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).
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.
The working paper version is available here.