### 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.

The corresponding paper by Hakan Yilmazkuday
has been published at Journal of International Economics.

**Abstract**

This paper models and estimates
bilateral trade patterns of U.S. states in a CES framework and identifies the
elasticity of substitution across goods, the elasticities of substitution
across varieties of each good, and the good-specific elasticities of distance
by using markup values obtained from the production side. Compared to the
international trade literature, the elasticity of substitution estimates are
lower across both goods and varieties, while the elasticity of distance
estimates are higher. Although home-bias effects at the state level are
significant, there is evidence for decreasing effects over time.

**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:

- Elasticities of substitution across varieties of each good are estimated by markup data.
- Elasticities of distance at the good level are identified through combining markups and bilateral trade estimates.
- 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.
- For each destination, composite price indices and total imports are calculated at the good level.
- 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.

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