Understanding Interstate Trade Patterns

One sentence summary: Interstate elasticity measures that are essential for any policy analysis within the U.S. are identified by combining state-level trade and production data.

Non-technical Summary

The elasticity of substitution and the elasticity of distance are two key parameters used by policy makers to derive quantitative results in international or intranational trade, because the effects of a policy change are evaluated by converting policy changes into price effects through these parameters. Therefore, there is no question that the measurement of these parameters is of fundamental importance in economic modeling where they connect quantities to prices. In empirical trade studies, especially the famous and successful gravity models, usual subproducts of an empirical analysis are some measures of these elasticities; however, in a typical gravity model estimation, one cannot identify the elasticity of substitution (across goods and/or varieties) and the elasticity of distance at the same time. This paper proposes a new approach by considering markups in the production side to estimate the elasticity of substitution across goods, the elasticities of substitution across varieties of each good, and the good-specific elasticities of distance, all identified in the empirical analysis.

A monopolistic-competition model consisting of a finite number of regions and a finite number of goods is employed in a constant elasticity of substitution (CES) framework. Each region consumes all varieties of each good, while it produces only one variety of each good. On the consumer side, as is standard in a CES framework, bilateral trade of a variety of a good across any two regions depends on the relative price of the variety and total demand of the good in the destination (importer) region. Similarly, total imports of a good in a region depends on the relative price of the good and total demand of all goods in the region. On the production side, having market power in the production of a variety of each good results in positive markups in each region. In equilibrium, markups at the good level are connected to the elasticities of substitution across varieties of each good.

We show that the simple CES framework is sufficient to estimate/calculate all structural parameters in the model when trade, distance, and markup measures are known. The estimated parameters correspond to:

• the elasticity of substitution across varieties of each good;?
• the elasticity of substitution across goods;?
• the good-specific elasticities of distance, which govern good-specific trade costs;?
• the heterogeneity of individual tastes, measuring geographic barriers and the so-called home-bias.

The key innovation is to bring in additional data for markups at the good level and use them to aid in identification of all types of elasticities mentioned above. The chain of logic is as follows:

1. Elasticities of substitution across varieties of each good are estimated by markup data.?
2. Elasticities of distance at the good level are identified through combining markups and bilateral trade estimates.?
3. In each region, source prices of each variety (of each good) are calculated using markup data and source fixed effects obtained by the bilateral trade estimation.?
4. For each destination, composite price indices and total imports are calculated at the good level.?
5. The elasticity of substitution across goods is estimated using the calculated composite price indices and total imports.

The empirical results show that

• the elasticity of substitution across varieties is about 3.01 on average across goods
• the elasticity of distance is about 0.45 on average across goods
• the elasticity of substitution across goods is about 1.09

Compared to the existing literature, the elasticity of substitution estimates are lower, and the elasticity of distance measures (thus, trade costs) are higher in this paper. The lower elasticity of substitution and the higher elasticity of distance measures in this paper likely arise through considering information from the production side that the demand-driven gravity models are unable to account for.

Besides providing identification solutions, this paper also investigates home-bias effects and shows that they are significant at the U.S. state level. Considering historical home-bias measures from earlier studies (that use data from 1993 and 1997), it is implied that home-bias effects are decreasing through time. Nevertheless, when home-bias effects are compared across goods and across states, they are significantly dispersed; much remains to be learned from such dispersion.

The published paper is available at Journal of International Economics.