Gravity Model of Trade - Econometric Estimation of Gravity Equations

Econometric Estimation of Gravity Equations

Since the gravity model for trade does not hold exactly, in econometric applications it is customary to specify

,

where represents volume of trade from country to country, and typically represent the GDPs for countries and, denotes the distance between the two countries, and represents an error term with expectation equal to 1.

The traditional approach to estimating this equation consists in taking logs of both sides, leading to a log-log model of the form (note: constant G becomes part of ):

.

However, this approach has two major problems. First, it obviously cannot be used when there are observations for which is equal to zero. Second, it has been argued by Santos Silva and Tenreyro (2006) that estimating the log-linearized equation by least squares (OLS) can lead to significative biases. As an alternative, these authors have suggested that the model should be estimated in its multiplicative form, i.e.,

,

using a Poisson pseudo-maximum likelihood (PPML) estimator usually used for count data (see the original paper for details). One of the authors' more surprising findings was that, when controlling for sharing a common language, having past colonial ties does not increase trade—a finding which contrasts with what more basic methods, such as OLS or even scatter plots of trade data, would indicate. Martin and Pham (2008) argued that using PPML on gravity severely biases estimates when zero trade flows are frequent. However, their results were challenged by Santos Silva and Tenreyro (2011), who pointed out that the simulation results of Martin and Pham (2008) are based on misspecified models and confirmed that the PPML estimator performs well even when the proportions of zeros is very large.

In applied work, the model is often extended by including variables to account for language relationships, tariffs, contiguity, access to sea, colonial history, exchange rate regimes, and other variables of interest.