The testable implications of competitive equilibrium in economies with externalities

Suppose that one has a data set consisting of prices and individual endowments for some economy. Brown and Matzkin (Econometrica 64:1249-1262, 1996) have shown that there are conditions that the data have to satisfy, if the observed prices are determined by the competitive equilibrium process, given the observed endowments, when there are no external effects in the economy's interactions. The results here show that the same conclusion does not apply, in general, if the economy exhibits externalities. On the other hand: (i) some restrictions exist if there exist at least two commodities on which the individuals' preferences are weakly separable; (ii) although extremely mild, restrictions exist too if one observed individual consumption for the economy that causes the external effects; and (iii) importantly, even if the previous two cases do not apply, restrictions exist when the externalities that exist are in the form of a public good.