Saturday, December 8, 2018

Understanding the International Elasticity Puzzle


Understanding the International Elasticity Puzzle


One sentence summary: The macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the corresponding elasticity of substitution across products of foreign source countries.

The corresponding paper by HakanYilmazkuday has been published at Journal of Macroeconomics.

The working paper version is available here.

 
Abstract
International trade studies have higher macro elasticity measures compared to international finance studies, which has evoked mixed policy implications regarding the effects of a change in trade costs versus exchange rates on welfare measures. This so-called international elasticity puzzle is investigated in this paper by drawing attention to the alternative strategies that the two literatures use for the aggregation of foreign products in consumer utility functions. Using the implications of having a finite number of foreign countries in nested CES frameworks that are consistent with the two literatures, the discrepancy between the elasticity measures is explained by showing theoretically and confirming empirically that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the corresponding elasticity of substitution across products of foreign source countries.


Non-technical Summary
International trade studies have higher macro elasticity measures compared to international finance studies. Since price movements due to policy changes are converted into welfare adjustments through these elasticities, this observation evokes mixed policy implications regarding the effects of trade costs in international trade versus the effects of exchange rates in international finance. Due to these mixed implications on welfare, this observation is called the international elasticity puzzle.

In the literature, international finance studies mostly have a macro elasticity value of about 1.5, while international trade studies mostly have a macro elasticity value of about 5. It is implied that if we directly employ these numbers in a policy analysis, say, in order to investigate the effects of a foreign price change due to tariffs or exchange rates, international trade studies imply quantity changes that are at least three times the international finance studies.

This paper attempts to understand the international elasticity puzzle by drawing attention to the alternative strategies the two literatures have for the aggregation of foreign products in consumer utility functions. In particular, while the majority of international finance models include a unique foreign country (in their two-country frameworks) in order to have an understanding of the macroeconomic developments in the home country, the majority of international trade models include multiple foreign countries in order to investigate the bilateral trade patterns of the home country. Since having alternative numbers of foreign countries is reflected as alternative macro elasticity measures between the two literatures in a nested constant elasticity of substitution (CES) framework, as shown in this paper, the international elasticity puzzle can be understood by paying attention to the alternative ways that foreign products are aggregated in the two literatures.

Regarding the details, when a finite number of goods and foreign countries is considered in nested CES frameworks that are consistent with both literatures, this paper finds alternative expressions for the price elasticity of demand as a function of the macro elasticity measures in the two literatures. In order to investigate the conditions under which the two literatures have the very same policy implications (e.g., regarding changes in trade costs versus exchange rates), this paper equalizes the price elasticity measures between the two literatures. This strategy results in an expression that connects the alternative macro elasticity measures in the two literatures, where good-level details are cancelled out during the equalization of the price elasticity measures. In particular, it is theoretically shown that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of different foreign source countries, where the weight is shown to depend on the number of foreign countries and home expenditure shares. Therefore, the alternative strategies in the two literatures for the aggregation of foreign products are reflected as alternative macro elasticity measures between the two literatures.



The implications of equalizing the price elasticity of demand measures between the two literatures are also tested empirically. Since this investigation requires data on both domestic and foreign trade, it cannot be achieved by using any international trade data set, where domestic trade data are not recorded. As an alternative, this paper uses the available trade data within the U.S. by considering interstate trade as foreign trade and intrastate trade as domestic trade. The results based on the estimation of macro elasticity measures in both literatures confirm the theoretical solution provided in this paper that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of different foreign sources. Therefore, the discrepancy between the macro elasticity measures in the two literatures can in fact be understood by paying attention to the alternative ways that foreign products are aggregated in the two literatures.


The corresponding paper by HakanYilmazkuday is available at Journal of Macroeconomics.


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