Estimating the Trade Elasticity over Time

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Estimating the Trade Elasticity over Time

One sentence summary: Based on a panel structural VAR approach that can distinguish between trade elasticity measures over time, short-run trade elasticity estimates (after one quarter) are about 1, medium-run trade elasticity estimates (after one year) are about 5, and long-run trade elasticity estimates (after five years) are about 7.

The corresponding paper by Hakan Yilmazkuday has been accepted for publication at Economics Letters.

The working paper version is available here.

 
Abstract

Using quarterly data on the U.S. imports from its major trading partners and the corresponding trade costs, this paper estimates the trade elasticity by using a panel structural vector autoregressive model that can distinguish between short-run versus long-run elasticity measures in a continuous way and is robust to any endogeneity problem. The estimated trade elasticity measures are highly consistent with studies in alternative literatures, suggesting a short-run value of about 1 (after one quarter), a medium-run value of about 5 (after one year), and a long-run value of about 7 (after five years).

Non-technical Summary

The main topic of investigation in international trade is the reaction of trade to changes in trade costs and thus the trade elasticity. This elasticity not only measures the effects of a trade policy change (e.g., a change in duties/tariffs) on trade but also connects the changes in home expenditure share of a country to its welfare gains from trade. Accordingly, estimating the trade elasticity is essential for a trade policy evaluation regarding the changes in trade and welfare.

Several studies in the literature have estimated the trade elasticity using the implications of static or dynamic trade models. The general agreement is the trade elasticity is lower in the short run and higher in the long run, both in calibrations and in estimations. Connected to several alternative frictions introduced by the literature, this observation has also been shown to explain several puzzles in international economics such as the international elasticity puzzle, the trade-comovement puzzle, or the missing globalization puzzle. Since trade elasticity estimates highly depend on the interaction between the variables governing dynamic patters of trade (i.e., general-equilibrium effects), it is implied that distinguishing between short-run and long-run trade elasticity measures is essential and several variables governing dynamic patters of trade are endogenously determined over time. Therefore, the causality between trade and its determinants should be taken into account in a dynamic framework in the estimation of the trade elasticity.

This paper achieves such an estimation (of the trade elasticity) by using a panel structural vector autoregression (VAR) approach that takes into account the causality and thus any potential endogeneity concerns in a dynamic framework. Theoretically, the bilateral-trade variables in the estimation are selected to be consistent with the implications of a large class of general equilibrium trade models, including quarterly data on the U.S. imports from its major trading partners, the corresponding import prices (measured at the port of the trading partner), the corresponding trade costs (including both duties/tariffs and transportation/shipment costs), and the U.S. real GDP (or the U.S. industrial production as an alternative). Empirically, the estimation of the trade elasticity is achieved by using its textbook definition, which corresponds to the total percentage changes in trade divided by the total percentage changes in trade costs. In the panel structural VAR framework, this definition corresponds to dividing the cumulative impulse response of trade to the cumulative impulse response of trade costs, both following a trade-cost shock. Since the cumulative impulse response can be estimated for any period after the shock, a continuous estimate of the trade elasticity can be achieved over time, which is a key innovation in this paper with respect to the existing literature.

The continuous estimate of the trade elasticity is connected to the existing literature by considering its value after alternative number of quarters. In particular, consistent with international finance studies that consider quarterly data in their empirical analyses, short-run trade elasticity is measured one quarter after the trade-cost shock; the estimated short-run trade elasticity is about one, on average across alternative model specifications and data used, which is highly consistent with international finance studies. Similarly, consistent with international trade studies that consider annual data in their empirical analyses, medium-run trade elasticity is measured one year after the trade-cost shock; the estimated medium-run trade elasticity is about five, on average across alternative model specifications and data used, highly consistent with international trade studies. Finally, as in economic growth studies that consider five-year intervals in their empirical analyses, long-run trade elasticity is measured five years after the trade-cost shock; the estimated long-run trade elasticity is about seven, on average across alternative model specifications and data used, highly consistent with studies that have estimated the trade elasticity over time by using implications of general-equilibrium models.

 

The corresponding paper by Hakan Yilmazkuday has been accepted for publication at Economics Letters.

The working paper version is available here.

Accounting for Trade Deficits

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Accounting for Trade Deficits

One sentence summary: Total trade deficit of a country can be decomposed into changes due to its effective terms of trade, its relative trade costs, and its macroeconomic developments with respect to its export partners.

 

The corresponding paper by Hakan Yilmazkuday has been accepted for publication at Journal of International Money and Finance.

 

The working paper version is available here.

 
Abstract

This paper proposes a decomposition for the total trade deficit of a country by using implications of a dynamic trade model. It is shown that the total trade deficit of a country can be decomposed into changes due to its effective terms of trade, its relative trade costs, and its macroeconomic developments with respect to its export partners. The implications for bilateral trade are estimated using both imports and exports data for 188 countries, and the decomposition of total trade deficit is achieved for each country. Empirical results show evidence for heterogeneity across countries regarding the decomposition of trade deficits, suggesting alternative policy tools to rebalance trade at the country level. A cross-country investigation further suggests that relative trade costs have contributed the most to the heterogeneity of trade imbalances.

Non-technical Summary

Trade deficits (defined as the difference between imports and exports) have been experienced by more than 70% of the countries around the globe between 1980-2015. Having a trade deficit is problematic, because it is simply financed by capital flows (from trade-surplus countries) of which sudden stop can be destabilizing not only at the country level but also globally; on the other hand, having a trade surplus is also problematic, because trade-surplus countries may become targets for protectionist measures by trading partners. Accordingly, having a balanced trade (or at least not having an excessive deficit/surplus) is desirable for any open economy, which requires the knowledge of the sources of trade deficit.

This paper investigates the sources of trade deficit by using an international trade approach. In particular, based on the implications of a dynamic trade model that incorporates implicitly additively separable nonhomothetic constant elasticity of substitution (CES) preferences, the trade deficit of any country is decomposed into the effects due to changes in effective terms of trade, relative trade costs, and relative macroeconomic developments. This is achieved in two steps. First, by using the implications of the dynamic trade model, bilateral imports and bilateral exports of 188 countries are estimated. As is standard in the international trade literature, these estimations result in fitted values representing bilateral trade costs, source-time fixed effects and destination-time fixed effects for both bilateral imports and bilateral exports in logs. Second, since the sum of logs is not equal to the log of sums due to Jensen's inequality (i.e., one cannot take the sum of log bilateral trade deficits to obtain log total trade deficit), the fitted values obtained from these estimations are connected to the changes in total trade deficit of each country over time by using the Taylor series of bilateral trade expressions. 

This innovation results in a decomposition of the level changes in total trade deficit of a country based on changes in its effective terms of trade (representing the difference between the weighted average of import prices and the weighted average of export prices), changes in relative trade costs of the country (representing the changes in the weighted average of import trade costs and the weighted average of export trade costs), and relative macroeconomic developments of the country (representing  changes in both relative economic activity and relative saving decisions with respect to its export partners). Since the sum of changes over time in the level of total trade deficit of any country is equal to its level of total trade deficit for any given period, a final decomposition can be achieved for the level of trade deficit for any country.

The empirical results suggest that each country has different patterns over time regarding the contribution of each gravity-based component in the decomposition of trade deficits, although relative trade costs followed by relative macroeconomic developments have contributed the most to the magnitude (of the trade deficit) during the sample period, on average across countries. The average OECD country has experienced a trade surplus that is mostly explained by effective terms of trade followed by relative macroeconomic developments, whereas the average non-OECD country has experienced a trade deficit that is mostly explained by relative trade costs followed by relative macroeconomic developments.

Regarding country-specific results, for example, the U.S. trade deficit is mostly explained by the positive contributions of relative trade costs followed by those of effective terms of trade. In contrast, the negative Chinese trade deficit (i.e., its trade surplus) is mostly explained by its negative effective terms of trade, despite high and positive contributions of its relative macroeconomic developments. Another interesting country is Japan of which negative trade deficit (i.e., its trade surplus) is mostly explained by its relatively negative macroeconomic developments, followed by its negative relative trade costs. 

 

The corresponding paper by Hakan Yilmazkuday has been accepted for publication at Journal of International Money and Finance.

 

The working paper version is available here.