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clevelandfed.org/research/workpaper/index.cfm Working Paver 9211 DYNAMICS OF THE TRADE BALANCE AND THE TERMS OF TRADE: THE S-CURVE by David K. Backus, Patrick J. Kehoe, and Finn E. Kydland David K. Backus is a professor of economics at the Stern School of Business, New York University; Patrick J. Kehoe is a professor of economics at the University of Pennsylvania and a consultant at the Federal Reserve Bank of Minneapolis; and Finn E. Kydland is a professor of economics at Carnegie-Mellon University, Pittsburgh, and a research associate of the Federal Reserve Bank of Cleveland. The authors thank the National Science Foundation, the Institute for Empirical Macroeconomics, and the Center for Japan-U.S. Business and Economic Studies faculty fellowship program fo'r financial support. They also thank Fabio Canova, Michael Gavin, Tiff Macklem, Patricia Reynolds, and participants at the University of Rochester Workshop, "International Transmission of Business Cycles," for helpful comments on earlier versions of this paper. 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 authors and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. October 1992 clevelandfed.org/research/workpaper/index.cfm ABSTRACT We provide a theoretical interpretation of two features of international data: t h e countercyclical movements in net exports and t h e tendency f o r the t r a d e balance t o be negatively correlated with current and f u t u r e movements in t h e t e r m s of trade, but positively correlated with past movements. We document these same properties in a two-country stochastic growth model in which t r a d e fluctuations reflect, in large part, the dynamics of capital formation. We find t h a t the general equilibrium perspective i s essential: The relation between t h e trade balance and the terms of t r a d e depends critically on the source of fluctuations. clevelandfed.org/research/workpaper/index.cfm We document some of the properties of short-term fluctuations in the t r a d e balance and the terms of trade in 11 OECD countries and interpret them The terms of from the perspective of a two-country stochastic growth model. trade, in this paper, is the relative price of imports t o exports and the t r a d e balance i s the ratio of net exports t o output. balance is uniformly countercyclical and, is negatively correlated with current and f u t u r e movements in the terms of trade, but positively correlated with past movements. t h e cross-correlation S-curve, in We find t h a t the trade general, We call this asymmetric shape of function f o r net exports and the terms of t r a d e the since i t looks like a horizontal S. This finding i s reminiscent of earlier work on the J-curve (Junz and Rhomberg 1973, Magee 1973, and Meade 1988). Our objective is t o provide a dynamic general equilibrium interpretation of these properties. The theoretical structure extends earlier work on trade and price dynamics by Hodrick (1988) and Stockman and Svensson (19871, who develop simple general equilibrium models in which both the t r a d e balance and t h e terms of trade a r e endogenous. imperfectly arise from purchases. substitutable persistent goods shocks In our economy, two countries produce with to capital aggregate and labor, and fluctuations productivity and government We find t h a t with plausible parameter values, t h i s theoretical economy generates both countercyclical trade and an S-curve. The dynamic responses t o productivity shocks suggest a straightforward explanation f o r both properties. A favorable domestic productivity shock leads to an increase in domestic output, a decrease in i t s relative price, and a rise in t h e terms of trade. Because the productivity shock is persistent, we also s e e a rise in consumption and a temporary boom in investment, a s capital i s shifted t o i t s most productive location. The increases in consumption and investment together a r e greater than the gain in output, and the economy clevelandfed.org/research/workpaper/index.cfm experiences a t r a d e deficit during this period of high output. This dynamic response pattern gives r i s e t o countercyclical movements in t h e balance of t r a d e and an asymmetric cross-correlation function much like t h e ones seen in t h e data. Investment dynamics play a central role in generating these properties of our theoretical economy. If we eliminate capital, t h e t r a d e balance is simply a reflection of output dynamics and consumption smoothing. Consider, once more, t h e dynamic responses t o a domestic productivity shock. In this economy, preference f o r smooth consumption results in a smaller increase in consumption than in output and an improvement in the balance of trade. Thus, the t r a d e balance i s procyclical r a t h e r than countercyclical, as i t is in t h e economy with capital. At the same time, the price of domestic goods f a l l s and the terms of t r a d e rises. Since the shocks (and hence the fluctuations in t r a d e and prices) a r e persistent, cross-correlation function: the economy generates a tent-shaped The asymmetric pattern we call t h e S-curve does not arise when the economy has no capital. We find t h a t the general equilibrium perspective i s essential, sense that the correlations critically on t h e source of between trade fluctuations. and relative in the prices depend Although t h i s implication of t h e theory is, in some ways, obvious, i t differs sharply from t h e large body of work in international macroeconomics based on the small assumption, in which relative price movements a r e exogenous. source of open economy Because the relative price movements i s not specified in these models, the relation between trade and prices is independent of them by assumption. In our general equilibrium setting, the source is critical. We illustrate t h i s feature of the theory in an economy with shocks t o government spending rather than productivity. In this case, the cross-correlation function f o r exports and the terms of trade i s tent-shaped, rather than S-shaped. net The clevelandfed.org/research/workpaper/index.cfm difference between cross-correlation functions with shocks to productivity and government spending makes i t clear t h a t there i s no simple structural relation, in our economy, between the t r a d e balance and t h e terms of t r a d e and suggests t h a t one cannot characterize the relation between t r a d e and prices without specifying t h e source of their fluctuations. These points a r e developed in the r e s t of I, Section with a description of postwar the paper. quarterly We s t a r t , in data, including the cyclical behavior of net exports and the correlations between net exports and In Section 11, we describe a t h e t e r m s of trade, f o r 11 developed countries. theoretical economy with two countries t h a t capital and purchases. labor and that face shocks produce different goods with to productivity and government In Section 111, we discuss the selection of parameter values and our method of computing equilibrium time paths f o r net exports, the terms of trade, and other variables. In Section IV, we turn to the model's properties, including the correlation between net exports and the terms of trade. capital Section V i s devoted t o two extreme experiments: and investment, and with shocks to the economy without government spending Section VI is devoted t o some additional features of the theory, alone. including two t h a t we term anomalies: properties f o r which there remains a substantial difference between theory and data. usefulness of our theoretical We conclude with a few remarks on t h e framework f o r interpreting t r a d e and price movements and other features of international time series data. I. P r o p e r t i e s of t h e Data We developed start by countries. looking The at postwar data Cooperation and Development's are quarterly from the trade statistics Organization for for 11 Economic (OECD's) Quarterly National Accounts and a r e described more completely in the Appendix. W e measure t h e t r a d e balance, clevelandfed.org/research/workpaper/index.cfm labeled nx, a s t h e r a t i o of net exports t o output, with both measured in current prices as reported in national income and product accounts. The terms of trade, labeled p, i s t h e r a t i o of t h e implicit price deflators f o r imports and exports -- the relative price of imported goods. either GNP o r GDP in constant prices, and i s labeled y. p and y r e f e r to logarithms of those variables. Real output i s Statistics f o r both Throughout the paper, properties of both international time series d a t a and theoretical economies r e f e r t o Hodrick-Prescott filtered variables. The properties of t h i s f i l t e r a r e described in some detail by Hassler e t al. (1992) and King and Rebelo (1989). We simply note that the filter leaves us with short-term fluctuations in t h e variables being studied. In Table 1, we report some of the salient properties of fluctuations in t h e t r a d e balance and t h e terms of trade. W e list, f i r s t , the standard deviations of net exports, the terms of trade, and output. A f a i r amount of heterogeneity exists across countries in the magnitudes of these statistics, particularly in t h e t r a d e variables. The standard deviation of the r a t i o of net exports t o output ranges from a low of 0.45 percent f o r the United S t a t e s t o a high of 1.75 f o r Finland. percent. The median value, in our sample, i s 1.06 The standard deviation of the terms of t r a d e varies somewhat more, from 1.63 in Austria t o 5.86 in Japan. Second, persistent. both t h e trade balance and the terms of t r a d e a r e highly The autocorrelation of net exports extends from 0.29 in Austria t o 0.90 in Switzerland, with a median of 0.71. The autocorrelation of the terms of t r a d e ranges from 0.50 f o r Austria t o 0.88 in Japan and Switzerland, with a median of 0.80. Third, net exports a r e countercyclical in every country in our sample. This f e a t u r e has been noted elsewhere by Blackburn and Ravn (1991) and Danthine and Donaldson (1991). among others, and i s implicit in t h e strong clevelandfed.org/research/workpaper/index.cfm relations between imports and income in most macroeconometric models. Fourth, t h e contemporaneous correlation between net exports and the terms of t r a d e varies somewhat across countries, but i s negative more often than not. In Finland, France, Italy, Japan, Kingdom, the correlations a r e less than -0.4. Switzerland, and the United The United S t a t e s i s the only country in our sample f o r which these two variables have a sizable positive contemporaneous correlation. Mendoza (1990) provides evidence f o r additional countries a t an annual frequency. The contemporaneous correlations between net exports and t h e terms of t r a d e ignore, however, the complex dynamic relation between these variables suggested by earlier work. In Figure 1, we graph cross-correlation functions for for these two variables, leads and lags up to two years: f o r k between -8 and 8. correlations, t h a t is, between pt and nx t+k the This function i s typically negative f o r negative values of k (the left side of t h e horizontal axis), but t u r n s positive f o r k between 2 and 4. This general pattern, moreover, does not seem t o be the result of the sample periods used. In Figure 2, we report cross-correlation functions f o r t h e periods before and a f t e r 1972 f o r the f o u r countries f o r which we have d a t a going back t o 1955. Japan and the United Kingdom exhibit the same shape in both the Bretton Woods period (1955-71) and the more recent floating-rate period (1972-90). shows little relation between the two variables, either period. Canada at any lead o r lag, f o r For the United States, the cross-correlation function f o r the earlier period i s similar t o t h a t of Japan and the United Kingdom, as well as 8 of the 11 countries in Figure 1. The United S t a t e s in this period differs slightly from these other countries in t h a t the function crosses the axis t o the left of k=O, r a t h e r than the right, but the shape i s otherwise similar. The United States in different pattern. the l a t t e r period, however, displays a substantially If we further divide the post-1972 period into the 1970s clevelandfed.org/research/workpaper/index.cfm and 1980s, we find (not reported) t h a t this change in U.S. t r a d e and price performance applies t o both decades: cross-correlation In neither decade i s t h e shape of the like t h a t of the Bretton Woods period in the United States, the United Kingdom, and Japan in both subperiods, o r in 8 of the 11 countries of Figure 1. We label the characteristic asymmetric shape of function f o r net exports and the terms of trade the cross-correlation the S-curve, since it resembles a horizontal S, but readers may notice a resemblance t o the J-curve of earlier work. In studies of devaluations, i t was frequently noted t h a t unfavorable movements in the terms of trade (increases, in our terminology) were generally associated with declines in the balance of t r a d e t h a t reversed themselves 6 t o 24 months J-curve. Artus later. This pattern was referred t o a s the A classic example ' i s the 1967 sterling devaluation described by (1975). This property of devaluations spawned subsequent studies, including those cited by Junz and Rhomberg (19731, Magee (19731, and Meade (19881, in which observed trade and price dynamics were attributed to, among other things, lags between order and delivery of imported goods and the time required f o r exporters t o change capacity. We return t o these issues in Section IV. In short, we find a number exports and the terms of trade: balance is consistently of regularities in the behavior of net both a r e highly autocorrelated; the t r a d e countercyclical; and the cross-correlation function f o r net exports and the terms of trade has an asymmetrical shape we call the S-curve. 11. A Theoretical Economy We compare these properties o f international data to those of a stochastic growth model with two countries, each inhabited by a large number clevelandfed.org/research/workpaper/index.cfm of identical agents. of Kydland produces and a This world economy i s a streamlined two-country version Prescott's different internationally (1982) closed good immobile. with economy, its Fluctuations own in which technology each and country labor is a r e driven by stochastic shocks t o productivity and government purchases of goods and services. Preferences of the representative agent in each country i are characterized by utility functions of the form where U(c.1-n) = 1c'(l-n1~"1'/~, and cit and n it a r e consumption and hours worked, respectively, in country i. With respect to the technology, each country specializes in the production of a single good, labeled "a" f o r country 1 and "b" f o r country 2. The goods are produced using capital, k, and labor, homogeneous production functions of the same form. n, with linear This gives rise t o t h e resource constraints, 8 1-8 in countries 1 and 2, respectively, with F(k,n) = k n . The quantity y denotes GDP in country i, measured in units of the local good, and a b. lt denote uses of the two goods in country i. country 1 t o country 2, and blt it it and Thus a2t denotes exports from represents imports into country 1. The vector z = (z , z 1 i s a stochastic shock t o productivity whose properties t It 2t will be described shortly. Consumption, investment, and government purchases g, respectively -- -- denoted c, x, and a r e composites of foreign and domestic goods: clevelandfed.org/research/workpaper/index.cfm - where G(a,b) = [ula p+02b-pl-1/P Hence, i s homogeneous of degree one and ph-1. a l l t h r e e final uses of goods and services have both foreign and domestic content, and in the same proportions. The substitution between foreign and domestic goods i s cr=l/(l+p). elasticity of This device f o r aggregating domestic and foreign goods was suggested by Armington (1969) and i s a standard f e a t u r e of general equilibrium t r a d e models (Whalley 1985, Deardorff and Stern 1990). aggregator. Accordingly, we r e f e r t o G as an Armington The weights oi in the aggregator function G allow us t o specify the domestic and foreign content of domestic spending. Government purchases, g, a r e stochastic; we describe their behavior below. Capital formation embodies the time-to-build Prescott (1982). structure of Kydland and As in their economy, i t takes J quarters t o augment the productive capital stock. A unit increase in the capital stock J q u a r t e r s from now involves purchases of 1/J units of the final good f o r J consecutive quarters. To express this mathematically, let sit be planned additions t o the capital stock of country i in period t+J. The capital stocks then evolve according t o where 6 i s the depreciation rate. In period t , total expenditure on gross capital formation i s the sum of capital expenditures on all currently active projects. In all experiments but one, we s e t J=1, s o investment expenditures made in period t clevelandfed.org/research/workpaper/index.cfm increase t h e stock of capital in period t+l. Finally, the underlying shocks t o our economy a r e independent bivariate autoregressions. Z where c The technology shocks follow i s distributed normally and independently over time with variance The correlation between the technology shocks, z and z is determined 1 2' VZ. by the off-diagonal elements of A and V Similarly, shocks t o government z' spending a r e governed by where g t = ( g ,g 1 and It 2t cg is distributed normally with variance V 8' Technology shocks, z, and government spending shocks, g, a r e independent. From these elements, we can construct national income and accounts f o r each country of our theoretical world economy. GDP in country 1 a t d a t e t , in units of the domestically produced good, i s ylt; components as follows. The the resource We relate national output t o constraint equates this t o the sum a +a I t 2t' expenditure product Armington a s a function of a and blt. absorption, c +x +g I t It It' It aggregator expresses Since t h e aggregator, G, i s homogeneous of degree one, we have, in equilibrium, where q It and q 2t a r e the prices of the two goods a t date t. Using t h e resource constraint, we can express output a s where p t absorption, = qZt/qlt i s the terms of ( c +x +g )/q I t I t It It' trade. and net exports, Thus output is the sum of a2t 'Pt bit' We measure t h e t r a d e balance in the model just a s we do in the data, a s the ratio of net clevelandfed.org/research/workpaper/index.cfm exports t o output, with both measured in current prices: nx -- t (a2t-~tblt)/~lt' We compute the terms of t r a d e in country 1 from t h e marginal r a t e of transformation between the two goods in country 1, evaluated a t equilibrium quantities. 111. P a r a m e t e r Values, Steady S t a t e , a n d Computation We describe, parameter values, equilibrium. Prescott's briefly, listed Both (1982) our in procedures Table 2, a r e adapted t o closed economy and the study; for selecting for computing open for economy the benchmark a competitive from details, see Kydland their and paper (Sections 4 and 5 ) and Backus, Kehoe, and Kydland (1992a, Sections I1 and 111). A s a rule, share parameters f o r preferences and production a r e chosen t o equate means of ratios of - aggregate U.S. time series t o analogous ratios for the theoretical economy's steady state. selected' from existing statistical studies. United States parameters of and an aggregate the technology of process, Curvature parameters are We use Solow residuals f o r the European countries which result to estimate in productivity t h a t a r e highly persistent and positively correlated across countries. the shocks The only new elements a r e the parameters of the Armington aggregator and those t h a t govern the behavior of shocks t o government spending, both of which we describe below. equilibrium by Given values f o r the model's parameters, solving numerically a quadratic we compute an approximation to a social planner's problem t h a t weights equally the utility of consumers in t h e two countries. The most important parameters in this paper a r e those of t h e Armington clevelandfed.org/research/workpaper/index.cfm aggregator, which govern the elasticity of substitution between foreign and domestic goods and the average r a t i o of imports t o output. The elasticity of substitution is cr=l/(l+p), and t h e r e is some uncertainty about what value of this parameter i s indicated by the data; see, f o r example, t h e survey of estimates provided by Stern, Francis, and Schumacher (1976). The most reliable studies seem t o indicate t h a t f o r the United States, t h e elasticity i s between one and two, and values in this range a r e generally used in empirical t r a d e models. the For Japan and an aggregate of European countries, elasticity seems t o be smaller; see, f o r example, the Deardorff and Stern (1990, ch. 3) and Whalley (1985, ch. 5). 1 and w 2 in W e use cr=1.5 a s our starting point, but experiment with other values a s well. w discussions W e determine from observed ratios of imports and exports t o GDP using the f irst-order condition In a symmetric steady s t a t e with y =y b =a and p=l, the r a t i o a /b can 1 1 1 2' 1 2' be expressed a s (1-bl/yl)/(bl/yl), in country 1. of w where bl/yl With p=l, this determines the ratio w /w 2 1' and w so t h a t the steady-state 2 1 normalization. i s the ratio of imports t o GDP value of y 1 We s e t the levels i s one, a convenient We use an import share of 0.15, which i s slightly greater than i t s average value in the United States, Japan, and Europe (in aggregate, with intra-European discussion of t r a d e excluded) over t h e last decade. government spending shocks until they a r e used We postpone in the next section. We use these parameter values as alternative values in the following sections. a benchmark, but also consider clevelandfed.org/research/workpaper/index.cfm IV. P r o p e r t i e s of t h e Theoretical Economy We a r e now in a position t o compute equilibrium time paths f o r variables in our theoretical economy and compare their properties t o those of the We do this f o r the benchmark parameter aggregate d a t a we reviewed earlier. values, described in the previous section and summarized in Table 2, and also f o r some other values. This analysis helps us to assess the role of various parameters in generating specific properties of the theoretical economy and gives us some feeling f o r the robustness of these properties. It also provides some intuition f o r the model's behavior. Our primary objective is t o document the theoretical relation between net exports and the terms of trade and t o determine, in particular, whether the theory can account f o r the asymmetric cross-correlation function f o r the trade balance and the terms of trade -- find i t useful t o start, with some summary statistics. statistics shed light on however, aspects of what we have called t h e S-curve. the model t h a t play We These a role in the dynamics of net exports and the terms of trade, and may also have some independent interest. Thus we report, in Table 3, the same properties of the theoretical economy that we documented f o r 11 OECD countries in Table 1. The f i r s t row, which we refer t o as the benchmark economy, uses the parameter values specified in the last section and listed in Table 2. We find, f i r s t , t h a t both net exports and the terms of t r a d e a r e highly autocorrelated in our theoretical economy. The autocorrelation of net exports is somewhat less than we see in the data (0.61 in t h e model v. a median of 0.71 in the data), but i s within the range observed f o r other countries. very The autocorrelation of the terms of trade in the model (0.83) is close t o i t s median properties is surprising: value in the data The variables of (0.80). Neither of these the model inherit t o a large extent the high degree of persistence in the technology shocks. clevelandfed.org/research/workpaper/index.cfm We turn next t o correlations between net exports and other variables. In the benchmark economy, net exports are countercyclical: contemporaneous correlation with output i s -0.64. stronger than we see in U.S. data (-0.221, but This characteristic i s i s within t h e range of variation observed across t h e 11 countries of our sample (-0.17 There is a countercyclical sense in which fluctuations investment in net is essential exports. The The in generating trade investment a r e connected, a s we know, by a n identity: t o -0.68). these balance and Net exports i s the difference, in our economy, between output and the sum of consumption and investment a t market prices. Consumers' desire f o r smooth consumption will lead, a s seen in Section VI, t o a standard deviation of consumption about half that of output. Countercyclical As a result, output net of consumption is procyclical. movements in the procyclical movements in investment. balance of trade also require strong In the model, a s in the data, these fluctuations a r e large enough t o make absorption more variable than output over the cycle and thus give rise t o a negative correlation between net exports and output. A third feature of the benchmark economy i s a strong inverse relation between net exports and the terms of trade: The t r a d e balance i s generally positive when the relative price of foreign goods is low. This correlation i s generally S t a t e s being a negative in the data, too, notable exception. with the United We also find that the correlation between t h e terms of t r a d e and output is strongly positive in the theoretical economy; in t h e data, there i s no obvious regularity. With this background, we turn t o the cross-correlation function f o r net exports and the terms of trade. We see, in Figure 3, t h a t this function takes the S-curve shape t h a t we documented f o r 8 of 11 countries in Figure 1. Thus, the theory delivers one of the striking features of t h e data. We can clevelandfed.org/research/workpaper/index.cfm get some intuition f o r the behavior underlying t h i s correlation from Figure 4, where we graph the dynamic responses of t h e terms of t r a d e and other variables t o a one-time positive shock t o domestic productivity. On impact, we see a n increase in domestic output and thus a decrease in i t s relative price, the inverse of the terms of trade. In the second panel of the figure we s e e t h a t this shock also raises consumption, but by less than half the increase in output. Investment, on the other hand, grows by more than consumption and t h e t r a d e balance moves initially into deficit. As time passes, the investment boom dissipates and the t r a d e deficit turns t o a surplus. This impulse response pattern gives rise, in the benchmark economy, t o a negative contemporaneous correlation between net exports and the terms of trade. The correlation between pt and nx t+k increases with k in the neighborhood of k=O, reflecting the positive slope of the dynamic response function f o r net exports in Figure 4. The reasoning behind the left side of the cross-correlation function i s somewhat different. To make this a s simple a s possible, suppose the economy has only one shock and t h a t the t e r m s of trade is Then the autoregressive of order cross-correlation geometrically a t r a t e a. one, function with autocorrelation for lags kc0 coefficient approaches a. zero In the benchmark economy, t h e dynamics a r e slightly more complex, and this example provides only an approximation t o the pattern reported in Figure 3. We see, then, t h a t the theory produces an S-curve and t h a t the dynamics of net exports and t h e terms of t r a d e in our theoretical economy reflect, t o a large extent, the influence of capital formation on t h e balance of trade. We return t o this issue in the next section. Table 3 particular illustrate parameters government purchases. the and sensitivity the of influence The remaining experiments of these on properties the economy to values of of shocks to clevelandfed.org/research/workpaper/index.cfm Perhaps t h e most important parameter f o r the trade-balance/terms-oftrade relation is t h e elasticity of substitution between foreign and domestic goods. In t h e benchmark economy, this elasticity i s 1.5; in t h e next two In t h e large e l a s t i c i t y experiments we choose larger and smaller values. experiment (cr=2.5), t h e contemporaneous correlation between net exports and the terms of t r a d e i s weaker, moving from -0.41 in t h e benchmark case t o -0.05. In t h e small e l a s t i c i t y experiment (cr=0.5), the correlation i s more Evidently the elasticity parameter, cr, has a significant strongly negative. influence on this correlation. In Figure 5, values of cr between zero and five. for small elasticities and positive we plot the correlation f o r We find t h a t the correlation i s negative for large elasticities, with the sign change occurring a t about cr=2.7. We get a more complete picture of the effect of the elasticity of substitution on t r a d e and price dynamics from the cross-correlation function. In Figure 6, we report such functions f o r the t r a d e balance and t h e terms of t r a d e f o r the f i r s t three theoretical economies. the three values function exhibits a n of the substitution S-curve. It is We find t h a t f o r each of elasticity, clear, then, the that elasticity does not change this implication of the theory. function shifts to the right. the value of the What changing the as we decrease cr, the elasticity does is s h i f t the function l e f t and right: cross-correlation cross-correlation Thus, the elasticity of substitution between foreign and domestic goods a f f e c t s the contemporaneous correlation between the t r a d e balance and the terms of trade, but not the asymmetric shape of the cross-correlation function. This dependence of the tiining of the S-curve on the elasticity of substitution suggests a more subtle interpretation of the data: t h a t there is the a relation correlation between function the and timing the of elasticity the of crossing point substitution. of Studies crossthat clevelandfed.org/research/workpaper/index.cfm estimate t h e elasticity of substitution between foreign and domestic goods typically find larger values f o r the United States than f o r Europe and Japan; see, f o r example, Whalley's (1985, ch. 51 survey of the evidence. We also see t h a t t h e cross-correlation function f o r the United States in Figure 1 i s shifted t o t h e l e f t relative t o those f o r other countries. work will indicate the robustness of the relation Perhaps f u r t h e r between these two properties. To this point, we have considered experiments in which productivity shocks a r e the only source of shocks i s government fluctuations. purchases, which have Another potential source of been emphasized contexts by Hodrick (19881, Obstfeld (19891, and Yi (19911. in related In our next experiment, labeled two shocks, we consider shocks t o both productivity and government spending. The parameter values f o r the government spending process a r e derived from international data and from Chari, Christiano, and Kehoe's (19911 estimates f o r the United States. The mean value of g in each country i s 2 0 percent of steady-state output, which we have normalized a t one. We s e t B = diag(0.95.0.951, so t h a t shocks a r e highly persistent. innovations a r e assigned standard deviations equal t o 2 percent of The mean These shocks a r e independent across countries government spending, o r 0.004. and of the productivity shocks, a s they tend t o be in international data. In most respects, the properties of the economy with government shocks are similar to countercyclical. those o f the benchmark economy. Net exports remain The cross-correlation function between net exports and the terms of trade, pictured in Figure 7, i s f l a t t e r than t h a t with only shocks t o productivity, but has the same general shape. Introducing shocks t o government spending, then, does not change these two features of t h e theory. Thus, our theoretical economy generates both the countercyclical movements of net exports and the asymmetrical pattern of cross-correlations clevelandfed.org/research/workpaper/index.cfm between net exports and the terms of trade t h a t we see in the data. With the benchmark parameter values, however, the dynamics of the theory a r e less persistent than those in the data, with the cross-correlation function changing i t s sign one t o two quarters f a s t e r in our theoretical economy than in the data. One approach t o this issue is, a s we have seen, t o postulate smaller values of the elasticity of substitution: When we lower c from 1.5 t o 0.5 (Figure 6). the point a t which the cross-correlation function crosses the axis s h i f t s t o t h e right by one t o two quarters. Another approach i s t o consider examples additional dynamic mechanisms. Common range from sluggishness in adding new productive capacity (Helkie and Hooper 1988, Junz and Rhomberg 1973, and Magee 1973 provide typical examples of this story) t o the fixed costs of changing export quantities of recent work on hysteresis (Dixit 1989 o r Baldwin and Krugman 1990). We look a t an example of each. We consider, f i r s t , modifications of the dynamics of capital formation. Most studies posit either adjustment costs o r multiperiod construction f o r the technology of capital formation. Baxter and Crucini (1992) and Mendoza (19911, f o r example, consider convex costs of changing t h e capital stock. Kydland and Prescott (19821, on the other hand, argue f o r "time t o build" and suggest t h a t a four-quarter construction period (J=4, in the notation of our theory) is closer t o what we see in the U.S. economy. We consider an intermediate experiment with J=2, labeled time to build in Table 3. f o r this experiment, different from modification the that the pattern of benchmark economy. shifts the cross-correlation cross-correlations As we function see in We find, is not Figure t o the right much 8, this about one quarter, bringing the theory closer t o what we see in the data f o r most countries. A second modification is a one-period lag in the trading process: Goods exported from country 1, say, in period t cannot be used in country 2 until clevelandfed.org/research/workpaper/index.cfm period t+l. We think of t h i s delay as including both time in t r a n s i t and in clearing customs. G(alt.blt-l) and The Armington aggregators in period t , in t h i s case, a r e G(alt-l' b I t ), respectively, in the domestic and We label t h i s one-period delivery lag time t o ship. countries. This shipping lag introduces a subtle measurement issue: clear foreign what concept of price corresponds constructing import price indexes. most closely t o One possibility that I t i s not used in i s the "delivery" price, which in our framework would give rise t o a terms of t r a d e in country 1 of pt = ~aG~altlblt-l)~ablt-l~~~~G(alt,blt-l)~aalt~. This relative price corresponds t o t h e value of customs. imports once they clear An alternative i s the "contract" price prevailing at the time the import goods a r e ordered. In this c a s e , the equilibrium terms of t r a d e would be where i s the intertemporal marginal r a t e of substitution f o r the domestic composite good. We report properties of the l a t t e r definition in Table 3, since this seems a better approximation of how prices a r e constructed in international data. We find t h a t the delivery lag in time t o ship does influence the timing of the relation between the t r a d e balance and the terms of trade. We see in Figure 8 t h a t the cross-correlation function i s shifted t o the right by about one quarter relative t o the benchmark economy, again making i t more similar t o those in the data f o r many countries. In this sense, both time t o build and time t o s h i p a r e useful extensions of the benchmark economy. clevelandfed.org/research/workpaper/index.cfm V. Two Extreme Experiments All of t h e experiments considered in t h e previous section a r e based on parameter values that we consider reasonable. Here we conduct two experiments with parameter settings t h a t we regard as unreasonable in order t o illustrate two central f e a t u r e s of t h e theory. The f i r s t f e a t u r e i s t h e relation between investment and t r a d e dynamics. In t h e l a s t section we stressed, as do Brock (19881, Gavin (19901, Matsuyama (19881, (19861, Murphy and Sachs (19811, the close fluctuations in t r a d e and investment in physical capital. connection, we set t h e capital share parameter 8 connection between To emphasize t h i s equal t o 0.001 in the experiment labeled no capital, which effectively eliminates capital from t h e economy. The behavior of t r a d e and prices changes dramatically. We find, in contrast t o t h e benchmark economy, t h a t t h e t r a d e balance i s procyclical and t h e contemporaneous correlation of strongly positive. tent-shaped: net exports and t h e t e r m s of t r a d e i s The cross-correlation There i s no evidence of economy with capital formation. function, pictured in Figure 9, i s t h e S-curve t h a t appeared in t h e These differences between t h e economy with and without capital indicate t h a t capital formation plays a central role in t h e dynamics of t r a d e and relative prices f o r t h e benchmark economy. The properties of t h e no capital economy can be understood, f o r t h e most part, as reflections behavior of trade. of consumption smoothing. Consider the cyclical We will see in t h e next section t h a t in t h i s economy, consumption i s less variable than income; a s a result, t h e t r a d e balance, which i s t h e difference between output and consumption at market prices, i s procyclical. With respect t o comovements between t r a d e and prices, dynamic response functions again provide some intuition. the A favorable shock t o domestic productivity leads t o an increase in domestic output, a smaller clevelandfed.org/research/workpaper/index.cfm rise in domestic consumption and, surplus. with these parameter values, a trade With greater output of the domestic good, i t s relative price f a l l s and t h e terms of t r a d e rises. correlation between the t r a d e This leads t o a positive contemporaneous balance that decays monotonically in both directions (see Figure 9). A second f e a t u r e of the theoretical economy i s the dependence of t r a d e and price dynamics on the type of shocks hitting the economy. In the experiment labeled government shocks, shocks t o government purchases serve as t h e sole impulse. With only government shocks we find, again, t h a t the properties of t h e model a r e much different from our benchmark experiment. The contemporaneous correlation between net exports and t h e terms of trade, f o r example, changes from -0.41 in t h e benchmark economy t o 1.00. most interesting aspect of these differences concerns t h e cross-correlation function f o r the t r a d e balance and t h e terms of trade. spending shocks alone, the cross-correlation i s tent-shaped: But the With government function, pictured in Figure 9, I t i s consistently positive, peaks at lag zero, and declines in both directions. A s in t h e n o c a p i t a l economy, there i s no sign of a n S-curve. Once more we can get some intuition f o r this behavior from t h e dynamic responses of the economy t o a one-time shock, reported in Figure 10. striking difference between government largely in the response of investment. and productivity shocks The shows up There i s no tendency, a s with productivity shocks, f o r a n investment boom t o follow t h e shock; we see, in fact, the between opposite with the economy these with parameter productivity values. and This sharp government difference spending shocks illustrates t h e hazard of predicting comovements between the t e r m s of t r a d e and t h e t r a d e balance without specifying the shock t h a t gives rise t o these movements. Galor and Lin (1991) and Stulz (1988) make similar points in clevelandfed.org/research/workpaper/index.cfm different contexts. This result i s much different from t h a t small open-economy obtained f r o m deterministic analysis, in which price movements a r e exogenous. In prominent papers by Dornbusch (19831, Obstfeld (19821, and Svensson and Razin (19831, f o r example, as well as most of the papers cited earlier in connection with t r a d e and investment dynamics, t h e source of relative price movements is not specified. The relation between t r a d e and relative price movements, then, i s assumed t o be independent of their source. This i s clearly not t h e case in our economy, where price movements resulting from shocks t o government purchases a r e associated with much different t r a d e responses than those resulting from shocks t o productivity. In short, the economy generates an S-curve when capital formation is an important p a r t of t h e propagation mechanism and fluctuations a r e driven by shocks t o productivity. Without capital, o r with shocks only t o government spending, i t does not. In this sense, both capital formation and t h e source of price and trade fluctuations a r e critical f a c t o r s in determining the shape of t h e cross-correlation function f o r net exports and the t e r m s of t r a d e in our theoretical framework. VI. Anomalies the cross- correlation function between t h e t r a d e balance and t h e terms of trade. Here We have emphasized the implications of the theory f o r w e expand our study t o other properties and point out two discrepancies between quantitative properties of theory and those of the data. The f i r s t discrepancy i s evident from Tables 1 and 3: For our benchmark parameter values and a wide range of alternatives, the variability of t h e t e r m s of t r a d e i s significantly smaller in our theoretical economy than i t i s i n t h e data. Zimmerman (19911 notes a similar discrepancy in a n analogous clevelandfed.org/research/workpaper/index.cfm economy with t h r e e countries of different sizes, as do Stockman and Tesar (1991) in a n economy with both traded and nontraded goods. The standard deviation of t h e terms of t r a d e is 0.48 percent in our benchmark economy (see Table 3) and 2.92 percent in U.S. data (Table 11, a difference of a f a c t o r of six. If we compare t h e theory t o d a t a f o r Japan, t h e difference i s even larger. The difference is smaller if we use a smaller elasticity of substitution (small e l a s t i c i t y ) o r add shocks t o government purchases (two shocks), but even in these cases t h e discrepancy between theory and d a t a i s substantial. Alternatively, we might argue t h a t the standard deviations of relative prices in the d a t a a r e overstated. has constructed improved indexes of U.S. Alterman (19911, f o r example, import and export prices. Using these indexes, t h e t e r m s of t r a d e exhibits about 30 percent less variability than the data used in our Table 1. We think i t unlikely, however, t h a t measurement e r r o r i s large enough t o account f o r most of t h e substantial difference in price variability between theory and data. A second class of discrepancies concerns t h e magnitude and character of fluctuations in aggregate quantities: the standard deviations of consumption and investment, f o r example, and the correlations of output and consumption across countries. parameter We report these properties in Table 4 f o r all of settings used in Table 3. the With respect t o the variability of investment, we found in our earlier study (Backus, Kehoe, and Kydland 1992a) t h a t when foreign and domestic goods a r e perfect substitutes and goods can be shipped costlessly between countries, t h e variability of greater than we see in t h e data. In U.S. data, reported in t h e f i r s t row of Table 4, t h e standard deviation of deviation of output. investment i s much investment is 3.15 times the standard When t h e time t o build parameter J i s one, as i t i s in the economy of this paper, this ratio is 31.5 (Backus, Kehoe, and Kydland 1992a, Table 5). We approximate this economy in the experiment labeled clevelandfed.org/research/workpaper/index.cfm perfect substitutes, where standard deviation of t h e benchmark we s e t cr=100 and w =w 1 2' investment, relative t o t h a t of economy, however, In t h i s case, the output, i s 30.3. In investment i s much standard deviation, relative t o output, i s 3.48. less variable: Apparently, The t h e concavity of technology implied by imperfect substitutability, even f o r values of cr a s large a s 2.5 (our l a r g e e l a s t i c i t y experiment), i s sufficient t o bring t h e theory close t o the data in this respect. For this reason, we do not view investment variability a s an anomaly of the theory. A more robust discrepancy i s what we termed, in our earlier paper, t h e consumption/output anomaly: In the data, the correlation of consumption across countries is generally smaller than t h a t of output; in our theoretical economies, we see the reverse. In d a t a f o r the United S t a t e s and an aggregate8of European countries, f o r example, the consumption correlation i s 0.46, the output correlation 0.70; perfect substitutes economy, see the data row of Table 4. these correlations are 0.67 In our and -0.58, respectively, s o there is clearly a large difference between theory and data. With imperfect benchmark substitutability experiment, for between example), foreign the and domestic consumption goods correlation (the (0.77) remains substantially larger than the output correlation (0.021, although the difference between them is smaller. Complementarity between foreign and domestic goods reduces this discrepancy even more (see the small e l a s t i c i t y experiment, in which cr i s reduced t o 0.5 from 1.5 in t h e benchmark case), but does not eliminate it. regard using nontraded Stockman and Tesar (1991) do somewhat better in t h i s goods and t a s t e shocks,, but they understate the correlation across countries of consumption of traded goods alone. In short, work t o date has documented two robust discrepancies between properties of the d a t a and those of this class of theoretical economies. f i r s t concerns relative price variability: The The terms of t r a d e appears much clevelandfed.org/research/workpaper/index.cfm more variable in t h e d a t a than in the theoretical economies. The second concerns international comovements: In t h e theory, we generally find that the countries correlation consumption; opinion, of output across is in the d a t a we see the reverse. are two of the central issues in stronger than that These anomalies, international of in our business cycle research and stand as clear challenges t o future work in this area. The question in t h e present context is how these anomalous features a f f e c t our assessment of the dynamics of the t r a d e balance and the terms of trade. This i s probably impossible t o answer without knowing how those anomalies a r e resolved. Nevertheless, we suspect t h a t t h e countercyclical movements in t r a d e and the S-shaped cross-correlation function f o r t r a d e and relative prices primarily may be robust properties on t h e persistence of of productivity the theory, since they rely shocks and the dynamics of capital formation, features t h a t apply t o a much broader class of economies than ours. Thus, we suspect that this account of the S-curve may survive the changes t h a t are called f o r by anomalies in other dimensions of the model's properties. VII. Concluding Remarks This study adds to a growing literature in which international time series d a t a a r e compared t o those of equilibrium models. properties of dynamic general Prominent examples include Baxter and Crucini (19921, Cardia (19911, Mendoza (19911, and Stockman and Tesar (1991); Backus, Kehoe, and Kydland (1992b) provide a more complete list. wide range of issues. These studies look at a The f i r s t three papers, f o r example, examine the correlation between saving and investment rates within countries. Stockman and Tesar (1991) study, among other things, the correlations of output and consumption across countries. W,e add t o this list a consideration of the clevelandfed.org/research/workpaper/index.cfm short-run dynamics of t r a d e and relative prices. theory mimics the cross-correlation We find t h a t while the function f o r t h e t r a d e balance and the terms of trade, in two other respects the theory d i f f e r s sharply from the data. Future work should tell us how these discrepancies between theory and d a t a a r e resolved and how f u r t h e r developments bear on the dynamics of t r a d e and relative prices. clevelandfed.org/research/workpaper/index.cfm REFERENCES William Alterman, in P. Hooper Transactions: University of "Price trends in U.S. trade: New data, new insights," and J.D. Richardson, eds., International Economic I s s u e s in Measurement and Empirical Research, Chicago: Chicago Press, 1991. Paul Armington, "A theory of demand f o r products distinguished by place of production," I M F Staff Papers, 27 (19691, 488-526. Jacques Artus, "The 1967 devaluation of the pound sterling," I M F Staff Papers, 22 (19751, 595-640. David Backus, Patrick Kehoe, and Finn Kydland, "International real business cycles," J o u r n a l of Political Economy, 101 (August 1992a1, 745-775. David Backus, Patrick Kehoe, and Finn Kydland, "International business cycles: theory and evidence," unpublished manuscript, August 1992b. Richard Baldwin and Paul Krugman, "Persistent t r a d e effects of large exchange r a t e shocks," Quarterly Journal of Economics, 104 (November 1990). 635-654. Marianne Baxter and Mario Crucini, "Explaining saving/investment correlations, " American Economic ~ e v i e w ,forthcoming 1992. Keith Blackburn and Morten Ravn, "Contemporary macroeconomic fluctuations: An international perspective," unpublished manuscript, January 1991. Philip Brock, "Investment, the current account, and the relative price of non-traded goods in a small open economy," J o u r n a l of International Economics, 24 (19881, 235-253. Emanuela Cardia, "The dynamics of a small open economy in response t o monetary, fiscal, and productivity shocks," J o u r n a l of Monetary Economics, 28 (December 19911, 411-434. V.V. Chari, Lawrence Christiano, and Patrick Kehoe, "Optimal fiscal policy in a business cycle model," unpublished manuscript, Federal Reserve Bank of Minneapolis, September 1991. Jean-Pierre Danthine and John Donaldson, "Methodological and empirical issues in real business cycle theory," unpublished manuscript, 1991. Alan Deardorff and Robert Stern, Computational Analysis of Global Trading Arrangements, Ann Arbor: University of Michigan Press, 1990. Avinash Dixit, "Entry and exit decisions under fluctuating exchange rates," Journal of Political Economy, 98 (June 19891, 620-638. Rudiger Dornbusch, "Real interest rates, home goods, and optimal external borrowing," Journal of Political Economy, 91 (February 19831, 141-153. Oded Galor and Shoukand Lin, "Terms of trade, interest rates, and current account dynamics, " unpublished manuscript, Brown University, January 1991. clevelandfed.org/research/workpaper/index.cfm Michael Gavin, "Structural adjustment t o a terms of t r a d e disturbance: The real exchange r a t e , stock prices, and t h e current account," J o u r n a l of Internationa l Economics, 28 (May 19901, 217-243. John Hassler, P e t t e r Lundvik, Torsten Persson, and Paul Soderlind, "The Swedish business cycle: Stylized f a c t s over 130 years," unpublished manuscript, Stockholm, 1992. William Helkie and Peter Hooper, "An empirical analysis of t h e external deficit, 1980-86," in R. Bryant, G. Holtham, and P. Hooper, eds., External Deficits and the Dollar: The Pit and the Pendulum, Washington: Brookings Institution, 1988. Robert Hodrick, "U.S. international capital flows: Perspectives from rational maximizing models," Carnegie-Rochester Conference S e r i e s on Public Policy, 30 (Spring 19881, 231-288. Helen Junz and Rudolf Rhomberg, "Price competitiveness in export trade among industrial countries," American Economic Review, 6 3 (May 19731, 412-418. Robert King and Sergio Rebelo, "Low frequency filtering and t h e business cycle," unpublished manuscript, University of Rochester, October 1989. Finn Kydland and Edward Prescott, "Time t o build and aggregate fluctuations," Econometrica, 50 (November 19821, 1345-1370. Stephen Magee, "Currency contracts, pass-through, and devaluation," Brookings P a p e r s on Economic Activity, 1: 1973, 303-323. Kiminori Matsuyama, "Terms-of-trade, factor intensities and t h e current account in a life-cycle model," Review of Economic Studies, 55 (19881, 247-262. Ellen Meade, "Exchange rates, adjustment, and t h e J-curve, " Federal Reserve Bul letin, 74 (19881, 633-644. Enrique Mendoza, "Some international evidence on t h e correlation between the t r a d e balance and the terms of trade," unpublished manuscript, International Monetary Fund, December 1990. Enrique Mendoza, "Real business cycles in a small open economy," American Economic Review, 81 (September 19911, 797-818. Robert Murphy, "Productivity shocks, nontraded goods, and optimal capital accumulation," European Economic Review, 30 (19861, 1081-1095. Maurice Obstfeld, "Aggregate spending and the terms of trade: Is there a Laursen-Metzler effect?" Quarterly Journal of Economics, 97 (May 19821, 251-270. Maurice Obstfeld, "Fiscal deficits and relative prices in a growing economy," Journal of Monetary Economics, 23 (May 19891, 461-484. Jeffrey Sachs, "The current account and macroeconomic adjustment in t h e 1970s," Brookings P a p e r s on Economic Activity, 1: 1981, 201-268. clevelandfed.org/research/workpaper/index.cfm Robert Stern, Jonathan Francis, and Bruce Schumacher, P r i c e Elasticities in International Trade, London: Macmillan, 1976. Alan Stockman and Lars Svensson, "Capital flows, investment, and exchange rates," Journal of Monetary Economics, 19 (19871, 171-201. Alan Stockman and Linda 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, April 1991. Rene Stulz, "Capital mobility and the current account," Journal of International Money and Finance, 7 '(19881, 167-180. Lars Svensson and Assaf Razin, "The terms of trade and the current account: The Harberger-Laursen-Metzler effect," Journal of Political Economy, 91 (February 19831, 97-125. John Whalley, Trade Liberalization Among Major Trading Areas, Cambridge, MA: MIT Press, 1985. Kei-Mu Yi, "Can government purchases explain recent U.S. net export deficits?" unpublished manuscript, presented a t the NBER Universities Conference, May 1991. Christian Zimmerman, "International real business cycles among large and small countries," unpublished manuscript, Carnegie Mellon University, December 1991. clevelandfed.org/research/workpaper/index.cfm APPENDIX Data Sources a n d Definitions The d a t a used in Table 1 and Figures 1 and 2 were taken from the Organization foy ~ c o n o m i c Cooperation and Development's Quarterly National Accounts. These a r e reported quarterly in a publication of the same name; our numbers come from a machine-readable d a t a base supported by the Board of Governors of t h e Federal Reserve System. real output: output in base-year on t h e country; net exports in current prices: The variables of interest a r e prices, either GNP o r GDP, depending exports minus imports in current prices; terms of trade: ratio of the implicit price deflator f o r imports t o the implicit price deflator f o r exports, with deflators computed a s r a t i o s of current-price imports and exports t o base-year-price imports and exports. The sample periods noted in Table 1 a r e the complete samples from the January 1991 version of the data b a s e . We seasonally Australia, Austria, and Finland using the X-11 method. adjusted the data for clevelandfed.org/research/workpaper/index.cfm Table 1 Properties of Net Exports, Real Output, and the Terms of Trade in 11 OECD Countries Std. Deviation (percent) Autocorrelation Correlation Country - - Australia Austria Canada Finland France Germany Italy Japan Switzerland U.K. U.S. Median Definition of Variables: nx = the ratio of net exports to output y =the logarithm of real output p = the logarithm of the ratio of the import deflator to the export deflator NOTES: Data are quarterly, from the Organization for Economic Cooperation and Development's Quarterly NationalAccounts. Numbers in parentheses are Newey-West standard errors. All statistics refer to Hodrick-Prescottfiltered variables. Sample periods are Australia, 1960:IQ-1990:IQ; Austria, 1964:IG1990:IQ; Canada, 1955:IQ-1990:IQ; Finland, 1975:IQ-1990:IQ; France, 1970:lQ-1990:IQ; Germany, 1968:lQ-1990:IQ; Italy, 1970:ICT1990:IQ; Japan. 1955:llQ-1990:IQ; Switzerland, 1970:ICT1990:IQ; United Kingdom, 1955:lQ-1990:IQ; and United States. 1950:IQ-1990:llQ. SOURCE: Authors' calculations. clevelandfed.org/research/workpaper/index.cfm Table 2 Benchmark Parameter Values Preferences P Technology 8 = .36, 6 = .025,J = 1, = .99, p = .34, y = -1.0 a = ll(l+p) = 1.5, import share = -15 Forcing processes A = [I: var = 6: g, = 0. SOURCE: Authors' calculations. var .906 .088 = I.088 . g o d E; = .00852*, corr(e:,e$) = 258 clevelandfed.org/research/workpaper/index.cfm Table 3 Properties of Net Exports, Real Output, and the Terms of Trade in Theoretical Economies - Std. Deviation (percent) Economy Benchmark m Y - - Autocorrelation P m Y Correlation P (my) (%P) -.41 .49 (.08) (.14) (Y,P) -30 1.38 -48 (.02) (.18) (.06) .61 .63 -83 (.07) (.lo) (.05) -.64 Large Elasticity .33 1.41 .35 (.03) (. 18) (-05) .63 .64 .88 (.07) (.18) (-03) -.57 -.05 .43 (.08) (.09) (.14) Small Elasticity .37 1.33 .76 (.03) (.18) (.07) .61 .63 .77 (.07) (.lo) (.05) -.66 -.80 .51 (.07) (.09) (. 16) Two Shocks .33 1.33 .57 (.03) (.IS) (.07) .62 .65 .78 (.08) (.08) (-06) -.57 -.05 .39 (.15) (.17) (.17) Time to Build .28 1.34 .51 (.02) (.17) (.06) .60 .63 .52 (.17) (.lo) (.16) -.61 -.40 .50 (.07) (.08) (.12) Time to Ship .24 1.35 -48 (.02) (. 18) (.05) .65 .66 .66 (.07) (.08) (.09) -.56 -.51 .61 (.08) (.09) (.11) No Capital .18 1.14 1.29 (.Ol) (.15) (.09) .71 .61 (.06) (. 11) Government Shocks .16 .17 -30 (.03) (.02) (.05) .67 .67 .67 ( 1 1 (.08) (.ll) Perfect Substitutes 16.90 2.22 (1.14) (.29)' --- -.lo (. 18) .76 (.05) -64 (.07) --- (.07) .66 (.06) .99 .68 (.OO) (.06) -.55 1.00 -35 (.13) (.13) (.OO) .10 (.w) --- --- NOTES: Statistics are based on Hodtick-Prescott filtered data. Entries are averages over 20 simulations of 100 quarters each; numbers in parentheses are standard deviations. Parameters are as in Table 2, except for large elasticity, o = 2.5; small elasticity, o = 0.5; two shocks, 2 mean of g = diag (0.2,0.2), B = diag (0.95,0.95), and Vg = diag (0.004 ,0.004~);government shocks, as in two shocks plus z, = 1, all t; time to build, J = 2; no capital. 0 = 0.001; time to ship, one-period shipping lag, as described in the text; and perfect substitutes, 0 = 100, and import share = 0.5. SOURCE: Authors' calculations. clevelandfed.org/research/workpaper/index.cfm Table 4 Business Cycle Properties of Theoretical Economies Ratio of Std. Dev. to mat of Output Economy c x Data .49 Correlation (c,Y> (x,Y) 3.15 .76 .90 .70 .46 .31 (-06) 30.32 (1.07) .75 (.12) .01 (.05) -.58 (. 15) .67 (. 17) Two Shocks .62 (.09) 4.29 (.59) .78 (.ll) .89 (.04) .00 03) .83 Time to Build .49 (.08) 3.35 (-30) .88 (.06) .93 (-02) .04 (. 18) -77 (. 10) .72 (. 11) - .42 .79 Perfect Substitutes @I,Y~) ( ~ 1 ~ ~ 2 ) Benchmark Large Elasticity Small Elasticity Time to Ship No Capital Government Shocks .93 3.66 -.95 -.95 Definition of Variables: c = the logarithm of real consumption x = the logarithm of real fixed investment y = the logarithm of real output Subscripts 1 and 2 refer to the domestic and foreign countries, respectively. NOTES: Parameter values are described in Tables 2 and 3. The data row is taken from Backus, Kehoe, and Kydland (1992a, Table 5); entries refer to the United States, except for the correlations between foreign and domestic output and consumption, which refer to the United States and Europe. As in Table 3, numbers in parentheses are standard deviations of the relevant statistic over 20 simulations of 100 periods each. SOURCE: Authors' calculations. 33 , clevelandfed.org/research/workpaper/index.cfm Figure 1 Correlation of p t and n x t+k Australia Austria Japan 0.75 0.00 --25 -.50 --7s -.25 -.75 . . . . - . - - - - - . . - Switzerland Finland 0.75 United Kingdom 0.25 0.00 - -2s -.50 -.75 -7 -3 I 5 -25 -.so - .75 -7 -3 -7 -3 1 United States Fmnce ! !$[ -.50 - .75 1 Germanu SOURCE: Authors' calculations. 5 5 . . clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm Figure 4 120 Dynamic Responses to Domestic Productivity Shock , i . \ .OUTPUT .. **. -.* * -- - - -.- - ------ -- - ------- -------____ -----------------P R D SHOCK ~ ~ O ------------------- 0- TERMS OF TRADE / .. . 1.00 t 0.80- INVESTMENT 'b, t t '. 0.60 - z P % ... ..'. Oa40- CONSUMPTION - a ---- -- ------_ *=-.__ 0.20 - - G ----------__-______ ----------- . 0 2 0 1 ! 2 / 3 : 4 , 5 , 6 , , 7 , 8 , 9 , 10 , 11 , , 12 , 13 QUARTERS SOURCE: Authors' calculations. , 14 , , 15 16 , , 17 , 18 ,, 19 , 20 , 21 , 22 23 clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm clevelandfed.org/research/workpaper/index.cfm Figure 10 Dynamic Responses to Domestic Government Shock 0.90 I 0.75 0.60 - GOVERNMENT SPENDING 0.45 - S P a Os300.15 - 5 -- -- --OUTPUT -- -- -- -- -- -- -- __ 0.00 4 0 -- - - - - ----TERMS OF TRADE -0.15- -- -- -- __ ---- . 0 3 1 0 2 1 3 4 i ~ 5 6 1 7 , 8 t 9 t 10 1 ~ 11 12 13 0.00 -0.05 - C C C C C CONSUMPTION 0 1 2 3 4 5 C 4 - 6 7 8 9 10 11 12 -- t 15 t 16 8 17 t 18 19 4-- 13 14 ~ 20 ~ 21 t 22 23 _ -- -- _--- -- ---- C QUARTERS SOURCE: Authors' calculations. ~ 14 15 16 17 18 19 --- 20 21 22 23 8 r ~ t