 2 77.85 (.91)3 61.41 (1.00) 3 44.65 (1.00) 3 66.85 (.99) 3 87.42 (.72)

Notes: ] All variables are in logs. The IPS(i) and MW statistics are constructed as t-bar = N−1 ∑i ti and

pλ = −2∑i log(pi) respectively, where ti are the country ADF statistics and pi corresponding p-values. For the IPS(i) the

critical values (-1.73 for 5%, -1.69 for 10% significance level — distribution is approximately t) are reported in Table 2,

Panel A of their paper. For the MW test the critical values are distributed χ2(2N). IPS(i) uses ‘ideal’ lag-length asdetermined via the AIC (see notes Table TA-1).

Table TA-3: Second generation panel unit root tests

Pesaran (2007) panel unit root tests — CIPS]

H0: unit root process; augmentation with lags as indicated

output value-added labour capital materialslags Z[t-bar] (p) lags Z[t-bar] (p) lags Z[t-bar] (p) lags Z[t-bar] (p) lags Z[t-bar] (p)0 -1.22 (.11) 0 -1.85 (.03) 0 2.39 (.99) 0 5.11 (1.00) 0 0.29 (.62)1 0.01 (.51) 1 0.06 (.52) 1 1.26 (.90) 1 3.79 (1.00) 1 0.89 (.81)1.42 1.13 (.87) 1.96 3.54 (1.00) 1.48 3.74 (1.00) 1.50 4.55 (1.00) 1.65 3.68 (1.00)2 2.65 (1.00) 2 2.30 (.99) 2 4.21 (1.00) 2 3.96 (1.00) 2 1.05 (.85)3 7.04 (1.00) 3 3.59 (1.00) 3 4.76 (1.00) 3 7.64 (1.00) 3 4.21 (1.00)

output/worker VA/worker capital/worker materials/workerlags Z[t-bar] (p) lags Z[t-bar] (p) lags Z[t-bar] (p) lags Z[t-bar] (p)0 -1.08 (.14) 0 -2.55 (.01) 0 1.92 (.97) 0 0.57 (.72)1 2.91 (1.00) 1 -0.73 (.23) 1 1.33 (.91) 1 3.74 (1.00)1.44 5.98 (1.00) 1.65 3.77 (1.00) 1.71 5.92 (1.00) 1.83 9.62 (1.00)2 5.02 (1.00) 2 2.37 (.99) 2 4.60 (1.00) 2 5.96 (1.00)3 8.73 (1.00) 3 5.48 (1.00) 3 7.34 (1.00) 3 8.08 (1.00)

Notes: ] All variables are in logs. In the third row for each variable in the lower panel we present the CIPS test statisticfor ‘ideal’ lag augmentation of the underlying ADF regression (based on Akaike information criteria); the value for lagsreported here is the average across countries.

iii

Kernel density plots for capital coefficient estimates

Figure TA-1: Kernel densities for technology parameter estimates (VA)

capital coeff.

beta mean: .270

0

.5

1

-1 -.5 0 .5 1 1.5

kernel = epanechnikov, bandwidth = 0.1374

[2] RCM (CRS)

capital coeff.

beta mean: .179

0

.2

.4

.6

.8

-2 -1 0 1 2


[1] MG (CRS)

capital coeff.

beta mean: .290

0

.2

.4

.6

.8

1

-2 -1 0 1 2


[3] AMG (i) (CRS)

capital coeff.

beta mean: .298

0

.2

.4

.6

.8

-2 -1 0 1 2


[4] AMG (ii) (CRS)

capital coeff.

beta mean: .466

0

.2

.4

.6

.8

1

-1 -.5 0 .5 1 1.5


[5] CCEMG (i) (CRS)

capital coeff.

beta mean: .313

0

.2

.4

.6

.8

1

-2 -1 0 1 2


[6] CCEMG (ii) (CRS)

capital coeff.

beta mean: .356

0

.5

1

1.5

-.5 0 .5 1 1.5


[7] ARCM (i) (CRS)

capital coeff.

beta mean: .353

0

.5

1

-.5 0 .5 1 1.5


[8] ARCM (ii) (CRS)

Notes: Each plot shows the kernel density of the capital coefficientsfrom the country regressions (value-added specification, CRS imposed,see Table 2 in the paper). Dashed line: normal distribution, verticalline: parameter mean.

iv

Residual diagnostics

The nature of our data prevents us from implementing a number of specification testsfrom the nonstationary panel econometric literature: firstly, existing procedures used toinvestigate cross-section dependence (PCA, mean absolute correlation, Pesaran (2004)CD statistic for residual diagnostics) rely on fairly balanced panels without missing ob-servations. Secondly, standard residual-based panel cointegration tests (Pedroni, 1999,2004) need to be adjusted for cross-section dependence and perform relatively poorly inmoderate T panels. We therefore opt for an error-correction model-based test suggestedby Gengenbach et al. (2009). Prior to this we resort to a mix of standard diagnostictests for pooled regression residuals and construct test statistics for country regressionresiduals following Fisher (1932).25

We begin with normality and homoskedasticity tests for regression residuals in Table TA-4. Using the D’Agostino, Balanger, and D’Agostino Jr. (1990) and Cameron and Trivedi(1990) tests virtually all of our pooled regression results reject the joint null hypothesisof normal, and normal and homoskedastic residuals respectively. In contrast the countryregression residuals can be assumed as jointly normal or jointly normal and homoskedas-tic, based on the respective Fisher statistics (pλ).

Tables TA-5 and TA-6 present panel unit root test results for pooled regression andcountry regression errors respectively. This analysis broadly suggests that residuals fromPOLS and FE are likely to be nonstationary. Country regression residuals are more likelyto be stationary across all specifications: nonstationarity is rejected for up to 4 lags inthe first generation Maddala and Wu (1999) test, and still for up to 3 lags in the Pesaran(2007) CIPS test (CIPS∗).

v

Table TA-4: Testing Residuals for Normality and Homoskedasticity

Regression residuals — normality, homoskedasticity]

H0 for respective test statistics: no heteroskedasticity, regular skewness, regular kurtosis;[

we report the χ2 or the Fisher pλ statistic and corresponding p-values

Cameron & Trivedi tests D’Agostino et al normality testPooled regression residuals: Gross output specifications (CRS)†

Joint test Heterosked. Skewness Kurtosis Joint test Skewness Kurtosisχ2 p χ2 p χ2 p χ2 p χ2 p p p

POLS 176.1 .01 139.5 .01 36.4 .36 0.2 .64 33.6 .00 .04 .00FE 1355.6 .01 1162.0 .49 180.2 .00 13.4 .00 69.2 .00 .00 .00CCEP - - - - - - - - 106.2 .00 .12 .00FD-OLS 541.3 .00 491.9 .00 43.1 .11 6.3 .01 214.2 .00 .00 .00

Pooled regression residuals: Value-added specifications (CRS)†Joint test Heterosked. Skewness Kurtosis Joint test Skewness Kurtosisχ2 p χ2 p χ2 p χ2 p χ2 p p p

POLS 194.3 .00 95.4 .01 95.3 .00 3.6 .06 51.2 .00 .00 .16FE 1324.2 .16 1194.0 .49 98.1 .08 32.2 .00 53.0 .00 .00 .00CCEP - - - - - - - - 84.7 .00 .12 .00FD-OLS 281.7 .00 237.2 .00 36.8 .26 7.8 .01 279.4 .00 .00 .00

Cameron & Trivedi tests D’Agostino et al normality testCountry regression residuals: Gross output specifications (CRS)†

Joint test Heterosked. Skewness Kurtosis Joint test Skewness Kurtosispλ p pλ p pλ p pλ p pλ p pλ p pλ p

MG 80.0 .88 70.4 .98 69.0 .98 39.7 1.00 51.0 1.00 55.4 1.00 43.2 1.00AMG(i) 81.7 .85 70.9 .97 67.5 .99 41.8 1.00 46.0 1.00 47.7 1.00 41.8 1.00AMG(ii) 64.7 .99 56.7 1.00 59.0 1.00 42.9 1.00 48.7 1.00 50.6 1.00 43.9 1.00CMG(i) 46.5 1.00 44.5 1.00 42.3 1.00 50.7 1.00 45.2 1.00 41.0 1.00 46.5 1.00CMG(ii) 41.7 1.00 39.0 1.00 47.7 1.00 43.9 1.00 34.4 1.00 32.4 1.00 39.8 1.00

Country regression residuals: Value-added specifications (CRS)†Joint test Heterosked. Skewness Kurtosis Joint test Skewness Kurtosispλ p pλ p pλ p pλ p pλ p pλ p pλ p

MG 93.6 .55 83.8 .81 72.3 .97 43.5 1.00 56.2 1.00 57.6 1.00 47.2 1.00AMG(i) 97.3 .44 80.1 .88 81.9 .85 46.6 1.00 56.0 1.00 57.0 1.00 47.2 1.00AMG(ii) 81.4 .86 71.9 .97 63.8 1.00 50.0 1.00 52.4 1.00 54.2 1.00 46.7 1.00CMG(i) 96.8 .46 71.8 .97 86.1 .76 43.0 1.00 58.7 1.00 63.4 1.00 45.3 1.00CMG(ii) 65.7 .99 59.4 1.00 56.1 1.00 43.9 1.00 51.6 1.00 51.0 1.00 47.6 1.00

Notes: ] We report heteroskedasticity and normality test statistics for residual series from(a) pooled estimators: POLS — pooled OLS, FE — pooled OLS with N country dummies, CCEP — Pesaran (2006) common correlatedeffects estimator (pooled version), FD-OLS — pooled OLS with variables in first differences; POLS, FE and FD-OLS are augmented withT − 1 year dummies; the regression results from which these residuals are taken are presented in Table ??; and(b) heterogeneous parameter estimators: MG — Pesaran and Smith (1995) Mean Group estimator, AMG(i) — Augmented Mean Groupestimator (µ•t imposed with unit coefficient), AMG(ii) — dto. (µ•t included as additional regressor), CMG(i) — Pesaran (2006) commoncorrelated effects estimator (mean group version), CMG(ii) — dto. with additional country trend; MG, AMG(i), AMG(ii), and CMG(ii)contain country-specific trend terms; the regression results from which these residuals are taken are presented in Table 2.The Cameron and Trivedi (1990) decomposition test analyses residual heteroskedasticity, skewness and kurtosis. The D’Agostino et al.(1990) test investigates skewness and kurtosis. Both tests provide joint hypothesis tests. If a test rejects skewness or kurtosis we can nolonger assume normality for the residual distribution.[ ‘Regular’ in this case is taken to mean in line with the normal distribution.† For the pooled regressions we report χ2 statistics and corresponding p-values. For the country regression we compute the Fisherstatistic pλ = −2

∑i log(pi), where pi is the p-value of the country-specific test statistic. The Fisher statistic pλ is distributed χ2(2N).

vi

Table TA-5: Testing Residuals for Stationarity (i)

Pooled regression residuals — stationarity tests]

H0 for each test: nonstationary residual series;[

Maddala and Wu (1999) (MW) and Pesaran (2007) (CIPS) test results;CIPS∗ does not apply cross-sectional demeaning prior to the testing procedure

Residuals from gross output specifications (CRS imposed)†lags: 0 lags: 1 lags: 2 lags: 3 lags: 4

MW pλ p pλ p pλ p pλ p pλ pPOLS 193.16 .00 169.00 .00 91.82 .60 105.65 .24 110.42 .15FE 188.54 .00 216.55 .00 127.73 .02 129.72 .01 98.44 .41CCEP 397.64 .00 370.93 .00 203.45 .00 148.20 .00 155.512 .00FD-OLS 1164.92 .00 632.24 .00 393.81 .00 297.95 .00 140.95 .00CIPS Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pPOLS -1.88 .03 -0.36 .36 1.27 .90 4.22 1.00 6.33 1.00FE -1.49 .07 -0.61 .27 1.65 .95 3.98 1.00 6.80 1.00CCEP -10.08 .00 -8.23 .00 -4.12 .00 2.40 1.00 7.08 1.00FD-OLS -20.88 .00 -10.26 .00 -1.47 .07 3.97 1.00 8.89 1.00CIPS∗ Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pPOLS -2.32 .01 -1.41 .08 1.51 .93 1.19 .88 3.09 1.00FE -1.98 .02 -2.00 .02 1.39 .92 2.86 1.00 4.21 1.00CCEP -10.08 .00 -8.23 .00 -4.12 .00 2.40 .99 7.08 1.00FD-OLS -22.28 .00 -14.19 .00 -8.51 .00 -5.00 .00 1.72 .96

Residuals from value-added specifications (CRS imposed)†lags: 0 lags: 1 lags: 2 lags: 3 lags: 4

MW pλ p pλ p pλ p pλ p pλ pPOLS 151.96 .00 176.19 .00 108.60 .18 74.32 .95 72.70 .96FE 146.64 .00 140.02 .00 94.70 .52 72.66 .96 92.21 .59CCEP 323.84 .00 306.74 .00 196.42 .00 136.74 .00 127.54 .02FD-OLS 2033.95 .00 1142.64 .00 580.42 .00 455.09 .00 314.48 .00CIPS Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pPOLS -0.96 .17 0.52 .70 3.59 1.00 8.14 1.00 9.82 1.00FE -1.76 .04 -1.13 .13 0.78 .78 5.17 1.00 6.53 1.00CCEP -8.32 .00 -7.53 .00 -2.74 .00 1.41 .92 8.26 1.00FD-OLS -27.11 .00 -20.16 .00 -6.73 .00 -1.17 .12 4.23 1.00CIPS∗ Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pPOLS -1.34 .09 -1.53 .06 1.67 .95 3.81 1.00 4.81 1.00FE -1.18 .12 -0.44 .33 2.28 .99 4.40 1.00 4.96 1.00CCEP -8.32 .00 -7.53 .00 -2.74 .00 1.41 .92 8.26 1.00FD-OLS -28.18 .00 -20.99 .00 -12.63 .00 -8.92 .00 -1.35 .09

Notes: † We apply the Pesaran (2007) (CIPS) and Maddala and Wu (1999) (MW) panel unit root tests; theformer accounts for possible cross-section dependence in the variable tested (here: regression residuals). We alsopresent the results for the CIPS where cross-sectional demeaning of the data prior to the testing procedure isprevented (marked as CIPS∗).See Table TA-4 for a description of the regressions from which these residuals are taken.

vii

Table TA-6: Testing Residuals for Stationarity (ii)

Country regression residuals — stationarity tests]

H0 for each test: nonstationary residual series;[

Maddala and Wu (1999) (MW) and Pesaran (2007) (CIPS) test results;CIPS∗ does not apply cross-sectional demeaning prior to the testing procedure

Gross output specifications (CRS)†lags: 0 lags: 1 lags: 2 lags: 3 lags: 4

MW pλ p pλ p pλ p pλ p pλ pMG 429.01 .00 386.48 .00 227.16 .00 166.57 .00 138.59 .00RCM 384.54 .00 359.93 .00 211.93 .00 154.20 .00 127.73 .02AMG(i) 444.71 .00 388.14 .00 251.08 .00 168.88 .00 132.25 .01AMG(ii) 551.52 .00 468.54 .00 299.32 .00 195.87 .00 145.25 .00CMG(i) 581.95 .00 585.88 .00 329.75 .00 285.80 .00 201.71 .00CMG(ii) 699.77 .00 624.26 .00 330.92 .00 242.79 .00 177.41 .00ARCM(i) 397.22 .00 355.32 .00 226.16 .00 145.11 .00 127.07 .02ARCM(ii) 485.06 .00 444.00 .00 275.65 .00 176.20 .00 132.18 .01CIPS Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pMG -9.63 .00 -9.28 .00 -2.65 .00 0.96 .83 8.05 1.00RCM -9.07 .00 -8.99 .00 -1.85 .03 1.10 .86 7.25 1.00AMG(i) -10.15 .00 -9.94 .00 -5.18 .00 1.62 .95 7.69 1.00AMG(ii) -12.23 .00 -11.32 .00 -5.62 .00 0.14 .56 5.63 1.00CMG(i) -12.88 .00 -11.18 .00 -5.61 .00 0.37 .65 8.03 1.00CMG(ii) -15.28 .00 -11.66 .00 -4.62 .00 0.49 .69 7.45 1.00ARCM(i) -9.35 .00 -8.20 .00 -4.37 .00 2.61 1.00 7.74 1.00ARCM(ii) -11.39 .00 -10.98 .00 -6.10 .00 0.66 .74 5.72 1.00CIPS∗ Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pMG -10.17 .00 -8.95 .00 -4.76 .00 -2.47 .01 0.42 .66RCM -9.18 .00 -8.31 .00 -4.25 .00 -2.07 .02 0.76 .78AMG(i) -10.69 .00 -9.09 .00 -5.48 .00 -2.79 .00 -0.14 .45AMG(ii) -13.35 .00 -11.26 .00 -7.05 .00 -3.66 .00 -0.35 .36CMG(i) -14.15 .00 -13.28 .00 -7.93 .00 -6.08 .00 -2.25 .01CMG(ii) -16.60 .00 -14.48 .00 -8.23 .00 -5.37 .00 -1.67 .05ARCM(i) -9.73 .00 -8.22 .00 -4.62 .00 -1.80 .04 0.25 .60ARCM(ii) -11.98 .00 -10.61 .00 -6.22 .00 -2.82 .00 0.21 .58

Value-added specifications (CRS)†lags: 0 lags: 1 lags: 2 lags: 3 lags: 4

MW pλ p pλ p pλ p pλ p pλ pMG 360.10 .00 365.52 .00 236.82 .00 274.77 .00 136.90 .00RCM 336.11 .00 349.73 .00 227.42 .00 285.17 .00 132.23 .01AMG(i) 351.49 .00 347.73 .00 234.17 .00 160.73 .00 134.66 .01AMG(ii) 434.12 .00 403.79 .00 254.07 .00 172.11 .00 137.53 .00CMG(i) 399.32 .00 393.45 .00 270.81 .00 176.23 .00 149.47 .00CMG(ii) 482.29 .00 440.86 .00 271.00 .00 184.36 .00 165.30 .00ARCM(i) 330.71 .00 327.87 .00 217.22 .00 148.04 .00 176.24 .00ARCM(ii) 384.88 .00 362.08 .00 224.68 .00 159.38 .00 162.32 .00CIPS Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pMG -8.22 .00 -7.64 .00 -3.90 .00 0.56 .71 7.78 1.00RCM -7.83 .00 -6.98 .00 -3.72 .00 0.50 .69 7.56 1.00AMG(i) -8.97 .00 -7.19 .00 -2.90 .00 2.59 1.00 7.90 1.00AMG(ii) -10.98 .00 -9.86 .00 -4.77 .00 1.25 .89 7.60 1.00CMG(i) -9.20 .00 -9.08 .00 -3.90 .00 1.96 .97 8.62 1.00CMG(ii) -11.78 .00 -9.57 .00 -4.05 .00 1.54 .94 6.26 1.00ARCM(i) -8.55 .00 -7.32 .00 -2.93 .00 1.50 .93 6.98 1.00ARCM(ii) -10.35 .00 -9.13 .00 -4.72 .00 2.43 .99 7.35 1.00CIPS∗ Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] p Z[t-bar] pMG -8.72 .00 -8.50 .00 -5.12 .00 -3.31 .00 0.01 .50RCM -8.18 .00 -8.07 .00 -4.82 .00 -2.91 .00 0.40 .65AMG(i) -8.72 .00 -8.13 .00 -4.87 .00 -2.14 .02 -0.12 .45AMG(ii) -10.60 .00 -9.76 .00 -5.83 .00 -2.45 .01 0.20 .58CMG(i) -9.59 .00 -8.97 .00 -5.96 .00 -2.35 .01 -0.03 .49CMG(ii) -11.78 .00 -10.45 .00 -6.26 .00 -3.35 .00 -1.21 .11ARCM(i) -8.23 .00 -7.55 .00 -4.35 .00 -1.48 .07 -0.14 .44ARCM(ii) -9.59 .00 -8.61 .00 -4.78 .00 -1.68 .05 0.16 .57

Notes: See Table TA-5 for details.

viii

Country regressions with unrestricted returns to scale

Table TA-7: Country regressions in levels (unrestricted returns to scale)

Country regressions in levelsstatic specification, no restriction on returns to scale; estimates presented are unweighted means of the country coefficients

(i) Gross output regressions

[1] [2] [3] [4] [5] [6] [7] [8]estimator MG RCM AMG AMG CMG CMG ARCM ARCM

dependent variable] lO lO lO-µ•t lO lO lO lO-µ•t lO

regressorslabour 0.2143 0.1908 0.1815 0.1806 0.2004 0.2226 0.1677 0.1690

[5.54]∗∗ [4.62]∗∗ [5.44]∗∗ [4.80]∗∗ [6.86]∗∗ [6.83]∗∗ [4.67]∗∗ [4.22]∗∗

capital 0.1206 0.0860 0.1794 0.1969 0.0764 -0.0017 0.1361 0.1250[0.82] [0.57] [1.43] [1.33] [1.11] [0.02] [1.06] [0.82]

materials 0.7315 0.7464 0.7474 0.7380 0.7172 0.7210 0.7627 0.7570[26.05]∗∗ [24.90]∗∗ [27.95]∗∗ [25.31]∗∗ [24.53]∗∗ [27.93]∗∗ [26.75]∗∗ [24.51]∗∗

common process 0.9259 0.9279[3.44]∗∗ [3.21]∗∗

country trend 0.0040 0.0024 -0.0004 0.0005 0.0045 -0.0018 -0.0007[1.36] [0.78] [0.15] [0.16] [1.44] [0.60] [0.20]

intercept 0.9570 1.7807 -0.4315 -0.7703 1.3273 2.7179 0.5327 0.8579[0.27] [0.48] [0.14] [0.21] [0.81] [1.08] [0.17] [0.23]

Returns to scaleCRS test (p) 0.24 (.63) 0.03 (.87) 0.82 (.36) 0.61 (.43) 0.01 (.92) 0.35 (.55) 0.29 (.59) 0.11 (.74)

Panel t-statistics, trendslabour 19.03 21.05 17.1 16.57 17.09 16.83 19.92 19.33capital 3.50 4.53 6.76 5.69 13.74 1.75 8.33 6.87materials 103.31 110.20 111.30 104.13 89.71 80.90 118.91 115.95country trends 20.60 19.49 18.65 15.16 14.28 17.36 14.60# of sign. trends (at 10%) 27 27 27 23 26 27 25

VA-equivalent coefficients‡labour (VA) mean 0.798 0.752 0.719 0.689 0.709 0.798 0.707 0.696

[7.25]∗∗ [5.90]∗∗ [7.51]∗∗ [6.82]∗∗ [7.59]∗∗ [9.35]∗∗ [6.23]∗∗ [5.82]∗∗

capital (VA) mean 0.449 0.339 0.710 0.751 0.270 -0.006 0.574 0.514[0.84] [0.58] [1.50] [1.43] [1.18] [0.02] [1.09] [0.86]

obs (countries) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48)

(ii) Value-added regressions


dependent variable] lY lY lY-µva •t lY lY lY lY-µva •t lY


[8.80]∗∗ [7.82]∗∗ [8.79]∗∗ [8.70]∗∗ [7.19]∗∗ [8.83]∗∗ [7.93]∗∗ [8.01]∗∗

capital 0.1770 0.3074 0.3216 0.3453 0.5179 0.3144 0.4201 0.4295[0.68] [1.15] [1.47] [1.52] [5.13]∗∗ [1.18] [1.85] [1.81]

common trend 1.0254 0.9019[5.27]∗∗ [4.14]∗∗

country trend 0.0105 0.0094 -0.0066 -0.0077 0.0090 -0.0069 -0.0053[1.53] [1.30] [0.91] [0.96] [0.81] [0.91] [0.62]

intercept 8.5557 5.6880 6.5479 6.0760 -0.0126 4.8980 4.2023 3.9300[1.48] [0.95] [1.34] [1.19] [0.01] [0.88] [0.83] [0.74]


Panel t-statistics, trendslabour 30.2 34.0 27.2 26.7 26.5 27.0 31.3 31.3capital 7.2 9.3 10.2 9.7 26.5 9.9 12.2 11.8country trends 20.2 19.5 16.8 14.9 18.8 16.3 13.6# of sign. trends (at 10%) 24 28 25 20 30 25 22

obs (countries) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48)

Notes: We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively. All variables are in logs.Dependent variable: lO — log output, lY — log value-added. µ•t and µ

•,vat are derived from the year dummy coefficients of a

pooled regression (no restriction on returns to scale) in first differences (FD-OLS) as described in the text. We omit reportingthe parameters on the cross-section averages for the CMG estimators (columns [5] and [6]) to save space.Values in parentheses are absolute t-statistics.] We subtract the common dynamic process µ•t from log output (log value-added) for country i in models [3] and [7].† We report averaged t-statistics for country-specific t-statistics ti of the factor estimates.‡ Standard errors are obtained using the delta method.

ix

Table TA-8: Country regressions in FD (unrestricted returns to scale)

Country regressions in first differencestatic specification, no restriction on returns to scale; estimates presented are unweighted means of the country coefficients


[1] [2] [3] [4] [5] [6] [7] [8]estimator ∆MG ∆RCM ∆AMG ∆AMG ∆CMG ∆CMG ∆ARCM ∆ARCM

dependent variable] ∆lO ∆lO ∆lO-∆µ•t ∆lO ∆lO ∆lO ∆lO-∆µ•t ∆lO

regressors∆labour 0.1931 0.1766 0.1623 0.1675 0.1659 0.1919 0.1543 0.1624

[6.35]∗∗ [5.00]∗∗ [5.73]∗∗ [5.42]∗∗ [5.79]∗∗ [5.47]∗∗ [4.65]∗∗ [4.60]∗∗

∆capital 0.0543 0.0075 0.1230 0.1293 0.0761 -0.1267 0.0617 0.0368[0.40] [0.05] [0.98] [0.86] [1.06] [0.82] [0.46] [0.23]

∆materials 0.7617 0.7715 0.7741 0.7643 0.7570 0.7449 0.7830 0.7763[39.79]∗∗ [34.92]∗∗ [39.28]∗∗ [38.40]∗∗ [39.52]∗∗ [34.35]∗∗ [34.72]∗∗ [34.14]∗∗

common process ∆µ•t 0.9982 0.8614[4.41]∗∗ [3.38]∗∗

country drift 0.0042 0.0032 0.0001 -0.0003 0.0007 -0.0004 -0.0006[1.72] [1.08] [0.05] [0.10] [0.23] [0.15] [0.20]


Panel t-statistics, driftslabour 12.66 16.41 10.89 12.23 10.88 11.52 15.04 15.68capital 0.00 0.78 1.90 1.52 5.31 1.08 2.83 2.16materials 85.18 112.60 96.17 92.00 82.73 74.90 115.18 116.35country drifts 8.22 8.38 6.78 7.64 7.66 6.92 7.00# of sign. drifts (at 10%) 10 11 8 10 11 11 7

VA-equivalent coefficients‡labour (VA) mean 0.810 0.7729 0.719 0.7108 0.6829 0.7526 0.7113 0.7258

[8.13]∗∗ [6.13]∗∗ [7.33]∗∗ [6.97]∗∗ [7.07]∗∗ [7.50]∗∗ [5.69]∗∗ [5.69]∗∗

capital (VA) mean 0.228 0.033 0.544 0.5488 0.3133 -0.4967 0.2845 0.1647[0.41] [0.05] [0.99] [0.88] [1.10] [0.85] [0.46] [0.23]

obs (countries) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48)


[1] [2] [3] [4] [5] [6] [7] [8]estimator ∆MG ∆RCM ∆AMG ∆AMG ∆CMG ∆CMG ∆ARCM ∆ARCM

dependent variable] ∆lY ∆lY ∆lY-∆µva,•t ∆lY ∆lY ∆lY ∆lY-∆µva,•t ∆lY


[9.62]∗∗ [8.02]∗∗ [9.59]∗∗ [9.95]∗∗ [9.91]∗∗ [10.37]∗∗ [7.91]∗∗ [8.30]∗∗

∆capital -0.1816 -0.0025 0.0044 -0.0070 0.2231 -0.1634 0.1478 0.1137[0.62] [0.01] [0.02] [0.03] [0.92] [0.50] [0.51] [0.37]

common process ∆µva,•t 1.0460 0.8763

[5.60]∗∗ [4.06]∗∗

∆country drift 0.0187 0.0195 0.0016 -0.0019 0.0173 0.0018 0.0040[2.58]∗ [2.24]∗∗ [0.22] [0.25] [1.93] [0.21] [0.44]


Panel t-statistics, driftslabour 24.41 29.73 21.6 22.08 21.30 22.35 27.07 28.57capital -1.03 0.50 0.81 0.43 8.94 -0.19 2.48 2.15country drifts 9.17 10.23 6.61 7.47 8.18 7.03 7.84# of sign. drifts (at 10%) 12 15 8 10 12 10 12

obs (countries) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48)

Notes: We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively. All variables are in logs.Dependent variable: ∆lO — output growth rate, ∆lY — value-added growth rate. See Table TA-7 for more details.

x

Country regressions with ‘demeaned’ data

Table TA-9: Country regressions — data in deviation from x-section mean

Country regressions (demeaned data)static specification with CRS imposed;

estimates presented are unweighted means of the country coefficients

Gross output regressions

[1] [2] [3] [4]estimator MG RCM estimator MG RCM

dependent variable lo lo dependent variable ∆lo ∆lo

regressors regressorscapital pw 0.1125 0.1128 ∆capital pw 0.0989 0.0997

[5.62]∗∗ [5.09]∗∗ [5.51]∗∗ [4.67]∗∗

materials pw 0.7429 0.7616 ∆materials pw 0.7845 0.7902[26.79]∗∗ [25.83]∗∗ [38.97]∗∗ [34.35]∗∗

trend term 0.0000 0.0000 drift term -0.0008 0.0000[0.04] [0.00] [1.08] [0.03]

intercept -0.0101 -0.0011[0.36] [0.04]

Panel -t-statistics, trends† Panel -t-statistics, trends†capital pw 14.0 17.2 ∆capital pw 10.5 13.4materials pw 98.8 111.0 ∆materials pw 96.4 108.5country trends 15.6 14.5 drift terms 4.1 4.0# of sign. trends (at 10%) 25 26 # of sign. trends (at 10%) 1 2

VA-equivalent‡ VA-equivalent‡capital-VA 0.437 0.473 capital-VA 0.459 0.475

[6.62]∗∗ [5.90]∗∗ [5.74]∗∗ [4.89]∗∗

RMSE .030 .031 .029 .030obs (countries) 1,162 (48) 1,162 (48) 1,094 (48) 1,094 (48)

Value-added regressions

[1] [2] [3] [4]estimator MG RCM estimator MG RCM

dependent variable ly ly dependent variable ∆ly ∆ly

regressors regressorscapital pw 0.1325 0.2005 ∆capital pw 0.1401 0.1483

[2.30]∗ [3.21]∗∗ [2.33]∗ [2.17]∗

trend term 0.0204 0.0192 drift term 0.0193 0.0214[9.29]∗∗ [8.33]∗∗ [8.47]∗∗ [6.57]∗∗

intercept 9.5765 9.6035[79.04]∗∗ [77.55]∗∗

Panel -t-statistics, trends† Panel -t-statistics, trends†capital pw 10.7 13.17 ∆capital pw 5.96 6.75country trends 50.7 48.55 drift terms 11.45 20.65# of sign. trends (at 10%) 43 43 # of sign. trends (at 10%) 18 44

obs (countries) 1,194 (48) 1,194 (48) obs (countries) 1,128 (48) 1,128 (48)

Notes: All variables are in logs and deviation from the cross-section mean. lo — log output per worker, ly — log value-added perworker (in deviation from cross-section mean).Values in parentheses are absolute t-statistics. These were obtained by regressing the N country estimates on an intercept term, exceptfor the Swamy t-stats, which are provided by xtrc in Stata and represent

∑i(Σ + Vi) where Σ is a measure of dispersion of the country

OLS estimates and V is the variance of the N OLS estimates scaled by∑x2i .

We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively.† We report averaged t-statistics for country-specific t-statistics ti of the factor estimates.‡ This is obtained using a non-linear combination of the capital and materials coefficients accounting for the precision of these estimates.

xi

Dynamic specification — pooled models

Table TA-10: Pooled regressions (Error Correction Model)

Pooled dynamic regressions (CRS)dynamic specification (Error Correction Model) with CRS imposed;

regression equations augmented with year dummies or period-means (Pesaran, 2006)

Gross output models Value-added models

[1] [2] [3] [4] [5] [6]estimator POLS FE CCEP POLS FE CCEP

dependent variable] ∆lo ∆lo ∆lo ∆ly ∆ly ∆ly

regressorslagged log output pw -0.0522 -0.3003 -0.4326

[4.89]∗∗ [13.67]∗∗ [14.75]∗∗

lagged log VA pw -0.0143 -0.2780 -0.3747[2.03]∗ [12.38]∗∗ [14.13]∗∗

lagged log capital pw -0.0022 0.0406 0.0585 0.0109 0.1661 0.22767[0.84] [5.09]∗∗ [5.00]∗∗ [1.81] [7.11]∗∗ [8.24]∗∗

lagged log materials pw 0.0557 0.2284 0.3498[4.80]∗∗ [12.95]∗∗ [14.19]∗∗

capital growth rate 0.0456 0.0487 0.0485 0.3299 0.3225 0.3416[1.65] [3.49]∗∗ [2.93]∗∗ [3.70]∗∗ [7.93]∗∗ [7.58]∗∗

materials growth rate 0.7981 0.7945 0.8095[32.63]∗∗ [66.02]∗∗ [58.85]∗∗

intercept 0.0101 0.4309 -0.0997 0.0178 0.8848 0.06028[0.77] [6.13]∗∗ [0.50] [0.49] [4.68]∗∗ [0.14]

long-run coefficients†capital -0.043 0.135 0.135 0.766 0.597 0.608

[0.84] [5.84]∗∗ [5.50]∗∗ [4.14]∗∗ [9.49]∗∗ [9.91]∗∗

materials 1.067 0.761 0.809[17.35]∗∗ [32.18]∗∗ [29.79]∗∗

long-run VA equivalent†capital (VA) 0.635 0.565 0.707

[2.26]∗ [7.21]∗∗ [8.35]∗∗

AR tests‡AR(1) (p) -2.6 (.01) -1.1 (.29) -2.4 (.02) -3.3 (.00) -1.9 (.06) -1.2 (.25)AR(2) (p) -1.6 (.11) 0.0 (.98) -2.35 (.02) -2.5 (.01) -0.5 (.60) -2.4 (.02)AR(3) (p) 1.5 (.13) 2.2 (.03) 0.1 (.93) 1.4 (.16) 2.6 (.01) 0.4 (.69)

Observations 1,094 (48) 1,094 (48) 1,094 (48) 1,128 (48) 1,128 (48) 1,128 (48)

Notes: Values in parentheses are absolute t-statistics. ∗ and ∗∗ indicate statistical significance at the 5% and 1% levelrespectively. † Long-run coefficients are computed from the pooled estimates using the Delta method (available via thenlcom command in Stata).‡ Arellano and Bond (1991) serial correlation test.

xii

Dynamic specification — country regression averages

Table TA-11: Country regression averages (dynamic model, CRS imposed)

Country regressions (ECM specification)dynamic specification with CRS imposed; estimates presented are unweighted means of the country coefficients

Value-added regressions


dependent variable] ∆ly ∆ly ∆ly-∆µ•t ∆ly ∆ly ∆ly ∆ly-∆µ•t ∆ly

regressorsvalue-added pw (t− 1) -0.6020 -0.4985 -0.6396 -0.6825 -0.5511 -0.7276 -0.5330 -0.5766

[11.29]∗∗ [8.34]∗∗ [17.28]∗∗ [12.43]∗∗ [9.68]∗∗ [8.86]∗∗ [11.58]∗∗ [9.34]∗∗

capital pw (t− 1) 0.2233 0.2018 0.1511 0.3559 0.2005 0.0589 0.1720 0.2679[2.27]∗ [1.94] [2.37]∗ [3.35]∗∗ [1.86] [0.20] [2.41]∗ [2.39]∗

common process (t− 1) 0.6153 0.7486[2.29]∗ [2.58]∗∗

∆capital pw (t) 0.1173 0.1522 0.1546 0.2623 0.3475 0.3579 0.2070 0.2446[1.05] [1.25] [1.44] [2.24]∗ [3.19]∗∗ [2.69]∗∗ [1.74] [1.92]

∆common process (t) -0.0978 0.1229[0.45] [0.52]

country trend 0.0050 0.0041 -0.0004 -0.0064 0.0052 -0.0008 -0.0068[2.18]∗ [1.62] [0.16] [1.96] [1.39] [0.33] [1.82]

intercept 3.2907 2.6032 4.4500 2.6316 5.5285 11.3752 3.2598 2.6042[3.78]∗∗ [2.76]∗∗ [6.34]∗∗ [2.63]∗ [1.30] [1.19] [4.12]∗∗ [2.43]∗

Panel-t statistic, trends†country trend 11.26 11.76 11.85 10.17 11.64 11.8 9.09# of sign. trends (at 10%) 22 21 24 14 18 25 15

long-run coefficients‡capital pw (from above) 0.3709 0.4048 0.2363 0.5214 0.3637 0.0810 0.3227 0.4646

[9.45]∗∗ [2.13]∗ [7.09]∗∗ [15.32]∗∗ [1.16] [1.66] [2.45]∗ [2.58]∗∗

capital pw (mean) 0.3168 0.3403 0.1933 0.4052 0.3825 0.5800 0.3153 0.4007[2.89]∗∗ [5.24]∗∗ [1.90] [3.10]∗∗ [2.50]∗ [1.68] [4.50]∗∗ [5.41]∗∗

Panel t-statistic 9.48 8.48 4.76 11.23 16.16 3.98 8.72 11.55

obs (countries) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48)

Notes: All variables are in logs. ly — log value-added per worker. µ•t and µva •t are derived from the year dummy coefficients of a staticpooled regression (CRS imposed) in first differences (FD-OLS) as described in the text.We omit reporting the parameters on the cross-section averages for the CMG estimators (columns [5] and [6]) to save space.Values in parentheses are absolute t-statistics. These were obtained by regressing the N country estimates on an intercept term, exceptfor the Swamy t-stats, which are provided by xtrc in Stata and represent

∑i(Σ + Vi) where Σ is a measure of dispersion of the country

OLS estimates and V is the variance of the N OLS estimates scaled by∑x2i .

We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively.] We subtract the common dynamic process µ•t from lagged value-added per worker (in logs) for country i, and common dynamic processµ•t from in models [3] and [7].† We report averaged t-statistics for country-specific t-statistics ti of the factor estimates.‡ This is obtained using a non-linear combination of the capital and materials coefficients accounting for the precision of these estimates.The first estimate (‘from above’) simply calculates the long-run capital coefficient based on the sample averages on capital pw (t− 1) andvalue-added pw (t− 1) reported in the upper section of the table. The second estimates (‘mean’) use the long-run coefficients computedfor each country i and averages them.

xiii

Parameter heterogeneity tests

The individual country coefficients emerging from our regressions imply considerable pa-rameter heterogeneity across countries. However, this apparent heterogeneity may bedue to sampling variation and the relatively limited number of time-series observationsin each country individually (Pedroni, 2007). We therefore carry out a number of param-eter heterogeneity tests for the results from the various CMG and augmented MG/RCMestimations.

As a first test, we compute the residuals in the case of parameter homogeneity for eachcountry

Hhet ≡ o•it − b kit − c mit − µt− A0

Hhet ≡ oit − b kit − c mit − µt− dµ•t − A0

where b, c and d (for Augmented models) are the mean estimates for capital per worker(k), materials per worker (m) and the common dynamic process taken from the results inTable 2 in the paper (Table ?? for the regressions with variables in first differences), withµ the average country trend term and A0 the average intercept term (the latter is notimportant for this analysis). The common dynamic process is either subtracted from theoutput variable (o•it) or included as indicated above. Similarly for the other models, theVA specifications and the specifications in first differences. In a second step, we regressthe residuals created on the input variables, a country trend or drift term and country-and year-dummies in a pooled regression

Hhet = πb kit + πcmit + πd t (+∑i

πe,i) (9)

The rationale behind this test is as follows: if factor input parameters were truly hetero-geneous across countries, we would expect the pooled regression to produce statisticallysignificant coefficients (πj 6= 0). Results are presented in Tables TA-12 and TA-13.

As can be seen the levels regressions imply that capital parameter homogeneity is re-jected, while the materials coefficients are more likely to be homogeneous (in the grossoutput specification). In the VA-specification capital parameter homogeneity is rejectedin all models. In contrast the tests for the first difference specifications on the whole donot provide much evidence for heterogeneity, with all covariates insignificant with theexception of the case of CMG in first differences. Note that the kernel densities for thetechnology parameters underlying the above heterogeneity tests do not differ considerablybetween levels and FD specifications (FD densities not reported). This stark differenceis therefore likely to be driven by the impact of nonstationarity on the test.

Secondly, we report the Swamy (1970) S statistic from the gross output and VA regres-sions in levels and first differences in Table TA-14.26 For a detailed discussion of thistest see Pesaran and Yamagata (2008). Note that the test for the equation in levels istesting heterogeneity of all parameters, including the intercepts; since the assumption ofheterogeneous TFP levels is rather uncontroversial, this test does not adquately address

xiv

our interest in the homogeneity of technology parameters. We therefore also provide atest for the levels specification where the intercept terms have been dispensed with viatransformation of the data into mean-deviations. Estimates for this specification are ofcourse identical to those of the untransformed levels equation (see references in footnote??).

The Swamy S test rejects parameter heterogeneity for all specifications tested. In general,this test was developed for panels where N is large relative to T . Using Monte Carlo ex-periments, Pesaran and Yamagata (2008) show that in case of a panel of T = 30, N = 50the test has power but tends to over-reject — a tendency which becomes worse with thenumber of parameters included in the model.27 Further, as Pedroni (2007) points out,the Swamy-based tests are not designed for nonstationary panel data.

Thirdly, we produce Wald statistics, as suggested by Canning and Pedroni (2008)

Wθ =∑i

(θi − θ)2

Var(θi)Wθ ∼ χ2(N)

where θi is the parameter coefficient from the country regression, θ is the unweightedaverage parameter estimate and Var(θi) its variance across all countries. If parametersare similar across countries, the test statistic will be small, whereas if parameters areheterogeneous Wθ will be larger. The validity of this test depends on T being moderateto large. The null for this test is that all countries have the same parameter value. TableTA-16 presents the summed Wald statistics for the entire sample, as well as an indica-tion of the share of country-specific tests rejecting the null of equality between countryestimate and full sample mean estimate (for both the levels and FD specifications).

The Wald tests reject homogeneity for the factor parameters derived from the levelsmodels in case of both the gross-output and value-added specifications. The statisticsare particularly large for the trend terms in the levels specifications, thus rejecting homo-geneity emphatically, which is not always the case for the drift terms in the first-differencespecifications. Turning to the share of countries rejecting parameter homogeneity, it canbe seen that roughly half of all countries reject homogeneity for all covariates in the levelsspecifications. This share falls to less than one third in the models in first differences.

Fourthly, following Pedroni (2007), we produce an F -statistic for the standard and aug-mented MG and RCM regression models (Pesaran & Yamagata, 2008, p.52)

F =

(RSShom −RSShet

RSShet

)(dfDdfN

)F ∼ F (dfN , dfD) dfN = k × (N − 1) dfD = N(T − k − 1)

where k is the number of parameters in each country-regression and RSShom and RSShetare the sums of the squared residuals of the homogeneous and heterogeneous models re-spectively — in the former case the mean coefficient estimates are imposed. This tests

xv

the full parameter heterogeneity versus the full homogeneity case. We do not computeF -tests for the CMG models, as the parameters on the period-average are not meant tobe identical.

The F tests are valid for fixed N , when the regressors are strictly exogenous and theerror variances are homoskedastic (Pesaran & Yamagata, 2008).28

All of the test results presented in Table TA-15 reject parameter homogeneity for thefactor input variables at the 1% level of significance. It is intuitive why the test statisticsmay emphatically reject the null: if the homogeneity restriction is incorrect, the countryregressions do not cointegrate under the null, such that the regression errors will be non-stationary. As a result the F -statistic will quickly diverge and reject the null (Pedroni,2007).

Like in the Swamy S Test we are faced with the problem that the tests evaluate the fullregression model for the null of parameter homogeneity, which is not sensible in the levelsregression case since heterogeneous intercepts are commonly accepted in the literature.In order to bypass this problem we also computed F -statistic for the levels MG and Aug-mented MG cases where the intercepts have been dispensed with by taking all variablesin deviations from the country-mean — all of these reject parameter homogeneity at the1% level.29

Taken together the various diagnostic tests we carried out in this section do give a strongindication that parameter homogeneity is rejected. The differences in the results for levelsand first difference specifications however indicate that nonstationarity may drive someof the results reported. Nevertheless, even if heterogeneity were not very significant inqualitative terms, our contrasting of pooled and country regression results in the paperhas shown that it nevertheless matters greatly for correct empirical analysis in the caseof nonstationary variable series.

Further parameter heterogeneity tests were considered for this analysis: Pesaran andYamagata (2008) compare their own version of Swamy’s test of parameter homogene-ity (denoted ∆) with the ‘traditional’ Swamy test and F -Test we computed above, aHausman-type comparison of Fixed Effects and Mean Group estimates and the Phillipsand Sul (2003) G-test. Their Monte Carlo experiments suggest that all of these tests havelow power in panels with the dimensions we observe (N = 48, T ≈ 24) and we thereforedid not further pursue any of these here.

xvi

Table TA-12: Parameter Heterogeneity — Pooled Tests (levels)

Parameter Heterogeneity — Pooled Tests (levels)pooled fixed effects regressions; dependent variable: residuals Hhet as defined in main text


[1] [2] [3] [4] [5] [6] [7] [8]estimator MG RCM AMG(i) AMG(ii) CMG(i) CMG(ii) ARCM(i) ARCM(ii)

dependent variable] Hhet Hhet Hhet Hhet Hhet Hhet Hhet Hhet

regressorscapital pw 0.1200 0.0993 0.1007 0.0910 0.0538 0.0912 0.0877 0.0780

[10.23]∗∗ [8.47]∗∗ [8.77]∗∗ [7.76]∗∗ [4.66]∗∗ [7.94]∗∗ [7.64]∗∗ [6.79]∗∗

materials pw 0.0224 0.0009 0.0119 0.0011 0.0157 0.0265 -0.0094 -0.0092[1.64] [0.06] [0.88] [0.08] [1.18] [1.99]∗ [0.70] [0.68]

country trends -0.0027 -0.0016 -0.0020 0.0014 0.0004 -0.0019 -0.0012 -0.0010[7.69]∗∗ [4.70]∗∗ [5.78]∗∗ [4.06]∗∗ [1.22]∗∗ [5.36]∗∗ [3.46]∗∗ [2.89]∗∗

intercept terms all sign all sign all sign all sign all sign all sign all sign all signat 1% at 1% at 1% at 1% at 1% at 1% at 1% at 1%

obs 1,162 1,162 1,162 1,162 1,162 1,162 1,162 1,162



dependent variable] Hvahet Hva

het Hvahet Hva

het Hvahet Hva

het Hvahet Hva

het

regressorscapital pw 0.4704 0.4242 0.3733 0.3511 0.197 0.3517 0.3072 0.3083

[15.94]∗∗ [14.38]∗∗ [12.95]∗∗ [11.90]∗∗ [6.55]∗∗ [12.00]∗∗ [10.65]∗∗ [10.68]∗∗

country trends -0.0112 -0.0026 -0.0088 0.0039 -0.0018 -0.0087 -0.0068 -0.0071[11.72]∗∗ [2.73]∗∗ [9.07]∗∗ [4.07]∗∗ [1.87]∗∗ [9.13]∗∗ [7.04]∗∗ [7.33]∗∗

intercept terms all sign all sign all sign all sign all sign all sign all sign all signat 1% at 1% at 1% at 1% at 1% at 1% at 1% at 1%

obs 1,194 1,194 1,194 1,194 1,194 1,194 1,194 1,194

Notes: All variables are in logs. Values in brackets are absolute t-statistics. The models underlying the constructionof Hhet are presented in Table 2 above. We indicate statistical significance at the 5% and 1% level by ∗ and ∗∗

respectively.

Table TA-13: Parameter Heterogeneity — Pooled Tests (FD)

Parameter Heterogeneity — Pooled Tests (FD)pooled fixed effects regressions; dependent variable: residuals Hhet


[1] [2] [3] [4] [5] [6] [7] [8]estimator ∆MG ∆RCM ∆AMG(i) ∆AMG(ii) ∆CMG(i) ∆CMG(ii) ∆ARCM(i) ∆ARCM(ii)

dependent variable] Hhet Hhet Hhet Hhet Hhet Hhet Hhet Hhet

regressorscapital pw -0.0102 -0.0169 -0.0264 -0.0367 -0.0663 -0.0416 -0.0280 -0.0274

[0.36] [0.60] [0.95] [1.32] [2.35]∗ [1.50] [1.01] [0.99]

materials pw 0.0226 0.0124 0.0163 0.0236 0.0198 0.0145 0.0073 0.0122[0.91] [0.50] [0.67] [0.98] [0.81] [0.60] [0.30] [0.50]

drift terms only 1 only 1 only 1 only 1 only 1 only 1 only 1 only 1sign. sign. sign. sign. sign. sign. sign. sign.

obs 1,094 1,094 1,094 1,094 1,094 1,094 1,094 1,094


[1] [2] [3] [4] [5] [6] [7] [8]estimator ∆MG ∆RCM ∆AMG(i) ∆AMG(ii) ∆CMG(i) ∆CMG(ii) ∆ARCM(i) ∆ARCM(ii)

dependent variable] Hvahet Hva

het Hvahet Hva

het Hvahet Hva

het Hvahet Hva

het

regressorscapital pw 0.0989 0.0546 0.0157 0.0069 -0.0791 -0.0202 -0.0162 -0.0106

[1.11] [0.61] [0.18] [0.08] [0.88] [0.22] [0.18] [0.12]

drift terms only 2 only 2 only 2 only 2 only 2 only 2 only 2 only 2sign. sign. sign. sign. sign. sign. sign. sign.

obs 1,128 1,128 1,128 1,128 1,128 1,128 1,128 1,128

Notes: See Table TA-12 for details. The results for the country regressions in first difference tested here for parameterheterogeneity are presented in Table ??.

xvii

Table TA-14: Parameter Heterogeneity — Swamy (1970) Tests

Swamy (1970) testsH0: homogeneity across countries; p-values are reported in parentheses;

‘MD’ refers to variables in deviations from country-specific means (‘within’ transformation)

Levels and mean-deviation (MD) specifications†RCM ARCM

Levels MD Levels MD Levels MDGross Output 30,598.1 (.00) 2,198.2 (.00) 41,427.1 (.00) 2,119.7 (.00) 45,871.5 (.00) 2,598.4 (.00)Value-Added 51,123.0 (.00) 1,531.6 (.00) 62,499.9 (.00) 1,440.4 (.00) 69,157.0 (.00) 1726.7 (.00)

Specifications in first differences (FD)

RCM ARCMFD FD FD

Gross Output 359.5 (.00) 332.3 (.00) 453.4 (.00)Value-Added 191.1 (.00) 153.5 (.00) 258.7 (.00)

Notes: Swamy S is distributed χ2 with k(N − 1) degrees of freedom. † Data in mean-deviations.

Table TA-15: Parameter Heterogeneity — F -Tests

Panel F-testsFull sample statistics; H0: model parameters are homogeneous


[1] [2] [3] [4] [5] [6]estimator MG RCM AMG(i) AMG(ii) ARCM(i) ARCM(ii)

levelsF 283.1 (.00) 199.7 (.00) 209.0 (.00) 207.1 (.00) 169.2 (.00) 151.4 (.00)distr F (188, 922) F (188, 922) F (188, 922) F (235, 874) F (188, 922) F (235, 874)

first differencesF 2.4 (.00) 1.9 (.00) 2.5 (.00) 1.7 (.00) 2.0 (.00) 2.2 (.00)distr F (141, 902) F (141, 902) F (141, 902) F (188, 854) F (141, 902) F (188, 854)


[1] [2] [3] [4] [5] [6]estimator MG RCM AMG(i) AMG(ii) ARCM(i) ARCM(ii)

levelsF 413.7 (.00) 334.1 (.00) 339.9 (.00) 279.4 (.00) 287.5 (.00) 232.3 (.00)distr F (141, 1002) F (141, 1002) F (141, 1002) F (188, 954) F (141, 1002) F (188, 954)

first differencesF 2.0 (.00) 1.5 (.00) 2.6 (.00) 2.4 (.00) 1.6 (.00) 1.8 (.00)distr F (94, 950) F (94, 950) F (94, 950) F (141, 902) F (94, 950) F (141, 902)

Notes: See main text for construction of the Panel F statistic. The models underlying the construction of the Fstatistics are presented in Table 2 and ?? above. The null hypothesis in all cases is parameter homogeneity.

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Table TA-16: Parameter Heterogeneity — Wald Tests (levels and FD)

Wald Tests (levels)Full sample Wald statistics (Wθ) and share of countries rejecting H0 of parameter homogeneity



full sample Wθ

capital pw (k) 667.3∗∗ 406.4∗∗ 517.1∗∗ 553.9∗∗ 397.7∗∗ 318.6∗∗ 323.9∗∗ 298.8∗∗

materials pw (m) 599.4∗∗ 368.3∗∗ 518.4∗∗ 626.5∗∗ 588.6∗∗ 375.0∗∗ 325.8∗∗ 329.7∗∗

country trends (t) 932.2∗∗ 603.5∗∗ 802.0∗∗ 264.7∗∗ 298.0∗∗ 530.3∗∗ 245.4∗∗

Country-specific Wθ,i

share rejecting H0: k 56% 46% 44% 54% 58% 40% 44% 50%share rejecting H0: m 56% 54% 44% 54% 58% 40% 44% 56%share rejecting H0: t 54% 56% 54% 50% 48% 54% 48%

obs (countries) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48) 1,162 (48)



full sample Wθ

capital pw (k) 578.1∗∗ 388.1∗∗ 474.0∗∗ 542.3∗∗ 515.5∗∗ 548.0∗∗ 320.1∗∗ 354.9∗∗

country trends 1,044.3∗∗ 720.9∗∗ 781.8∗∗ 267.7∗∗ 374.4∗∗ 636.7∗∗ 194.5∗∗


share rejecting H0: k 52% 46% 52% 56% 54% 46% 50% 54%share rejecting H0: t 65% 56% 58% 44% 42% 52% 40%

obs (countries) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48) 1,194 (48)

Wald Tests (FD)Full sample Wald statistics (Wθ) and share of countries rejecting H0 of parameter homogeneity



full sample Wθ

capital pw (k) 130.2∗∗ 119.0∗∗ 102.2∗∗ 116.0∗∗ 101.7∗∗ 134.9∗∗ 92.8∗∗ 113.6∗∗

materials pw (m) 263.2∗∗ 160.3∗∗ 248.2∗∗ 290.0∗∗ 176.2∗∗ 206.2∗∗ 156.2∗∗ 174.3∗∗

country drifts 87.2∗∗ 81.7∗∗ 69.0∗ 112.9∗∗ 109.7∗∗ 67.0∗ 68.0∗


share rejecting H0: k 23% 23% 27% 29% 25% 25% 23% 21%share rejecting H0: m 23% 29% 27% 29% 25% 25% 27% 29%share rejecting H0: drift 15% 13% 13% 13% 23% 17% 13%

obs (countries) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48) 1,094 (48)



full sample Wθ

capital pw (k) 166.1∗∗ 147.1∗∗ 117.1∗∗ 139.8∗∗ 125.2∗∗ 141.5∗∗ 115.9∗∗ 132.4∗∗

country drifts 80.5∗∗ 73.5∗ 51.7 109.5∗∗ 74.7∗∗ 54.0 86.8∗∗


share rejecting H0: k 25% 33% 33% 31% 35% 29% 31% 33%share rejecting H0: drift 19% 17% 15% 21% 15% 15% 21%

obs (countries) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48) 1,128 (48)

Notes: See main text for construction of the Wald statistic Wθ . The models underlying the construction of the Wald statistics are

presented in Table 2 above. In the full sample tests Wθ ∼ χ2(48), with 5% and 1% critical values 65.17 and 73.70 respectively(Wθ =

∑iWθ,i); for country-specific tests (Wθ,i) we apply the 10% critical value of 2.7. The null hypothesis in all cases is parameter

homogeneity. For Wθ we indicate statistical significance at the 5% and 1% level by ∗ and ∗∗ respectively.

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productivity analysis in global manufacturing...

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