Here we present some descriptive statistics on trade flows that help to motivate our model of trade in durables. We use our 25 OECD country data from NBER-UN World Trade Data and use the latest available data (year 2000) to calculate the share of durable goods in international trade. The original data are at 4-digit SITC levels. We aggregate them into 1- and 2-digit levels for each country. Then we use the information of the SITC classifications to classify imports and exports into durable and nondurable goods. At the 1-digit SITC level, there are 10 categories (0-9). Categories 0 (FOOD AND LIVE ANIMALS), 1 (BEVERAGES AND TOBACCO), and 4 (ANIMAL AND VEGETABLE OILS, FATS AND WAXES) are obviously nondurable goods. It is also straightforward that category 7 (MACHINERY AND TRANSPORT EQUIPMENT) belongs to durable goods. Category 2 is raw materials that exclude fuels such as petroleum. Category 3 contains energy products such as coal, petroleum, gas, etc. The remaining categories however are difficult to classify. This is particularly true for category 5 (CHEMICALS AND RELATED PRODUCTS, N.E.S.). Even if we go down to the 3-digit level, it is still unclear which categories belong to durable goods.
We find that this category includes many nondurable goods, such as fertilizers, medicines, cleaning products, etc. To avoid exaggerating the share of durable goods, we put the whole category 5 into nondurable goods. But we note that this category does include some durable goods, such as plastic tubes, pipes, etc.
For categories 6, 8 and 9, we go down to the SITC 2-digit levels for more information about the durability of goods. Category 6 (MANUFACTURED GOODS CLASSIFIED CHIEFLY BY MATERIALS) classifies goods according to their materials. We assume that goods produced from leather, rubber, or metals are durables (61-62 and 66-69). Goods produced from wood (other than furniture), paper, or textile (63-65) are nondurables. Category 8 includes other manufactured products that are not listed in categories 6 and 7. We assume that construction goods (81), furniture (82), professional instruments (87), photographic equipments
(88) are durable goods. Travel goods (83), clothing (84), footwear (85) and remaining goods (89) are classified as nondurables. Category 9 includes products that are not classified elsewhere. In this category, we assume that coins and gold (95-97) are durables. All remaining products are classified as nondurables.
It reports the share of durable goods in imports and exports in our 25 OECD country dataset.An average durable goods account for about 60% of total imports and exports in these countries. If we exclude raw materials (SITC 2) and energy products (SITC 3), the share increases to 70% . We find that about three quarters of trade is in durable goods in the US if we exclude energy products, which is in line with the finding of Erceg, Guerrieri, and Gust (2006). We note some outliers for exports. More than 50% of exports in Australia and New Zealand are in categories zero (FOOD AND LIVE ANIMALS) and two (CRUDE MATERIALS, INEDIBLE, EXCEPT FUELS). 65% of exports in Iceland are FOOD AND LIVE ANIMALS. Norway exports a significant amount of energy products. After we exclude
raw materials and energy products, Australia and Norway become close to our sample mean. Iceland and New Zealand still export a much lower share of durable goods than other OECD countries. But our overall results confirm that durable goods account for a large portion of international trade for OECD countries. In particular, category 7 (MACHINERY AND TRANSPORT EQUIPMENT) on average accounts for more than 40% of trade for OECD countries.
A Two-country Benchmark Model
There are two symmetric countries in our model, Home and Foreign. We depart from the standard models that were once used in performing these calculations, by having two production sectors in each country: the nondurable good and durable good sectors. All firms are perfectly competitive with flexible prices. Nondurable goods can only be used for domestic consumption. Durable goods are traded across countries and used for durable consumption and capital accumulation. Because of the symmetry between these two countries, we describe our model focusing on the Home country.
Our modeling strategy is motivated by the empirical regularities discussed below. As we have noted, in order to explain the high volatility of imports and exports, it is not promising to rely on the response of these variables to price changes. That would tend to make imports and exports negatively correlated, but in fact they are positively correlated. Instead, we note that changes in capital stocks can be very volatile in response to persistent changes in productivity. It is well known that investment is very volatile and pro-cyclical. However, it would be unrealistic to attribute all of the movements in imports and exports to trade in capital goods. In order to match the movements in trade volumes, we would need to ascribe an unrealistically high share of trade to trade in capital goods. Instead, we add trade in durable consumption goods to the model. This is a plausible avenue to explore, because Baxter (1995) has shown that about two-thirds of trade is in either capital goods or durable consumption goods. We suspect that in fact this is an underestimate of the share of durables, since many goods that have characteristics of durables - such as clothing - are classified as nondurables. It is intuitive.We list all equilibrium conditions for both countries in developed as well as underdeveloped categories and that a large fraction of trade is in durables. Nondurable goods are typically more perishable, and thus more expensive to ship than durables.The standard RBC models are able to capture the pro-cyclicality of imports and exports, and the countercyclicality of the trade balance by introducing capital goods. But they are unable to match the volatility because most trade is in consumption goods, so the fraction of trade accounted for by investment goods is too small to account for the overall volatility of trade volumes. However, recognizing that much of trade in consumption goods is trade in consumer durables, we are able to simultaneously reconcile the volatility and cyclical behavior of imports and exports. We are able to match the business cycle facts on trade without giving up realism in other dimensions, particularly in the characteristics of consumption behavior over the business cycle. That is because we recognize that a large fraction of consumption is in services, which we model as a nondurable nontraded good.
Trade in capital goods and consumer durables would introduce too much volatility in trade if we did not allow for some sort of installation cost. This is a well-known feature of international RBC models. But this also allows us to build a model consistent with another widely-recognized fact: that trade elasticities
are higher in the long run in response to persistent shocks than they are in the short run. In our model, home and foreign durable consumption and capital goods are close substitutes, but the sensitivity over the business cycle to relative price changes is low because of these costs of adjustment. In addition, we introduce an iceberg cost of trade. Here, we want to capture the idea that there is “home bias” in consumption of durables, as well as in the use of capital goods in production. Especially for large economic areas such as the US or the European Union, imports are a relatively small component of the overall consumption basket, or mix of inputs used in production. Because we model traded goods as being highly substitutable in the long run, it does not seem natural to simultaneously introduce home bias directly into the utility function or production function. Instead, and consistent with much of the recent literature in trade, we posit that there are costs to trade which lead to this home bias even in the long run.We note that there is a tension in modeling the behavior of trade volumes over the business cycle. Imports and exports are pro-cyclical and their standard deviation (in logs) is much larger than that of GDP.At the same time, they are apparently not very responsive in the short run to price changes. The model of consumer durables and investment goods captures these features for reasonable parameter values. We discuss the calibration in below, after the theoretical presentation of the model.
We calibrate our model such that in the steady state, the structure of the economy is the same as in below. Details about how to solve the steady state can be found below. In our benchmark economy,
nondurable goods account for 60% of total output and durable goods account for the remaining 40%. Among the durable goods, half of them are used for consumption (equivalent to 20% of total output) and the other
half are used for investment (equivalent to 20% of total output).17 Among durable consumption goods, 65% are used for domestic consumption (equivalent to 13% of total output) and 35% are used for exports (equivalent to 7% total output). Among durable investment goods, 70% are used for domestic investment
(equivalent to 14% of total output) and 30% are used for exports (equivalent to 6% of total output). In this economy, the investment accounts for 20% of total output and the consumption (durable plus nondurable) accounts for the remaining 80%. The trade share of output is 13%. Those features match the US data
closely. It shows parameter values that we use to match our benchmark model with the described economy structure. We set the shares of home goods in capital ( ) and durable consumption ( ) at 50%. That is, there is no home bias exogenously built in our economy structure. Instead, we generate the observed low
trade share from the iceberg trade cost . We will discuss this more later. As in Backus, Kehoe, and Kydland (1992), the capital share in production is set to 36%, and the subjective discount factor is set to 0.99, which gives a 4% annual real interest rate. The depreciation rate of durable consumption is set
to 0.05, which implies a 20% annual depreciation rate for consumption durables. A similar depreciation rate has been used in Bernanke (1985) and Baxter (1996).
Given those parameters, we choose other parameters to match the economy structure as discussed below. We first choose the preference parameter μ and the depreciation rate of capital jointly to match the relative size of durable and nondurable good sectors, and the size of investment in durable goods. μ is set to 0.23 and
is set to 0.013 such that 1. the durable good sector accounts for 40% of total output and, 2. the investment accounts for 50% of durable goods, or equivalently 20% of total output. Consumption durables account for the remaining 50% of durable goods, or equivalently 20% of total output. The trade cost ( ) and the elasticity of substitution between the home and foreign goods are calibrated to match two empirical findings:
1. The trade share of total output is about 13%;
2. The long-run elasticity of substitution between the home and foreign goods is high. In our calibration, the long-run elasticity of substitution between the home and foreign capital () is set to 9.1. The elasticity of substitution between the home and foreign durable consumption is set to 6.85. In the steady state, the trade in capital goods (durable consumption goods) accounts for 46% (54%) of total trade. The above calibration of and implies an overall elasticity of 7.9, which is the same as in Head and Reis (2001).18 The trade cost ( ) is calibrated to 0.1, that is, 90% of goods arrive in their destination countries in the international trade. For given and , this trade cost generates a trade share of 13%.We use different values for and to generate different home bias levels for capital and durable consumption.
Capital is more biased towards home goods than durable consumption (70% vs 65%). For given trade cost, the degree of home bias increases with the elasticity of substitution. So we assign a higher elasticity of substitution to capital goods. Alternatively, we can assume the same elasticity of substitution, but higher trade cost for capital goods. In either method, capital can have a higher level of home bias than durable consumption. We used the first method because it matches a pattern observed in the data. For given decrease in trade cost, the first method predicts that the share of investment goods in international
trade increases relative to the share of durable consumption. Intuitively, the investment goods are more substitutable across countries than durable consumption under this setup. So when the trade cost decreases, there is more substitution for investment goods than for durable consumption. As a result, the share of
investment goods in the trade increases. We then plot this prediction from the model. The same pattern is also found in the US data: from 1994 to 2006, the share of capital goods except automotive in total export
goods increased from 34.4% to 45.1%.19 The preference parameters and are set to their standard levels used in the GHH utility function. The parameter is chosen such that the labor supply is one third in the steady state. We assume that the elasticity of substitution between the durable and nondurable consumption is low. The adjustment cost parameters of durable consumption (1) is chosen to match the volatility of durable consumption, which is about three times as volatile as output in the data. The adjustment cost of capital stock (2) is calibrated to match the volatility of investment, which is about three times as volatile as output in the data.
We follow Erceg and Levin (2007) in calibrating the productivity shocks in the durable and nondurable goods sectors. However, there is no information about the cross-country spillovers of those shocks in their closed-economy model. Empirical findings usually suggest small cross-country spillovers. For instance,
Baxter and Crucini (1995) find no significant international transmission of shocks, except for possible transmission between US and Canada. In Kollman’s (2004) estimate between the US and three EU countries, the spillover is 0.03. In Corsetti, Dedola, and Leduc (forthcoming), the spillover is −0.06 for traded goods and 0.01 for nontraded goods. We will first set those spillovers at zero and then choose some values used in the literature to check whether our results are robust under different shock structures.
Performance of Benchmark Model
The model is solved and simulated using the first-order perturbation method. The model’s artificial time series are logged (except for net exports) and Hodrick-Prescott (H-P) filtered with a smoothing parameter of 1600. The reported statistics in this section are averages across 100 simulations. Our benchmark model
performs well in three broad categories. First, the model can match the observed IRBC statistics, including the “trade volatility” and “positive comovement” of imports and exports as documented in a suervey. Second, the model can replicate the elasticity puzzle in the trade literature. Finally, our model can replicate
the Backus-Smith puzzle and offers some new insights on this puzzle.
International RBC Statistics
It shows simulation results for four models. In the benchmark model, we assume that there is no spillover of productivity shocks across sectors and countries. But innovations in durable good sector are positively correlated across countries. In the model of High Correlation, the correlation of innovations is
set to a higher level as in Corsetti, Dedola, and Leduc (forthcoming). Models High Spillover and Medium Spillover allow spillover of productivity shocks across countries. In the model High Spillover, the spillover coefficients is set to 0.088, which has been used by BKK. In the literature, smaller values have also been
used. So in the model of Medium Spillover, we set this parameter to 0.044. All of these models can match data fairly well in the following respects:
1. The models can replicate the volatility (relative to that of GDP) of aggregate variables such as consumption, investment, durable consumption, and labor.
2. Real imports, exports and net exports are as volatile as in the data. That is, our model can successfully replicate the excessive volatility of imports and exports.
3. Both imports and exports are pro-cyclical and positively correlated with each other. Net exports are
counter-cyclical.
4. The CPI-based real exchange rate is about twice as volatile as GDP.
A noticeable difference between our benchmark model and the models with cross-country correlation of technology shocks is that the volatility of imports and exports decreases when we allow spillovers. This result is consistent with BKK’s finding that net exports become less volatile when cross-country spillovers
increase. But even when we set the spillover coefficient at 0.088, which is relatively large in the literature,imports and exports are still about two times as volatile as output. If we set the spillover coefficient to a moderate level of 0.044, the simulation results are very close to our benchmark results.In all of our calibrations, we note the following shortcomings: As in almost all RBC models, real exchange rate volatility is still lower than in the data. However, our model does quite well relative to the literature. The
standard deviation of the real exchange rate in our benchmark model is roughly 50% of the standard deviation in the data. Across all specifications, our model produces somewhat lower correlations of real imports with GDP than appear in the data. And, perhaps as a consequence, net exports are not as negatively correlated
with GDP as in the data. Cross-country output correlation is nearly zero in the standard IRBC models, though this correlation is usually large in the data.24 Our model provides little insight on this issue. We find that the cross-country correlation of output increases if we allow innovations to be correlated across countries. For instance, if we set cross-country correlation of innovations to 0.258 for both durable good and nondurable good sectors in the model of Medium Spillover, the cross-country output correlation increases from −0.01 to 0.1. However, it is still far less than it in the data. Kose and Yi (2003) find that their model can generate stronger cross-country correlations for pairs of countries that trade more. But the increased correlation still falls far short of the empirical findings.
When productivity shocks are persistent, it is well understood that investment will be volatile. Agents wish to change the capital stock quickly to take advantage of current and anticipated productivity shocks. This effect contributes to the high volatility our model produces for imports and exports, because capital
goods are traded. A positive productivity shock leads to a desire to increase Homes stock of domestically produced and foreign produced capital. This leads to the increase in demand for imports when there is a positive productivity shock. A positive productivity shock also increases the supply of Homes export good,
lowering its world price, and thus increasing exports. These effects are standard in RBC models, and explain why the models can generate procyclical imports and exports. However, if only investment goods are durable, and consumption goods are nondurable, the model does not produce sufficient volatility in imports and exports. For instance, if we change the depreciation rate of durable consumption ( D) to one and the adjustment cost to zero, the (relative) standard deviation of imports and exports decreases from 2.6 to 2.25 When we introduce a consumer durable sector, there is an additional source of volatility. Demand for consumer durables, like demand for investment goods, is forward looking. It is not expected productivity per second, but rather higher wealth from higher expected future income that leads to volatility in demand for durable consumer goods.
Consider the effect of a positive productivity shock in the production of durable goods. Because the shock is persistent, there is a significant wealth effect that pushes up demand for both home and foreign durable consumption goods. In addition, there is an increase in the relative price of nondurable goods, which leads to substitution from nondurables to durables. The price of home-produced durables relative to foreign-produced durables also increases, which leads to substitution toward home-produced durables. But overall, the wealth effect and the effect of the decline in the price of nondurables lead to an increase in import demand, despite the increase in the price of foreign durables relative to home durables. Indeed, total expenditure on imports increases more than the value of exports, leading to a decline in the trade balance.
However, part of that increase in import expenditure comes from the increased price of imports. But overall, the model still generates procyclical movements of import and export quantities. This shows the correlations between US GDP and real imports, exports and net exports at various leads and lags. As noted by Ghironi and Melitz (2007), the correlation between GDP and imports exhibits a tent-shaped pattern, while the correlations of exports and net exports with GDP are S-shaped.26 Our model captures these qualitative patterns well. Note in particular that the model captures the fact that, while current imports are positively correlated with GDP, imports are negatively correlated with lagged GDP at longer horizons. However, our model’s correlation of both imports and exports with lagged GDP declines quickly - too quickly - as the horizon increases. It appears especially that exports increase with a lagged response to a positive shock to GDP. It might be possible to capture this dynamic behavior by incorporating a lag between orders of durable goods and delivery.
Elasticity Puzzle
The elasticity of substitution between the home and foreign goods is defined as the percentage change of demand for imports relative to home goods, given a one percent change of the import price relative to the home-good price. Two methods have been used in the literature to estimate this elasticity. In the literature of
trade liberalization, studies investigate how much the demand for foreign goods increases after a permanent relative price change caused by tariff reduction. In the data, the trade share of output increases substantially over time after a small but permanent decrease in the tariff. This empirical finding suggests that the home
and foreign goods are highly substitutable. So the estimates from this strand of literature range from 6 to 15 with an average of 8. For instance, see Feenstra and Levinsohn (1995), Head and Ries (2001), Lai and Trefler (2002).
In another strand of literature, the same elasticity is estimated from transitory relative price changes at the business cycle frequency. We show with a simple example below that under a general setup used in the literature, those two methods are estimating the same parameter. However, estimates from business cycle frequency data are much smaller, in a range of 0.2 to 3.5. This result is robust for both disaggregate and aggregate data. For instance, see Reinert and Roland-Holst (1992), Blonigen and Wilson (1999), and Reinert and Shiells (1993) for studies on disaggregate data, and Heathcote and Perri (2002) and Bergin(2006) for estimates from aggregate data. These findings have been labeled as the “elasticity puzzle” in the trade literature.Several studies have offered explanations for this puzzle with a common feature that the long-run elasticity of substitution is high, but the short-run elasticity is low due to some market frictions.Our model is closely related. By the calibration of our model, the home and foreign goods are highly substitutable in the long run.
The short-run frictions in our model are adjustment costs of durable consumption and capital stocks. We calibrate those costs to match the volatility of investment and durable consumption. Under these conditions, we investigate whether adjustment costs can also deliver a reasonable short-run elasticity.
To calculate the short-run elasticity of substitution, we regress the (log) relative demand on the (log) relative price. We need the following variables in our regression: demand for foreign goods, domestic demand for home goods and the relative price. The demand for foreign goods is measured by real imports (RIMt).
The domestic demand for home goods is measured by domestic absorption (DAt), which is calculated by subtracting real imports from the sum of consumption and investment It is not surprising, of course, that we are able to generate an elasticity that is lower in the short run than in the long run by introducing costs of adjustment. Our point is simply that in a model in which trade is in durables, this is natural and accords with a long tradition in macroeconomics of modeling the gradual accumulation of capital. That is, the trade elasticity puzzle is easy to understand in a context in which trade is in durables which are accumulated slowly over time.Backus-Smith Puzzle Backus and Smith (1993) show in a model with nontraded goods that the real exchange rate should be perfectly correlated with cross-country relative consumption if households can trade a full set of contingent claims. This prediction is at odds with the data: the correlation of the real exchange rate and relative consumption among OECD countries is generally negative. Corsetti, Dedola, and Leduc (forthcoming) find the median of this correlation between the US and the remaining OECD countries is −0.42. These empirical findings are interpreted as lack of international risk sharing.31 However, Chari, Kehoe, and McGrattan (2002) show that incomplete financial markets are not sufficient: even a DSGE model with only bond markets implies a strong positive correlation. Some recent papers offer models to solve this puzzle. Corsetti, Dedola, and Leduc (forthcoming) find that if the elasticity of substitution between the home and foreign goods is small enough, the terms of trade improve, instead of deteriorate, in the face of a positive productivity shock it the home country. This could generate a negative correlation between the real exchange rate and relative consumption. Begnigo and Thoenissen (2007) show that even if the terms of trade deteriorate after a positive shock in the trade sector, the Balassa-Samuelson and wealth effects could be strong enough to generate a real appreciation in a model with nontraded goods. They argue that the price of nontraded goods increases after a positive shock in the tradable good sector, which calls for an appreciation of the real exchange rate.
This effect could dominate the deterioration of the terms of trade and induce a real appreciation. In this paper, we can also replicate the Backus-Smith empirical findings. The dynamics of consumption and the real exchange rate in response to a shock to productivity in the durable sector look very much like
those in Benigno and Thoenissen (2007). A positive shock lowers the price of the durable export, and because of home bias, that tends to work toward a real CPI depreciation. But that effect can be more than offset by the increase in the price of nondurable goods, which are not traded across countries. There are two forces working to push up the price of non-traded goods: First, there is the traditional Balassa-Samuelson effect. The increase in productivity pushes up the real wage, thus pushing up the relative price of non-tradables. In addition, overall consumption in the home country increases from a wealth effect, because higher productivity increases lifetime income for the home country. Even if there were no factors mobile between sectors, that would tend to push up the price of the nontradable goods, and help foster a real appreciation. We have that aggregate consumption is increasing, and under our calibrations, a real appreciation – these correspond to the data.However, our model also offers some new insight on this puzzle. The durable consumption measured in national accounts data is expenditures on new durable consumption goods. However, it is the service flow from the stock of durable consumption that enters the utility function. As emphasized by Obstfeld and Rogoff (2006), the consumer smooths the service flow from the stock of durable consumption, instead of the path of expenditures on durables.
Conclusion
The behavior of imports and exports is, of course, a key component of the linkages among economies. Our model confronts and, to a degree, successfully explains some strong empirical regularities. By modeling trade in durables, we can understand the high volatility of imports and exports relative to output. Trade in durables also offers a natural explanation for the trade elasticity puzzle – that the response of imports to changes in the terms of trade is low at business cycle frequencies, but is high when considering the long-run effect of permanent price changes. Our model performs well compared to other models, because it offers an
explanation that is also consistent with the observation that imports and exports are both procyclical, and positively correlated with each other, even when the terms of trade and real exchange rate are as volatile as
in the data. We believe the forward-looking nature of investment decisions and decisions to purchase consumer durables are a key feature of trade behavior. Our model noticeably fails to account for the high correlation of output across countries, which is a failure shared by essentially all rational expectations equilibrium models. However, we think that modeling trade as durables may still be a promising avenue for dealing with this puzzle as well, through channels that are not explored in this paper. One possibility is that while the common (across countries) component of productivity shocks may account for a small share of the variance of productivity, it may be that agents typically receive strong signals about the future common component. If news helps to drive business cycles (as in Beaudry and Portier, 2005), then perhaps news about the common component of productivity shocks helps contribute to the high correlation of business cyclesfailure shared by essentially all rational expectations equilibrium models. However, we think that modeling trade as durables may still be a promising avenue for dealing with this puzzle as well, through channels that are not explored in this paper. One possibility is that while the common (across countries) component of productivity shocks may account for a small share of the variance of productivity, it may be that agents typically receive strong signals about the future common component. If news helps to drive business cycles (as in Beaudry and Portier, 2005), then perhaps news about the common component of productivity shocks helps contribute to the high correlation of business cycles across countries. News about future productivity is especially important for durables, so the impact of news may be especially strong on the investment and consumer durables sectors. Another avenue that may deserve further exploration is a model with nominal price stickiness, as in DSGE models. Our model of durable trade creates large swings in demand for imports, which indeed is what allows it to account for trade volatility. But an increase in Home demand for Foreign output has only a small effect on Foreign’s output level. Instead, in our model, prices adjust so that more of Foreign’s output is channeled toward Home. In a model with sticky prices, changes in demand may lead to changes in aggregate output, and so create a channel for international spillovers. While these channels do exist in current DSGE models, they are not strong because the models do not account for large procyclical movements in imports and exports.It is an empirical fact that a large fraction of trade is in durables. Indeed, we view explaining this phenomenon - rather than assuming it, as we do in this study - to be another interesting topic for future research. What we have accomplished here is to demonstrate that trade in durables significantly alters the behavior of imports and exports in an RBC model in a way that can account for some striking empirical facts.
