## The View from Space: Theory-based Time-varying Distances in the Gravity Model

Julian Hinz.
*Under review*.

In this paper I use a general representation of the gravity model in international economics to derive a theory-consistent spatial aggregation of bilateral frictions. I apply the method to compute *time-varying* country-to-country distances, used in estimations of the gravity model in fields ranging from international trade, to foreign direct investment and migration.
The aggregation takes the form of a weighted generalized mean, where the weights reflect the spatial distribution of economic activity in a country and the elasticity of the bilateral friction in question is a key parameter.
I use annually available satellite imagery on nighttime light emissions for highly-detailed information on the economic geography of countries, capturing urban and rural areas and reflecting changes over time.
Employing the computed distances in an application to the gravity equation of international trade yields a number of noteworthy results. Exploiting the time variation, I can estimate the distance elasticity while controlling for unobserved country-pair characteristics. Estimates for the distance coefficient are in the range of *-0.5* and *-1*.
Furthermore, the distances’ use yields important consequences for estimates of other gravity variables: the border coefficient, i.e. the often puzzlingly large relative difference between internal and external trade, is reduced by between 30% and 50%.
Regressions using simulated data confirm the theoretical and empirical findings.