One of the most established empirical regularities in international business cycle analysis is the countercyclical behavior of net exports. Backus, Kehoe and Kydland (1992, 1994) (BKK henceforth) explain thisempirical finding with the dynamics of capital formation: in the face of a positive productivity shock, the increase of investment exceeds the increase in saving.
1 In contrast, the behavior of imports and exports themselves has been largely neglected in the literature.
2 They are much more volatile than GDP and both are pro-cyclical, facts which are at odds with the predictions of standard models. Inspired by the evidence that a large fraction of international trade is in durable goods, we propose a two-country two-sector model, in which durable goods are traded across countries. Simulation results show that our model can match the trade sector data much better than the standard models. Our model also sheds light on two other puzzles in the literature: the elasticity puzzle and Backus-Smith puzzle.
We first document two robust empirical findings:
1. Real imports and exports are much more volatile than total output. Their standard deviations are on average about two to three times as large as GDP’s in our OECD-country dataset.
2. Real imports and exports are pro-cyclical and also positively correlated with each other. We label the first finding “trade volatility”, and the second one “positive comovement”.These findings are very robust across our 25-OECD-country data. We also confirm in our dataset the well-documented negative correlation between net exports and output.In a standard international real business cycle (IRBC) model with incomplete financial markets, we show that imports and exports are far less volatile than in the data. They are actually even less volatile than GDP.One can modify the standard IRBC model with monopolistic competition, sticky prices and monetary policy rules. This class of models is labeled as open-economy Dynamic Stochastic General Equilibrium (DSGE) models and has been used widely in open-economy policy analysis. These extensions do not help the model’s
performance in replicating the behavior of imports and exports. However, the IRBC and DSGE model also fail to replicate real exchange rate volatility. A natural question is whether a model with more variable exchange rates can replicate the “excessive volatility” in imports and exports. We follow recent DSGE
modeling, and add a shock to the interest-parity relationship in order to increase exchange-rate volatility.
We also try the “elasticity method” suggested by Chari, Kehoe and McGrattan (2002) to increase exchangerate volatility. Although a more volatile exchange rate helps to increase the volatility of imports and exports, it generates a negative correlation between imports and exports. This is at odds with the finding of “positive comovement”. Import and export volatility in those models is mainly driven by the effects of fluctuations in the terms of trade. When the terms of trade (relative price of imports and exports changes) change, the
imports and exports go to opposite directions. Therefore, these models generate a counterfactual strong negative correlation between the imports and exports.We propose a model in which countries trade durable goods only. This setup is inspired by the fact that a large portion of international trade is durable goods. Baxter (1995) shows that about two thirds of trade is in durable goods (including capital goods.) Erceg, Guerrieri, and Gust (2006) document a more recent (year 2004) breakdown of US imports and exports. They find that consumer non-durables account for only 28% of non-energy imports and 25% of non-energy exports. In contrast, consumer durables and capital goods account for 32% and 30% of non-energy imports. For non-energy exports, they account for respectively, 16% and 45%. Non-energy industrial supplies, which are used in producing durables, account for the remaining 10% of imports and 14% of exports. We find similar patterns in our OECD country dataset. Trade in durable goods on average accounts for more than 60% of imports and exports for OECD countries. The share increases to 70% after excluding raw materials and energy products in the trade. The importance of capital goods in international trade has also been documented by Eaton and Kortum (2001).
Boileau (1999) examines a model with trade in capital goods to explain the volatility of net exports and the terms of trade. Erceg, Guerrieri, and Guest (2006) also emphasize that trade in capital goods helps model
to replicate trade volatility. They argue that trade balance adjustment may be triggered by investment shocks from either home or foreign country and such adjustment may not cause substantial real exchange rate fluctuations. Warner (1994) finds that global investment demand has been an important determinant
of U.S. exports since 1967. However, we find that a model with trade in capital goods but not consumer durables is inadequate. In order to match the volatility of the trade data, a large share of traded goods must be durable. But if we take all of those traded goods to be capital, then the model would require, for example, that the U.S. obtains almost all capital goods from imports while simultaneously exporting large quantities of capital.
In our two-country two-sector model, nondurable goods are nontraded. Durable consumption flows require both home and foreign durable goods varieties and capital goods are aggregated from home and foreign varieties of capital. Simulation results show that the benchmark model can successfully replicate “trade
volatility” and “positive comovement”. In addition, net exports in our model are counter-cyclical and as volatile as in the data. So our model can match the trade sector data much better than the standard models.
This improvement is not at the cost of other desirable features of standard models. The aggregate variables such as output, consumption, investment and labor, can also match the data well. Our benchmark model can also replicate the behavior of short- and long-run elasticities documented in the trade literature. One strand of literature estimates the long-run elasticity of substitution between the home and foreign goods from permanent relative price changes, such as from tariff reductions. Those studies usually find a large elasticity of about 8 (for instance Feenstra and Levinsohn, 1995 and Head and Ries, 2001.)
But when the same elasticity is estimated from relative price fluctuations at the business cycle frequency, the estimate is much smaller - even less than one (for instance, Bergin, 2006, Heathcote and Perri, 2002.)Several studies have offered explanations for this puzzle, and ours is closely related. A common feature of the hypotheses is that the long-run elasticity of substitution is high, but the short-run elasticity is low due to some market frictions. Ruhl (2005) proposes a model in which firms have to pay a fixed cost to change their export status. Benefits from changing export status are not enough to recover the fixed cost under transitory shocks. So the elasticity of substitution between the home and foreign goods is low when shocks are transitory. However, in the face of persistent chocks, firms will pay the fixed cost and change their export status, which leads to a large increase of trade share even for a small, but permanent price change. Drozd and Nosal (2007) use the friction of international marketing to reduce the response of output to relative price changes. Ramanarayanan (2007) models this problem from the side of importers. In this model, importers use foreign goods as intermediate inputs in production. Home and foreign intermediate goods are perfectly
substitutable in the long run, but switching between them in the short run is very costly. We follow the same idea in our model, where we assume that the home and foreign goods are highly substitutable in the long run,but in the short run there is a quadratic cost for adjusting the durable consumption and capital stocks.
Unlike the above studies, we do not provide a micro-story for the market friction. Our contribution is quantitative.After calibrating the adjustment costs to match the volatility of durable consumption and investment, we investigate whether our model can also deliver a reasonable short-run elasticity of substitution.
When agents can trade a complete set of contingent claims, but face potentially different goods prices,in a variety of contexts models imply that relative cross-country consumption should be perfectly positively correlated with the real exchange rate. Backus and Smith (1993) demonstrate this result in a model with nontraded goods, while Chari, Kehoe, and McGrattan (2002) show that even a DSGE model with incomplete markets implies a strong but imperfect positive correlation. But, beginning with Backus and Smith, several studies find empirically that the correlation between relative consumption and the real exchange rate is
generally low, even negative in many countries. Some recent papers offer models to explain this correlation when capital markets are not perfect, and only bonds are traded.6 Our model shares some of the features of these models, but also offers some new insight. Consumption measured in national accounts data does
not capture the service flow from consumer durables. Our model does a good job of replicating the data for measured consumption, which includes purchases of new durable goods. Positive wealth shocks increase purchases of new consumer durables as well as nondurables, and drive up the relative price of nontraded
(nondurable) goods, as in Benigno and Thoenissen (2007). But the consumption flow from durable goods adjusts slowly to shocks, so the behavior of “true” consumption can be quite different than that of measured consumption.
Our model’s success in accounting for several aspects of international trade data suggests that it may be important to incorporate the trade in durable goods when constructing an open-economy model for policy analysis. There are several challenges remaining, however. A well-known departure of the IRBC model from
the data is that cross-country outputs have low correlation in those models, while this correlation is positive and relatively high in the data. Our model provides little insight on this issue. In this paper, we also take trade in durable goods as exogenously given. Future work might endogenize the durability of traded goods,
relating the types of goods traded to the cost of storage and time to ship.The remainder of the paper is organized as follows: Section 2 displays statistics on “trade volatility” and “positive comovement”. We show that the standard models and their simple extensions cannot simultaneously replicate those empirical findings. Section 3 describes our two-country two-sector benchmark model.Section 4 explains our calibration of the model. Section 5 shows simulation results of the benchmark model and Section 6 concludes.
Empirical Findings and Performance of Standard Models
In this section, we first show some facts about international real business cycles: 1. Real imports and exports are about two to three times as volatile as GDP.
2. Both real imports and exports are pro-cyclical and positively correlated with each other.
3. Real net exports are counter-cyclical. Then we investigate whether standard models in the literature can replicate those features. We also present evidence that trade in durable goods accounts for a large portion of imports and exports in OECD countries.
Empirical Findings
Our data-set includes quarterly real GDP, real imports, real exports, and real net exports of OECD 25 countries during the period between 1973Q1 and 2006Q3.7 The data are from OECD Economic Outlook database. All variables are logged except net exports8 and H-P filtered with a smoothing parameter of 1600.
It shows the volatility of those variables. The standard deviation of GDP on average, is 1.51%. Both real imports and exports are much more volatile than GDP. On average, the imports are 3.3 times,and exports are 2.7 times as volatile as GDP.9 This result is not driven by outliers. The sample median is very close to the sample mean. The volatilities of imports and exports in the US are close to the sample mean. However, the ratio of net exports to GDP in the US is less volatile than it is in any other countries. This reports comovement of real imports and real exports with GDP. Two things stand out. First, both imports and exports are pro-cyclical. This result is very robust: the imports are positively correlated with GDP in all 25 countries. The average correlation is 0.63. The same is true for exports except in two countries: Denmark and Mexico. The average correlation between exports and GDP is 0.39. Second, imports and exports are positively correlated in all countries except Australia, Mexico, New Zealand and Spain. The average correlation between imports and exports is 0.38. We also confirm a well-documented finding in previous studies: net exports are counter-cyclical. This is true in all countries except Austria and Hungary.The average correlation between net exports and GDP is -0.24.
Performance of Standard Models
We investigate whether some standard models can replicate the facts presented below shows simulation results for these models. These simulations demonstrate that the standard models and their extensions cannot replicate trade volatility and positive comovement simultaneously. Since the model
setups are very standard in the literature.We consider two types of models: the IRBC model and the DSGE model. We use exactly the structure of the bond-economy model in Heathcote and Perri (2002) as our standard IRBC model. This model has the same structure as BKK’s model, but limits the financial market to a real-bond market only. Baxter and Crucini (1995) compare this incomplete financial market model with the model with perfect risk-sharing and find they behave very similarly if the productivity shock is not extremely persistent or the cross-country spillover of productivity shocks is high. This also reports results for the DSGE model. This is the extension of the IRBC model that assumes monopolistic competition, trade in nominal bonds, Calvo staggered price setting, and a monetary policy (Taylor) rule. Those models are often used in the studies of monetary policy in open economies.
GHH is the DSGE model with the preference function proposed by Greenwood, Hercowitz and Huffman (1988). We include this model to show that our benchmark model results are not driven by this choice of utility function. We also report the results for two more extensions of the DSGE model: the model with low intertemporal elasticity of substitution (Lo-elast) and one with an uncovered interest rate parity
shock (UIP). The standard international RBC model and DSGE models cannot replicate the volatility of the real exchange rate. We use those two methods to increase this volatility to see if it helps the model’s performance in matching the behavior of imports and exports. Here it reports the standard deviations of aggregate variables relative to that of GDP. In our standard IRBC model (HP), imports and exports are even less volatile than GDP. The same discrepancy has also been reported in Heathcote and Perri (2002).11 They find that the assumption of financial autarky can improve the volatility of imports and exports in a very limited way. The added features in DSGE model and GHH models cannot solve this problem. Imports and exports are still far less volatile than what they are in the data. However, the GHH utility function does make the volatility of net exports much closer to the data. This follows because imports and exports are more volatile (due to more variable consumption in the GHH model), and imports and exports are less correlated than what they are in the DSGE model. Panel B shows the correlations of real imports, real exports, and real net exports with GDP, as well as the correlation between real imports and exports. Imports and exports are measured by their steady state prices (constant price). The models of HP, DSGE and GHH match the data in that real imports and exports are pro-cyclical and positively correlated with each other. Net exports are counter-cyclical in these models. That is, the standard models can replicate the “positive comovement” feature, though they fail the “trade volatility”.12 Panel C reports the same statistics as Panel B, but imports, exports and net exports are measured in terms of final consumption goods, instead of constant prices. The results are similar to those in Panel B.Besides the volatility of imports and exports relative to GDP, another feature missing from the standard DSGE model is the high volatility of the real exchange rate. A natural question is whether we can increase the volatility of imports and exports in a model with more volatile real exchange rates. We follow Chari, Kehoe and McGrattan’s (2002) “elasticity method” to increase real exchange rate volatility by decreasing the value of the intertemporal elasticity of substitution 1/ . Some authors have also used an uncovered interest rate parity (UIP) shock to generate exchange rate variations in DSGE models.13 In our simulation results, we find that the volatilities of real imports, exports and the exchange rate all increase in those models. Under certain calibrations of the UIP shock, the model can also replicate the pro-cyclical movement of imports and exports, though the correlation between exports and output is nearly zero. However, there is a striking departure of these models from the data: real imports and exports are highly negatively correlated in those models.It shows the production structure in the standard models. Home and foreign intermediate goods are used to produce final goods. The final goods are used for consumption and investment. There are two factors affecting the volatility of imports:
1. The volatility of demand for final goods and,
2. The substitution between home and foreign goods. Under the standard calibration, the majority (about 75%) of final goods (and therefore imports) goes to consumption. Consumption is less volatile than GDP in the data. So if we want to match the volatility of consumption, demand for final goods will not be very volatile. Given the low volatility of demand for final goods, we can still have very volatile imports and exports if there is a lot of substitution between home and foreign goods. This is actually what the high elasticity and the UIP models do.Exchange rate movements induce fluctuations in the relative price of imports and exports. In return, the substitution between home and foreign goods increases the volatility of imports and exports. But when the
terms of trade changes, the imports and exports move in opposite directions. So this method produces a negative correlation between imports and exports, which is contradictory to the data. Baxter and Stockman (1989) find little evidence of systematic difference in the volatility of real imports and exports when countries
switch from fixed to flexible exchange rate regimes, though the real exchange rates became substantially more variable during this period. This finding also suggests that the high volatility of international trade flows is unlikely to come from the exchange rate fluctuations.
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