During the last thirty years the gravity equation has been extensively applied in empirical studies of international economics to provide valuable insights into the functioning of both interregional and international bilateral trade flows. Specifically, the gravity equation has been used to analyze the impact of a variety of policy issues such as trading groups, political blocks, patent rights and various trade distortions. Despite of it’s extensive use, the early applications of the gravity model had lacked rigorous theoretical underpinnings and was long criticized for being rather ad hoc.
Recently Deardorff (1998) and Baier and Bergstrand (2001) have shown that the gravity equation of bilateral trade can be derived from a factor endownment model consistent with classical theories of trade. This was an extension of the earlier works by Anderson (1979), Helpman and Krugman (1985), Bergstrand (1985; 1989) and Hummels and Levinsohn (1995) who also derived theoretically the gravity equation as a reduced form from a general equlibrium model of international trade. Although the theoretical foundations seems that have been established, the empirical estimation of the gravity model has not been addressed in detail.
In it’s simplest form the gravity equation assumes that the amount of trade between two countries or regions is increasing in size, as measured by national income, and decrease in the cost of transportation between them, as measured by the bilateral distance between countries.1 In other words, exporter and importer GDPs can be interpreted as the production and absorption capacities of the exporting and importing countries, respectively.
Linnemann (1966) suggested an augmented form of the gravity equation including population or per capita income as an alternative measure of country’s size. As noted by Bergstrand (1989), regardless the particular specification of the gravity model, the prime purpose of any empirical application is to allow for non-homothetic preferences in the importing country and to proxy for the capital-labor ratio in the exporting country.
Through years other variables reflecting factors that make trade easier or more difficult, such as political considerations, preferential and free trade agreements, customs unions, tariff levels and neighborhood have been taken into account in gravity model specification. However, not all the factors affecting bilateral trade flows are readily observable. Variables such as historical links, cultural similarities etc., though they affect significantly bilateral trade flows, are usually unobservable and thus difficult to quantify empirically. For instance, if US consumers due to cultural reasons have a stronger preference for British made goods over German made goods, then if all else are equal, the US will import more from UK than from Germany.
Hence, exogenous factors not readily observable introduce a country-pair heterogeneity which should be taken into account in the econometric estimation of the gravity equation. With such heterogeneity a country may trade different amounts from two other countries even though the two markets have the same GDP and are equidistant from each other. This may happen due to historical, cultural, political or geographical factors that affect the level of bilateral trade flows and are correlated with the independent variables included in the gravity equation. In this case the standard econometric estimation (i.e. OLS, MLE) of the gravity equation, it is more likely to provide biased estimates.
Several attempts have been made in the literature to control for this heterogeneity bias including variables such as whether trading partners share a common language, have had a colonial history, are in military alliance etc. Nevertheless, these exogenous factors are often difficult to quantify empirically. In order to overcome the problem several authors have introduced dummy variables as an approach to include in the model specification these exogenous factors. However, dummy variables are simplistic in nature and thus they do not account for real trade diversion effects. It is quite important therefore, to find alternative ways to account for the impact of these factors in bilateral trade flows in the empirical estimation of the gravity equation.
In a recent paper Cheng and Wall (1999) found that in the presence of country- pair heterogeneity the standard estimation methods tend to underestimate trade between high-volume traders and overestimate it between low-volume traders. They suggest the use of standard panel data estimators to allow for the intercepts of the gravity equation to be specific to each trading pair in order to account for pairwise heterogeneity. Bayoumi and Eichengreen (1997) and Mátyás (1997) have also proposed models to handle pairwise heterogeneity each of which can be expressed as a restricted version of the fixed effects panel data model.
Besides the need of panel data, in this case the impact of the unobservable variables on bilateral trade flows is assumed to be neutral with respect to each trading pair. The estimated parameters of the gravity equation are assumed to be the same across country-pairs except of the intercept term. Nevertheless, it is logically to assume that the impact of the explanatory variables included in the gravity equation is not affecting uniformly bilateral trade flows among country-pairs. The diversity of pairwise trade behavior, would lead to parameter variation across country pairs. In such cases the constant slope but varying intercept coefficients do not appear to be meaningful.
The objective of this paper is to present an alternative way for estimating the gravity equation that accounts for country-pair heterogeneity. A stochastic varying coefficient gravity model is suggested that allows for modeling the heterogeneity in the functional relationship between bilateral trade flows and explanatory variables. The model is based on Hildreth and Houck (1968) random coefficient regression popularized by Swamy (1970). The empirical application is based on cross-section data of bilateral trade flows between EU member states.
