Thursday, December 22, 2016

Unifying Macro Elasticities in International Economics


Unifying Macro Elasticities in International Economics


One sentence summary: International elasticity puzzle is solved when expenditure shares are taken into account while calculating price elasticities of demand; moreover, international trade and finance literature imply the very same welfare gains from trade when international finance studies have unitary (Armington) elasticity of substitution between home and foreign products or unitary terms of trade.

The corresponding SSRN working paper by Hakan Yilmazkuday is available here.

The Dallas-Fed Globalization Institute working paper version is available here.
 

Abstract
International trade studies have higher macro (Armington) elasticity measures compared to international finance studies. This observation has evoked not only mixed policy implications regarding tariffs and exchange rates but also mixed welfare gains from trade. Regarding the policy implications, this so-called international elasticity puzzle is solved in this paper by distinguishing between elasticities of substitution and price elasticities of demand that are connected to each other through expenditure shares. It is shown theoretically and confirmed empirically 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 foreign countries. It is implied that one can always find an elasticity of substitution across foreign countries that would be consistent with different macro elasticities in the two literatures; therefore, the puzzle is something artificial due to the way that the foreign products are aggregated at destination countries. Regarding the welfare gains from trade, the two literatures are shown to have the very same implications when international finance studies have a unitary macro elasticity of substitution between home and foreign products or unitary terms of trade. As opposed to the existing literature that has offered many supply-side solutions to the puzzle, the results in this paper are independent of the supply side and thus are consistent with any production structure.


Non-technical Summary
International trade studies have higher macro (Armington) elasticity measures compared to international finance studies. Since price changes are converted into quantity changes and thus real effects through these elasticities, this observation has evoked mixed policy implications regarding tariffs and exchange rates in the two literatures (e.g., see Ruhl (2008)). Moreover, since welfare gains from trade are directly connected to these macro elasticity measures (as in Arkolakis, Costinot, and Rodríguez-Clare (2012)), this observation has also evoked mixed welfare gains between the two literatures. Due these mixed implications, this observation has been called the international elasticity puzzle.

In order to have a better idea about the magnitude of this puzzle, we would like to consider the elasticity measures used in the literature. Although elasticity measures differ across studies, international finance studies mostly follow Backus, Kehoe, and Kydland (1994) with a macro elasticity value of about 1.5, while international trade studies mostly follow Anderson and Van Wincoop (2004) or recently Simonovska and Waugh (2014a) and Simonovska and Waugh (2014b) with 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. Similarly, if we use the formula for the welfare gains from trade as introduced by Arkolakis, Costinot, and Rodríguez-Clare (2012), which is a function of home expenditure share and the macro elasticity, international finance studies imply welfare gains (in percentage terms) that are about eight times the international trade studies (for any given home expenditure share).

This paper unifies these macro elasticities that lead into mixed results in the two literatures. Since the upper-tier aggregation is achieved across source countries (including home country) in international trade studies, and it is achieved across home and foreign products in international finance studies, the two literatures are connected to each other by an additional tier of aggregation across different foreign countries in international finance. Although such an additional tier is missing in international finance studies, it is well understood to exist in the background.

Within this framework, we show that there is no connection between the macro elasticities of the two literatures when expenditure shares are negligible in the calculation of price elasticities. The tables turn when such expenditure shares are taken into account in this paper, which results in having price elasticities of demand connected to elasticities of substitution through such expenditure shares. We show that such a strategy helps us understand several differences across studies in the literature regarding the elasticity measures such as the differences due to simulating versus estimating, differences due to the level of disaggregation (e.g., having different digits of data), and differences between long-run and short-run elasticity measures. More importantly, such a strategy also allows us connect macro elasticities in the two literatures through the elasticity of substitution across different foreign countries in international finance that is newly introduced in this paper. In particular, when expenditure shares are considered, we show 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 foreign countries. It is implied that one can always find an elasticity of substitution across foreign countries that would be consistent with different macro elasticities in the two literatures; therefore, the puzzle is solved theoretically. Then, how can one make sense of the mixed policy implications and mixed welfare gains from trade implied by the two literatures? We focus on this question next.

From a researcher’s or a policy maker’s perspective, since policy implications for any individual good coming from an individual foreign country should not depend on how foreign goods are artificially aggregated at the destination country, we equalize the micro price elasticities of demand (depending on expenditure shares) between the two literatures to show theoretically and confirm empirically that the elasticity of substitution across different foreign countries plays an important role in the determination of the puzzle. Therefore, the policy implications at the individual foreign good level are automatically equalized, although the artificially created upper-level elasticities are allowed to change between the two literatures; this inductive approach is different from the deductive approach followed by the existing literature, where the upper-level variables (e.g., utility) are taken as given, while lower-level variables are allowed to change. Since policy implications are equalized between the two literatures for each and every foreign good, the international elasticity puzzle disappears at the disaggregated micro level. It is implied that the policy analysis should be first achieved at the disaggregated micro level and then aggregated up to obtain macro implications; such a strategy has also been used by Imbs and Mejean (2015) who have calibrated macro elasticities using a weighted average of sector elasticities.

After solving the puzzle due to its policy implications at the micro level, we continue with focusing on different implications by the two literatures regarding the welfare gains from trade at the macro level (which also correspond to the macro-level effects of a foreign shock in home country). Rather than using the simplified version of the formula given by Arkolakis, Costinot, and Rodríguez-Clare (2012), we consider the full definition of welfare gains (measured by the costs of autarky) in order to have a comparison between the two literatures by searching for aggregate price indices that would have to adjust to keep the consumer utility the same between the current openness to trade and a hypothetical autarky, for any given expenditure. We show that the two literatures have the very same welfare gains from trade when there is unitary macro elasticity of substitution between home and foreign products or when there is unitary terms of trade in international finance. Hence, there is no international elasticity puzzle from the perspective of welfare gains from trade as long as there is unitary macro elasticity or unitary terms of trade in international finance and as long as we do not make any simplifying assumptions regarding the implications of our models for welfare gains from trade; we should rather derive our model-specific formulas.

The theoretical framework in this paper is closest to the study by Feenstra, Luck, Obstfeld, and Russ (2014) who have three tiers of aggregation in their CES framework; the disaggregation is across goods in the upper-tier, across home and foreign products in the middle-tier, and across foreign sources in the lower tier. They call their middle-tier elasticity (across home and foreign products) as the "macro" elasticity, while they call their lower-tier elasticity (across foreign source countries) as the "micro" elasticity. They consider these "macro" and "micro" elasticities as the elasticities used in international finance and international trade studies, respectively, which they estimate at the good level and show that their "macro" elasticity is higher than their "micro" elasticity only for half of the goods investigated; hence, they have a good-level investigation while comparing their "macro" and "micro" elasticities. However, this aggregation strategy is not consistent with either international trade or international finance studies, where the former aggregates across source countries in the upper-tier (e.g., see Anderson and Van Wincoop (2003), Anderson and Van Wincoop (2004), Head and Ries (2001), Hummels (2001), or Yilmazkuday (2012), among many others), and the latter aggregates across home and foreign countries in the upper-tier (e.g., see Backus, Kehoe, and Kydland (1994), Blonigen and Wilson (1999), Corsetti, Dedola, and Leduc (2008), Enders, Müller, and Scholl (2011), or Heathcote and Perri (2002), among many others). Since the international elasticity puzzle is about the comparison of these upper-tier macro elasticities in the two literatures (rather than the middle-tier or the lower-tier), the aggregation strategy used by Feenstra, Luck, Obstfeld, and Russ (2014) is useless to address this puzzle. In contrast, our aggregation strategy successfully employs the upper-tier macro elasticities as they are exactly used in the two literatures.

It is important to emphasize that the results in this paper are independent of the supply side and thus are consistent with any production structure in the literature. In contrast, the existing literature has focused on many solutions to the puzzle based on the supply side. For example, Ruhl (2008) has proposed a solution based on firm-level entry costs and uncertainties on future productivities in a Melitz (2003) framework; Fitzgerald and Haller (2014) have both fixed and sunk costs of export participation, where participation in different export markets are considered as independent decisions after conditioning on a common marginal cost of production; Crucini and Davis (2016) consider the speed of adjustment of capital in the distribution sector; Ramanarayanan (2015) considers intermediate inputs in which heterogeneous producers face a plant-level irreversibility in the structure of inputs used in production; Arkolakis, Eaton, and Kortum (2012) consider the difference between the adjustments in extensive and intensive margins of trade in an Eaton and Kortum (2002) framework. Accordingly, it is implied by the demand-side investigation in this paper that we do not need such supply-side complications in order to understand the puzzling difference between macro elasticities of the two literatures. The puzzle is rather something artificial due to the way that the foreign products are aggregated at destination countries.

The corresponding working paper by Hakan Yilmazkuday is available here.


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