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www.clevelandfed.org/research/workpaper/index.cfm Workinn Paper 9115 ON THE ECONOMETRICS OF WORLD BUSINESS CYCLES by Finn E. Kydland Finn E. Kydland is a professor of economics at Carnegie-Mellon University, Pittsburgh, Pennsylvania. This paper was written while he was a visiting scholar at the Federal Reserve Bank of Cleveland. Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment. The views stated herein are those of the author and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. October 1991 www.clevelandfed.org/research/workpaper/index.cfm Introduction Over the past 10 or 15 years, academic interest in business cycles has recovered to a level not matched perhaps since the 1930s. In his editorial statement in the first issue of Econometric8 in 1933, Ragnar Frisch not only introduced a new word, econometrics, which he defined as quantitative economic theory, but also listed business cycle theory among four fields of particular interest to econometricians. This inclusion reflected the views not only of Frisch, but also of Hayek (1931). Tinbergen (1935), and others. This interest waned, however, in the 1950s and 1960s. A major factor leading to its reawakening was the paper by Robert Lucas (1977) on "Understanding Business Cycles." Perhaps this course of events was not surprising. A prerequi- site for making much progress in this field was dynamic general equilibrium theory. By the 1970s, the basic theory had been developed, and neoclassical growth theory evolved as the dominant framework for business cycle analysis. Most of the business cycle research has been conducted within closedeconomy frameworks. Only recently has the focus started to shift toward international model environments. In the next section, I describe briefly the econometrics of the general equilibrium approach to business cycles. 1 The following section includes two applications to international questions. The final section provides a brief summary. The Econometric Au~roach Central to the econometric approach are the computational experiments. Leading up to these experiments are three steps. The first is a clear state- A' more extensive discussion of the econometric approach is Prescott (1991b). in Kydland and www.clevelandfed.org/research/workpaper/index.cfm ment of the question to be addressed. For example, some of the recent busi- ness cycle literature asks how much of the variation in postwar U.S. aggregate economic activity would have remained if technology shocks, also called Solow (1957) residuals, were the only source of fluctuation. In business cycle theory, questions about the source of impulse are, of course, standard. This phrasing of the question leaves open the possibility that the contributions from different sources may interact. The next step is to choose a model economy with a bearing on the question at hand. Other considerations in the model selection are tractability and computability. If existing tools overly constrain the freedom to analyze a suitable model economy, then, of course, the development of new methodology is needed. The main point is that model-economy selection depends on the question being asked and not on the answer. The model economy must be calibrated. Unlike the system-of-equations approach to macroeconomics, under which the parameters are the coefficients of behavioral equations and are estimated using the data series whose behavior the researcher is studying, the approach here is to determine parameter values on the basis of non-business-cycle measurements. The parameters are those of preferences, technology, information structure, and institutional arrangements. For example, with constant-elasticity-of-substitution (CES) functional forms for preferences and technology, there are share parameters and elasticity parameters. The former generally follow from average rela- tions between aggregates that change little from one cycle to another. These relations may follow from national income and product accounts data or from panel data. Values of elasticity parameters sometimes are implied by dramat- ic experiments provided by history, such as a change in relative quantities '- www.clevelandfed.org/research/workpaper/index.cfm (or the absence thereof) associated with a large change in relative prices. In some cases, the necessary experiment or information is not yet available to the researcher. Before a new parameter is introduced, however, it ought to be evident that,' at least in principle, it can be measured. The parameters should not be chosen so as to produce the best fit of the model to the business cycle data. The goal is to provide the clearest possible answer to the question. In some cases, deviations of the theory from the data even provide independent verification of the answer. Kydland and Prescott (1991a. p. 791). (See, for example, Moreover, given the simplicity of abstractions, some discrepancies or anomalies will remain. Attempting to fit the model to the data is not helpful in making the anomalies stand out as clearly as possible, providing motivation for further research. If all parameters could be accurately calibrated, then in principle only one computational experiment would be needed:.. In practice, however, the researcher will not have access to that much information. additional experiments, with different parameter values range, may be useful. Consequently, some in a reasonable These experiments may tell us either of two things. One possibility is that the answer is not sensitive to different values of a given parameter, in which case its measurement is not urgent. Alternatively, if the answer is indeed sensitive to values of an imprecisely measured parameter, then efforts directed toward its measurement could have considerable payoff. The description of the findings could include a summary of the outcomes of the experiments along with a quantitative assessment of the precision with which the question has been answered. For example, in answer to the question about the role of technology shocks for the cycle, Kydland and Prescott '-. www.clevelandfed.org/research/workpaper/index.cfm (1991a) estimate that Solow residuals have accounted for about 70 percent of U.S. business cycle fluctuations since the Korean War. The numerical answer to the research question, of course, is dependent on the model. The degree of confidence in the answer depends on the degree of confidence placed in the economic theory being used and in the underlying measurements. b ~ ~ l i c a t i o nto s International Business Cvcles In using the neoclassical growth paradigm for addressing international business cycle questions, several problems arise. on two. Here, I shall concentrate First, with technology shocks as a major impulse, one must allow for the possibility that Solow residuals in different countries interact somehow. There are at least two basic ways in which that can happen. technology innovations are correlated across countries. One is that Another is that an innovation in either country over time spills over to other countries. This suggests the estimation of interrelated technology-shock processes. A related issue is that the data needed for computing Solow residuals in different countries may not be consistent. Most countries have collected quarterly data for substantially shorter periods than has the United States. Moreover, the quality of either the output or the input data may be questionable. Most countries do not report quarterly capital-stock data. The exper- ience from the United States, however, suggests that omitting the capital input makes little difference for the measurement of Solow residuals. may be two reasons: There First, the capital stock fluctuates relatively little; and second, its cyclical behavior is essentially uncorrelated with that of output. The case of the labor input could be more serious, however. countries have not collected comprehensive hours-per-worker data. 8 - Many In the - www.clevelandfed.org/research/workpaper/index.cfm United States, roughly one-third of the total hours variation takes this form. For now, however, we make do with employment data. The second problem relates to the need for relaxing the assumption of homogeneous goods. Examples of relevant classifications of goods are traded versus nontraded goods and consumption versus investment goods. A difficulty is that, with .most potentially useful classifications, large quantities of the same class of goods are simultaneously being shipped in both directions between any pair of countries or group of countries. The Role of International Borrowing A natural question to ask is whether a significant bias exists when the role of technology shocks is estimated from closed-economy models. A missing feature, then, is the possibility of shifting resources to the country with relatively high technology. At the same time, risk-sharing in the form of borrowing or lending through international trade theoretically may make the consumption paths quite similar. Indeed, one can construct simple multi- country economies in which the consumption paths are perfectly correlated while the output paths are not. This result would not hold with leisure entering preferences in a nonseparable way, and other model features as well could modify the result. A question is, then, whether allowing for world trade affects the quantitative estimate of the role of technology shocks. Presumably, this question could be. asked while maintaining a framework of only one traded good, so that one would not need to take a stand on the second problem mentioned at the beginning of this section. This is what Backus, Kehoe, and Kydland (1991a) set out to do. Experiments with a calibrated two-country economy based on estimated technology-shock processes with spillover effects demonstrated anomalies of '- - www.clevelandfed.org/research/workpaper/index.cfm such magnitude relative to the data that the original question could not reasonably be asked in this simple extension-of the closed-economy framework. The theoretical flow of resources across borders simply responded too much to productivity differences, while too much risk-sharing was taking place. In the data for the United States versus almost any other major country, the correlation between consumption in the two countries is about the same or lower than the correlation between the two countries' outputs. In the model, the consumption correlation was much too large. Consequently, we shifted our focus to asking what salient features of international data would be consistent with a simple real business cycle theory and how robust the anomalies are to parameter variation within reasonable ranges. It turns out, for example, that the consumption anomaly remains if a transport cost or tariff is introduced that slows down international trade. In fact, with the estimated spillover effects, it remains even with absolutely no trade. Why I s There a J-Curve? Some devaluation studies have shown that the trade balance initially moves against the devaluing country, but then, after a few quarters, improves steadily. This pattern over time resembles a tilted J, and hence its name. Attempts at an explanation tend to focus on various sources of inertia, such as import quantities being slow to respond to price changes, perhaps because of delivery lags or costs of changing suppliers. More generally, if we plot the correlation coefficient between contemporaneous terms of trade and leads and lags of the trade balance, the picture for most major countries also looks like a tilted J. The example of the U.K. in Figure 1 is typllcal. The question asked in Backus, Kehoe, and Kydland (1991b) is whether this pattern can be reconciled with a general equilibrium framework in which technology *- - www.clevelandfed.org/research/workpaper/index.cfm shocks are a major source of fluctuations. To have a theoretical concept of terms of. trade, one obviously needs at least two traded goods. This means that one is faced with the second problem mentioned at the beginning of this section. In embarking on this project, we did not feel we had the information required to use trade classifications such as consumption versus investment goods. Tesar [1991]). (See, however, Stockman and Instead, we adopted a modeling approach with a long tradition in computable models in international trade. (1969) assumption. We made use of the Armington Following him, home-produced goods simply are assumed to be different from foreign-produced goods. Domestic goods need at least some imported goods to be useful. Thus, omitting time subscripts, one can write c1 + x1 = C2 + X2 = G(al, bl) and G(b2, a2), where ci and x are consumption and investment in country i, i-1,2; and a i i and b i are the quantities of the home- and foreign-produced goods, respec- tively, used in country i. These quantities are constrained by al + a2 - F(kl , nl) b1 + b2 - F(k2. and n2i, where k and n are the capital and labor inputs in country i. Using a CES i i function for the aggregator function, G I the share parameters follow from average import or export shares, leaving the elasticity of substitution to be determined. Whalley (1985) cites dozens of studies at various levels of - aggregation that have produced estimates of this elasticity. Generally, they are larger than one, with a central tendency toward 1.5. - Using .this'value as a benchmark, a calibrated two-country economy indeed produces the J-curve pattern. The intuition is that when the home country d . . www.clevelandfed.org/research/workpaper/index.cfm experiences a favorable technology shock, output of home-produced goods rises relative to foreign-produced goods, resulting in an increase in the terms of trade. At the same time, with positive serial correlation in technology changes, this she-ck signals high future productivity of capital, which is exploited initially by a net increase in imports. In other words, the in- crease in the sum of what the home country wishes to consume and invest exceeds the output increase -- the trade balance becomes negative. Over time, investment slows, and the productivity differential narrows, resulting in the trade balance eventually becoming positive. As in the data for most countries, the United States being an exception (see figure I), the benchmark economy's contemporaneous correlation between terms of trade and net exports is negative. Some have suggested that the elasticity of substitution between homeand foreign-produced goods varies across countries. For example, supposedly it is larger for the United States than for most European countries. With a larger elasticity, say three or four instead of 1.5, the model still produces a J-curve pattern, but the contemporaneous correlation then is positive. Again, the description of the findings would be incomplete without a presentation of the discrepancies or anomalies relative to the data. In this case, while the J-curve arises naturally through interaction between the technology-shock processes and the dynamics of capital formation, the volatility of the terms of trade is substantially greater in the data than in the model. Zimmermann (1991) finds that this general pattern persists in three/ country models with differences across countries in size and/or-proximity. Some of the deviation from theory may be the result of a measurement problem associated with the export and import price indices used. A recent study by 1 - - www.clevelandfed.org/research/workpaper/index.cfm ~lte&an (1989) shows that for the 1980s. a decade for which data are available to construct better indices, t h e ~ ealternative indices display substantially less volatility. Yet, even with such a modification in measurements, the model volatility of the terms of trade still would be substantially larger than that in the data. Summary In this paper, I describe briefly an econometric (that is, quantitativetheoretic) approach to business cycles along with two examples of applications to questions or issues in international business cycles. The focus is on its use in obtaining quantitative answers to well-defined questions. Moreover, since much .of the progress in economic science is motivated by remaining deviations or anomalies relative to established theory, I emphasize that disciplined use of this econometric approach indeed enables the researcher to document such deviations clearly. The model economies referred to are formulated within the neoclassical growth framework, which has come to dominate in business cycle theory. In economies with only technology shocks as impulses, use is made of measurements of the degree of interrelation between these shocks across countries, including spillovers over time. A finding is that the tilted J-curve pattern we see in the cross correlations between contemporaneous terms of trade and the trade balance, going from leads of several quarters to lags of several quarters, arises naturally in such economies. An example of a deviation is a robust tendency in the model economies for the volatility of the terms of trade to be too low. Another deviation is that, in the model environments, the correlation between domestic and foreign consumption is much higher than '_ www.clevelandfed.org/research/workpaper/index.cfm that between domestic and foreign output. In the data for the United States versus other major countries, however, these correlations are either about the same or reversed i n r e l a t i v e magnitudes. www.clevelandfed.org/research/workpaper/index.cfm Figure 1: Correlations of terms of trade with net exports at lag j, j Source: Backus, Kehoe, and Kydland (1991b). - -8,8 www.clevelandfed.org/research/workpaper/index.cfm References Alterman, W. "Price Trends in U.S. Trade: New Data, New Insights," Working Paper, Bureau of Labor Statistics, 1989. Armington, P. "A Theory of Demand for Products Distinguished by Place of Production," Staff Papers 27, International Monetary Fund, 1969, pp. 488-526. Backus, D.K., P.J. Kehoe, and F.E. Kydland. "International Real Business Cycles," Journal of Political Economy, 1991a, forthcoming. . "Dynamics of the Trade Balance and the Terms of Trade: the J-Curve Revisited," Working Paper, Federal Reserve Bank of Minneapolis, 1991b. Hayek, F.A. Prices and Production. London: George Routledge and Sons, 1931. Kydland, F.E., and E.C. Prescott. "Hours and Employment Variation in Business Cycle Theory," Economic Theory 1, 1991a, pp. 63-81. . "The Econometrics of the General Equilibrium Approach to Business Cycles," Scandinavian Journal of Economics 93, 1991b, pp. 161-78. Lucas, R.E. Jr. "Understanding Business Cycles," in K. Brunner and A.H. Meltzer, eds., Stabilization of the Domestic and International Economy. Amsterdam: North-Holland, 1977, pp . 7-29. Solow, R.M. "Technical Change and the Aggregate Production Function," Review of Economics and Statistics 39, 1957, pp. 312-20. Stockman, A.C., and L.L. Tesar. "Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Co-Movements," Working Paper 9019, Federal Reserve Bank of Cleveland, 1991. Tinbergen, J. "Annual Survey: Suggestions on Quantitative Business Cycle Theory," Econornetrica 3, 1935, pp. 241-308. Whalley, J. Trade Liberalization among Major Trading Areas. Mass.: MIT Press, 1985. Cambridge, Zimmerman, C. "International Real Business Cycles among Heterogeneous Countries," Working Paper, Carnegie-Mellon University, 1991.
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