Dual gravity: using spatial econometrics to control for multilateral resistance

We propose a quantity-based `dual' version of the gravity equation that yields an estimating equation with both cross-sectional interdependence and spatially lagged error terms. Such an equation can be concisely estimated using spatial econometric techniques. We illustrate this methodology by applying it to the Canada-U.S. data set used previously, among others, by Anderson and van Wincoop (2003) and Feenstra (2002, 2004). Our key result is to show that controlling directly for spatial interdependence across trade flows, as suggested by theory, significantly reduces border effects because it captures `multilateral resistance'. Using a spatial autoregressive moving average specification, we find that border effects between the U.S. and Canada are smaller than in previous studies: about 8 for Canadian provinces and about 1.3 for U.S. states. Yet, heterogeneous coefficient estimations reveal that there is much variation across provinces and states.