International Business Cycles: World, Region, and Country-Specific Factors By M. AYHAN KOSE,CHRISTOPHER OTROK, AND CHARLES H. WHITEMAN* The paper investigates the common dynamic properties of business-cycle fluctua- tions across countries, regions, and the world. We employ a Bayesian dynamic latent factor model to estimate common components in macroeconomic aggregates (output, consumption, and investment) in a 60-country sample covering seven regions of the world. The results indicate that a common world factor is an important source of volatility for aggregates in most countries, providing evidence for a world business cycle. We find that region-specific factors play only a minor role in explaining fluctuations in economic activity. We also document similarities and differences across regions, countries, and aggregates. (JEL F41, E32, C11, C32) Is there a world business cycle? Recent stud- ies have indeed provided evidence that there are many cross-country links in macroeconomic fluctuations. 1 For example, studies of pairwise correlations by David Backus et al. (1995) and Marianne Baxter (1995) find that business cy- cles in major industrialized economies are quite similar. Enrique G. Mendoza (1995) and Kose (2002) document that business cycles of devel- oping economies have characteristics similar to those of developed countries. 2 More structured time-series analyses also find comovement in subsets of countries. In particular, Allan Greg- ory et al. (1997) use Kalman filtering and dy- namic factor analysis to identify the common fluctuations across macroeconomic aggregates in G7 countries. 3 Todd E. Clark and Kwanho * Kose: International Monetary Fund, 700 19th Street NW, Washington, DC 20431 (e-mail: [email protected]); Otrok: Department of Economics, 114 Rouss Hall, Univer- sity of Virginia, Charlottesville, VA 22903 (e-mail: [email protected]); Whiteman: Department of Econom- ics, W380 John Pappajohn Business Building, University of Iowa, Iowa City, IA 52242 (e-mail: Whiteman@uiowa. edu). Earlier versions of this paper were presented at the 1998 Midwest Macroeconomics Meetings in Indiana, 1999 Econometric Society Winter Meetings in New York, 1999 NBER Summer Institute, 2000 Growth and Business Cycles Conference in Manchester, the Federal Reserve Banks of Chicago and Kansas City, Duke University, Ohio State University, Oklahoma State University, Princeton Univer- sity, and the University of Iowa. We would like to thank David Backus, Marianne Baxter, Mario Crucini, Paul Evans, Michael Kouparitsas, and seminar participants for their comments and suggestions. Otrok and Whiteman grate- fully acknowledge support from the National Sci- ence Foundation under Grant Nos. SES-0082237 and SES- 0082230. The views presented are those of the authors and do not necessarily reflect the views of the IMF or IMF policy. 1 Understanding the similarities of business-cycle fluc- tuations across countries has long been a subject of interest to macroeconomists. See Victor Zarnowitz (1992) for a survey of this research program. 2 Stefan Gerlach (1988), using spectral methods, finds that movements in industrial production indices in a number of OECD countries are correlated. In a recent paper, U. Michael Bergman et al. (1998) study cross-country correla- tions of several macro aggregates of 13 industrialized coun- tries and find that business-cycle fluctuations are highly synchronized across countries and across monetary regimes. Mario J. Crucini (1999) establishes a link between those studies employing stochastic dynamic macroeconomic models that try to explain common fluctuations across coun- tries, and those empirical studies documenting features of international business cycles. Kose and Kei-Mu Yi (2001, 2003) study whether standard multicountry business-cycle models can generate the observed relationship between in- ternational trade and business-cycle comovement. Michael Kouparitsas (1997a, b) studies the transmission of interna- tional business cycles from the developed countries in the North to the developing economies in the South. 3 Alan Stockman (1988) employs an error-correction method and finds that a substantial fraction of variation in industrial production is due to global sector-specific and country-specific disturbances in major industrialized econ- omies. Stefan C. Norrbin and Don E. Schlagenhauf (1996) also employ a dynamic factor model to examine the role of world, nation-specific, and industry-specific factors in ex- plaining common movement across G7 countries, Belgium, and Netherlands. Their results indicate that while the world and country-specific factors explain some fraction of 1216
Transcript
International Business Cycles: World, Region,and Country-Specific Factors
By M. AYHAN KOSE, CHRISTOPHER OTROK, AND CHARLES H. WHITEMAN*
The paper investigates the common dynamic properties of business-cycle fluctua-tions across countries, regions, and the world. We employ a Bayesian dynamiclatent factor model to estimate common components in macroeconomic aggregates(output, consumption, and investment) in a 60-country sample covering sevenregions of the world. The results indicate that a common world factor is animportant source of volatility for aggregates in most countries, providing evidencefor a world business cycle. We find that region-specific factors play only a minorrole in explaining fluctuations in economic activity. We also document similaritiesand differences across regions, countries, and aggregates. (JEL F41, E32, C11,C32)
2 Stefan Gerlach (1988), using spectral methods, finds
Is there a world business cycle? Recent stud-ies have indeed provided evidence that there aremany cross-country links in macroeconomicfluctuations.1 For example, studies of pairwisecorrelations by David Backus et al. (1995) andMarianne Baxter (1995) find that business cy-cles in major industrialized economies are quitesimilar. Enrique G. Mendoza (1995) and Kose(2002) document that business cycles of devel-oping economies have characteristics similar to
* Kose: International Monetary Fund, 700 19th StreetNW, Washington, DC 20431 (e-mail: [email protected]);Otrok: Department of Economics, 114 Rouss Hall, Univer-sity of Virginia, Charlottesville, VA 22903 (e-mail:[email protected]); Whiteman: Department of Econom-ics, W380 John Pappajohn Business Building, University ofIowa, Iowa City, IA 52242 (e-mail: [email protected]). Earlier versions of this paper were presented at the1998 Midwest Macroeconomics Meetings in Indiana, 1999Econometric Society Winter Meetings in New York, 1999NBER Summer Institute, 2000 Growth and Business CyclesConference in Manchester, the Federal Reserve Banks ofChicago and Kansas City, Duke University, Ohio StateUniversity, Oklahoma State University, Princeton Univer-sity, and the University of Iowa. We would like to thankDavid Backus, Marianne Baxter, Mario Crucini, PaulEvans, Michael Kouparitsas, and seminar participants fortheir comments and suggestions. Otrok and Whiteman grate-fully acknowledge support from the National Sci-ence Foundation under Grant Nos. SES-0082237 and SES-0082230. The views presented are those of the authors and donot necessarily reflect the views of the IMF or IMF policy.
1 Understanding the similarities of business-cycle fluc-tuations across countries has long been a subject of interestto macroeconomists. See Victor Zarnowitz (1992) for asurvey of this research program.
121
those of developed countries.2 More structuredtime-series analyses also find comovement insubsets of countries. In particular, Allan Greg-ory et al. (1997) use Kalman filtering and dy-namic factor analysis to identify the commonfluctuations across macroeconomic aggregatesin G7 countries.3 Todd E. Clark and Kwanho
that movements in industrial production indices in a numberof OECD countries are correlated. In a recent paper, U.Michael Bergman et al. (1998) study cross-country correla-tions of several macro aggregates of 13 industrialized coun-tries and find that business-cycle fluctuations are highlysynchronized across countries and across monetary regimes.Mario J. Crucini (1999) establishes a link between thosestudies employing stochastic dynamic macroeconomicmodels that try to explain common fluctuations across coun-tries, and those empirical studies documenting features ofinternational business cycles. Kose and Kei-Mu Yi (2001,2003) study whether standard multicountry business-cyclemodels can generate the observed relationship between in-ternational trade and business-cycle comovement. MichaelKouparitsas (1997a, b) studies the transmission of interna-tional business cycles from the developed countries in theNorth to the developing economies in the South.
6
3 Alan Stockman (1988) employs an error-correctionmethod and finds that a substantial fraction of variation inindustrial production is due to global sector-specific andcountry-specific disturbances in major industrialized econ-omies. Stefan C. Norrbin and Don E. Schlagenhauf (1996)also employ a dynamic factor model to examine the role ofworld, nation-specific, and industry-specific factors in ex-plaining common movement across G7 countries, Belgium,and Netherlands. Their results indicate that while the worldand country-specific factors explain some fraction of
1217VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
Shin (2000) use a VAR factor model to studythe importance of common and country-specificshocks in accounting for variation in industrialproduction in European countries. Robin L.Lumsdaine and Eswar S. Prasad (2003) developa weighted aggregation procedure, and examinethe correlations between the fluctuations in in-dustrial output in 17 OECD countries and anestimated common component, and find evi-dence for a world business cycle and for aEuropean business cycle.4
What is common to these studies of interna-tional business cycles is that they are not studiesof the world. Data limitations and econometricintractability have heretofore limited attentionto small groups of countries, or to ad hoc worldaggregates, and there has not been a detailedstudy of whether fluctuations are associatedwith worldwide, regional, or country-specificshocks. We address this and related issues byemploying a Bayesian dynamic latent factormodel to estimate common dynamic compo-nents in macroeconomic aggregates (output,consumption, and investment) in a 60-countrysample covering seven regions of the world. Inparticular, we simultaneously estimate (i) a dy-namic factor common to all aggregates, regions,and countries (the world factor); (ii) a set ofseven regional dynamic factors common acrossaggregates within a region; (iii) 60 country fac-tors to capture dynamic comovement across ag-gregates within each country; and (iv) acomponent for each aggregate that captures id-iosyncratic dynamics. By design, the dynamic fac-tors capture all intertemporal cross-correlationamong the observable variables.
The econometric methodology we employpermits us to examine multiple common factors.Otrok and Whiteman (1998) developed aBayesian single dynamic factor model to studycoincident and leading economic indicators us-ing the data of the state of Iowa. We extendtheir work to a multiple-factor setting and em-ploy it in an international business-cycle con-text. One of the major advantages of our
4 Nicos Christodoulakis et al. (1995), Michael J. Artis etal. (1997), Artis and Wenda Zhang (1997), Bergman et al.(1998), and Jean Imbs (1999) also find high correlationsacross output fluctuations in several European countries.
Bayesian procedures over those used in earlierstudies in the dynamic factor framework is thatthe method works well with the large crosssection of data necessary to uncover worldwidecomovement. In addition to working efficientlywith large cross sections of data, our methodcan also easily handle a large number of dy-namic factors.
We are therefore able to examine regionaland country-specific cycles simultaneously withthe world business cycle. The importance ofstudying all three in one model is that studyinga subset of countries can lead one to believe thatobserved comovement is particular to that sub-set of countries when it in fact is common to amuch larger group of countries. For example, inlight of our results, the distinct “European”business cycle apparent in studies of comove-ment in European countries appears to be anartifact of limited samples—we find that thecomovement among European countries is dueto comovement common to all countries in theworld.
Understanding the sources of internationaleconomic fluctuations is important both for de-veloping business-cycle models and makingpolicy. For example, if most of the variation ineconomic activity in a set of countries withdifferent economic policies, institutions, andeconomic structures is explained by a worldbusiness cycle, this lends support to the predic-tions of theoretical models emphasizing thecommon characteristics in the operations ofmarkets rather than the differences in economicpolicies or institutional environments in thosecountries.5 Similarly, if a significant fraction ofdomestic business cycles is due to the commonworld factor, this implies that policies targetingexternal balances to stabilize sudden move-ments in economic activity might be ineffective.
Our results indicate that there is a distinctworld business cycle—the world factor seemsto account for a significant fraction of outputgrowth fluctuations in many countries. The fac-tor is quite persistent, and reflects many majorworldwide economic events, including the
5 In a recent paper, Gregory and Head (1999) document
industrial output, the industry-specific factor plays a mi-nor role.
that common movements explain a significant fraction ofproductivity fluctuations and a much smaller part of theinvestment movements. They construct a stochastic dy-namic model that is consistent with these features.
1218 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
steady expansionary period in the 1960’s, theglobal recession of the mid-1970’s, the reces-sion of the early 1980’s, and the downturn in theearly 1990’s. Likewise, the country factors,though less persistent, also exhibit some impor-tant historical episodes. For example, the U.S.country factor moves in accord with many ofthe NBER reference cycles, and the countryfactors of Latin American economies affectedby the debt crisis in 1982 reflect that event.
Upon decomposing the variance of each ag-gregate into the fractions attributable to eachtype of factor, we find that the world factoraccounts for a larger fraction of business-cyclevariability in developed countries than in devel-oping countries. The variance decompositionsalso show that the world factor accounts for alarger share of the fluctuations in output than inconsumption in the majority of the countries inour sample. Further, except for the North Amer-ica factor, we find little evidence for region-specific fluctuations.
There are of course countries for which theworld factor is less important than country-specific events. To study the pattern of variancedecompositions, we use regressions of the frac-tion of the variance of each country’s observ-ables (output growth, consumption growth,investment growth) attributable to a factor(world, regional, country) on a variety of ex-planatory variables related to country character-istics. We find that the world factor is moreimportant in explaining fluctuations in devel-oped, stable economies, whereas country-specificfactors are more important in developing, vola-tile economies.
The next section briefly lays out our ap-proach. Section II presents the world and otherfactors, and studies the relationship among thecountry-specific, regional, and worldwide fluc-tuations. Section III investigates the persistenceproperties of the world factor. Section IV stud-ies the relative importance of the various factorsacross countries using variance decompositions;Section V provides the characterization of thepattern of variance decomposition results. Sec-tion VI concludes.
I. Methodology
The econometric model used here is a multi-factor extension of the single dynamic unob-
served factor model in Otrok and Whiteman(1998). Such models are the dynamic counter-parts to static unobserved factor models that arecommon in psychology. A static factor modelprovides a description of the variance-covariancematrix of a set of random variables; the methodof principal components is one implementationof this idea. A dynamic factor model provides adescription of the spectral density matrix of aset of time series, and thus the factor(s) describecontemporaneous and temporal covariationamong the variables.
Specifically, suppose xj is a vector of Q mea-surements of person j’s academic achievement(e.g., GPA, class rank, scores on the PSAT,SAT, ACT, GRE, GMAT, etc.) and � is theassociated covariance matrix. Then xj is said tohave factor structure if � can be written in theform
� � ��� � U
where � is Q � K, K � Q, and U is diagonalwith positive entries on the diagonal. This struc-ture implies that xj can be thought of as beingexplained by a set of K common factors andidiosyncratic noise. That is,
xj � af � uj
where f is a K � 1 vector of factors, a is theQ � K vector of “factor loadings,” and uj is theperson-specific noise. Typically, one employsthe identification assumptions that the factorsare independent and have variance 1.0, and thatthe uj’s are independent and identically distrib-uted across individuals. If there is no otherinformation on the factors f, they are “unobserv-able” and their characteristics must be learnedindirectly via the pattern of correlation in thexj’s. It might be thought that the vector of scoreswould be determined in large part by a smallnumber of factors (“intelligence,” “test-takingability,” etc.), but there is no direct way ofidentifying what the factors are, only indirectones via the factor loadings.
In the time-series context, suppose yt is aQ-dimensional vector of covariance stationarytime series at date t (e.g., growth rates of output,consumption, and investment in 60 countries),and Syy is its associated spectral density matrix.Then the time series {yt} is said to have dy-
1219VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
namic factor structure if Syy can be written inthe form
Syy � LL� � V
where L is Q � K, K � Q, and V is diagonalwith positive entries on the diagonal. This struc-ture means that all of the comovement amongthe variables is controlled by the M-dimensionalset of “dynamic factors.” In addition, in the timedomain, yt can be represented as
yt � a�L�ft � ut
where a(L) is a Q � K matrix of polynomialsin the lag operator, {ft} is a K-dimensionalstochastic process of the factors, and the errorsin ut may be serially but not cross-sectionallycorrelated. The factors are in general seriallycorrelated, and may be observed or unobserved.
In our implementation, there are K dynamic,unobserved factors thought to characterize thetemporal comovements in the cross-countrypanel of economic time series. Let N denote thenumber of countries, M the number of timeseries per country, and T the length of the timeseries. Observable variables are denoted yi,t, fori � 1, ... , M � N, t � 1, ... , T. There arethree types of factors: N country-specific factors( f n
country, one per country), R regional factors( f r
region, e.g., one each for North America,Latin America, Africa, Developed Asia, Devel-oping Asia, Europe, and Oceania), and the sin-gle world factor ( f world). Thus for observable i:
(1) yi,t � ai � biworldf t
world � biregionf r,t
region
� bicountryf n,t
country � �i,t
E� i,t� j,t � s � 0 for i � j,
where r denotes the region number and n thecountry number. The coefficients bi
j are the fac-tor loadings, and reflect the degree to whichvariation in yi,t can be explained by each factor.Notice that there are M � N time series to be“explained” by the (many fewer) N � R � 1factors. The “unexplained” idiosyncratic errors�i,t are assumed to be normally distributed, but
may be serially correlated. They follow pi-orderautoregressions:
(2) � i,t � � i,1� i,t � 1 � � i,2� i,t � 2 � ...
� �i,pi�i,t � pi
� ui,t
Eui,t uj,t � s � � i2 for i � j and s � 0,
0 otherwise.
The evolution of the factors is likewise gov-erned by an autoregression, of order qk withnormal errors:
(3) fk,t � � fk ,t
(4) � fk ,t � � fk ,1� fk ,t�1 � � fk,2� fk,t�2 � ...
� �fk,qk�fk,t�qk
� ufk ,t
Eufk ,tufk ,t � � fk
2 ; Eufk ,tui,t � s � 0
for all k, i, and s.
Notice that all the innovations, ui,t, i � 0, ... ,M � N and ufk,t
, k � 1, ... , K, are assumed tobe zero mean, contemporaneously uncorrelatednormal random variables. Thus all comovementis mediated by the factors, which in turn allhave autoregressive representations (of possiblydifferent orders).
There are two related identification problemsin the model (1)–(4): neither the signs nor thescales of the factors and the factor loadings areseparately identified. Signs are identified by re-quiring one of the factor loadings to be positivefor each of the factors. In particular, we requirethat the factor loading for the world factor bepositive for U.S. output; country factors areidentified by positive factor loadings for outputfor each country, and the regional factors areidentified by positive loadings for the output ofthe first country listed for each region in theAppendix A. Scales are identified followingThomas J. Sargent and Christopher A. Sims(1977) and James H. Stock and Mark W.Watson (1989, 1993) by assuming that each �fk
2
is equal to a constant.Because the factors are unobservable, special
methods must be employed to estimate the
7 Technically, our procedure is “Metropolis withinGibbs,” as one of the conditional distributions—for theautoregressive parameters given everything else—cannotbe sampled from directly. As in Otrok and Whiteman(1998), we follow Chib and Greenberg (1996) in employinga “Metropolis-Hastings” procedure for that block.
8 We add regional and country factors, which appear inequations for a subset of the observable variables, to thesingle factor model in Otrok and Whiteman (1998). Thisresults in some additional modifications to the conditionaldistributions of the observables given the factors (as thereare additional factors). The conditional distributions foreach of the factors given the parameters and the otherfactors is derived as in Otrok and Whiteman (1998, pp.1003–4): derivation of each factor conditional requires the
1220 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
model. Gregory et al. (1997) follow Stock andWatson (1989, 1993) and treat a related modelas an observer system; they use classical statis-tical techniques employing the Kalman filterfor estimation of the model parameters, andthe Kalman smoother to extract an estimate ofthe unobserved factor. Otrok and Whiteman(1998) used an alternative based on a recentdevelopment in the Bayesian literature onmissing data problems, that of “data aug-mentation” (Martin A. Tanner and Wing H.Wong, 1987).
In our context, data augmentation builds onthe following key observation: if the factorswere observable, under a conjugate prior themodel (1)–(4) would be a simple set of regres-sions with Gaussian autoregressive errors; thatsimple structure can in turn be used to deter-mine the conditional (normal) distribution ofthe factors given the data and the parameters ofthe model. Then it is straightforward to generaterandom samples from this conditional distribu-tion, and such samples can be employed asstand-ins for the unobserved factors. Becausethe full set of conditional distributions isknown—parameters given data and factors, fac-tors given data and parameters—it is possible togenerate random samples from the joint poste-rior distribution for the unknown parametersand the unobserved factor using a Markov-Chain Monte Carlo (MCMC) procedure. In par-ticular, taking starting values of the parametersand factors as given, we first sample from theposterior distribution of the parameters condi-tional on the factors; next we sample from thedistribution of the world factor conditional onthe parameters and the country and regionalfactors; then we sample each regional factorconditional on the world factor and the countryfactors in that region; finally, we complete onestep of the Markov chain by sampling eachcountry factor conditioning on the world factorand the appropriate regional factor.6 This se-quential sampling of the full set of conditional
6 The sampling order within each step is irrelevant. Allthat matters is that samples are taken from each of the“blocks” of unknowns (parameters, world factor, regionalfactors, country factors) conditional on the data and all theother blocks. We in fact experimented with changing theorder, and the results obtained were identical to those pre-sented below.
distributions is known as “Gibbs sampling” (seeSiddhartha Chib and Edward Greenberg, 1996;John Geweke, 1996, 1997).7 Under regularityconditions satisfied here, the Markov chain soproduced converges, and yields a sample fromthe joint posterior distribution of the parametersand the unobserved factors, conditioned on thedata. Additional details can be found in Appen-dix B and Otrok and Whiteman (1998).8
A practical benefit of our procedure is that itcan easily be applied to a large cross section ofcountries. The reason is that a large cross sec-tion merely means a large number of very sim-ple conditional normal distributions of the formof equation (1). What makes the problem chal-lenging is a long time series—because thecovariance matrices in the conditional distribu-tions for the factors are of dimension T; if it isnot practical to invert these directly, specializedrecursive procedures must be employed. Thuswhile the estimation problem can be difficult inthe time-series dimension, it easily decomposesinto independent, simple calculations in thecross section. Classical maximum likelihoodmethods generally do not so decompose, andare difficult to apply to a problem of this dimen-sion, because with over 1,600 parameters and68 dynamic factors, the dimension of the prob-lem poses a serious challenge to current hill-climbing techniques.9
completion of a square to obtain the mean and variance ( f,H�1 in their notation) of the Gaussian distribution in theirexpression (9). Thus the covariance matrix (H�1) for afactor involves squares of quasi-differencing matrices (theirSi matrices) from equations in which that factor appears,and the mean involves the matrix weighted average ofresiduals from those equations.
9 A classical alternative that does exploit the decompo-sition involves using the “EM” algorithm to maximize the
1221VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
The data are from the Penn World Tables(PWT), version 5.5 (see Robert Summers andAlan Heston, 1991, and Heston et al., 1994).We use output, consumption, and investmentdata, and restrict attention to those countrieswith a data quality grade of C� or higher, andfor which data are available for each of theyears 1960–1990.10 Each series was log first-differenced and demeaned (as in Otrok andWhiteman, 1998).11 Thus we used M � 3 seriesper country for N � 60 countries, with T � 30time series observations for each. The countriesin our data set and our R � 7 regional defini-tions are given in Appendix A. One concernwith procedures that extract measures of theworld business cycle is that large countriesdrive the world component simply because oftheir size. In the procedure used here we areworking in growth rates, so the size of thecountry can have no direct impact on the results.That is, the econometric procedure that extractscommon components does not distinguish be-tween a 2-percent growth rate in the UnitedStates and a 2-percent growth rate in the IvoryCoast.12 Put another way, the procedure is a
10 We do not consider the periods of fixed and flexibleexchange rate regimes separately, for two reasons. First,there is not conclusive evidence about whether one ought tosplit the sample in this way. For example, Baxter andStockman (1989), Baxter (1991), and Shaghil Ahmed et al.(1993) find that different types of exchange rate regimes donot result in significant changes in the behavior of the mainmacroeconomic aggregates, though Gerlach (1988) con-cludes that the exchange rate regime has a significant impacton the stylized business-cycle facts. Second, we do not haveenough data to examine the fixed and flexible exchange rateperiods separately. There are only 12 observations for thefixed exchange period and 18 for the flexible period.
11 The qualitative results in the paper do not changemuch when we use Hodrick-Prescott filtered versions of thelogarithms of the raw data series. The one notable exceptionis that the importance of the world factor for explainingoutput volatility in the United States falls to 16 percent. Allother results documented below remain unchanged.
12 We also estimated the model using per capita growthrates, and the results were virtually identical.
decomposition of the second moment propertiesof the data (e.g., the spectral density matrix).
In our implementation, the length of both theidiosyncratic and factor autoregressive polyno-mials is 3. The prior on all the factor loadingcoefficients is N(0, 1). For the autoregressivepolynomials parameters the prior was N(0, �),
where � � �1 0 00 0.5 00 0 0.25
� . Because the
data are growth rates, this prior embodies thenotion that growth is not serially correlated;also, the certainty that lags are zero grows withthe length of the lag.13 Experimentation withtighter and looser priors for both the factorloadings and the autoregressive parameters didnot produce qualitatively important changes inthe results reported below. As in Otrok andWhiteman (1998), the prior on the innovationvariances in the observable equations is InvertedGamma (6, 0.001), which is quite diffuse.
Because we are not sampling from the pos-terior itself (the elements of the Markov chainare converging to drawings from the posterior),it is important to monitor the convergence of thechain. We did so in a number of ways. First, werestarted the chain from a number of differentinitial values, and the procedure always con-verged to the same results. Second, we experi-mented with chains of different lengths rangingfrom lengths of 5,000 to 50,000. For chains oflength 10,000 or greater the results were thesame. The results we report in the paper arebased on a chain of length 50,000.
II. The Dynamic Factors
Figure 1 presents the median of the posteriordistribution of the world factor, along with 33-and 66-percent quantile bands; the narrownessof the bands indicates that the factor is esti-mated quite precisely. The fluctuations in thefactor reflect the major economic events of thelast 30 years: the steady expansionary period ofthe 1960’s, the recession of the mid-1970’s(associated with the first oil price shock), the
likelihood function. In this procedure, given an initial guessat the factors, regressions are used to maximize the likeli-hood (the “M” step); then the Kalman smoother is used toestimate (the “E” step) the factors given the regressionestimates. This sequential process continues until the like-lihood is maximized. This can take a very long time. Ingeneral applications, the accepted practice is to use EM toget “close,” and then switch to a direct hill climb; the switchis not feasible for a problem as large as ours.
13 Otrok and Whiteman (1998) discuss the procedure forensuring stationarity of the lag polynomial. The methodinvolves drawing from a truncated normal distribution in theMetropolis-Hastings step described in footnote 7.
1222 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
recession of the early 1980’s (associated withthe debt crisis and the tight monetary policies ofmajor industrialized nations), and the downturnand recession of the early 1990’s.
Our estimate of the world factor suggests thatthe downturn in the early 1980’s was as severeas the recession of the mid-1970’s. In contrast,Gregory et al. (1997), who restricted their at-tention to a sample of output, consumption, andinvestment series for the G7 countries, foundthat the world component exhibited a more se-vere recession in 1974 than in 1982. Thus itseems that our inclusion of developing econo-mies as well provides a different picture of thetwo recessions.14 In particular, the debt crisismarking the recession of 1982 heavily affectedeconomic activity in a number of developingcountries, especially those in Latin America. Ev-idently, developed countries were hit harder by theoil shock of the 1970’s, while the rest of the worldwas hit harder by the shocks of the 1980’s.
FIGURE 1. WORLD FACTOR
14 To ensure that this result is due to the scope of thesample, and not our approach, we employed our proceduresto estimate a dynamic factor model using the G7 dataemployed by Gregory et al. (1997), and found a resultsimilar to theirs, that the unobserved aggregate factor dis-plays a deeper downturn in 1974 than 1982. To furtherexamine the depth of these two different recessionary peri-ods, we also computed an aggregate world output measure(following Raymond Riezman and Whiteman, 1992) usingthe size-weighted aggregate output of the countries in oursample, and compare this measure with the estimated worldfactor. This world aggregate output also has the propertythat the mid-1970’s recession is slightly less severe than thatin 1982.
Because the factor is unobservable and wehave merely extracted an estimate of it based onits hypothesized relationships to time series wecan observe, it is much easier to determine whatthe factor is not than to agree on what it is. Forexample, the relationship between internationalmacroeconomic activity and changes in oilprices has received considerable attention in theliterature;15 is the world factor anything morethan a stand-in for oil prices? Indeed, it displaysits largest troughs just after large sudden in-creases in the price of oil.16 But to be moreprecise, the contemporaneous correlation be-tween the median world factor and the changein the oil price is negligible (�0.07), and thecorrelation between the oil price change and theworld factor one year later is only �0.26. Thiscorrelation is driven in large part by two obser-vations in the data set. Dropping the 1974 oilprice increase (and the corresponding fall in theworld factor in 1975) lowers the correlation to�0.16. Eliminating the 1980 oil price increaseand subsequent fall in the world factor drops thecorrelation to �0.06. Thus while oil prices maybe an important source of international shocks,understanding world business cycles will likelyrequire going beyond oil price changes alone.
To attempt to discover whether the worldfactor is an amalgam of oil shocks and some-thing else, e.g., monetary policy shocks, westudied a variety of dynamic systems with mul-tiple world factors. Yet across multiple identi-fications, we found no significant evidence of asecond world factor. We employed identifica-tion schemes for the second world factor rang-ing from a positive loading for the output of amajor oil-exporting country (Venezuela), a pos-itive loading for the output of a developed Asiancountry (Japan), to a positive loading for theoutput of a developing country (Kenya). Fi-nally, we estimated a model with the secondworld factor normalized to German investmentgrowth. In all cases, the second factor washighly correlated with the first, and displayed avariance several orders of magnitude smallerthan that of the first. Further, its introduction to
15 See Backus and Crucini (2000).16 To be more specific, major oil price increases of 1974
and 1980–1981 were followed by the global recessions of1975 and 1982. The oil price data is from Backus andCrucini (2000).
1223VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
FIGURE 2. RESCALED OUTPUT AND DYNAMIC FACTORS
country-specific factor along with the world fac-tor, the North American regional factor, and thegrowth rate of U.S. output. To make the scalescomparable, the country, region, and world fac-tors are multiplied by their median factor load-ings in the U.S. output equation. Thus the sumof the three scaled factors and the idiosyncraticcomponent of U.S. output is equal to the U.S.output (growth) series.
Several of the peaks and troughs of the U.S.country factor coincide with NBER referencedates: the recessions of 1970, 1975, 1980, and1982, and the booms of 1973, 1981.17 Similarly,movements in the world factor are consistent
17 The NBER reference business-cycle dates: Troughs:February 1961, November 1970, March 1975, July 1980,November 1982, March 1991. Peaks: April 1960, December1969, November 1973, January 1980, July 1981, July 1990.
the analysis changed very little else, and inparticular did not change estimates of the firstfactor in a qualitatively meaningful way. Fi-nally, while formal Bayesian model comparisonvia odds ratios is problematic with models ascomplex as ours, we did calculate values of theJushan Bai and Serena Ng (2002) factor modelselection criteria at the posterior median of allour parameters. None of their six criteria fa-vored increasing the number of world factorsfrom 1 to 2.
To gain some insight into what the worldfactor is capturing, and how the various factorsinteract, we also studied relationships amongthe world factor, country factors, regional fac-tors, and output in four selected countries: theUnited States, Germany, Japan, and Mexico.The results are presented in Figures 2(a)–2(d).
In Figure 2(a) we plot the median of the U.S.
1224 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
with some of the business-cycle reference dates:the troughs of 1975, 1980, 1982, and the peaksof 1969, and 1973. While the U.S. factor and theworld factor exhibit some common movements(e.g., the troughs of 1975, 1980, and 1982, andthe peak of 1973), there are also some notabledifferences between the two factors: the worldfactor is booming in 1970, whereas the U.S.country factor reflects the domestic contraction.An additional difference is that the world factorshows a relatively prolonged recession duringthe 1980’s, while the U.S. country factor exhib-its back-to-back booms in 1981 and 1984. Thecorrelation between the median world factorand U.S. output growth is 0.616, indicating thatthe United States represents an important sourceof world economic fluctuations.
Figure 2(b) presents the median of the Ger-man country-specific factor along with theworld factor, the European regional factor, andthe growth rate of German output. Again, thecountry, region, and world factors are multi-plied by their median factor loading coeffi-cients. The country factor captures the Germanrecessions of 1967, 1975, and 1982, and exhib-its the peaks of 1964, 1973, and 1979.18 Thepattern of fluctuations suggests that the Germanrecession of 1982 and the boom of 1973 wereworldwide events, while the recovery of themid-1970’s, the peaks of 1979 and 1983, andthe troughs of 1969 and 1975 were more dis-tinctly German phenomena. The European re-gional factor only loosely reflects Germanoutput, though it does reflect the German reces-sions of 1967, 1975, and 1982, and peaks of1964 and 1973.
Figure 2(c) displays the medians of the Japan,world, and developed-Asia factors, togetherwith the growth rate of Japan’s output. Note thatthe very rapid growth of the late 1960’s wasdistinctly Japanese—the world factor does notshow strong comovement with Japanese outputduring this period, but the country-specific fac-tor does. The OPEC recession hit harder andfaster in Japan than the rest of the world, re-flecting Japan’s strong dependence on importedoil. While the estimated country-specific factordisplays minor recessions in 1965, 1971, and
18 These peak and trough dates are taken from Artis et al.(1997).
1980, the growth rates of output during theseyears are positive. The reason is that whileJapanese output increased in 1965, 1971, and1980, there were marked declines in Japaneseinvestment just before or during these years,and the estimated country factor captures thecommon movements in output, consumption aswell as investment. For the first half of the1980’s, as Japan went, so went the world. Butthe downturn of the latter half of the decade wasidiosyncratically Japanese.
The country-specific factors of developingeconomies also exhibit some important histori-cal episodes. For example, the country factorsof several Latin American economies (such asChile and Argentina) display the downturn as-sociated with the debt crisis in 1982. Figure2(d) plots the median of the Mexican factoralong with the medians of the world and regionfactors and Mexican output growth. The patternof comovements reveals that since the mid-1970’s, fluctuations in Mexico have been verydifferent from those in the rest of the world andeven in Latin America—the country factormoves very closely with output growth duringthe large swings surrounding the debt crisis.
The results reported in this section suggestthat to the extent that there are country-specific,regional, and worldwide sources of economicshocks, these play different roles at differentpoints in time and around the globe. In someepisodes, the country factor was more stronglyreflective of domestic economic activity, whilein others the domestic growth reflected the com-mon worldwide pattern embodied in the worldfactor. After assessing the persistence propertiesof the dynamic factors in the next section, weexamine the quantitative importance of thecommon factors in explaining variations in out-put, consumption, and investment growth moreformally in Section IV.
III. Persistence Properties of the DynamicFactors
Are common, worldwide fluctuations morepersistent than those in individual countries orregions? To measure persistence, we calculatethe first-order autocorrelation implied by theparameters of the estimated autoregressive co-efficients [equations (3) and (4)] at each step ofthe estimation procedure so that we can calcu-
1225VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
TABLE 1—AUTOCORRELATIONS OF DYNAMIC FACTORS
World 0.482 Latin America �0.059 Asia (Developed) 0.018 Europe �0.095North America �0.042 Africa 0.014 Asia (Developing) �0.057 Oceania 0.071
19 We also calculated autocorrelations for the factors bycalculating the first autocorrelation of the factors themselvesat each step of the estimation procedure. The differencesbetween results obtained using the two approaches are mi-nor.
try factors exhibit positive autocorrelation.However, in most cases the autocorrelation ismuch smaller than that of the world factor. Thehigh serial correlation in the Spanish factor isnot surprising given that Spain’s output, con-sumption, and investment time series are morepersistent than those of other countries. Indeed,the Spanish factor is the only country factormore persistent than the world factor. Countrieswhose country factors exhibit relatively lownegative autocorrelation, such as Bangladesh,Colombia, Senegal, and Sri Lanka all have neg-atively autocorrelated output, consumption, andinvestment growth. Similarly, countries whosecountry factors exhibit relatively high positiveautocorrelations, such as Spain, Philippines,Singapore, and Norway have positively auto-correlated growth in output, consumption, andinvestment series.20
The results indicate most of the persistent, orlow frequency, comovement across economiesis captured by the world factor. The higher-frequency comovement seems to be captured bythe regional and country factors.
IV. Variance Decompositions
To measure the relative contributions of theworld, region, and country factors to variationsin aggregate variables in each country, we
20 Our results regarding persistence properties of worldand country factors are different than those of Gregory et al.(1997) on some dimensions. For example, their resultssuggest that the Japan and Germany factors are negativelyautocorrelated, while the Canada, France, and Italy factorsare positively autocorrelated. We find that the Canada,Germany, France, and Japan factors are positively autocor-related, and the Italian factor is negatively autocorrelated.Considering the different scopes (recall that they use onlyG7 countries, while we use 60 developing and developed
late the distribution of the estimates.19 The me-dians of the estimated autocorrelations for theworld and region factors are presented in Table1. The medians of the country factor autocorre-lations are presented in a histogram in Figure3. To save space we do not report the quantilesof the distribution, but the estimates are gener-ally fairly tight.
The world factor has large and positive auto-correlation (0.48); the 33 percent and 67 percentquantiles of this distribution were 0.44 and 0.52.Compared to the autocorrelations of the re-gional factors and most of the country factors,the world factor is much more persistent—thelargest regional factor autocorrelation is 0.07for Oceania, while the North American, LatinAmerican, developing Asia, and European fac-tors are negatively autocorrelated and thusstrongly mean reverting.
The autocorrelations of the country-specificfactors vary substantially across countries, rang-ing from a low of �0.35 (Senegal) to a high of0.52 (Spain). More than two-thirds of the coun-
FIGURE 3. AUTOCORRELATIONS OF THE COUNTRY FACTORS
countries), data (they use quarterly data for 1970–1993 andwe use annual data for 1960–1991), and the differencesbetween models, some discrepancies are to be expected.One important similarity between the two sets of findingsshould be highlighted: in each study, the world factor ismore persistent than the country factors and countries’aggregate output in most cases.
1226 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
TABLE 2—VARIANCE DECOMPOSITIONS FOR THE NORTH AMERICA REGION
21 Even though the factors are uncorrelated, samplestaken at each pass of the Markov chain will not be, purelybecause of sampling error. To ensure adding up, we took afurther step for these calculations, and orthogonalized thesampled factors, ordering the world factor first, the regionalfactor second, and the country factor third. The samplecorrelations between the raw factors was small (the standarderror of a correlation with 30 observations is 0.18), so theorder of orthogonalization has little impact on the results.All of the results remain qualitatively the same under alter-native orderings, and the quantitative differences are small.
We present the variance shares attributable tothe common factors for North America andEurope in Tables 2 and 3. As summary mea-sures of the importance of the factors, thesetables present regional medians of posteriorquantiles as well as 33-percent and 67-percentquantiles of posterior shares for each country.Complete tables with the variance decomposi-tions for each of the remaining countries aregiven in the Appendix (Tables A1–A5).
As Table 2 shows, the world factor explains asignificant fraction of the fluctuations in allthree aggregates in North American countries.The world factor edges out the regional factor asdominant, though both play an important role inNorth America. In these economies, the country-specific factor plays an important role in ac-counting for the investment dynamics: for themedian country, 40 percent of the investmentvariation is due to the country-specific factor.
Table 3 presents variance decompositions forEuropean countries. The world factor explainsmore than 33 percent of output- and 26 percentof consumption-growth variability. However,the world factor share of output-growth volatil-ity ranges widely across these countries, from alow of less than 4 percent in Iceland to a high of68 percent in France. Roughly half of the vol-atility in output growth and about 35 percent ofvariation in investment growth is explained bycountry-specific factors. Notably, the Europeanregional factor plays a relatively minor role inaccounting for the economic activity in these
estimate the share of the variance of each mac-roeconomic aggregate due to each factor. Wedecompose the variance of each observable intothe fraction that is due to each of the threefactors and the idiosyncratic component. Withorthogonal factors the variance of observable ican be written:21
(6) var�yi,t � � �biworld�2var� f t
world�
� �biregion�2var� f r,t
region�
� �bicountry�2var� f n,t
country�
� var��i,t �.
The fraction of volatility due to, say, the worldfactor would be:
�biworld�2var� ft
world�
var�yi,t �.
These measures are calculated at each pass ofthe Markov chain; dispersion in their posterior
1227VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
22 Because there are only two countries (six series) in ourversion of Oceania, identification of the two country factorsand the region factor is weak at best. The static factor modelfor six series and three factors (the world factor can bethought of as identified in the remainder of the world) is notrestrictive, meaning that identification of the dynamic re-gion and country factors for Oceania rests on subtleties inthe dynamics of the observables and factors. Thus we drawno conclusions about the country and region factors forOceania.
can economies; evidently, African economicfluctuations are not like those in most of the restof the world.
Another region with little apparent comove-ment with the rest of the world is Asia (Devel-oped and Developing; see Tables A3 and A4).In this region, country factors again play thedominant role in explaining the volatilities ofgrowth in output and consumption. Country fac-tors explain about 70 percent of output variationand half of consumption volatility. Moreover,as in African countries, most of the variation ininvestment is attributable to the idiosyncraticcomponent, and the world factor plays a modestrole, explaining only 5 percent of output vola-tility. Japan is the only outlier in Asia; for it, theworld factor is much more important, and thecountry and idiosyncratic factors less important,than in the rest of the region. The finding thatthe world factor explains 38 percent of Japaneseoutput growth volatility and 36 percent of con-sumption growth volatility is much closer to theresults for other G7 economies than the Asianregion.
Tables 2–4 and the tables in Appendix Aexhibit some important regularities. The first isthat there is a world business cycle. As Table4 indicates, the world factor (the world businesscycle) accounts for almost 15 percent of aggre-gate variation in output growth, almost 9 per-cent of consumption growth variation, and 7percent of investment growth volatility. Thehistogram in Figure 4 further illustrates thispoint. This figure shows that in the majority ofcountries the world factor explains a significantamount of output growth volatility. Further,most countries’ output and consumption growthfactor loadings on the world factor are distinctlypositive (the posterior distributions of the factorloadings have very little mass in symmetric
countries: it accounts for more than 5 percent ofoutput volatility in only one country (Belgium).The country-specific factor and the idiosyn-cratic components seem to be important ininducing variations in consumption and invest-ment in European countries: together they ex-plain 77 percent of consumption volatility and63 percent of investment volatility.
Though less important than in North Americaand Europe, the world factor explains a notice-able fraction of aggregate volatility in countriesin Latin America, Developed Asia, and Oceania(see Tables A1, A3, and A5). For example, theworld factor accounts for more than 14 percentof output and 7 percent of consumption volatil-ity in Latin American countries, and between 6and 15 percent of the output variance in theDeveloped Asia and Oceania regions. As inEurope, country-specific factors capture thegreatest share of output fluctuations in theregions.22
Unlike North America and Europe, for Af-rica, the country factors explain the majority ofvolatility in output and consumption (see TableA2), accounting for more than 68 percent ofoutput volatility and 76 percent of consumptionvariation. A large fraction, 88 percent, of invest-ment variability is due to the idiosyncratic com-ponents in African countries. The world factorexplains little of output variation in most Afri-
25 Backus et al. (1995) refer to apparent inconsistencybetween the theory and the data as “the quantity anomaly.”(A simple model with risk sharing would suggest that con-sumption across countries ought to be more correlated thanoutput.) We computed cross-country correlations of outputand consumption and found that 1,087 out of 1,770 con-sumption growth correlations across countries are lowerthan the associated output growth correlations.
26 Zimmermann (1995) uses the quarterly data of 19
1229VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
intervals about zero).23 Thus because the worldfactor is identified by a positive factor loadingfor U.S. output growth, there is a sense in whichwhat is good for the United States is good forthe world.
Second, the world factor plays a more impor-tant role in explaining economic activity in ad-vanced industrialized countries than it does indeveloping economies. Table 4 compares theworld median to the G7 median: while theworld factor explains 37 percent of outputgrowth volatility in the G7 economies, 15 per-cent of output growth variation in other coun-tries is attributable to the world factor. Thispattern extends to consumption and investmentgrowth: the world factor captures almost 19percent of the variation in investment growth,and approximately 36 percent of consumptiongrowth volatility in the G7 economies.24
Third, the world and regional factors togetheraccount for a larger share of fluctuations inoutput growth than in consumption growth in42 out of 60 countries. While these two factorstogether explain more than 11 percent of con-sumption growth volatility, they account foraround 17 percent of aggregate output growthvolatility. This implies that in most countries
FIGURE 4. OUTPUT VARIANCE DUE TO WORLD FACTOR
23 There are too many factor loadings (540) for us toreport the posterior distributions.
24 Our results regarding the world factor being moreimportant in explaining the business-cycle fluctuations inthe developed economies than those in the developing onesare consistent with the findings in Kouparitsas (1997a). Hefinds that productivity shocks originating in the developednorthern countries play a much smaller role in explainingthe volatility of the developing southern countries’ outputthan those productivity shocks originating in the South.
the country factor plays a more important role inexplaining consumption movements than theworld and regional factors. This result is con-sistent with a widely documented observation inthe international business-cycle literature:cross-country correlations of output growth arelarger than those of consumption growth.25
Fourth, country factors and idiosyncraticcomponents play a much larger role in account-ing for investment dynamics than the world andregion factors. The country factor explains 35percent of investment growth fluctuations, andthe idiosyncratic (unexplained) components ac-count for 47 percent (see Table 4). The worldand regional factors combined account for only9 percent of investment growth volatility.The idiosyncratic behavior of investment vola-tility in our model is consistent with observedcross-country investment correlations: thesecorrelations are low and generally lower thanthe cross-country correlations of output (seeChristodoulakis et al., 1995; Christian Zimmer-man, 1995).26
Fifth, investment dynamics are much moreidiosyncratic in developing countries than indeveloped ones. More than 83 percent (Devel-oping Asia) and 88 percent (Africa) of in-vestment volatility must be attributed to idio-syncratic components, while for developedeconomies the largest role for such componentsis in Developed Asia, where roughly 41 percentof the variation in investment is idiosyncratic.27
In contrast, 15 percent of G7 and 28 percent of
industrialized countries. His results indicate that 70 out of110 cross-country investment correlations are lower thanthose of output. Christodoulakis et al. (1995) use the annualdata of 12 EU countries. They find that 48 out of 66cross-country investment correlations are lower than thoseof output. We also computed cross-country correlations ofoutput and investment for the economies in our sample:1,098 out of 1,770 cross-country investment correlations arelower than those of output correlations.
27 One explanation for the large role of the idiosyncraticfactor in developing economies is measurement error. Ifmeasurement error is larger in developing economies, which
1230 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
European investment volatility is idiosyncratic.The investment and output dichotomies be-tween the developing and developed economiespose questions for future research: what forcesdrive output and investment dynamics in devel-oping economies to be so different from oneanother and the world, and why are fluctuationsin developed economies so similar?
Sixth, our findings indicate that regional fac-tors play a minor role in explaining macroeco-nomic variation: they explain less than 3 percentof output, consumption, and investment growthvolatility in the median country (see Table 4).The regional factor seems to be playing its mostimportant role in the North America region.28
The histogram in Figure 5 illustrates how smalla role the regional factors play in explainingoutput variability.
Finally, we find no evidence of the Europeancycle, for little of the volatility of the Europeanaggregates can be attributed to the commonEuropean factor. This result stands in contrast tothose of several recent studies that have arguedto the contrary. Lumsdaine and Prasad (2003)estimated a European common component us-ing industrial production data for 14 Europeancountries; they found high positive correlations
FIGURE 5. OUTPUT VARIANCE DUE TO
THE REGIONAL FACTOR
28 This result is consistent with those of Bergman et al.(1998) who find, through cross-country correlations of out-put fluctuations for the 1880–1995 period, business cyclesin Canada and the United States move very closely dur-ing the 1880–1995 period for all monetary regimes theyexamine.
between country fluctuations and the Europeancomponent. They interpret this result as an ev-idence for a European business cycle. In a re-lated study, Artis et al. (1997) examined cyclesusing industrial production data for G7 and fiveother European economies. They concluded thatthere exists a European business cycle. In arecent paper, Bergman et al. (1998) found highand significant correlations between outputfluctuations of six European countries and in-terpreted this result as an outcome of a Euro-pean common market. Our findings indicate thata significant fraction of the common variationsacross economies is captured by the world fac-tor. That is, while the European aggregates dodisplay comovement, the source is not distinctlyEuropean, but rather, worldwide. Moreover,this result is robust to redefinitions of the Eu-ropean region. We estimated a model with twoEuropean factors, one for a group of “core”European countries (France, Germany, Bel-gium, Netherlands, Italy, and Ireland), and asecond factor for the remaining European coun-tries, with the other regions defined as previ-ously. The results are virtually unchanged. Theregional factor for the core group of Europeancountries explained 6 percent of output volatil-ity, 3 percent of consumption volatility, and 7percent of investment volatility.
V. The Relation Between Economic Structureand the Dynamic Factors
To aid in interpreting the 180 variance de-compositions of the previous section and theAppendix, in this section we attempt to charac-terize the relationship between the structuralcharacteristics of economies and the relativeimportance of the three types of factors. To dothis, we employ a simple data summary deviceinvolving regressions. In particular, we regressthe fraction of variance of an observable (out-put, consumption, investment) attributable toa particular factor (world, regional, country-specific) on a variety of explanatory variablesthat are related to country characteristics. Itshould be emphasized that the regressions inTables 5A–5C are merely suggestive of a re-sponse surface; the reported t-statistics onlysuggest which regularities merit further study.Reading too much into the t-statistics is prob-lematic because there appears to be some
the quality ratings in the Penn World tables indicate is true,then this error will be picked up by the idiosyncratic factor.
1231VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
TABLE 5A—REGRESSION OF OUTPUT VARIANCE DECOMPOSITION ON ECONOMIC STRUCTURE VARIABLES
29 PCGDP: Real GDP per capita in constant dollars(expressed in international prices, base 1985) from PWT;Gov Shr: Real Government share of GDP [percent] (1985intl. prices) from PWT; Man Shr: Manufacturing valueadded (percent of GDP) from World Tables 1994; outputvolatility is the standard deviation of output growth over thesample period. We have experimented with a variety ofexplanatory variables such as population, area, compositionof exports, composition of imports, terms of trade volatility,openness, composition of GDP, and industrial structure.None of these variables is important in our regressions whenthey are considered together with volatility and per capitaGDP.
output fluctuations. This is consistent with thefinding in Section IV, that the world factorplayed a more important role in explaining out-put fluctuations in developed economies: moredeveloped economies have less volatile aggre-gate output fluctuations. The level of incomeand the relative sizes of government and themanufacturing sectors do not help explain thecross-country pattern of world factor variancedecompositions.
The country and regional factors are moreimportant the more volatile the economy; whatdistinguishes them from one another involvesthe level of income and the size of the manu-facturing sector. Consistent with the developing—developed distinction developed above, thecountry factor plays a more important role inpoorer economies.30 In contrast, though, thecountry factor is more important the larger ismanufacturing’s share of output. The regionalfactor is more important in economies with theopposite characterization, those with higher percapita GDP and smaller manufacturing sectors.The relationship between richer countries andthe regional factor is consistent with previousresults that link the economies of more devel-oped countries more tightly together.
Table 5B shows the connection betweencountry characteristics and the role of the dy-namic factors in explaining consumptiongrowth volatility. The pattern of results is sim-ilar to that for output volatility: the world factor
heteroskedasticity (“Developed” vs. “Develop-ing”) in the error terms.
Table 5A summarizes our results about thelink between the structural characteristics of aneconomy, and the role of the dynamic factors inexplaining output growth volatility. Summarystatistics from three regressions are reported inthe table. For example, the columns under“World factor” report results of regressing the(median) fraction of variance of each country’soutput growth attributable to the world factor ona set of four explanatory variables. The columnsunder “Country factor” report results from asimilar regression using the median fraction ofoutput volatility accounted for by the countryfactor, and so on. In this and the consumptionand investment growth regressions to follow,the four explanatory variables are ratio of percapita GDP to U.S. per capita GDP (PCGDP),the share of government expenditure in GDP(Gov Shr), manufacturing’s share of output(Man Shr), and volatility of GDP growth (GDPVol).29
The coefficient on the volatility of GDPgrowth in the regressions using the world factorvariance decompositions is sizeable and nega-tive, indicating that in less volatile economies,the world factor is more important in explaining
30 Head (1995) finds that country size is negatively cor-related with the volatility of main macroeconomic aggre-gates. He develops a model that generates this feature of thedata as the aggregate shocks affecting all countries have arelatively larger impact on smaller countries. Crucini (1997)constructs a multicountry general-equilibrium model tostudy business cycles in countries of different size and findsthat the model is consistent with several features of the data.
1232 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
TABLE 5B—REGRESSION OF CONSUMPTION VARIANCE DECOMPOSITION ON ECONOMIC STRUCTURE VARIABLES
analysis of comovement across the world,across regions, and within countries. Our paperalso makes a methodological contribution as itprovides a framework to study multiple types ofcomovement simultaneously using a large crosssection of data.
We find that there is a significant commonworld component present in the fluctuations inalmost all of the countries in the sample. Whilea substantial fraction of economic fluctuationsis explained by the world factor in developedeconomies, the country-specific factor and theidiosyncratic component account for more ofthe volatility in developing economies. Giventhe world factor, we find that regional businesscycles, except for North America region, do notplay an important role in explaining aggregatevolatility. We argue regional factors found to beimportant in previous studies are in fact proxiesfor a broader, worldwide factor.
In contrast to output growth fluctuations, con-sumption and investment dynamics are drivenmore by country and idiosyncratic factors. Inparticular, the country dynamic factors play amore important role in explaining consumptionfluctuations than the world and regional factors,a result that is consistent with imperfect con-sumption risk sharing among countries. We findthat the country-specific and idiosyncratic com-
is more important the less volatile the economy,the country-specific factor is more important thepoorer the economy, and the regional factor ismore important the richer the economy. We alsofind that government’s share is positively re-lated to the importance of the country factor.
Table 5C reports results on the link betweenthe structural characteristics and the role ofcommon factors in explaining investmentgrowth volatility. Recalling that roughly half ofinvestment growth volatility is idiosyncratic(Table 4), it is likely to be difficult to discernpatterns in the importance of the three factors inexplaining it. Indeed, the three factors are allmore important in explaining investmentgrowth volatility the richer the economy. Wealso find that as GDP volatility falls the worldfactor explains more of the variance in invest-ment growth, a result that is consistent with thegreater comovement of developed economiesthat we document above.
VI. Conclusion
In this paper we employ a Bayesian dynamiclatent factor model to study the dynamic co-movement of macroeconomic aggregates in abroad cross section of countries. We provide an
1233VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
ponents account for the bulk of the volatility ininvestment.
Our results also suggest that countries forwhich the world factor seems to be important—countries that comove with the world businesscycle—are those with less volatile GDP. Fur-ther, less developed economies are more likelyto experience country-specific cycles. Evi-
dently, there is a world business cycle, and,unsurprisingly, it reflects economic activity inthe developed economies. Further study of thetemporal evolution of the world factor we haveidentified and its relationship to other macro-economic aggregates may prove fruitful in thesearch for the sources of comovement docu-mented in this paper.
APPENDIX A: DEFINITIONS AND DETAILED RESULTS
Regional Definitions
North America Latin America Europe AfricaAsia
(Developing)Asia
(Developed)
USA Costa Rica Bolivia France Italy Cameroon Bangladesh Hong Kong SARCanadaMexico
OceaniaAustraliaNew Zealand
DominicanRepublic
El SalvadorGuatemalaHondurasJamaicaPanamaTrinidadArgentina
1237VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
APPENDIX B: THE MCMC APPROACH TO
DYNAMIC FACTOR ANALYSIS
The dynamic factor analysis model in equa-tions (1)–(4) can be thought of as consisting ofa specification of a Gaussian probability densityfor the data { yt} conditional on a set of param-eters � and a set of latent variables { ft}. Callthis density function gy(Y��, F) where Y de-notes the MNT � 1 vector of data on theobservables, and F denotes the KT � 1 vectorof dynamic factors. In addition, there is a spec-ification of a Gaussian probability density gf (F)for F itself. Given a prior distribution for �,�(�), the joint posterior distribution for theparameters and the latent variables is givenby the product of the likelihood and prior,h(�, F�Y) � gy(Y��, F) gf (F)�(�).
As is shown in Otrok and Whiteman (1998),although the joint posterior h(�, F�Y) is ex-tremely cumbersome, under a conjugate priorfor � the two conditional densities h(��F, Y)and h(F��, Y) are quite simple. Moreover, it ispossible to use this fact and Markov-ChainMonte Carlo methods (MCMC) to generate anartificial sample {�i , Fj} for j � 1, ... , J asfollows:
1. Starting from a value F0 in the support of theposterior distribution for F, generate a ran-dom drawing �1 from the conditional densityh(��F0, Y).
2. Now generate a random drawing F1 from theconditional density h(F��1, Y).
3. This process is repeated, generating at eachstep drawings �j h(��Fj � 1, Y) and Fj h(F��j � 1, Y).
Under regularity conditions satisfied here (seeTanner and Wong, 1987), the sample so pro-duced is a realization of a Markov chain whoseinvariant distribution is the joint posteriorh(�, F�Y).
What makes this process feasible is the sim-plicity of the two conditional distributions. Forexample, h(��F, Y) is easily constructed fromequation (1) when F is known. In particular,equation (1) is just a normal linear regressionmodel for yi given the factors (albeit a regres-sion that has autocorrelated errors). Because theprior for the intercept and factor loadings isGaussian, the conditional posterior for the pa-
rameters (�i , ai , and the bi’s) is also Gaussian.The other conditional density, h(F��, Y) is alittle more complicated because it is the solutionto a Gaussian signal extraction problem. Kal-man filter techniques are commonly used tosolve such problems, but when the time series isshort, as in this application, it is straightforwardto solve the problem directly. Solving the prob-lem without using the Kalman filter is especiallyuseful when the number of factors is large, as inthe problem we study. (With a large number offactors the state equation in the Kalman filtercan become computationally very burdensome.)Otrok and Whiteman (1998) do this as follows:first, they write the joint density for the data andthe dynamic factors given the parameters as aproduct of NMK independent Gaussian densi-ties (NM of them are associated with the ob-servable time series, K with the dynamicfactors). Second, from this joint distribution,simple normal distribution theory is used toobtain the conditional distribution for any oneof the factors given the rest and the parameters.These normal distributions involve inverses ofT � T covariance matrices that can be handledusing conventional procedures provided T is notlarge. In the model analyzed here, T � 30 is notproblematic.
REFERENCES
Ahmed, Shaghil; Ickes, Barry W.; Wang, Pingand Yoo, Byung S. “International BusinessCycles.” American Economic Review, June1993, 83(3), pp. 335–59.
Artis, Michael J.; Kontolemis, Zenon G. and Os-born, Denise R. “Business Cycles for G7 andEuropean Countries.” Journal of Business,April 1997, 70(2), pp. 249–79.
Artis, Michael J. and Zhang, Wenda. “Interna-tional Business Cycles and the ERM: IsThere a European Business Cycle?” Interna-tional Journal of Finance and Economics,January 1997, 2(1), pp. 1–16.
Backus, David K. and Crucini, Mario J. “OilPrices and the Terms of Trade.” Journal ofInternational Economics, February 2000,50(1), pp. 203–31.
Backus, David K.; Kehoe, Patrick J. and Kydland,Finn E. “International Business Cycles: The-ory and Evidence,” in Thomas F. Cooley, ed.,
1238 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003
Frontiers of business cycle research. Prince-ton, NJ: Princeton University Press, 1995, pp.331–57.
Bai, Jushan and Ng, Serena. “Determining theNumber of Factors in Approximate FactorModels.” Econometrica, January 2002,70(1), pp. 191–222.
Baxter, Marianne. “Business Cycles, StylizedFacts, and the Exchange Rate Regime: Evi-dence from the United States.” Journal ofInternational Money and Finance, March1991, 10(1), pp. 71–88.
. “International Trade and Business Cy-cles,” in Gene M. Grossman and KennethRogoff, eds., Handbook of international eco-nomics, volume 3. Amsterdam: North-Holland,1995, pp. 1801–64.
Baxter, Marianne and Stockman, Alan C. “Busi-ness Cycles and the Exchange Rate Regime:Some International Evidence.” Journal ofMonetary Economics, May 1989, 23(3), pp.377–400.
Bergman, U. Michael; Bordo, Michael D. and Jo-nung, Lars. “Historical Evidence on BusinessCycles: The International Experience,” inJeffrey C. Fuhrer and Scott Schuh, eds., Be-yond shocks: What causes business cycles?Boston, MA: Federal Reserve Bank of Bos-ton, 1998, Federal Reserve Bank of BostonConference Series No. 42, pp. 65–113.
Chib, Siddhartha and Greenberg, Edward.“Markov Chain Monte Carlo SimulationMethods in Econometrics.” EconometricTheory, August 1996, 12(3), pp. 409–31.
Christodoulakis, Nicos; Dimelis, Sophia P. andKollintzas, Tryphon. “Comparisons of Busi-ness Cycles in the EC: Idiosyncracies andRegularities.” Economica, February 1995,62(245), pp. 1–27.
Clark, Todd E. and Shin, Kwanho. “The Sourcesof Fluctuations Within and Across Coun-tries,” in Gregory Hess and Eric van Win-coop, eds., Intranational macroeconomics.Boston, MA: Cambridge University Press,2000, pp. 189–220.
Crucini, Mario J. “Country Size and EconomicFluctuations.” Review of International Eco-nomics, May 1997, 5(2), pp. 204–20.
. “International Comovement: Is TheoryAhead of International Business Cycle Mea-surement?” Working paper, Ohio State Uni-versity, 1999.
Gerlach, Stefan. “World Business Cycles UnderFixed and Flexible Exchange Rates.” Journalof Money, Credit, and Banking, November1988, 20(4), pp. 621–32.
Geweke, John. “Monte Carlo Simulation andNumerical Integration,” in Hans M. Amman,David A. Kendrick, and John Rust, eds.,Handbook of computational economics, vol-ume 1. Amsterdam: North-Holland, 1996, pp.731–800.
. “Posterior Simulators in Economet-rics,” in David M. Kreps and Kenneth F.Wallis, eds., Advances in economics andeconometrics: Theory and applications.Cambridge: Cambridge University Press,1997, pp. 128–65.
Gregory, Allan W. and Head, Allen C. “Commonand Country-Specific Fluctuations in Produc-tivity, Investment, and the Current Account.”Journal of Monetary Economics, December1999, 44(3), pp. 423–51.
Gregory, Allan W.; Head, Allen C. and Raynauld,Jacques. “Measuring World Business Cy-cles.” International Economic Review, Au-gust 1997, 38(3), pp. 677–702.
Head, Allen C. “Country Size, Aggregate Fluc-tuations, and International Risk Sharing.”Canadian Journal of Economics, November1995, 28(4), pp. 1096–119.
Heston, Alan; Summers, Robert; Nuxoll, DanielA. and Aten, Bettina. Penn World Table Ver-sion 5.5, Center for International Compari-sons at the University of Pennsylvania(CICUP), November 1994.
Imbs, Jean. “Co-fluctuations.” Working paper,London Business School, 1999.
Kose, M. Ayhan. “Explaining Business Cycles inSmall Open Economies: How Much DoWorld Prices Matter?” Journal of Interna-tional Economics, March 2002, 56(2), pp.299–327.
Kose, M. Ayhan and Yi, Kei-Mu. “InternationalTrade and Business Cycles: Is Vertical Spe-cialization the Missing Link?” AmericanEconomic Review, May 2001 (Papers andProceedings), 91(2), pp. 371–75.
. “The Trade-Comovement Problem inInternational Macroeconomics.” Working pa-per, IMF, 2003.
Kouparitsas, Michael. “North-South BusinessCycles.” Working paper, Federal ReserveBank of Chicago, 1997a.
1239VOL. 93 NO. 4 KOSE ET AL.: INTERNATIONAL BUSINESS CYCLES
. “North-South Financial Integrationand Business Cycles.” Working paper, Fed-eral Reserve Bank of Chicago, 1997b.
Lumsdaine, Robin L. and Prasad, Eswar S. “Iden-tifying the Common Component in Interna-tional Economic Fluctuations.” EconomicJournal, January 2003, 113(484), pp. 101–27.
Mendoza, Enrique G. “The Terms of Trade, theReal Exchange Rate, and Economic Fluctua-tions.” International Economic Review, Feb-ruary 1995, 36(1), pp. 101–37.
Norrbin, Stefan C. and Schlagenhauf, Don E.“The Role of International Factors in theBusiness Cycle: A Multicountry Study.”Journal of International Economics, Febru-ary 1996, 40(1–2), pp. 85–104.
Otrok, Christopher and Whiteman, Charles H.“Bayesian Leading Indicators: Measuringand Predicting Economic Conditions inIowa.” International Economic Review, No-vember 1998, 39(4), pp. 997–1014.
Riezman, Raymond and Whiteman, Charles H.“World Business Cycles.” Working paper,University of Iowa, 1992.
Sargent, Thomas J. and Sims, Christopher A.“Business Cycle Modeling Without Pretend-ing to Have Too Much A Priori EconomicTheory,” in Christopher A. Sims et al., eds.,New methods in business cycle research.Minneapolis, MN: Federal Reserve Bank ofMinneapolis, 1977, pp. 45–108.
Stock, James H. and Watson, Mark W. “NewIndexes of Coincident and Leading Eco-
nomic Indicators,” in Olivier Jean Blanchardand Stanley Fischer, eds., NBER macroeco-nomics annual: 1989. Cambridge, MA: MITPress, 1989, pp. 351–94.
. “A Procedure for Predicting Reces-sions with Leading Indicators: EconometricIssues and Recent Experience,” in James H.Stock and Mark W. Watson, eds., Businesscycles, indicators, and forecasting. Chicago:University of Chicago Press, 1993, pp. 95–153.
Stockman, Alan. “Sectoral and National Aggre-gate Disturbances to Industrial Output inSeven European Countries.” Journal of Mon-etary Economics, March/May 1988, 21(2/3),pp. 387–409.
Summers, Robert and Heston, Alan. “The PennWorld Table (Mark 5): An Expanded Setof International Comparisons, 1950–1988.”Quarterly Journal of Economics, May 1991,106(2), pp. 327–68.
Tanner, Martin A. and Wong, Wing H. “TheCalculation of Posterior Distributions byData Augmentation.” Journal of the Ameri-can Statistical Association, June 1987,82(398), pp. 84–88.
Zarnowitz, Victor. Business cycles: Theory, his-tory, indicators, and forecasting. Chicago:University of Chicago Press, 1992.
Zimmermann, Christian. “International TradeOver the Business Cycle: Stylized Facts andRemaining Puzzles.” Working paper, Univer-sity of Quebec at Montreal, 1995.
