International business cycle accounting: the case of Japan and the US

International business cycle accounting: the case of Japan and the US 198-28 Keisuke Otsu y Sophia University, Faculty of Liberal Arts April 25, 29 Abstract It is well known that replicating bilateral international business cycle comovements across countries with the two-country international real business cycle model is challenging. In this paper, I apply the business cycle accounting method a la Chari, Kehoe and McGrattan (27) to a two-country setting and quantitatively account for the impacts of the disturbances in the labor, investment, resource, e ciency, and international markets on business cycle comovements between Japan and the U.S. I show that the disturbances in the U.S. labor market, Japanese production e ciency and international relative prices are important in accounting for the recent business cycle correlation patterns between Japan and the U.S. over the 198-28 period. JEL Classi cation: E32; F41 Keywords: Business Cycle Accounting; International Business Cycles I would like to thank Ippei Fujiwara, Hidehiko Ishihara, Masaya Sakuragawa, Etsuro Shioji, Tomoyoshi Yabu and participants at the Istitute of Statistical Research seminar. This reasearch was supported by the Murata Science Foundation. y e-mail: k-otsu@sophia.ac.jp. 1

1 Introduction International real business cycle models are intended to explain international cross-correlations of aggregate variables such as output and consumption. Backus, Kehoe and Kydland (1994) showed that the correlation of output among developed countries is positive. This is not true in the case of Japan and the U.S. in the recent years. The quarterly correlation of output over the 198-28 period is approximately zero and is negative during the 9s. In this paper, I extend the business cycle accounting method a la Chari, Kehoe and McGrattan (27) to a two country international business cycle model and quantify the e ect of wedges in relevant markets on the business cycle correlation between Japan and the US and show that disturbances in the labor market, production e ciency and international trade market are important in accounting for the business cycle correlation pattern between Japan and the US. In this paper, I focus on the recent business cycle correlation between Japan and the US. Table 1 shows the cross-country correlations of quarterly data over the 198-28 after detrended with the Hoddrick-Prescott lter. As shown in Ambler, Cardia and Zimmerman (24), recent data of Japan and the US show positive but low cross-country correlation of output and labor. In fact, output correlation is almost zero during the 198s and negative during the 199s. Surprisingly, cross country correlations of consumption and investment are negative on average over the whole period. Figure 1 shows the linearly detrended uctuations in key macroeconomic variables in both countries. Consumption, labor and investment are all procyclical in each country over the 198-28 period. This gure shows the reason why the business cycle correlations are weak in the 198s and negative in the 199s. During the early 198s, US experienced a recession while Japan was relatively stable. In the late 198s, Japan experienced a large expansion referred to as the bubble economy while the US was relatively stable. The business cycle correlation is negative in the 199s since the US experienced a steady growth 2

while Japan went through a decade long recession known as the lost decade. In the 2s, the business cycle correlation is stronger. The model s foundation is one-good two-country model a la Baxter and Crucini (1995), which consists of nal good rms, households and governments in both countries. The nal good rms in both countries produce an identical nal good from capital and labor using constant returns to scale production technology. The nal good rms face Hicks-neutral disturbances in production e ciency. The in nitely-lived representative households in both countries gain utility from consumption and leisure. The households in each country earn income from capital stock and labor supplied to the nal good rms with which they purchase consumption and investment. They also trade state contingent bonds whose returns are a ected by international nancial disturbances. The governments in each country collect distortionary labor income and investment taxes from the household, purchase nal goods, and rebate the remainder as a lump sum transfer. Chari, Kehoe and McGrattan (27) shows that distortions created by various frictions can be mapped into a prototype model with distortionary taxes. Following their study, instead of analyzing the e ects of actual distortionary taxes on the business cycles, as in Braun (1994) and McGrattan (1994), I assess in which market exists the important distortions in accounting for the business cycle correlation between Japan and the U.S. The disturbances in resource, labor, investment, production e ciency and international nancial markets are computed as wedges from equilibrium conditions and are taken as exogenous. Resource, labor, investment and production e ciency wedges are identical to those introduced in Chari, Kehoe and Mc- Grattan (27). Resource wedges are disturbances in the resource constraints which correspond to government expenditure in the data. Labor wedges are disturbances in the labor rst order condition that capture the discrepancy between the intratemporal marginal rate of substitution of leisure to consumption and the marginal product of labor. Investment wedges are distur- 3

bances in the capital Euler equation that captures the discrepancy between the intertemporal marginal rate of substitution of future consumption to current consumption and the return on capital. Production e ciency wedges are equivalent to total factor productivity, i.e. Solow residuals. Wedges in the international market are additions I made to the original literature. International price wedges are disturbances in the cross-country arbitrage condition which drives wedges between the marginal utility of consumption across countries. Trade wedges are disturbances in the international resource constraint that captures the discrepancy in the trade balances of the two countries evaluated at international prices. Taking productivity shocks as given, canonical international real business cycle models, such as Baxter and Crucini (1995), Backus, Kydland and Kehoe (1994) and Stockman and Tesar (1995), can replicate the positive output correlation between developed countries. However, the cross-country correlation of consumption generated by the model is too high due to international risk sharing. Furthermore, the cross-country output correlation generated by these models is lower than data since they cannot replicate the positive correlation of inputs across countries. That is, in a canonical model, production factors should shift towards the country that faces a relatively higher productivity shock. Therefore, although output has positive correlation due to positive productivity correlation, production factors have negative correlations across countries. These are known as the quantity anomalies. In addition, the correlation between the marginal rate of substitution for consumption across countries and the real exchange rate is opposite from the data. This is known as the price anomaly. This paper shows that the sources of these anomalies can be quanti ed by the wedges in each markets. The business cycle accounting results show that Japanese e ciency wedges and U.S. labor wedges are important in accounting for the correlation pattern of output and that international price wedges are important in accounting for the cross-country consumption (un)correlation between Japan and the 4

U.S. I also con rm that international price wedges imply counterfactual real exchange rate movements. A sophisticated model aimed to explain the correlation between the Japanese and U.S. economies should be based on these results. The remaining of this paper is organized as follows. In section 2, I describe the model. In section 3, I explain the quantitative method and present the simulation results. Section 4 concludes the paper. 2 The Model The model is a competitive market version of a standard two-country model a la Baxter and Crucini (1995) in which there is a single nal tradable good produced in both countries. Each country i = JP; US consists of a representative household, nal good rm, government and trading rm. Following Chari, Kehoe and McGrattan (27), I introduce wedges in relevant markets represented as distortionary shocks. The full description of the model is as follows. 2.1 Final Good Firms The nal good rms in each country produce aggregate output Y t from capital stock K t and labor supply L 1 t using a Cobb-Douglas production technology which is a ected by aggregate TFP, A t : Y i t = A i t(k i t) i (l i t) 1 i 1 Output and capital stock are divided by the adult population. Labor supply consists of average hours worked per worker and the number of workers per adult population. Average hours worked per worker is de ned as the average weekly hours worked per worker divided by 14 7 assuming that 14 hours is the maximum each worker can work per day. 5

where represents the capital share. I decompose the aggregate TFP into the trend, t = (1 + ) t 1, and stationary shocks z t : A i t = exp(z i t)( i t) 1 i : Using this decomposition, the production function can be rewritten as Y i t = exp(z i t)(k i t) i ( i tl i t) 1 i : Thus, the trend component t is also known as the labor augmenting technical progress. Then, dividing both sides of the equation by t, the production function can be rewritten as y i t = exp(z i t)(k i t) i (l i t) 1 i (1) where yt i and kt i refer to output and capital detrended by t, respectively. Then, the detrended pro t maximization problem for the nal good rm can be written as max i t = exp(z i t)(k i t) i (l i t) 1 i w i tl i t r i tk i t where w t are real wages and r t are real capital rental rates 2. 2.2 Households The households in each countries maximizes lifetime utility: U = E 1 X t= t i ln c i t + (1 i ) ln(1 l i t) (2) 2 According to the Kaldor growth facts, real wages grow as labor augmenting technical progress t grows. Thus they are detrended by t. On the other hand, real interest rates do not have a trend. 6

where c t and l t denote detrended consumption and labor supply, respectively, subject to a budget constraint: (1 i lt)w i tl i t + r i tk i t + p i td i t + i t = c i t + (1 + i xt)x i t + p i tq t d i t+1 + t k i t (3) where x t is investment, d t is the state contingent international bond, q t is the price of the bond, lt and xt represent distortionary taxes on labor income and investment, respectively, and t is the lump-sum transfers from the government. I assume that there is a disturbance in the international nancial market p i t where p JP t = 1 and p US t cost t is assumed to take the form of = p t. The capital adjustment t = i 2 x i t k i t d i 2 where d i = i (1 i ) 3. Investment is assumed to follow the capital law of motion: i k i t+1 = x i t + (1 i )k i t: (4) 2.3 International Financial Market The state contingent international bonds are traded at the price q t. However, I assume that there are disturbances in the market such that the e ective price of the claim is q t for Japan and p t q t for the U.S. I also assume that there is a disturbance to resource that ows across borders, t t 4. That is, [q t d JP t+1 d JP t ] + p t [q t d US t+1 d US t ] = t t 3 This guarantees that the adjustment cost is equal to zero in the steady state. 4 This can be considered as a variable iceberg cost. This term is important accountingwise since it captures the trade of each country with other countries, which is not modeled in this paper. 7

or tb JP t + p t tb US t = t t : (5) 2.4 Government The government collects taxes from households, purchases goods and services and rebates the remaining to the household as a lump-sum transfer. That is, i ltw i tl i t + i xtx i t = i t + g i t: (6) As mentioned above, the main focus of this paper is not to analyze the e ect of distortionary taxes, but to assess which wedge is important in accounting for the business cycle correlation in Japan and the U.S. 2.5 Shocks The 1 exogenous variables are exo = fg i ; i l ; i x; z i ; p; tg. follow a VAR process I assume they exo t = P + P exo t 1 + " t (7) where " = f" i g; " i l ; "i x; " i z; " p ; " ts g: Agents expect the future levels of the exogenous variables according to this process. 2.6 Equilibrium The competitive equilibrium is characterized by the prices and quantities fy i ; c i ; l i ; x i ; tb i ; k i ; w i ; r i ; i ; g i ; i l ; i x; z i ; q; p; tg such that, households optimize given prices and wedges fw i ; r i ; q; p; i ; i l ; i xg, nal goods rms optimize given prices and wedges fw i ; r i ; z i g, government budget constraint (6) holds, the resource constraints hold, and shocks follow the process (7). 8

The equilibrium can be summarized by the following equations. capital Euler equation in both countries i (1+ i xt+ t ) c i t i = i E t i c i t+1 i yi t+1 k i t+1 the labor rst order condition in both countries The + (1 i )(1 + i xt+1) + k t+2 t+1 + t+1 ; k t+1 (8) 1 i 1 l i t = (1 i lt)(1 i ) yi t l i t c i t i ; (9) the production function in both countries (1), the capital law of motion in both countries (4), the resource constraint in both countries x yt i = c i t + x i t + gt i + tb i i t + t kt; i (1) the trade balance constraint (5), and the international rst order condition k i t p t = JP =c JP t US =c US t : (11) These 12 equations characterizes the equilibrium of the following 12 endogenous variables fy i ; c i ; l i ; x i ; tb i ; k i g given 1 exogenous variables fg i ; i l ; i x; z i ; p; tg: 3 Quantitative Analysis The quantitative analysis is done in the following order. First I use the equilibrium conditions and data over the 198-28 to calibrate and estimate the parameter values. Second, I obtain linear decision rules for endogenous variables using the method of undetermined coe cients. Third, I compute the wedges using data and the linear decision rules. Finally, I simulate the model using the computed wedges and linear decision rules. 9

3.1 Parameter Values The structural parameter values are calibrated using the data of Japan and the U.S. over the 198-28 period. I assume symmetry across Japan and the U.S. and use the average of these numbers as common parameter values in both countries. The values of structural parameters are listed in Table 2. The capital share parameter is calibrated as follows for each country. First, the capital income share p = unambiguous capital income + xed capital consumption GDP - ambiguous capital income is directly calculated from national income and product accounts 5. The values are.36 for Japan and.29 for the US, respectively 6. Since output is de ned as GDP plus the ow income from durable and government capital stock (F LOW ), the capital share is computed as = p GDP + F LOW GDP + F LOW : The depreciation rate is computed directly from data using the capital law of motion (4) 7. The growth trend is computed as the average growth rate of per capita output. The subjective discount rate is calibrated to data of average capital to output ratio with the steady state version of capital Euler equation (8) i (1 + x ) = i i y i k + (1 i i )(1 + i x) : The utility parameter is calibrated to match data of average labor and 5 For details, see Cooley and Prescott (1995). 6 I use the Hayashi and Prescott (22) data set over the 198-22 period for Japan, and BEA data over the 198-26 period for the US, respectively. 7 The capital stock series is constructed by the perpetual inventory method. For further discussion see the appendix. 1

consumption to output ratio with the steady state version of the labor rst order condition (9) i 1 = (1 i 1 l l)(1 i ) yi i l i I assume that the steady state values of wedges f i l ; i x; z i g are zero for simpli- cation. The steady state level of government wedges g are computed directly from data. The steady state levels of international prices p and trade shocks ts are computed by steady state versions of (11) and (5), respectively. The parameter of capital adjustment cost is set so that the marginal Tobin s q is equal to one. i c i : The persistence parameters of the shock process (7) is obtained using Bayesian estimation 8. For estimation, I use output, consumption, labor, investment and government purchases of both countries as observable variables. Since there are 1 shocks and 1 observable variables, the system is just identi ed. For simplicity, I put a restriction on the persistence parameters as follows. 1 2 3 1 11 12 13 2 21 22 23 3 31 32 33 exo t = P + 44 45 46 47 exo t 54 55 56 57 64 65 66 67 74 75 76 77 88 89 98 99 1 + " t 8 Resource wedges, labor wedges, production e ciency wedges and international wedges can all be directly computed from the equilibrium conditions. However, computing investment wedges involves expectational terms so they cannot be directly computed. Therefore, the entire system must be estimated. 11

In other words, I assume that the wedges in each country do not have spill over e ects across the country border. This is a very convenient assumption since it allows the estimation to be done separately for each country which economizes estimation time dramatically 9. Notice that I do not restrict the variance covariance matrix of the error term so that they have contemporaneous correlation. Unlike the structural parameters, I do not assume symmetry across countries in the stochastic process 1. 3.2 Wedges Once the parameter values are obtained, the model can be solved for decision rules numerically. In this paper, I use the linear solution method a la Uhlig (1999) to solve the model. I compute the wedges using the data of the observable variables used for the estimation, their obtained linear decision rules and the obtained linear decision rules of the endogenous state variables, capital stock in each country. The linear decision rules of endogenous variables are functions of state variables fk i ; g i ; i l ; i x; z i ; p; tg. Initial capital stock in each country is assumed to be at the steady state level. Once the initial capital stock level is given, in the initial period there are 12 known variables including initial capital stock in both countries and 12 unknown variables including the second period capital stock in both countries. Thus, we can solve the linear system of equations and compute the unknown variables. The same procedure can be used for the next period using the computed level of the second period capital stock from the rst step. We can continue this procedure until the 9 I estimated the processes of wedges assuming exonogenous trade balance being independent from other wedges in each country. 1 Unfortunately, for the U.S. estimation, the acceptance rate of the MCMC process is very low indicating a poor estimate for the stochastic process. This is most likely because over the data period, 198-28, consumption, labor and output are too highly correlated. The original CKM paper uses data over the 1959-24 period. As CKM, I check that the key results presented below hold for a wide range of parameter values for the stochastic process. 12

whole series of wedges are computed. Figure 2a and 2b plot output and the wedges in each country. In Japan, government wedges are not that volatile and do not have clear correlation with GDP. Labor wedges are growing after early 199s. E ciency wedges are highly correlated with GDP. Investment wedges are growing during the 199s. These observations are consistent with Otsu and Pyo (29) which compares the Japanese and Korean economies using business cycle accounting 11. In the US, government wedges are quite volatile relative to GDP. Labor wedges are highly countercyclical. E ciency wedges are procyclical but not as volatile as in Japan. Investment wedges are constantly declining after 199. Figure 2c plots the international price and trade wedges. The international price wedge plotted in the upper panel shows that the relative price of Japanese goods should have fallen relative to US goods during the 1985-1995 period. The key economic e ects of changes in each wedges are as follows. A rise in resource wedges or trade wedges will generate a negative income e ect for the household in whichever country. This tends to reduce consumption and leisure. An increase in labor wedges increases the relative price of leisure to consumption. The substitution e ect leads the household to reduce consumption and increase leisure. An increase in current investment wedges increases the relative price of investment to consumption so the household should increase consumption and reduce investment, and hence reduce future consumption. An increase in production e ciency wedges causes a real business cycle e ect in which output, consumption, labor and investment should all increase. Finally, a rise in the price of Japanese goods relative to U.S. goods should lead to a fall in Japanese consumption and a rise in U.S. consumption. 11 One di erence is that I linearly detrend labor while Otsu and Pyo (29) does not. Theoretically speaking, labor is a stationary variable. However, there is a declining trend in Japanese labor re ecting demographic trends which are not dealt in the model. This treatment of the labor series does not have great impacts on the results. 13

3.3 The Backus-Smith Puzzle The wedge analysis shows that the price of Japanese goods relative to U.S. goods should have been falling during the late 198s and early 199s. However, yen appreciated in real terms against the US dollar during this period. This is an example of the well known Backus-Smith puzzle, introduced by Backus and Smith (1993), that international real business cycle models fail to replicate the negative relationship between real exchange rates and the international marginal rate of substitution. In order to assess whether this discrepancy is created by a misspeci cation of the preference function, I consider alternative forms of preference functions and compute international price wedges 12. First, I consider a preference function that is non-separable between consumption and leisure u(c; l) = (c t (1 l t ) 1 ) 1 : 1 The curvature parameter represents risk aversion of the household. The preference in (2) is simply a special case of this preference function in which = 1. I compute the implied international relative prices for two other cases in which = 2; 5. Figure 3 shows the results. With non-separable preferences, marginal utilities in each countries are not only a function of consumption, but also labor. However, altering the risk aversion parameter does not seem to be able to reduce the gap between the implied international relative price and the real exchange rate. Next I consider a case in which the household consumption forms habit 12 Backus, Kehoe and Kydland (1994) generate endogenous uctuation in international relative prices by introducing a structure of intermediate goods production into the two country economy setting. Stockman and Tesar (1995) generate endogenous uctuation in international relative prices through preference shocks which directly a ect the mariginal utility of consumption. In either model, the international relative price is still de ned as the ratio of marginal utilities of consumption across countries. Therefore, the discrepancy between international relative price implied by the model and the data of real exchange rate remains. 14

persistence u(c; l) = log(c t bc t 1 ) + (1 ) log(1 l t ): The habit persistence parameter b is assumed to be equal to.65 following the estimation of Christiano, Eichenbaum and Evans (25). The results are plotted in the Figure 3. With habit persistence, marginal utility is a function of consumption growth rather than the level of consumption. This change in preference also does not seem to be able to reduce the gap. Therefore, I carry on with the analysis assuming that there was a shock to the e ective international relative price regardless of the discrepancy with it and the real exchange rate. Finally, I consider the GHH preferences a la Greenwood, Hercowitz and Hu man (1988) u(c; l) = log(c t lt ): GHH preferences are widely used in the small open economy literature due to its ability to generate high volatility in consumption and countercyclical trade balance through the lack of income e ects on labor supply. Ra o (28) shows that the GHH preference can generate a countercyclical trade balance in a two-country Backus, Kehoe and Kydland (1994) model which rely more on countercyclical uctuation of goods rather than prices. Figure 3 shows that the international price wedges computed with GHH preferences are less volatile than the benchmark case. That is, the international price wedges are less important in accounting for the consumption correlation. However, since the uctuation of the international price wedges are negatively correlated to the real exchange rate, the Backus-Smith puzzle is not resolved. 3.4 Simulation Results Simulation is done using the linear decision rules and the computed wedges. Since there are 1 wedges, I can provide 1 separate simulations for each 15

wedge as well as simulations using multiple wedges. For simplicity, I focus on results for simulations using the following 5 sets of wedges: government wedges in both countries, labor wedges in both countries, investment wedges in both countries, e ciency wedges in both countries and international price and trade wedges. Figure 4 and 5 plots the endogenous uctuations of output, consumption, labor and investment in response to uctuations of each set of wedges. In Japan, output and investment mainly responds to e ciency wedges, consumption mainly responds to international wedges and labor mainly responds to labor wedges. In the US, output and labor mainly react to labor wedges, consumption reacts to both labor and international wedges, investment reacts to investment and e ciency wedges. The results are summarized in Table 3. The left panel of the table reports the correlation of each simulated variable across countries as well as the standard deviation of them in each country computed from the results of the simulation described above. The results show that labor wedges are important in explaining the positive correlation of output. Also international wedges are essential in explaining the negative correlation of consumption. These results illustrate the common problem with single good international business cycle models such as Baxter and Crucini (1995) that consumption correlation across countries would be too high relative to data. This can be shown by the international risk sharing condition (11) which guarantees that consumption across countries would be perfectly correlated without international price wedges. Another common problem with international business cycle models is that production factors will have negative correlations across countries with only e ciency wedges i.e. productivity shocks. In the case of Japan and the US, e ciency wedges in Japan are more volatile than in the US so the e ect of uctuations in Japanese e ciency wedges dominates the e ect of uctuations in US e ciency wedges. High productivity in Japan leads to high labor supply in Japan and low labor supply in the US. Labor 16

wedges in the US are important in accounting for the uctuation in US labor and output. 3.5 Error Terms The assumption in (7) is that there are no lagged spill over e ects between domestic wedges and international wedges. However, there are no restrictions on the contemporaneous correlation among the error terms. Table 4 shows the correlation between the error terms. Labor wedges are positively correlated while investment and e ciency wedges are negatively correlated across countries. International price wedges are negatively correlated to Japanese investment and production e ciency wedges whereas they are positively correlated to US investment and production e ciency wedges. It is clear that the international price wedges is strongly correlated to the Japanese e ciency wedges. Early studies on international business cycles such as Backus, Kehoe and Kydland (1994) and Stockman and Tesar (1995) can be considered as models connecting international price wedges to domestic wedges. In Backus, Kehoe and Kydland (1994), productivity shocks to intermediate goods rms in both countries endogenously shift the terms of trade which shows up as international price wedges in the business cycle accounting model. In Stockman and Tesar (1995), preference shocks a ect the international relative prices directly where preference shocks show up as labor wedges in the business cycle accounting model. Business cycle accounting does not provide for an evaluation on which model is correct. Christiano and Davis (26) show that in order to understand the nature of shocks to the economy, one has to orthogonalize the error terms. Only by doing so, we can de ne fundamental economic shocks and understand how they form wedges. However, this involves an identi cation process which is usually problematic since there is not enough information. Sophisticated international business cycle models, such as the ones mentioned above, identify 17

the contemporaneous relationship of error terms by assuming certain structure of the economy. However, these assumptions may or may not be true. A further investigation of the error terms is needed to truly understand the nature of international business cycle correlations. 4 Conclusion This study focuses on the Japan and US business cycle correlation over the 198-28 period. The cross-country correlation of GDP is weak in the 198s and negative in the 199s while after 2 the correlation turns positive. I extend the business cycle accounting method a la Chari, Kehoe and McGrattan (27) to a two-country open economy framework and show that production e ciency wedges in Japan and labor wedges in the US are important in accounting for the output correlation while international price wedges are important in accounting for the consumption correlation between the two countries over this period. A successful model for business cycle correlations between Japan and the US must account for this fact. This study should serve as a foundation for future research to construct a more sophisticated international business cycle model. References [1] Ambler, Cardia and Zimmerman, 24, International Business Cycles: What are the facts?, Journal of Monetary Economics [2] Backus, Kehoe and Kydland, 1994, Dynamics of the trade balance: the J-curve?, American Economic Review [3] Backus and Smith, 1993, Consumption and real exchange rates in dynamic economies with non-traded goods, Journal of International Economics 18

[4] Baxter and Crucini, 1995, Business cycles and the asset structure of foreign trade, International Economic Review [5] Braun, 1994, The Interaction of Distortionary Taxes and Aggregate Variables in Postwar Data, Journal of Monetary Economics [6] Chari, Kehoe and McGrattan, 27, Business Cycle Accounting, American Economic Review [7] Christiano and Davis, 26, Two aws in business cycle accounting, NBER working papers [8] Christiano, Eichenbaum and Evans, 25, Nominal rigidities and the dynamic e ects of a shock to monetary policy, Journal of Political Economy [9] McGrattan, 1994, The macroeconomic e ects of distortionary taxation, Journal of Monetary Economics [1] Otsu and Pyo, 29, Comparative estimates of nancial frictions in Japan and Korea, Seoul Journal of Economics [11] Ra o, 28, Net exports, consumption volatility and international business cycle models, Journal of International Economics [12] Stockman and Tesar, 1995, Tastes and technology in a two-country model of the business cycle: explaining international comovements, American Economic Review [13] Uhlig, 1999, A toolkit for analyzing nonlinear stochastic models easily, in Computational methods for the study of dynamic economics, Marimon and Scott eds. 19

A Tables and Figures Table 1. Japan-US Business Cycle Correlation y c x g l 198 28 :14 :12 :3 :12 :37 198 1989 :59 :56 :21 :26 :43 199 1999 :7 :8 :79 :2 :68 2 28 :84 :83 :57 :5 :54 Table 2. Parameter Values Japan US :457 :387 :2 :14 1:4 1:5 :982 :986 :269 :214 l :252 :22 c=y :592 :659 x=y :258 :22 g=y :134 :145 2

cor std(jp ) std(us) Table 3. Results of Simulations y c l x g JP &g US :54 1: :9 :95 JP l & US l :18 1: :12 :1 JP x & US x :89 1: :62 :85 z JP &z US :88 1: :99 1: p&ts :91 :89 :9 :81 DAT A :14 :12 :37 :3 g JP &g US :9 :13 :16 :49 JP l & US l 1:6 1:2 1:83 2:23 JP x & US x 1:5 :56 1:18 6:89 z JP &z US 5:34 1:34 3:21 15:4 p&ts 1:15 1:72 2:15 :56 DAT A 3:76 3:25 2: 1:56 g JP &g US :12 :13 :18 :57 JP l & US l 1:9 1:2 3:11 :69 JP x & US x 2:29 :56 1:86 13:92 z JP &z US 4:52 1:34 3:96 14:9 p&ts 1:67 1:98 2:73 :55 DAT A 1:85 1:23 3:14 7:5 21

" JP g " JP l " JP x Table 4. Correlation of Shocks " JP z " US g " US l " US x " US z " p " ts " JP g 1: :69 :11 :5 :18 :29 :15 :56 :2 :11 " JP l 1: :2 :57 :23 :51 :13 :66 :5 :19 " JP x 1: :55 :7 :8 :94 :1 :61 :14 " JP z 1: :19 :41 :76 :52 :38 :1 " US g 1: :3 :1 :4 :6 :6 " US l 1: :22 :55 :11 :27 " US x 1: :27 :63 :7 " US z 1: :28 :26 " p 1: :3 " ts 1: 22

Output Consumption Government Expenditure Labor Investment Deviation from HP trend (Investment).4 Figure 1a. Japan Business Cycles.8.3.6.2.4 Deviation from HP trend.1 -.1.2 -.2 -.2 -.4 -.3 -.6 -.4 198 1985 199 1995 2 25 -.8

Output Consumption Government Expenditure Labor Investment Deviation from HO trend (Investment).4 Figure 1b. US Business Cycles.16.3.12.2.8.1.4 Deviation from HP trend -.1 -.2 -.4 -.8 -.3 -.12 -.4 -.16 -.5 198 1985 199 1995 2 25 -.2

Output Government Wedges Labor Wedges Efficiency Wedges Investment Wedges.6.4 -.4 -.6 Deviation from HP trend (Investment Wedges).4 Figure 2a. Japan Wedges 1.3.8.2 Deviation from HP trend.1 -.1.2 -.2 -.2 -.3 -.8 -.4 198 1985 199 1995 2 25-1

Output Government Wedges Labor Wedges Efficiency Wedges Investment Wedges 1.5 -.5-1 Deviation from HP trend (Investment Wedges).8 Figure 2b. US Wedges 1.5.6.4 Deviation from HP trend.2 -.2 -.4 -.6 -.8 198 1985 199 1995 2 25-1.5

.3 Figrue 2c. International Wedges.2.1 Deviation from HP trend -.1 -.2 -.3 -.4 198 1985 199 1995 2 25 Price Trade Shock

log Sigma=2 Sigma=5 Habit GHH Real Exchange Rate.4.2 -.4 Deviation from Linear trend (Real Exchange Rate).2 Figure 3. International Prices.6.15.1 Deviation from Linear trend.5 -.5 -.2 -.1 -.15 -.2 198 1985 199 1995 2 25 -.6

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.4 Figure 4a. Results Japan-Output.3.2 Deviation from HP trend.1 -.1 -.2 -.3 -.4 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.2 Figure 4b. Results Japan-Consumption.15.1 Deviation from HP trend.5 -.5 -.1 -.15 -.2 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.3 Figure 4c. Results Japan-Labor.2.1 Deviation from HP trend -.1 -.2 -.3 -.4 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.15 Figure 4d. Results Japan-Investment.1.5 Deviation from HP trend -.5 -.1 -.15 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.4 Figure 5a. Results US-Output.3.2 Deviation from HP trend.1 -.1 -.2 -.3 -.4 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.3 Figure 5b. Results US-Consumption.2 Deviation from HP trend.1 -.1 -.2 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.3 Figure 5c. Results US-Labor.2.1 Deviation from HP trend -.1 -.2 -.3 -.4 -.5 198 1985 199 1995 2 25

Government Wedges Labor Wedges Investment Wedges Efficiency Wedges International Wedges Data.2 Figure 5d. Results US-Investment.15.1 Deviation from trend.5 -.5 -.1 -.15 -.2 198 1985 199 1995 2 25