Centre de recherche sur l'emploi et les uctuations �economiques (CREF�E)Research Center on Employment and Economic Fluctuations (RCEEF)

Universit�e du Qu�ebec �a Montr�eal

International Trade

over the Business Cycle:

Stylized Facts

and Remaining Puzzles

Christian Zimmermann �

Universit�e du Qu�ebec �a Montr�eal

March 1995(�rst draft June 1993)

CREF�E/RCEEFUniversit�e du Qu�ebec �a Montr�ealC.P. 8888, Succ. Centre-VilleMontr�eal, Qu�ebecH3C 3P8T�el�ephone: (514) 987{6181FAX: (514) 987{4707

�Department of Economics and Research Center on Employment and Economic Fluctuations, Universit�e

du Qu�ebec �a Montr�eal, P.O. Box 8888, Station Centre-Ville, Montr�eal, Qu�ebec, Canada H3C 3P8. Email:

zimmermann.christian@uqam.ca. I acknowledge the support of the William Larimer Mellon Foundation and

the Swiss National Science Foundation. This is a revised version of the fourth chapter of my dissertation at

Carnegie Mellon University. Finn Kydland, Bennett McCallum, Jos�e-V��ctor R��os-Rull and seminar partici-

pants at the Universit�e du Qu�ebec �a Montr�eal have provided insightful comments, but are not responsible

for any errors.

Abstract

Using quarterly national accounts for 19 industrialized economies, the business cycle behaviorof trade related aggregates and prices is assessed. Emphasis is put on the distinction betweensmall, relatively open, and large, relatively closed, economies. Comparing those facts withthe computational experiments of international real business cycle models, several puzzlesare studied or uncovered. Finally, we determine which facts are crucial for international realbusiness cycle models, that is, in which direction current research should pursue.

R�esum�e

Nous �etudions, pour 19 pays industrialis�es, le comportement cyclique d'agr�egats et de prixtrimestriels li�es au commerce international. La distinction entre les petits pays, plus ouverts,et les grands pays, relativement ferm�es au commerce ext�erieur, est mise en �evidence. Encomparant ces faits stylis�es avec les pr�edictions de mod�eles internationaux du cycle r�eel, nousanalysons plusieurs �enigmes, dont certaines sont nouvelles. Finalement, nous d�eterminonsquels faits stylis�es sont cruciaux pour un mod�ele international du cycle, donc dans quelledirection la recherche doit s'orienter.

Journal of Economic Literature Classi�cation: E32, F41Keywords: Open economymacroeconomics; International trade; Business cycles; Small coun-tries.

1 Introduction

The study of business cycles has traditionally concentrated on the United States. This comesfrom the availability and quality of the data, the fact that this country constitutes the largesteconomy and that the scholars are mostly based in this country. But this comes also fromthe belief that there is no need to study other economies, Lucas (1977, page 10):

[...] There is, as far as I know, no need to qualify these observations [on bu-siness cycle co-movements] by restricting them to particular countries or timeperiods: they appear to be regularities common to all decentralized market eco-nomies. Though there is absolutely no reason to anticipate it, one is led by thefacts to conclude that, with respect to the qualitative behavior of co-movementsamong series, business cycles are all alike. To theoretically inclined economists,this conclusion should be attractive and challenging, for it suggests the possibilityof a uni�ed explanation of business cycles, grounded in general laws governingmarket economies, rather than in political or institutional characteristics speci�cto particular countries or periods.

I have omitted the behavior of foreign trade statistics from the above catalogueof phenomena-to-be-explained, in part because, for a large economy like the U.S.,trade statistics do not exhibit enough conformity to be cyclically interesting. Fora smaller country, to be sure, export movements would do much to \explain"cycles, but to focus on open-economy explanations would, I think, beg the moredi�cult and crucial question of the ultimate origins of cyclical movements.

This paper studies the business cycle behavior of 19 industrialized countries, focussing ontrade related series. With Hodrick & Prescott (1980), Kydland & Prescott (1982) andLong & Plosser (1983) and the techniques developed therein, the need to establish stylizedfacts about the behavior of economies through the business cycle has reemerged. The currentpractice nowadays is to study the volatility of the cyclical components of economic aggregatesas well as their comovements, as advocated by Lucas (1977).

Usually, business cycle researchers establish a limited number of facts, those relevant to themodel to be presented. But there is the need to determine more generally what are thestylized facts of a business cycle. In recent years, a growing literature has performed thisfor individual countries,1 but without comparing them to others more than super�cially. Afew recent studies make some international comparisons, but for a limited number of broadaggregates.2 The most ambitious undertaking so far is that of Backus & Kehoe (1992),who publish statistics on annual data for ten countries over a century. Also, Baxter &

1So Blackburn & Ravn (1992) for Great Britain, Brandner & Neusser (1992) for Austria and Germany,

Danthine & Girardin (1989) for Switzerland, Englund, Persson, & Svensson (1992) for Sweden, Kydland &

Prescott (1990) for the United States, and others.2See Backus, Kehoe, & Kydland (1992, 1994), Blackburn & Ravn (1991), Cooley & Ohanian (1991),

Fiorito & Kollintzas (1994), Head (1991), Tesar (1991) and Zimmermann (1994a).

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Stockman (1989) compare the properties of cyclical components for many countries acrossexchange-rate regimes.

This study focusses on the business cycle comovements relating to trade. We use a uniquedatabase with quarterly national accounts and other data from 19 industrialized economiesover 30 years. We investigate the cyclical behavior of output, imports, exports, their pricede ators, the trade balance, savings, investment and consumption by looking at their volati-lity, their autocorrelations and their comovements with output or other aggregates. We lookalso at cross-correlations, that is the comovements of one a given variable across countries.Emphasis is put on the distinction between large and small countries, as they usually di�eralso in their \openness" as measured by the share of trade to output.

Finally, we compare our �ndings with the moments of standard international business cyclemodels with heterogeneous economies, as well as some more specialized models. We canthen highlight some of the strengths and shortcomings of these models, as well as con�rmor dismiss some known puzzles on the basis of a broader data sample.

The paper proceeds as follows. In the next section, statistics are presented and brie ycommented for various trade related variables. We try to crystallize stylized facts for theirbusiness cycle comovements and compare them to the predictions of international real busi-ness cycle models. Section three makes a summary of these �ndings and discusses on whichstylized facts research should focus on. A �rst appendix gives the sources for the data pre-sented, a second one gives details on the interpretation of the tables. The latter follow atthe end of the paper along with the �gures. The data used will be made available on theInternet. Additional tables relating to statistics mentioned in the text are available from theauthor.

2 Stylized Facts

We provide a series of tables presenting business cycle statistics for several variables andcountries. The HP-�lter has been applied to all data, and the statistics relate to the cyclicalcomponents. Appendix A lists the sources of the data, and appendix B gives details aboutthe interpretation of these tables.

Whenever possible, the data samples range from 1960.I to 1991.II. The samples are shorter forsome countries, but a shorter sample per se does not in uence the statistics. It is possible,with Monte-Carlo experiments, to show that the statistics do not change too much if weremove ten years from the sample. Regressing the moments before and after the truncationgives a correlation coe�cient of around 0.8. However, it is always possible that interestingepisodes are left out in the data.

These facts are compared to sample moments of international real business cycle models.These computational experiments feature general equilibrium models with dynamic opti-mization where the sources of uctuations are idiosyncratic shocks to technology. As areference, we take published and unpublished results from Zimmermann (1994b), which is

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an extension of Backus et al. (1994) with a partition of the world into three countries ofdi�erent sizes. We do not take a symmetric, two country model as a benchmark, becauseit does not allow for di�erences across countries within the same model economy. Further-more, a two country model coerces some behavior that can be prevented with the inclusionof a third one, such as perfectly negative correlations between the trade balances. We will,however, occasionally also refer to other models in the literature.

On several instances, we will make the distinction between large and small countries. Theselection criteria for large countries are: (a) having a signi�cantly large economy, (b) havinga low import share. Using those two criteria we split the sample of 19 countries in two. Forthe �rst, we take the logarithm of total output in 1985 from Summers & Heston (1988)'sdata. The most signi�cant split of the sample is by considering the G-7 countries plus Spainas large countries. Using the average import share, the second criterion distinguishes thesame countries with the addition of Australia and Greece. The latter fail, however, markedlyunder the �rst criterion. We settle therefore with G-7 and Spain as large countries. We thenproceed with providing statistics for large and small countries. These are not computed fromaggregations of country speci�c data, as not all series cover the whole 1960-1991 period, butare weighted averages of the individual statistics.

2.1 Output

Table 1 presents the business cycle statistics for output, as measured by real GDP or realGNP. The standard deviation of its cyclical components shows a wide range across countries,from 1.06% in Spain to 2.31% in Norway. It is striking that countries seemingly highlyintegrated to each other exhibit very di�erent volatilities of output, so Norway and Sweden,or Austria and Germany [see also Brandner & Neusser (1992)]. Aggregating the statisticsinto groups of countries does not yield obvious regularities. If anything, the volatility seemsto be slightly higher in small countries than in larger ones. One would expect a much largerdi�erence, according to the conventional wisdom that sectoral shocks in a large economy aremore likely to be diluted, see Crucini (1993). However, our result is partly driven by thebehavior of the U.S. economy. Indeed, Zimmermann (1994c) �nds that the high volatilityof output in the United States is not replicated with an open-economy real business cyclemodel, whereas it is easily possible for all other countries. Excluding the United States fromthe summary statistics, the average volatility in the world and the large countries is 1.54%.In Zimmermann (1994c), it is shown that diversity of output volatilities even wider than inthe data are attainable with a standard calibration for each country.

Comparing these quarterly statistics to the annual ones of Backus & Kehoe (1992), it isstriking how the represented countries rank di�erently regarding the output volatility. Theirarticle lists Japan as the country with the highest volatility, by far, in the postwar period,followed by the United States, Canada and Italy, the last being Sweden. The quarterlyresults list, for the countries common to both studies, Norway as �rst, then Denmark, theUnited States and Canada. Last are Sweden and Japan. Part of the explanation residesin the di�erent sample, generally 1950-86 for the yearly data and 1960-91 for the quarterly

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data or in the varying degrees of autocorrelation in the quarterly data. Other reasons needto be explored.

Autocorrelations of cyclical components of output have an even larger spread than volatilitiesacross countries, evenly distributed between 0.34 and 0.92. On average, however, autocorre-lations are noticeably higher in large countries. Their correlation with the logarithm of theoutput level is 0.56, signi�cantly di�erent from zero at the 2% level. This will be the case forthe autocorrelation coe�cients of most of the series studied here. This fact is well replicatedin model economies. Notice also that the autocorrelation is generally much lower in Europe.

The cyclical components of output described above are the representation of the businesscycle. Whenever we say that a variable is procyclical, we mean its cyclical components havea positive comovement (correlation) with those of real output.

2.2 Real Imports of Goods and Services

The volatility of real imports is about 5% to 6%, somewhat higher for small countries thanfor large ones. Looking at individual countries, one notices that the spread is much largerthan for the volatility of output. For output, it is from simple to double, while for imports thespread is from 3% to 11%. Even if we take account of the volatility of the overall economicactivity (divide the volatility of imports with the volatility of output), the spread still rangesfrom 2 to 6 (second column). But most countries are clustered around 3.5 times the volatilityof output. Note that the \remote" countries (Japan, Australia, and South Africa) have veryvolatile imports. Imports are procyclical and exhibit generally neither lead nor lag, with theexception of Australia, the Netherlands and Portugal.

This is consistent with the intuition that when the business cycle is high, the excess do-mestic demand can easily be met by imports. This leads to procyclical imports, which areproportionally more volatile than output. Model economies have, however, trouble genera-ting imports su�ciently volatile, especially for large countries. Also, the procyclicality ofimports is generally very close to one. Finally, simulated economies indicate that importstend to lag slightly in large economies, a fact that did not show up in the data here, but willwhen looking at import shares.

2.3 Correlations of Imports with Private Investment

In international real business cycle models, imports are much more driven by productivitydi�erentials generating investment needs than driven by consumption needs. This can beveri�ed in the data by looking at the correlation between real imports and real privateinvestment. We �nd that these two aggregates are indeed strongly correlated, in most caseswithout imports leading or lagging investment. The instantaneous correlation averages at0.66, contrasting with 0.64 for the correlation between consumption and imports (not inthe tables), despite the fact that consumption has a much larger share of imports than

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investment. Only �ve countries have a higher correlation with consumption, among themthe United States and Germany.

Small countries have a somewhat lower correlation between imports and investment. How-ever, the correlations of the average import share with the instantaneous correlations is onlysigni�cantly di�erent from zero at the 20% level with a correlation of 0.32: the higher theimport share, the more imports and investment are correlated. Indeed, with a higher importshare, the domestic producers are less able to absorb demand uctuations, especially ininvestment.

Correlations of imports with investment in international real business cycle models are hig-her than with consumption, as in the data. Both correlations are, however, higher thanobserved, especially in large countries. Simulated results for small countries indicate a nearperfect correlation between imports and investment, while the correlation with consumptionis around 0.75{0.80. In large countries, the �rst correlation is about 0.92, the second rangesfrom 0.82 to 0.95.

Taste shocks, as in Stockman & Tesar (1991), generate stronger correlations imports withconsumption than with imports, as a positive shock increases the marginal utility of con-sumption, consumption and imports, while having only a small impact on investment. Ourresults indicate that taste shocks do not seem to be very important.

2.4 Import Shares to Output

Import shares are a lot more volatile in small countries, mainly due to the higher share ofimports there. Indeed, the �rst column of Table 4 has to be interpreted in percentage points.The average import share of small countries in our sample is 32%, while it is 15% for largeones (World: 17%). So, while the import share is 2.1 times higher, its volatility is 2.2 timeshigher (1.9 times when considering volatility relative to output). Regressing these standarddeviations with the import share yields a correlation coe�cient of 0.62, signi�cant at the0.25% level.

The import share is procyclical in many countries, with the notable exceptions of Germanyand Japan. Procyclicality of the import share occurs if real imports are su�ciently procycli-cal and much more volatile than output. In most cases, a one quarter lag is observed, whichmay hint at some delay in the response of imports to the domestic business cycle, a delay toosmall to appear in the comovements of real imports, but that does appear in simulations.Model economies exhibit the same dependence of volatility on the average import share.However, in small countries, import shares are strongly procyclical, while they are stronglycountercyclical in large countries. This anomaly appears for the following reason: in modeleconomies, the volatility of imports is close to that of output, and these two aggregates arealmost perfectly correlated. The import share is then almost constant, and a little change involatility or procyclicality for imports may lead to pro- or countercyclical import shares. Ina small country, imports are much more volatile, leading always to procyclical import shares.

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2.5 Real Exports of Goods and Services

Exports are less volatile than imports, without exception, with a standard deviation of about4%, or about 2.7 times that of output. There is not a signi�cant di�erence between largeand small countries, but European countries experience less export volatility than others.The standard deviation varies quite a lot across countries, but less than for real imports.However, high volatility of imports often means also high volatility of exports: the twostandard deviations have a correlation with each other of 0.80.

Autocorrelations are generally lower than those of imports, and the contemporaneous cor-relations with output are positive, but low. Only few countries show relatively strong pro-cyclicality of exports: Austria, Canada, the Netherlands, and Switzerland, which all havestrong trade ties with a large neighbor. The \remote" countries do not show any cyclicality,as well as a few other small countries.

This may lead to think that exports are not an important factor in the business cycle.Rather, they seem to be driven much more by the conditions in the other countries: import(demand) is much more procyclical than export (supply). Indeed, only the Netherlands donot verify this rule.

Is it possible to �nd some feedback e�ect from this data? U.S. exports lag the cycle byabout two quarters. Small countries exhibit higher correlations for leads of exports over thecycle, while large ones do for lags. The correlation coe�cients are, however, so low, that itis di�cult to argue that there is a sizable feedback e�ect in the large countries, whereby astrong phase at home (with high imports) leads to high exports only one or quarters later.Among large countries, this can be observed only in the United States and Japan, althoughnot strongly, when looking at comovements between imports and exports (not in the tables).

Model economies share the same properties as the data: exports are less volatile than im-ports, they are procyclical, although not very much, and tend to lag slightly the businesscycle. However, this lag appears for all countries, not only large ones. This comes fromthe shock di�usion process. A good shock in the home country propagates to the otherscountries in the subsequent periods, generating upswings and stronger imports abroad. Ofcourse, this e�ect is less apparent in small countries.

2.6 Export Shares to Output

While the volatility of real exports was barely distinguishable between large and small coun-tries, there is a strong di�erence with the export share: it is 2.4 times as volatile in the smallcountries than in the large ones, while the average export share is 2.1 times higher. Thecorrelation between this standard deviation and the average export share is 0.78, signi�cantat the 0.1% level. The volatility of the export share is higher than that of the import sharein only two countries: Germany and the United States.

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The export share is acyclical, with few exceptions (notably Canada). It is, however, pro-cyclical with a �ve quarter lag in the United States, a unique feature among the countriesstudied here. This may give some fuel to the idea that the United States are a locomotiveof the world economy: a strong U.S. economy leads to strong economies abroad and then tostrong U.S. exports, a feedback that was hinted at in the analysis of real exports. As for thelatter aggregate, we �nd also for the export share that correlations at leads are higher forsmall countries while higher at lags for large countries.

The dependence of the export share volatility on the average export share is also very presentin model economies. However, it is countercyclical, strongly so in small countries.

2.7 Trade balance

As the trade balance is sometimes negative, it is not possible to take logarithms before�ltering to prevent its volatility to increase with time. Therefore, we �lter the ratio of netexports to output, which is not heteroskedastic. The volatilities of net export shares exhibitsimilar features as the import or export shares. That is, they are much more volatile in thesmall countries due to their higher trade share. So the volatility is 2.4 times higher in smallcountries compared to large ones, while the trade share is 2.1 times higher.

The behavior of the trade balance through the cycle shows that the e�ect of the importsare dominating in many countries: net exports are countercyclical, although not much. Onenotable exception is Norway, whose procyclical trade balance may be explained by its largeoil exports. While small countries tend to have net exports slightly lagging the cycle, largeones may show a lead, as in the United States (�ve quarters!) and Germany. In the U.S.case, this is clearly the result of the export share behavior dominating that of the importshare in this respect.

The above analysis is based on the ratio of the nominal trade balance to nominal output.Using real exports, real imports and real output changes the results only slightly. Also,annual data yields very similar results, as shown in Backus & Kehoe (1992).

Model economies replicate qualitatively the facts above, although the volatility is too lowand the countercyclicality somewhat high, depending on the speci�c model economy. Nohard evidence for a lead or a lag appears. There is only a hint of a lead, somewhat strongerfor large countries. One exception is the symmetric two-country model of Backus et al.(1992), which features a four quarter lead as well as a very high volatility. This model has,however, the major drawback that it does not permit cross-hauling (imports and exports atthe same time).

2.8 Import Prices

Import prices are about 3.6 times as volatile as output, quite less in small countries. Theyare unusually volatile in Japan, due to the high share of energy in the imports. The opposite

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is the case for Canada. Import price volatility is independent from business cycle volatility,with a correlation of 0.02 for the 19 countries sampled. Size is however a important factor(correlation of 0.39, signi�cant at the 10% level), the share of fuel in total imports leads toa correlation of 0.77.

Import prices show a strong lead in several countries, especially large ones. The outputof small countries seems relatively uncorrelated with contemporary import prices, despitetheir higher import share. But for large countries, an increase in import prices is likelyto coincide with lower output about a year later. This result may come from oil price uctuations generating supply shocks. Indeed, oil constitutes a larger share of imports inlarger countries than in smaller ones (while the share of energy to output is relatively constantacross countries) and therefore has a larger weight in the import price index.

Model economies without oil input have some trouble replicating the behavior of import pri-ces. Indeed, these prices are by far not as volatile as in the data and are strongly procyclical.However, a signi�cant negative correlation appears at 4-5 quarter leads, as in the data.

2.9 Correlations of Import Prices with Real Imports

The four quarter lead of import prices on the business cycle can be associated with a similarlead of import prices on real imports (remember, the latter were very procyclical). OnlyGermany and Spain do not have such a lead.

Such a lead also appears in simulated data, although stronger for small countries thanfor large ones. However, the contemporaneous correlation is around 0.50{0.60, while it isslightly negative in the data. In a model with exchange rate shocks, Zimmermann (1994a)is, however, able to generate negative contemporaneous correlations, but loses the lead ofimport prices on imports.

2.10 Export Prices

Export prices are less volatile than import prices, about 2.2 times output. They are morevolatile in small countries, to the contrary of import prices. In fact, export and import priceshave the same volatility on average in the small countries, whereas large countries have amuch lower standard deviation of export prices.

Most small countries do not show a signi�cant comovement of export prices with output.Large countries experience, as for import prices, a strong lead of about a year. Note thatexport prices are the only variable where the autocorrelation is not much higher in largecountries.

In international real business cycle models, exports prices are indeed less volatile than importprices and are more volatile in small countries. Quantitatively however, they are much lessvolatile than in the data. Furthermore, there is no sign of a lead, and exports prices are very

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countercyclical. In those models, the export price corresponds to the price of the domesticgood. Backus & Kehoe (1992) show that domestic price levels are indeed countercyclical,in most cases, for the postwar period, using annual data. Meltzer (1986) �nds the same forquarterly postwar data in Canada, Germany, the United Kingdom and the United States.Introducing exchange rate shocks makes a distinction between export prices and domesticprices, and the former are then much less countercyclical.

2.11 Correlations of Export Prices with Real Exports

An increase in export prices coincides often with a decrease in exports after a year in smallcountries, lowering the GNP. These comovements are, however, weak, which explains theacyclicality of export prices. For large countries, we cannot �nd, on average, a signi�cantlagged comovement of export prices on exports, but for the United States and France.

Simulated data exhibits these facts: no strong comovements between real exports and exportprices, indications that there is a lead of export prices, and contemporaneous correlationsare positive in large countries, but negative in small ones, despite the fact that no exportdemand is explicitely modeled.

2.12 Terms of Trade

The terms of trade are de�ned here as the ratio of import prices to export prices, measured bynational accounts de ators when available. They are about 2.3 times as volatile as output,without clear distinction between large and small countries. There is, however, a largediversity across countries, from 1.50% to 6.36%. As argued before, this last �gure for Japancomes mainly from the high share of oil in imports, and may not originate in a measurementproblem, as argued in Backus, Kehoe, & Kydland (1995).

From Table 12, it is apparent that import prices have a stronger e�ect than export prices interms of comovements with output: The terms of trade are generally acyclical and inheritfrom the import prices the strong lead over the business cycle they exhibit for many countries.For small countries, the evidence is, however, dim.

Standard international business cycle models have di�culties matching the volatility of theterms of trade. Backus, Kehoe, & Kydland (1993) call this the price anomaly. The inclu-sion of exchange rate shocks, however, reconciles empirical and theoretical evidence, as inZimmermann (1994a). These monetary shocks also correct to a large extend the strong pro-cyclicality of the terms of trade in standard models. But only small negative comovementsare then generated for leads over the business cycle.

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2.13 Correlations of the Trade Balance to Output Ratio with the Terms of

Trade

Scholars in international economics have traditionally been interested in the relation betweenthe trade balance and the terms of trade in the light of the e�ect of a devaluation on netexports. This has been labelled as the J-curve: imports become initially more expensive,leading to a trade de�cit, but better priced exports eventually pick up in volume, leading toa trade surplus after some time.

The economies we study here are subjected to many shocks, not only devaluations. Instead oflooking at impulse responses, Backus et al. (1994) suggest therefore to consider correlationsbetween the trade balance and the terms of trade. The empirical regularity described aboveis con�rmed in most countries: the contemporaneous correlation is generally negative andgets positive with lags of the trade balance after the terms of trade. As these correlationstay negative for leads, but eventually get positive (something the devaluation story cannotdescribe) , Backus et al. (1994) have termed this feature of the data as the S-curve, whichcame be seen in Figures 1 and 2.

There are a few exceptions to this empirical regularity: Canada, which may have di�erentprice-trade dynamics as a net fuel exporter (however, Norway displays a S-curve), Spain,and, again, the United States. The spread of the S-curves seems to be much narrower forsmall countries, while the S-curves in large countries are generally higher. The curve reachesits highest point after four quarters, on average, but several countries need more than �vequarters.

Note that the net export share is computed using nominal aggregates. Using real aggregatesfor trade and output does not changes the comovements with output, as mentioned above,but in many cases makes the S-curve disappears. Then, only Italy, Japan, the Netherlands,South Africa, and Switzerland exhibit this type of shape. The others have either tent-shapedor at correlation curves.

Standard international business cycle models generate S-curves. The inclusion of transpor-tation costs even induces an earlier trough of the S-curve, at around three quarters, as in thedata for the \remote" countries (Australia, Japan, South Africa). However, the models donot seem to yield steeper curves for large countries. Including government expense shocksimplies higher correlations at all leads and lags, which may explain some of the positivecorrelations observed.

2.14 Correlations of Investment Shares with Savings Shares to Output

Feldstein & Horioka (1980) and Murphy (1984) view the correlation of investment and savingsshares to output as an indicator of the international capital mobility. In a closed economy, itis one. In a very small economy with no restrictions or frictions to capital mobility, it is zero.In between, the larger the country, the higher the correlation, as it becomes more di�cultto �nd external sources to �nance investment and the national pool of savings is larger, see

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Gertler & Rogo� (1990) or Crucini (1993). Through a careful measurement with annualdata on 23 OECD countries, Tesar (1991) �nds that this correlation is generally positive.

This is veri�ed in our quarterly data: large countries have a mean contemporaneous corre-lation of 0.50, whereas small countries average at 0.09. Several small countries even havenegative correlations. But both Italy and the United Kingdom, which we consider as largecountries, have correlations very close to zero. Regressing the contemporaneous correlati-ons on country size reveals a correlation of 0.48, signi�cant at the 5% level. Notice thatsavings shares are leading investment shares in many countries, a feature that does not showup when using annual data. One country is rather puzzling: the correlation is negative inSouth Africa (-0.50), which has been far from experiencing free and frictionless movementsof capital.

Note that savings are measured as output less private consumption and government purcha-ses. As argued in Backus et al. (1992), these are not savings stricto sensu, but are easy tomeasure and capture the distinction needed in the question motivating Feldstein & Horioka(1980). Furthermore, the application of this de�nition is straightforward in model economies.Baxter & Crucini (1993) use a di�erent measure of savings, which is derived from completerisk-pooling across the world. Such a measure can yield signi�cantly lower, even negative,correlations with investment in model economies.

The correlation on quarterly data is lower than those given in the literature for data at lowerfrequencies or cross-sections. Obstfeld (1986) observes that for countries with a high shareof foreign investment or savings, typically small, open countries, a measurement bias leadsto a higher correlation than in reality. Given that the average correlation for small countriesis barely above zero and sometimes even negative, this bias must quite small.

We have not mentioned the volatility. It is higher for savings shares, but as the procyclicalityof the investment shares is stronger, this does not prevent the trade balance from beingcountercyclical (think of X �M = S � I). Both volatilities depend strongly on the size ofthe economy.

Model economies show that the correlation is higher in large countries. Apart from thisregularity, they can generate pretty much any correlation, depending on the dynamics ofthe shocks [Finn (1990)], even very close to one for small economies. Savings shares are,however, a little less volatile than investment shares.

2.15 Correlations of Real Investment with Real Savings

Looking at the same correlations, but using investment and savings levels instead of sha-res, the contemporaneous correlations are with few exceptions higher. Also, the di�erencebetween large and small countries becomes even clearer. Now all large countries have acorrelation well above the average of the small ones, 0.26. Regressing those correlations onsize, we obtain a correlation coe�cient of 0.60, signi�cant at the 0.5% level. Note also thatsavings lead investment now only in one country, Australia, probably because of the missing

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inventories in the de�nition of savings. Simulated results are not signi�cantly di�erent fromusing shares to output rather than levels.

2.16 Cross-correlations

Cross-correlations indicate to what extend economies are synchronized. We look at sixvariables for which international real business cycle models have very strong predictions.For each variable, we �rst consider the cross-correlations for the 171 pairs of countries3,then summarize them to averages for various groupings of pairs. Finally, we compare thosestatistics with model predictions.

Previous discussions, as in Backus et al. (1995), limited themselves to cross-correlationsof various countries with the United States, the justi�cation being that this country takesaround 40% of OECD output. This should not necessarily be so. For example, Europeancountries have probably closer ties with each, be it because of policy coordination, managedexchange rates or lower transportation costs. The European environment is much closer, inthese respects, to the premises of international real business cycle models. Also, the UnitedStates is the country with the lowest import share, and, as we quoted Lucas (1977) in theintroduction, is not really interesting to study as an open economy.

Output

The average cross-correlation of output is positive, at 0.24. For some country pairs (12% of allcases), it is negative, with a high concentration of such cases in pairs with Portugal (whichhas a short data sample) and South Africa (whose synchronization has been hindered byembargoes). We can therefore de�nitely say that the cross-correlation of output is positive.Note that the cross-correlations of output are consistent with those reported by Backus &Kehoe (1992) for annual postwar data. Theirs average at 0.26, with a correlation of 0.73with ours.

Looking into subcategories gives us a more precise view. Output cross-correlations are higheramong neighbors and lower with remote countries, which should not be a surprise. Largecountries appear to be more in synch with each other than small countries do. This pertainsto contemporaneous cross-correlations. If we consider for each pair of countries the highestcross-correlation within leads and lags of 15 quarters, the distinctions disappear: the averagelies at 0.36, and only neighboring countries di�er with an average of 0.47. We may justifyconsidering these delays by observing that there can be frictions, or that markets maybeincomplete, be it de jure or de facto.

In model economies, this cross-correlation is close to zero, independently of size. Neighboringcountries do exhibit a larger cross-correlation, which depends on the di�usion process of theshocks, but may attain 0.40 with a reasonable calibration.

3These tables are available from the author.

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Consumption

For cross-correlations of consumption, the picture is slightly di�erent. Occurrences of nega-tive numbers are more frequent, 27% of all cases. The average correlation is also lower thanoutput: 0.14. Otherwise, the same facts arise from the subcategories: higher among largecountries or neighbors, lower with remote countries. Considering the highest values withinleads and lags, the cross-correlations among large countries stay higher then average, and itis not higher among neighbors.

Real business cycle models assume utility smoothing across time and space. In an interna-tional setting, this means that consumption is also smoothed across countries. This implies�rst that the cross-correlations of consumption are always positive. It is higher among neigh-bors, and maybe also among large countries. The main consequence of this smoothing isthat consumption is more correlated across countries than output. The data does not givesupport to this assumption in most cases. This is what Backus et al. (1993) call the quan-tity anomaly. Indeed, only 30% of all cross-correlation pairs exhibit a higher correlationfor consumption. But it is striking that this rate is much lower among neighbors, whichseem to experience highly correlated cycles, while relatively little cross-country consump-tion smoothing occurs. Also, small countries tend to experience more often than large onesstronger output smoothing than consumption smoothing. Indeed, the average correlationsof output seem not very dependent on size, while this seems to matter more for the averagecorrelations of consumption.

There have been several attempts to address the quantity anomaly. By introducing a distinc-tion between traded and non-traded goods, Stockman & Tesar (1991) can reduce the cross-correlations of consumption levels. So does the introduction of preference shocks. However,the cross-correlation of consumption of traded goods remains very high. Other attempts,like Baxter & Crucini (1993, 1992), introduce restriction in the asset market. While thesecorrect to some extend the puzzle, they generate new anomalies.

If we allow for leads or lags in the cross-correlations, quantity puzzle becomes less obvious.Indeed, the correlations of output are higher in half of the cases, more than half for countrypairs involving large or remote countries. It remains to be studied whether various delays orfriction may bring us closer to solving the quantity anomaly.

Investment

In real business cycle models, uctuations of investment arise when shocks move productivityaway from its steady state path. In open economies, a shock to other countries generates alsoa productivity di�erential, which leads to additional investment uctuations. As investmentincreases in the country where productivity is relatively high to the other (where investmentdecreases), a negative cross-correlation of investment is expected. However, as shown inZimmermann (1994b, 1994c), the shocks themselves are often positively correlated, in whichcase the cross-correlation could get positive. Note that the productivity shocks, which areempirically measured by Solow residuals, are often criticized for their lack of accurateness.

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One way to see whether the measured process produces the correct dynamics is to look atthe generated cross-correlations of investment.

The cross-correlation of investment is negative for 27% of the country pairs, for an averagecross-correlation of 0.16. Shocks appear to be more strongly correlated among neighboringcountries. The cross-correlations of investment are indeed the highest among this class ofcountry pairs, with a mean of 0.38, none of them negative. Among large countries, thosecorrelations reach 0.23 on average, while it is 0.10 among small ones.

The case of European countries is particularly interesting. The average cross-correlation ofinvestment among European economies is 0.15, in line with the World average. Removingthe pairs of neighboring countries, the average drops to 0.10, while it is 0.39 for Europeanneighbors. One can therefore suspect that the easy movement of goods in Europe leads tovery low cross-correlations of investment, which are compensated by a very strong correlationof the idiosyncratic shocks only in neighboring countries.

International real business cycle models may produce a wide range of cross-correlations ofinvestment. A standard model generates, however, more often correlations that are negativeor close to zero than positive ones, the latter usually for pairs of neighboring countries. Also,cross-correlations of investment are lower than those of output. This is also found in thedata (64% of the country pairs), especially in Europe. Notice that model economies withtwo countries only generate invariably negative cross-correlations, unless the correlation ofthe shocks is very high. With more countries, they are close to zero and even positive, as apositive shocks to productivity in one country induces a domestic push in investment, whileit decreases in all others.

Productivity

Cross-correlations of total productivity, as measured by Solow residuals, are quite close tozero, but in majority positive. Again, the cross-correlations are higher among large countriesand among neighbors. This last fact is replicated in model economies. However, they havetrouble generating cross-correlations of productivity lower than those of output. Indeed,only 19% of all country pairs concur with the predictions of the theory in this respect. Onewould need strongly negatively correlated shocks with little di�usion over time in order formodel economies to behave as observed, but the shocks are generally positively correlatedand their spillovers are quite strong. This is a puzzle that remains to be solved.

Labor

The �nal series we consider is the labor input. In most business cycle models, it correspondsto total hours worked. However, this measure is not available for all countries. Thereforewe present two sets of results, one for employment, which encompasses all countries, one fortotal hours worked, with 14 out of 19 countries.

In most cases, the cross-correlations of employment are positive and average at 0.20. Con-trarily to the previous cross-correlations, they are larger among small countries, but theyare also larger among neighbors. For total hours worked, the cross-correlations are gene-

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rally higher, especially among the large countries (but consider that the country sample isdi�erent).

International real business cycle models predicts that the labor input has a negative cross-correlation, a fact that is, in most bases, not veri�ed with either de�nition. Also, thesemodels predict that the cross-correlation of output should be higher. This is true in morethan half of the cases. In this respect, there are some interesting distinctions between totalhours and employment: the last prediction is con�rmed in all most all cases among neighborsfor employment, but much less with total hours. It is veri�ed only among 42% of pairs withsmall countries with employment, while it is 52% with total hours. Again, the countrysamples are not the same (and in some categories quite small), but it is striking that suchdi�erences can arise through a change in de�nitions.

3 Summary of the Facts and Discussion

We used quarterly data for 19 industrialized countries to establish some stylized facts evolvingaround trade and open economies, emphasizing the distinction between large and smallcountries. We looked at the standard deviations, autocorrelations and comovements of thecyclical components detrended with the Hodrick & Prescott (1980) �lter. These facts werecompared to moments resulting from a standard international real business cycle modelwith heterogeneous countries from Zimmermann (1994b), as well as other more specializedmodels. The most interesting stylized facts are the following:

Output: The volatility of output varies a lot from one country to the other. This does notdepend much on size.

Autocorrelations: They are always higher for large countries. Only exception: exportprices.

Real imports: Very volatile, highly procyclical, no lead or lag on the business cycle.

Imports and investment: They are highly correlated, indicating that investment is dri-ving a large part of the import uctuations. This e�ect is stronger in large countries.

Import shares: High volatility depends on the mean import share, procyclical with a onequarter lag.

Real exports: Less volatile and procyclical than imports, no lead or lag, but a two quarterlag in the United States.

Export shares: Volatility depends on mean export share, usually acyclical, no lead or lag,but in the United States.

Net export shares: Volatility depends on mean trade share, moderately countercyclical.

Import prices: Very volatile, more so in large countries, strong lead.

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Import prices and imports: Import prices lead real imports by four quarters, especiallyin large countries.

Export prices: Less volatile than import prices, especially in large countries, strong leadin large countries.

Export prices and exports: Exports prices lead (weakly) real exports in small countries.

Terms of trade: Highly volatile, with a large spread across countries, acyclical with astrong lead over the business cycle, mainly in large countries.

S-curve: This shape appears in the correlations of the net export share with the terms oftrade in all countries but Canada, Spain, and the United States.

Investment and savings shares: They are more correlated in large countries, the corre-lation being negligible in small countries (sometimes even negative). The savings shareis leading the investment share in some countries.

Real investment and savings levels: Correlations are stronger than for shares, no leadapparent.

Cross-correlations of output: They are usually positive, higher among neighbors andamong large countries.

Cross-correlations of consumption: They are mostly positive, higher among neighborsand among large countries. Consumption cross-correlations are generally lower thanoutput cross-correlations, more so among neighboring or small countries. Taking intoaccount leads and lags, this is the case in only half of the country pairs.

Cross-correlations of investment: Usually positive, but also often negative. High forneighboring or large countries, low for non-neighboring European countries. Lowerthan output cross-correlations in most countries.

Cross-correlations of total productivity: Slightly positive, higher among neighbors andamong large countries. Generally lower than output cross-correlations.

Cross-correlations of labor input: Generally positive, higher among neighbors, amongsmall countries for the employment series, and among large countries for the totalhours worked series.

International real business cycle models replicate many of those stylized facts, either gene-rically or through various model alterations. This is remarkable, as these are quite simplemodels. But some facts still remain to be explained by such model economies:

� The high volatility of trade components and their relevant price indices.

� Imports that are not almost perfectly correlated with output.

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� The import share is not countercyclical in large countries.

� The export share is acyclical.

� Import prices are acyclical and have a negative comovement with real imports.

� The correlation between savings shares and investment shares is in some instancesnegative.

� Cross-correlations of output are higher than for consumption.

� Cross-correlations of investment are in most cases positive.

� Cross-correlations of productivity are generally lower than for output.

Undoubtedly, this is a large list of facts, and it is di�cult to expect models to replicateall of them. However, some of them are replicated with even the simplest models, as theprocyclicality of imports or the dependence of the volatility of the import and export shareson their average values. Furthermore, some facts are closely linked to others. For example,the countercyclical trade balance depends on exports being acyclical and imports beingprocyclical. Also, some facts are more crucial than others. This depends on the questionasked. For example, a model for the study of the terms of trade should be able to replicatethe above facts for import and export prices, the terms of trade, and the S-curve. Also,some facts should absolutely be replicated whatever the question, or it would be a badsignal about the model structure or calibration. For example, having cross-correlations ofinvestment departing signi�cantly from the observed ones shows that the di�usion processof the technology shocks is poorly calibrated or that other shocks may be relevant. Or,the current failure of international real business cycle models to replicate the relative cross-correlations of consumption and output indicates that there is to much smoothing in thesemodels.

Based on such criteria, we can compose a short list of critical stylized facts that internationalreal business cycle models should meet. Some of these facts pertain only to some models,for example allowing for asymmetries. This list is ambitious, as no such model meets all ofthem currently:

Trade is very volatile. Imports, exports and the trade balance all are more volatile thanwhat the large majority of current models can predict.

Terms of trade are very volatile. This is the price anomaly from Backus et al. (1995).

Import shares are procyclical. This implies that imports are procyclical and more vo-latile than output.

Cross-correlations of consumption are lower than those of output. This is the quan-tity anomaly from Backus et al. (1995).

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Cross-correlations of investment are positive. This is a signal that correlated techno-logy shocks have an appropriate e�ect on productivity di�erentials that drive invest-ment and trade.

Models with asymmetric countries needs to ful�ll additional conditions. So, one should �ndthat, in large countries, autocorrelations are higher, import, export and trade balance sharesare less volatile, import prices are more volatile and lead imports, exports prices are lessvolatile than import prices and lead exports, terms of trade lead the cycle, investment andsavings are more correlated, cross-correlations are higher.

For a model calibrated to some speci�c countries, some of the above facts may need tobe reconsidered. For example, the import share is acyclical in several countries (Denmark,Germany, Greece, Japan, Norway). Also, such models may also need to replicate somepeculiarities, as the high volatility of import prices in Japan, the procyclical export share inNorway and Canada, the strong lead of the trade balance in the United States, the absence ofa S-curve in the United sates and Spain, the near zero correlation of investment and savingsshares in the United Kingdom and Italy (and negative in South Africa).

4 Conclusion

Using quarterly data for 19 countries we have established stylized facts for international tradeover the business cycle. Comparing them to the simulated moments from international realbusiness cycle models, we have identi�ed critical facts that such models should replicate. Nosuch model does so far. There is therefore still much research to be done.

Also, we have identi�ed some peculiarities, that is, facts that are drastically di�erent insome countries. While one can often make a quite clear distinction between large and smallcountries (something models should therefore take account of), some country speci�c seemto elude such an explanation.

In the introductory quote, Lucas (1977) mentions that the United States may not be inte-resting regarding trade statistics. In a certain way, he is right: the United States behaveatypically on several dimensions. But this means also that business cycles may not be allalike, at least from one country to another. Business cycle researchers should also ponderthis.

A Sources of the Data

We used the OECD Main Economic Indicators and the OECD Quarterly National Accounts

as the basis for the data used here. If necessary, the X11 procedure has been applied todata not previously deseasonalized. Import and export prices are computed by the ratioof nominal to real variables. Savings are output less private consumption and governmentexpenditures. The following is a list of exceptions to the above, if not stated in the tables:

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� Australia: Employment data is from the Australian Bureau of Statistics.

� Denmark: The data is from theMONA quarterly database of Danmarks Nationalbank.

� Finland: The data have been provided by Suomen Pankki / Finlands Bank.

� France: Employment data is from the Institut National de la Statistique et des �Etudes�Economiques.

� Germany: Nominal data before 1968 are from Deutsche Bundesbank publications.

� Greece: Import and export prices are from the International Financial Statistics of theInternational Monetary Fund. All real data is from the Athens Institute of Economic

Policy Studies. Nominal data is computed from import / export prices or the consumerprice index applied to real data.

� Japan: All data is from the Bank of Japan.

� Netherlands: The data are provided by the Central Planning Bureau. Real data aregiven as volume indices, that have been transformed to guilders using annual nationalaccounts. Nominal data have been computed from real data and the relevant priceindices.

� Norway: All data is from the Statistisk Sentralbyr�a.

� South Africa: All data is from the South African Reserve Bank.

� Spain: All data is from the Instituto Nacional de Estadistica.

� Sweden: All data is from the Statistiska Centralbyr�a.

� Switzerland: All data is from the O�ce f�ed�eral des questions conjonturelles.

Thanks to Villy Bergstr�om, Sophia Dimelis, Riccardo Fiorito, Dan Knudsen, Tryphon Kollin-tzas, Eva Ortega, Maritta Paloviita, Morten O. Ravn, Hette Rolland, Kuniho Sawamoto,Hans Timmer and Geert L. de Wet for providing assistance in collecting the data. This datawill be made available through the Internet.

B Reading the Tables

This section provides additional explanations regarding the tables with the business cyclestatistics. All series are logged before applying the HP-�lter, the exception being the seriesmeasured as a the ratio to GDP or GNP. The HP-�lter allows to separate cyclical and trendcomponents, while letting the slope of the trend vary depending on a penalty. This penaltyis set to 1600, along with most other business cycle studies for quarterly data. See Hodrick& Prescott (1980) or Kydland & Prescott (1990), for descriptions of this �lter.

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The �rst column of Tables 1, 2, 4 to 8, 10, 12, 14, and 15 give the standard deviation ofthese cyclical components, the second this standard deviation relative to that of GDP orGNP over the same period, the third the autocorrelation. The rest of the tables provideslead and lag comovements. For example, it is shown that the correlation between GDPt andimportst�5 in Australia is -0.36 (Table 2). Gray shadings show where correlations are thehighest. For example, Australian imports lead output by a quarter in Table 2. If a �gure isitalicized, the highest correlation is outside the � 5 quarter range.

The aggregates in the lower part of the table are computed as a weighted average of thestatistics above. The weights used are real GNP/GDP for 1985 for Tables 1, 14, and 15,real GNP/GDP times an average of import and export shares for the other tables. RealGNP/GDP is taken from Summers & Heston (1988). The following countries are considered\large": France, Germany, Italy, Japan, the United Kingdom and the United States.

Tables 16 and 17 summarize the cross-correlation tables which are available from the author.The additional country categories are de�ned in the following way: The remote countries areAustralia, Japan and South Africa. Neighbors are pairs of countries with a common landboundary. The productivity data are Solow residuals taken from Zimmermann (1994c): foreach country, we take the series with the most input aggregates available (among employ-ment, hours per worker, and capital).

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