Net Exports, Consumption Volatility and International Business Cycle Models

Transcription

1 Net Exports, Consumption Volatility and International Business Cycle Models Andrea Ra o y University of California, Los Angeles March 2005 Abstract The central feature of international business cycles is that net exports are countercyclical. Alternatively, domestic spending is more volatile than output. Small and large countries, developing and developed economies, all share this property. What do international business cycle models require to reproduce this feature of the data, when driven mainly by productivity shocks? Two-country models à la Backus et al. [1992] have proved to be successful in delivering countercyclical net exports. We point out that this result is obtained through large changes in international prices (terms of trade e ect), whereas in the data we observe uctuations in quantities. The model su ers from excessive smoothness in consumption: domestic spending is systematically less volatile than output. We then consider a class of preferences, proposed by Greenwood et al. [1988], that embeds home production in a reduced form. Introducing these preferences in the two-country setup enables us to generate su cient volatility in consumption so that domestic spending is more volatile than output, as in the data. Net exports are countercyclical primarily because of changes in quantities. Varying country size, the elasticity of substitution between traded goods or the presence of incomplete asset markets does not a ect our ndings. JEL Classi cation: E32; F32; F41 Keywords: Net exports; Home production; Consumption volatility. I would like to thank my advisor Andy Atkeson for encouragement and advice provided during all stages of this research. I am also grateful to Ariel Burstein, Hal Cole, Luca Dedola, Eduardo Ganapolsky, Lee Ohanian, Randall Wright and seminar participants at ECB, Kansas City FED, UCLA for helpful comments. Part of this project was conducted while visiting the Research Department at the Atlanta FED whom I thank for hospitality and useful suggestions. Financial support from UCLA s Dissertation Year Fellowship is gratefully aknowledged. y Ph.D. Student, Department of Economics, UCLA. ara o@ucla.edu

2 1 Introduction The central feature of international business cycle data is that net exports are countercyclical. Table 1 presents correlations between net exports and output for several OECD countries and emerging economies 1. The countercyclicality of net exports is a general property of the data, independent of country size and stage of development. This property has a counterpart in terms of volatilities, as we document in Table 2A: domestic absorption is more volatile than output. Countercyclical net exports indicate that countries borrow from international capital markets during booms and repay during recessions, which is at odds with the implications of optimizing models: consumption smoothing, in fact, provides a force for procyclical saving (that is, procyclical net exports). In this paper, we study what are the essential characteristics required to reproduce countercyclical net exports in DSGE models, when business cycles are driven primarily by productivity shocks. We adopt a two-country two-good framework à la Backus-Kehoe- Kydland [1994] (BKK henceforth) which has been successful in reproducing countercyclical net exports and, for this reason, has been extensively used in the literature to address issues related to international comovements, market incompleteness and terms of trade 2. Our rst nding is that the mechanism by which the BKK model generates countercyclical net exports is counterfactual. In the model, large changes in international prices (terms of trade e ects) generate countercyclical net exports, whereas quantities are indeed procyclical. In the data, however, the opposite is true: Table 2B shows that countercyclical net exports are associated with uctuactions in quantities of goods traded across national borders, while international prices play a minor role. We show that in the model domestic spending is systematically less volatile than output. In all our exercises, we include adjustment costs to investment to avoid the volatility of 1 Data for emerging economies are from Aguiar and Gopinath [2004]. 2 See, for example, Kehoe and Perri [2002], Heatcote and Perri [2002]. 1

3 domestic spending from being arti cially increased through this channel. We conclude that the model su ers from excessive smoothness in consumption: the dynamics of trade in goods is dominated by the consumption smoothing motive, thus producing procyclical net exports in terms of quantities. We then consider a class of preferences, proposed by Greenwood, Hercowitz and Hu man [1988] (GHH preferences), that include home production in a reduced form. We show that introducing these preferences in the BKK setup generates su cient volatility in consumption so that domestic spending is more volatile than output. Countercyclical net exports are associated with uctuations in traded goods, consistent with the data. A large literature has documented that the interaction between home and market activities has important quantitative implications for business cycle predictions of DSGE models 3. Supported by a large evidence on the allocation of time and on the cyclical uctuactions in the consumption of market goods that are substitute for home production (for example, eating at restaurants, housecleaning, child care...), these studies incorporate the idea that households substitute between home and market activties depending on the wage rate. High wages during economic expansions are associated with an increase of hours worked in the market and a corresponding reduction in home production, which increases purchases of market goods. Our previous discussion suggests that the home production structure implicit in the GHH preferences is a fruitful way to deal with the excessive smoothness in consumption implied by standard isoelastic preferences. We illustrate that this is indeed the case. Furthermore, sensitivity analysis shows that our ndings hold for a wide range of parametrizations, with particular interest for two experiments. First, we study the e ects of varying the elasticity of substitution between traded goods. In the BKK model, low values of this 3 See, for example, Benhabib et al. [1991], Greenwood et al. [1988], McGrattan et al. [1997]. Baxter and Jermann [1999] argue that home production helps explaining the excessive sensitivity of consumption to predictable changes in income. 2

4 parameter are needed to generate countercyclical net exports 4. In light of our ndings, it is clear why this is the case: high complementarity between traded goods implies that shocks to productivity, by altering the relative scarsity of goods in international markets, produce strong terms of trade e ects. Ultimately, this change in the relative price translates into countercyclical net exports. With GHH preferences, instead, the model relies on a mechanism that involves directly uctuations in quantities. As a consequence, the value of this elasticity does not a ect the cyclicality of net exports. In our second experiment, we study the e ects of varying country size, our motivation being that small and large countries, all share this feature of the data. We present an economy in which a small country (Canada) interacts with the rest of the world under isoelastic preferences. The model exhacerbates the failures of the symmetric case in that excessive smoothness in consumtpion generates procyclical net exports. Adding GHH preferences produces countercyclical net exports independent of country size, as in the data. The rest of the paper is organized as follows. Section II presents the BKK model, discussing its counterfactual implications for the dynamics of international trade in goods. Section III introduces the GHH preferences in the BKK setup, illustrating how home production provides a mechanism to increase the volatility in consumption and deliver countercyclical net exports. We then discuss the sensitivity of our results to changes in parameter values. Section IV concludes. 2 The Model 2.1 Preferences and Technology Time is discrete. Denote by s t an event drawn each period from a (possibly in nite) set S t ; by s t the history of events up to date t and by (s t ) the probability at time 0 of a particular history s t : 4 This point is due to Pakko [2003]. 3

5 There are two countries populated by identical in nitively lived agents. We will allow the size of the two countries to di er and indicate with i the measure of each country, where i = 1; 2: There are two intermediate goods (j = A; B) and two nal goods (C i ): Factors of production are immobile across countries and each country specializes in the production of one intermediate good. Households derive utility from consumption and leisure. Preferences are of the standard isoelastic form U(C i (s t ); 1 N i (s t )) = [C i (st )(1 N i (s t )) 1 ] 1 (1) 1 where C i is consumption, N i is labor and the time endowment has been normalized to one. Households supply labor and rent capital to rms producing intermediate goods in a perfectly competitive market. These rms solve a standard pro t maximization problem subject to a Cobb-Douglas production constraint, that is Max i (K i (s t ); N i (s t )) = q j i (st )e z i(s t) F (K i (s t ); N i (s t )) W i (s t )N i (s t ) R i (s t )K i (s t ) s:t: F (K i (s t ); N i (s t )) = Ki (s t )N 1 i (s t ) (2) where q j i (st ) is the price of the intermediate good j in country i relative nal good of country i, W i (s t ) and R i (s t ) are wages and rental rates in nal good units, K i (s t ) is capital and z i (s t ) is an exogenous technology shock. The two country-speci c shocks z i (s t ) follow a rst order vector autoregression process. After intermediates are produced, households trade goods in an international market without frictions (hence the law of one price holds) and sell all their holdings of intermediate goods to rms that produce domestic nal goods. The nal good can be either consumed or 4

6 invested. In each country, capital is subject to a convex adjustment cost so that it evolves according to the following law of motion K i (s t+1 ) = (1 )K i (s t ) + X i (s t ) + Xi (s t ) K K i (s t i (s t ) (3) ) where X i (s t ) is investment and is the depreciation rate. (:) is such that 0 (:) > 0; 00 (:) < 0: Final good producers are competitive and solve the problem Max i (A i (s t ); B i (s t )) = G i (A i (s t ); B i (s t )) q A i (s t )A i (s t ) q B i B i (s t ) s:t: 8 >< $i A 1 G i (A i (s t ); B i (s t )) = >: i (s t ) + (1 $ i )B 1 i (s t ) 1 1 i = 1 (1 $i )A 1 i (s t ) + $ i B 1 i (s t ) 1 1 i = 2 (4) where $ i > 0:5 determines home bias in the composition of nal goods 5. We denote by = 1 the elasticity of substitution between intermediate goods A and B. In our benchmark case asset markets are complete. Let D i (s t ; s t+1 ) be the quantity of bonds purchased by consumer in country i after history s t that entitles to one unit of country 2 consumption if event s t+1 happens in period t + 1. Let Q(s t ; s t+1 ) be the price of such an asset. We can then write the budget constraint for the representative citizen of country i as C i (s t ) + X i (s t ) + rx(s t ) X s t+1q(s t ; s t+1 )D i (s t ; s t+1 ) = = W i (s t )N i (s t ) + R i (s t )K i (s t ) + rx(s t )D i (s t 1 ; s t ) (5) 5 The function G(.) is known in the literature as the Armington aggregator. 5

7 where rx(s t ) denotes the real exchange rate 6. The household in each country maximizes utility subject to this budget constraint and the law of motion for capital. We will also consider the case in which agents can trade only a riskless bond. Denote by D i (s t ) the quantity of bonds purchased by consumer in country i after history s t that entitles with certainty to one unit of (country 2) consumption in period t + 1. Let Q(s t ) be the price of such an asset. We can then write the budget constraint for the representative citizen of country i as C i (s t ) + X i (s t ) + rx(s t )Q(s t )D i (s t ) = W i (s t )N i (s t ) + R i (s t )K i (s t ) + rx(s t )D i (s t 1 ) (6) 2.2 Equilibrium and the e ect of country size An equilibrium is an allocation and a set of prices for all s t and for all t 0 such that, given prices, all agents optimize, both types of rms optimize and markets clear. Market clearing for nal goods requires C i (s t ) + X i (s t ) = G i (A i ; B i ) i = 1; 2 (7) In the complete markets case, bond market clearing requires 1 D 1 (s t ; s t+1 ) + 2 D 2 (s t ; s t+1 ) = 0 8s t+1 2 S (8) If only a risk-free bond is traded, the market clearing condition for bonds is: 1 D 1 (s t ) + 2 D 2 (s t ) = 0 (9) 6 Given that bonds are issued in country 2 units of consumption, the real exchange rate does not appear in country 2 budget constraint. 6

8 Intermediate goods market clearing requires 1 A 1 (s t ) + 2 A 2 (s t ) = F (K 1 (s t ); N 1 (s t )) (10) and 2 B 2 (s t ) + 1 B 1 (s t ) = F (K 2 (s t ); N 2 (s t )) (11) In order to solve the model, we rst compute the non stochastic steady state by setting the innovations in productivity equal to their unconditional mean values. We then linearize the system of equations characterizing the solution of the model around the steady state and solve the resulting system of linear di erence equations. Notice that the only equations in which country size appears are the market clearing conditions for intermediates. The log-linearized version of these two expressions are and ex 1 b A2 + (1 ex 1 ) b A 1 = b Y 1 (12) ex 2B1 b + (1 ex 2 ) B b 2 = Y b 2 (13) where a hat denotes percentage changes from steady state for the corresponding variable and ex i (i = 1; 2) are the export shares of each country. We can then establish the following proposition: Proposition 1 For complete markets, country size does not matter independently of export shares. In what follows, we will make use of this result by studying the implications of country size on the volatility of domestic spending and the cyclical properties of net exports. We are interested in this modi cation of the benchmark set up because, as illustrated in Table 7

9 1, the countercyclicality of the trade balance is a general property of both small and large countries. In other words, it does not depend on country size. We will conduct our experiments under two scenarios. The rst is the BKK standard symmetric case, which has been extensively studied in the literature as an approximation for trade between U.S. and EU. The second scenario involves a small country (Canada) trading with a large country representing the rest of the world represented (EU, Japan and U.S.) 7. Notice that the only quali cation required by the model to study the e ect of country size is that as country size shrinks, openess increases Additional variables of interest In our analysis, we will be interested in observing the behavior of two additional variables. We de ne the terms of trade as the price of import relative to export P (s t ) = qb 1 (s t ) q A 1 (s t ) (14) Net exports over GDP (expressed in terms of nal good units) is de ned as nx = 2q A 1 (s t )A 2 (s t ) 1 q B 1 (s t )B 1 (s t ) 1 q A 1 (s t )F (K 1 (s t ); N 1 (s t )) Notice that changes in net exports are determined by changes in quantities (exports and imports) and prices (terms of trade). We isolate the rst component by de ning the variable NXQTY as the di erence between export and import when both terms evaluated at steady state prices 9, that is (15) nxqty = rowq A soea row (s t ) soe q B soeb soe (s t ) soe F (K soe (s t ); N soe (s t ))q A soe (16) 7 Appendix A provides details about how this aggregate for the rest of the world is constructed. 8 In the bond economy, country size a ects the bond market clearing condition as well. 9 The counterpart of NXQTY in the data will be net exports over GDP measured at constant prices. 8

10 2.4 Benchmark parameter values Table 3 reports the parameter values used in our benchmark simulation. Preference parameters are from the original BKK model. The discount factor is set equal to 0:99 which implies a steady state real interest rate of 1 percent per quarter. The share parameter ( = 0:34) is chosen so that in steady state the consumer allocates 30 percent of her time endowment to market activities. The curvature parameter, which determines both risk aversion and intertemporal elasticity of substitution, is set equal to 2 which is in the range of the evidence from U.S. time series. With respect to technology parameters, the capital share parameter in the Cobb- Douglas production function is set equal to 0:36; consistent with U.S. postwar data. The depreciation rate is 0:025 which implies an annual value of about 10 percent. All previous parameters are common across experiments. In the bottom panel of Table 3 we present the parameters that di er once we change country size: trade shares and productivity process. Under "BKK" we report the values used in the original BKK model, while under "Small Country" we present our estimates for Canada (trading with a rest of the world aggreagate). We calibrate the shares in the Armington aggregator $ i so that the implied import shares are consistent with the average values over the sample 1980:1-2004:1. In the case of Canada, this value is 0.32, while for the rest of the world is arbitrarily set equal to so that it resembles a closed economy. The corresponding value used by BKK is 0:15. We compute the two sequences of productivity shocks using the expression z t = ln(y t ) (1 ) ln(n t ) (17) where y t is real output and n t is total employment. Two issues arise in constructing productivity in this way. First, from a theoretical perspective, we should include capital given that our productivity sequence is derived from the assumption of Cobb-Douclas 9

11 production function. Unfortunately data on the capital stock at quarterly frequency are not available. However, as argued in the BKK work 10, the absence of data on capital should not be a serious problem given that its variability is small at high frequency. The second issue concerns the measurement of labor input. It would be preferable to have a measure of hours worked in our index for labor, but for most countries time series at quarterly frequency are not available. Given the two sequences of technology shocks, we then estimate a 2 x 2 vector autoregression process. For the symmetric case, our estimates did not di er signi cantly from the original BKK values, despite the use of a di erent sample 11. We decided to use the latter for easy of comparison. For the small country case, we set the spillover parameter from Canada to the rest of the world to be equal to zero because of lack of statistical signi cancy 12. Hence, the coe cients on the main diagonal are also the eigenvalues associated with the process, thus determining the persistence of the solution associated with two sequences of shocks. The last row of the table reports the ratio of population between countries. We use working age population in the year 2000 for Canada and our rest of the world aggregate to calibrate this parameter. This parameter does not a ect the simulation under complete markets, but s only the bond economy case. Overall, the bottom part of Table 3 shows how country size breaks the symmetry between countries in the parametrization of the model. First, trade shares di er thus allowing for one country to be more/less open than the other. This result is a direct consequence of Proposition 1 and it states that small countries are expected to trade more with foreigners than large ones. Second, spillover e ects are present only from the rest of the world to the 10 Kydland and Prescott [1982] originally documented this fact. 11 The OECD computes quarterly time series for EU-15 over the sample 1980:1-2002:4, while data in the BKK paper included the 70 s but not such a large group of European countries. 12 The estimated value turned out to be really small and insigni cant. Further, the p-value for Granger causality test is around 40 percent for this coe cient. Notice that, under this speci cation, rest of the world shocks a ect Canada with lag, but the viceversa is not true. 10

12 small country, thus a ecting wealth transfers across countries only in one direction. Third, the correlation between innovations is much lower than in the standard case. 2.5 Results: Benchmark Case In this section we use impulse response analysis and model simulations to illustrate that the BKK model generates countercyclical net exports through counterfactual large terms of trade e ects. We will show that this failure is related to the inability of the model to deliver su cient volatility in domestic spending relative to output. Throughout our analysis, we include adjustment cost to capital so that the volatility of domestic spending is not arti cially increased by the excessive responsiveness of investment to productivity shocks. We adopt a convex adjustment cost function that speci es the units of output foregone to increase the capital stock. This speci cation introduces an extra parameter, elasticity of the investment-capital ratio with respect to Tobin s q, that is calibrated to reproduce the same investment volatility (relative to output) as in the data. Finally, our parametrization of the adjustment cost function ensures that no cost is incurred in maintaining the steady-state capital stock (i.e. in the steady state Tobin s q is one) Impulse Responses We rst study our benchmark case by analyzing the impulse responses for the main variables we are interested in. Figure 1 and 2 present the impulses responses in country 1 after a 1 percent increase on its own productivity. Figure 1 shows that an increase in productivity increases the wealth of the country and provides investment opportunities. As a consequence, both consumption and investment rise. However, the top right panel shows that the combined change in these two variables is lower than the increase in output: the impulse response for domestic absorption is in fact below the one for output. As discussed in Table 2, this lack of su cient variability in domestic spending has a counterpart in terms of evolution of the trade balance. In Figure 2 we decompose the dynamics of net exports 11

13 into changes in quantities (NXQTY) and price e ect (changes in the terms of trade).the linearized version of the trade balance provides the mechanics of this decomposition. In fact, i cnx = im h^a ^b ^p (18) where ^p represents changes in the terms of trade and the rst component is obtained from the linearization of net exports evaluated at steady state prices, that is 13 h \nxqty = im ^a i ^b (19) Figure 2 shows that the model does indeed generate countercyclical trade balance (Net Exports starts from below zero), as originally argued in the BKK study. However, this result is entirely explained by the strong reaction in the terms of trade. The intuition for this result is quite straightforward: positive productivity shocks increase domestic output relative to foreign output thus raising the relative price between the two intermediate goods in the international market 14. The trade balance becomes then negative because the value of imports increases, while quantities imported do not vary. The impulse response of real net exports, instead, starts from zero and stays in the positive region. Our impulse response analysis indicates that in order for the model to deliver countercyclical trade balance, strong terms of trade e ects are needed. This mechanism contrasts with the data presented in Table 2A, where we observed that countercyclical net exports are associated with countercyclical real net exports. In other words, countercyclical net exports are a property characterizing the exchange of goods across countries, while prices (terms of trade) seem not to play such an important role. Our discussion of Table 2B provides also directions to understand why the model is not consistent with the data: the variability of domestic spending is lower than output, while the opposite is true in the data. 13 See Appendix B for details, where we show that our variable nxqty is exactly the di erence between output and domestic spending. 14 The terms of trade are de ned as price of imports over price of exports. 12

14 In the next section we con rm this intuition by comparing simulation-generated moments from the models and statistics from the data Model Simulations Table 4 reports the statistics generated by simulating the model for the variables of interest 15 under both scenarios, "symmetric BKK" (Table 4A) and "large vs small country" (Table 4B) In the rst column of Table 4A we present the data for U.S. The volatility of domestic absorption is higher than output volatility, to which it corresponds countercyclical trade balance in nominal and real terms. The terms of trade, on the other side, do not show any clear cyclical pattern, its correlation with output being almost zero. In the second column we report the result of our simulations for complete asset markets with capital adjustment cost. While it is immediate to see that the trade balance is negatively correlated with output (-0.61), the driving force behind this result is the strong terms of trade e ect generated by the change in relative scarcity of goods across countries. Positive productivity shocks cause increase in the production of home goods thus reducing its international value. The subsequent appreciation of the terms of trade makes foreign goods more expensive than home goods, hence generating negative trade balance mainly because of price e ect. However, as indicated in Table 2, this is not what we observe: in the data, the variations in nominal trade balance are explained by movements in real trade balance. It is worth noticing that in the model real net exports are instead procyclical, which indicates that the trade o between saving (consumption smoothing) and investment (productive opportunities) in real terms is resolved in favor of the rst. This discussion suggests that the roots of the problem are to be found in the panel reporting standard deviations 15 Moments for the model are calculated as averages of 100 simulations of series of length 100 periods. HP lter with smoothing parameter of 1600 is applied before computing each statistics. Standard errors are not reported, but available upon request. 13

15 relative to output volatility. After reproducing the volatility of investment, the model generates excessive smoothness in consumption so that domestic absorption is less volatile than output. In order to be able to invert this inequality, it has to be the case that consumption becomes more variable. We also experiment with incomplete asset markets, by having only a non-contingent bond internationally traded 16. Our results are reported in the third column of Table 4A and indicate that there is no signi cant di erence between bond economy and complete markets. In fact, it is well known that in this class of models one internationally traded bond is enough to achieve allocation similar to the complete market case 17. In Table 4B we depart from the symmetric world of the benchmark BKK and analyze the consequences of varying country size. The motivation for this exercise is in Table 1: countercyclical net exports characterize both large and small countries, so that a theory trying to explain this phenomenon has to be able to be su ciently general to include both cases. In the rst column we report business cycle statistics for our small country (Canada) that con rm the tight link between countercyclical net exports on one side, volatility of domestic spending on the other side. In the second column we present our results: the small country case exacerbates the problems of the standard BKK model. In fact, we now nd that terms of trade movements are not large enough to even generate negative correlation between nominal terms of trade and output. As a counterpart, the volatility of consumption is much lower than in the data (0.45 vs 0.77). Given our previous discussion, we decide not to report the results for the bond economy and perform a di erent experiment by allowing the elasticity of substitution to di er across countries. The rationale for this exercise is twofold. First, it would be natural to imagine that a small country has a larger dependency from imported goods than a big country. Second, Pakko [2003] shows that 16 Limiting asset trade to a riskless bond introduces non-stationarity in bond holdings. We include convex portfolio adjustment costs to induce stationarity. See Schmitt-Grohé and Uribe [2003] for details. 17 The intuition behind this result was already in Cole and Obstfeld [1991]. Baxter and Crucini [1995] report the same result for a two country-one good model. Heathcote and Perri [2002] document that this property is preserved in the 2 country-two good model. 14

16 adjustment costs on investment require small elasticity of substitution in order to preserve the countercyclicality of the trade balance. However, we nd that the model does not improve in any dimensions. In the table, we show that with values equal to 0.5 and 2 for this parameter, the trade balance is already procyclical. In conclusion, this section has shown that the success of the BKK model in delivering countercyclical net exports requires large changes in the terms of trade, which is counterfactual. We also illustrate that the source of the problem stems from the excessive smoothness in consumption which makes domestic spending not su ciently volatile relative to output. 3 Introducing GHH preferences In the small open economy literature, it is common practise to adopt a particular class of preferences introduced by Greenwood, Hercowitz and Ho man [1988] (GHH preferences from now on) to increase the volatility of consumption and generate countercyclical trade balance 18. In this section we argue that GHH preferences are needed in two country-two goods model à la BKK as well to avoid terms of trade e ect being the driving force behind the negative correlation between net exports and output. 3.1 GHH Speci cation Under GHH preferences, the momentary utility takes functional form of the type U(C; N) = [C N ] 1 1 where > 1; > 0: The important characteristics of this class of utility functions is the absence of income e ect in the supply of labor. (20) To illustrate this point, let us compare the static rst order condition that equates the marginal rate of substitution between consumption and leisure with the marginal product of labor to the same condition 18 This point is explicitly made in Correia et al. [1995]. See also, among others, Schmitt-Grohé and Uribe [2003] and Neumeyer and Perri [2004] for applications. 15

17 obtained under standard Cobb-Douglas preferences. In the latter case we have 1 while under GHH preferences this condition becomes C 1 N = A(1 )K N (21) $N 1 = A(1 )K N (22) that is $N = (1 )Y (23) With Cobb-Douglas preferences, after a positive productivity shock two forces are at work. The substitution e ect induces the household to supply more work because now leisure has become more expensive. The income e ect, on the contrary, induces the household to work less because higher income calls for higher demand of all normal goods (consumption and leisure). Overall, the substitution e ect dominates and labor input is procyclical. In the second case this is no longer true. Consumption (i.e. the income e ect) does not appear in this condition so that after a positive productivity shock only the substitution e ect operates. In other words, there is no intertemporal substitution of labor. As a consequence, labor reacts more to changes in productivity. However, notice that in the GHH utility function consumption and leisure enter linearly. Hence, a bigger response in labor (leisure) requires a bigger response in consumption to compensate for the decrease in utility associated with a positive income shock. This mechanism creates higher volatility in consumption.. The previous discussion has direct implications for the behaviour of net exports. After a positive productivity shock the country faces the trade o between saving to smooth (the marginal utility of) consumption and leisure and borrowing to invest more. Under GHH preferences, the higher reaction in consumption decreases domestic saving thus creating the need for borrowing more to nance productive investments. 16

18 We now turn to the quantitative implications of introducing GHH preferences in to the BKK model. 3.2 Simulation Results with GHH Preferences We nd the solution of the model by linearizing around the non stochastic steady state. The parameters used in our simulation are the same as before. However, two additional parameters need to be calibrated, namely and 19 :The parameter governs the elasticity of labor supply and is calibrated so that this elasticity is the same as in the Cobb-Douglas case. In particular, under Cobb-Douglas preferences the elasticity of labor supply (with marginal utility held constant) is equal to " CD = (1 N)[1 (1 )] N (24) while the value for this elasticity implied by GHH preferences is " GHH = 1 1 (25) Once is calculated, we can compute from static rst order condition such that in steady state the household allocates 30 percent of her time endowment to market activities. Figure 3 reports the impulse responses for the relevant variables in country 1 after it experiences a productivity shocks 20. The top left panel illustrates that the impact response of domestic spending is larger than output, contrary to the case with isoelastic preferences. The top right panel shows the impulse response of consumption: the ratio between consumption and output impact coe cients is close to 0:8 under GHH preferences, while it was close to 0:5 with isoelastic preferences. In other words, given that we are xing the dynamics of investment through adjustment costs, the larger response of domestic spending 19 In the original GHH speci cation, a growth term to the disutility of labor is included so that labor supply is bounded. The underlying assumption that home production grows at the same rate as productivity ensures consistency with balanced growth path. We consider a stationary environment, so there is no need for the inclusion of such a term. 20 Capital adjustment costs are included in all simulation involving GHH preferences as well. 17

19 to productivity shocks originates from the larger response of consumption. In the bottom part of Figure 3 we report the implications of GHH preferences for net exports: net exports are countercyclical, but in this case they are mainly driven by changes in real net exports (NXQTY). In fact, the two impulse responses are basically aligned. We then turn to our simulation to con rm our intuition. Table 5 compares the performance of the BKK model under standard isoelastic preferences and under GHH preferences. The rst striking di erence is the increase in the volatility of domestic absorption relative to the standard case: under GHH preferences, the volatility of domestic spending is indeed greater than output volatility, as in the data. Given that investment volatility is constant across experiments, this e ect is due primarily to increase in consumption volatility. As a consequence, the volatility of net exports increases by a factor of four, compared to the standard BKK, thus con rming that the adjustment comes from uctuations in quantity. In terms of correlation, we show that net exports is countercyclical, and almost all of its countercyclicality stems more from changes in quantities rather than prices. The model with GHH preferences, then, is able to replicate the mechanism at work in the data without need of resorting to terms of trade e ects. In Table 6 we carried out sensitivity analysis to the elasticity of substitution between intermediate goods. As already mentioned, this parameter plays an important role because it a ects the volatility of the terms of trade and, as a direct consequence, the countercyclicality of net exports. Table 6 illustrate that our ndings are not sensitive to the particular value for this parameter. In all cases, the countercyclicality of net exports is explained by the countercyclicality in real net trade and consumption remains su ciently volatile. Notice that for large values of this elasticity, the terms of trade become negatively correlated with output, features that we encountered in some countries of Table 1. The intuition for this result can be found by analyzing the linearized expression determining the terms of trade in the model. In Appendix B, in fact, we derive the following relationship 18

20 ^p = [ nxqty + (y 1 y 2 )] (26) where both and are positive coe cients. This equation determines changes in the terms of trade as the result of o setting movements in demand and supply. The second term (y 1 y 2 ) can be interpreted as a supply e ect and captures the idea that productivity shocks alter the relative scarcity of goods in the international markets. Hence, positive productivity shocks at home imply that foreign goods become more expensive. The rst term (nxqty), on the other hand, represents a shift in demand (real net exports equal the di erence between real output and domestic spending). Given that the terms of trade re ect the balancing of these two forces, it is not with surprise that with GHH preferences we can observe negative correlation between terms of trade and output: relative demand shifts are larger than supply movements In our discussion, we emphasized that a mechanism to increase domestic spending was needed in order to generate countercyclical real net exports. GHH preferences do provide such a mechanism by eliminating income e ect on labor supply. Higher volatility in consumption and, consequently, larger changes in real net exports provide a shortcut to mimic a demand shock, thus compensating the e ect on the terms of trade due to relative scarcity. Finally, Table 7 con rms that our results are robust to changes in country size and the elasticity of substitution between intermediates in this environment as well. 4 Conclusions In this paper we study what are the key determinants to obtain countercyclical net exports in models driven primarily by productivity shocks. The importance of this stylized fact stems from its generality: it is consistent across countries, independent of country size or stage of development. In addition, it indicates that countries borrow from international markets during booms, which is at odds with the implications of models led by consumption 19

21 smoothing motive only. To investigate this issue, we adopt a two-country two-goods model à la Backus et al. [1992] which has proved to be successful in reproducing this feature of the data. We illustrate that, however, the mechanism behind this result is counterfactual: the model requires changes in international prices that a ect the value of traded goods, while in the data changes in real net exports are the driving force. We establish that the reasons for this failure are to be found in the lack of volatility implied by the model for domestic spending relative to output. In the data, in fact, domestic absorption is more volatile than output, while the model, after controlling for investment volatility, delivers excessive smoothness in consumption. We study the implications of restricting asset trade by allowing only for trade on a riskless bond. We analyze the e ects of varying country size by having a small country trading with a large one. Finally, we experiment with di erent elasticity of substitution between traded goods. In all cases, our conclusions in terms of lack of volatility for consumption are not a ected. Our discussion leads us to introduce a class of preferences commonly used by the small open economy literature (GHH preferences) in the BKK set up. The main characteristic of these preferences is the absence of income e ect for labor supply. As a consequence, GHH preferences have the potential for generating su cient volatility in consumption to induce countercyclical real net exports. Our ndings con rm this intuition. We show that, under GHH preferences, the BKK model does not need to rely on counterfactual terms of trade e ects to generate negative correlation between real trade balance and output. Domestic absorption, in other words, becomes more volatile than output. Sensitivity analysis con rms the robustness of our ndings, with particular regards to the elasticity of substitution between intermediate goods, which is considered a critical parameter for this class of models. 20

22 5 Appendix A. Data For all countries, data are from OECD Quarterly National Accounts at current and constant prices and cover the sample 1980:1-2004:2. Consumption is the sum of both private nal consumption and government expenditures. Terms of trade are constructed as the ratio of import price index (import at current prices over import at constant prices) and export price index (export at current price over export at constant prices). Employment is the series Civilian Employment from OECD-Main Economic Indicators. Whenever a signi cant seasonal component was found, we deasesonalize the series using Census X-12 routine. To compute all statistics, we take log and then apply HP lter with smoothing parameter of 1600 except for Net Exports, for which we do not take log. The series for Rest of the World is an aggregate of EU-15, Japan and U.S. The OECD computes series for EU-15 in $ using PPP-adjusted indices. For Japan, we rst transform all series into 2000 yen because the Japanese base year is 1995 and then use 2000 PPP index to convert them into $. We nally use 2000 population as weight and construct aggregate series. We experiment using 2000 PPP- adjusted GDP per capita as weights, but the results are not a ected. 6 Appendix B. Linearization We compute the solution of the model by calculating the non-stochastic steady state and linearizing around this point. In solving for the linearized equations, we make large use of the properties of constant returns to scale functions. In particular, given the function G(a; b) homogenous of degree one, it can easily be shown that the following properties are satis ed: [1] G(:) = G a a + G b b [2] 0 = G aa a + G ab b [3] = GaG b G ab, where is the elasticity of substitution between a and b. G 21

23 Given that the Armington aggregator is homogenous of degree one, it immediate to calculate its log-linearize version as 21 dg(:) = G a a G ^a + G b b G ^b = (1 im 1 ) ^a 1 + im 1 ^b1 (B.1) where im is the import share. This expression shows that $ is calibrated by computing import shares from the data. The trade balance over GDP is de ned in equation (15) and has the following linear representation i cnx = im 1 h^a 2 ^b1 ^p (B.2) Notice that changes in net exports are determined by changes in quantities (exports and imports) and prices (terms of trade). We isolate the rst component by de ning the variable NXQTY as the di erence in export minus import evaluated at steady state prices, which has an empirical counterpart in the same variables measured in constant dollars. Hence the variable NXQTY, de ned in equation (16)has the following linear approximation \nxqty = im 1 h ^a 2 ^b1 i (B.3) Market clearing condition for good A, equation (10) yields ^y 1 = (1 im 1 )^a 1 + im 1^a 2 (B.4) It is immediate to show that expression (B.3) can be obtained by combining expression (B.1) and (B.4), that is \nxqty = ^y 1 ^G1 = im 1 h ^a 2 ^b2 i (B.5) Finally, we derive expression (26) for the terms of trade. The de nition of the terms of trade is 21 In what follows we denote with an hat percentage deviations from steady state and with a bar steady state values. We present the equation only for country 1, but analogous expressions apply to country 2. 22

24 whose linear approximation is bp = 1 P = G b G a h^a 1 ^b1 i (B.6) (B.7) Combining (B.7), (B.5), (B.4) and its analogous for country 2 we obtain ^p = [ nxqty + (y 1 y 2 )] (B.8) where = 1 2(1 im 1 ) and = 1 2im 1 im 1 : 23

25 References [1] Aguiar, M. and G. Gopinath, [2004], "Emerging Market Business Cycles: The Cycle is the Trend", working paper. [2] Backus, D., P. Kehoe and F. E. Kydland [1994], "Dynamics of the Trade Balance and the Terms of Trade: The J-Curve?", American Economic Review, March, 84, [3] Backus, D., P. Kehoe and F. E. Kydland [1995], "International Business Cycles: Theory and Evidence", in Frontiers of Business Cycle Research, ed. T. F. Cooley. Princeton University Press. Princeton, pp [4] Baxter, M. [1995]. "International Trade and Business Cycles", NBER working paper No [5] Baxter, M. and M. Crucini [1995], "Business Cycles and the Asset Structure of Foreign Trade", International Economic Review, 36, [6] Baxter, M. and U. Jermann [1999], "Household Production and The Excess Sensitivity of Consumption to Current Income", American Economic Review, September, 89, [7] Benhabib, J., R., Rogerson and R. Wright, [1999], "Homework in Macroeconomics: Household Production and Aggregate Fluctuations, Journal of Political Economic, December, 1991, 99(6), pp [8] Cole, H. and M. Obstfeld [1991], "Commodity Trade and International Risk Sharing: How Much DO Financial Markets Matter?", Journal of Monetary Economics, 28, [9] Correia, I., J. C. Neves and S. Rebelo [1995], " Business Cycles in Small Open Economies", European Economic Review 39,

26 [10] Cooley, T. and E. Prescott [1995], "Economic Growth and Business Cycles", in Frontiers of Business Cycle Research, ed. T. F. Cooley. Princeton University Press. Princeton, New Jersey. [11] Devereux, M., A. Gregory and G. Smith [1992], "Realistic cross-country consumption correlations in a two-country, equilibrium, business cycle model", Journal of International Money and Finance. [12] Greenwood, J., Z. Hercowitz and G. W. Hu man [1988], "Investment, Capacity Utilization and Real Business Cycle", American Economic Review, June 1988, 78, [13] Heathcote, J. and F. Perri [2002], "Financial Autarky and International Business Cycles", Journal of Monetary Economics, 49, [14] Kehoe, P. and F. Perri [2002], "International Business Cycles with Endogenous Incomplete Markets", Econometrica, 70/3, [15] Mendoza, E., [1991], "Real Business Cycle in a Small Open Economy", American Economic Review, September, 81, [16] McGrattan, E., R., Rogerson and R. Wright, [1997], "An Equilibrium Model of the Business Cycle with Household Production and Fiscal Policy", International Economic Review, September, May 1997, 38(2), pp [17] Neumeyer, P. A. and F. Perri [2002], "Real Business Cycles in Emerging Markets: The Role of Interest Rates", forthcoming Journal of Monetary Economics. [18] Pakko, M. R. [2003], "Substitution Elasticities and Investment Dynamics in Two- Country Business Cycle Models", Topics in Macroeconomics. [19] F. Perri [2003], "Comment to: Current Account in the Long and Short Run" by Kray A. and J. Ventura, NBER Macro Annual, MIT Press, Cambridge. 25

27 [20] Sachs, J.D. [1981], "The Current Account and Macroeconomic Adjustment in the 1970s", Brooking Papers on Economic Activity, [21] Schmitt-Grohé, S. and M. Uribe [2003], "Closing Small Open Economy Models", Journal of International Economics, 61, [22] Stockman, A. C. and L. Tesar [1995], "Tastes and Technology in a Two-Country Model of Business Cycle: Explaining International Comovements", American Economic Review, March 1995, 85,

28 Table 1. Correlation Between Net Exports and Output Developed Economies Emerging Economies Australia 0:36 Argentina 0:70 Belgium 0:18 Brazil 0:01 Canada 0:17 Ecuador 0:79 Finland 0:27 Israel 0:12 France 0:41 Korea 0:61 Germany 0:07 Malaysia 0:74 Greece 0:39 Mexico 0:74 Italy 0:37 Peru 0:24 Japan 0:40 Philippines 0:41 Netherlands 0:15 Slovak Republic 0:44 Norway 0:01 Thailand 0:83 Spain 0:38 Turkey 0:69 Sweden 0:04 Switzerland 0:57 UK 0:52 US 0:49 Eu-15 0:54 Average 0:25 0:51 Median 0:36 0:61 N ote. Developed Economies: data from OECD-MEI (1980:1-2004:2). Series were ltered using HP lter with smoothing parameter of Emerging Economies: data are from Aguiar and Gopinath (2004). 27

29 Table 2A. Domestic Absorption and Net Exports Std(DA)/Std(Y) Corr(NX,Y) Australia 1:35 0:36 Belgium 1:16 0:18 Canada 1:12 0:17 Finland 1:48 0:27 France 1:07 0:41 Germany 1:05 0:07 Greece 0:39 Italy 1:45 0:37 Japan 1:05 0:40 Netherlands 1:11 0:15 Norway 1:74 0:01 Spain 1:69 0:38 Sweden 1:03 0:04 Switzerland 1:12 0:57 UK 1:22 0:52 US 1:05 0:49 EU-15 1:19 0:54 Average 1:24 0:25 N ote. Domestic absorption (DA) is the sum of real consumption and investment. NX is net exports. Y is output. All series were logged (except NX) and HP- ltered using smoothing parameter of

30 Table 2B. Net Exports and Terms of Trade Correlation with Output NX TOT NXQTY Australia 0:36 0:18 0:40 Belgium 0:18 0:18 0:05 Canada 0:17 0:22 0:19 Finland 0:27 0:28 0:46 France 0:41 0:30 0:18 Germany 0:07 0:41 0:23 Greece 0:39 0:21 0:23 Italy 0:37 0:16 0:19 Japan 0:40 0:43 0:14 Netherlands 0:15 0:11 0:14 Norway 0:01 0:04 0:08 Spain 0:38 0:06 0:59 Sweden 0:04 0:28 0:26 Switzerland 0:57 0:23 0:16 UK 0:52 0:35 0:32 US 0:49 0:08 0:44 EU-15 0:54 0:16 0:38 Average 0:25 0:07 0:21 Note. Terms of trade (TOT) are calculated as ratios of import prices over export prices. NXQTY is the di erence between real export and real import over gdp. All series were logged (except NX) and HP- ltered using smoothing parameter of

31 Table 3. Benchmark Parameters Preferences = 0:99 = 0:34 = 2 Technology = 0:36 = 0:025 = 1:5 BKK Small Country Trade shares im 1 = 0:15 im 1 = 0:32 im 2 = 0:15 im 2 = 0:001 Productivity Transition Matrix 0:906 0:088 0:088 0:906 0:959 0: :998 Std Dev innovations 1 = 0: = 0: = 0: = 0:0499 Corr innovations 1;2 = 0:258 1;2 = 0:1288 Population N 1 N 2 = 1 N 1 N 2 = 0:04 30