The perils of aggregating foreign variables in panel data models

The curse of dimensionality refers to the difficulty of including all relevant variables in empirical applications due to the lack of sufficient degrees of freedom. A common solution to alleviate the problem in the context of open economy models is to aggregate foreign variables by constructing trade-weighted cross-sectional averages. This paper provides two key contributions in the context of static panel data models. The first is to show under what conditions the aggregation of foreign variables (AFV) leads to consistent estimates (as the time dimension T is fixed and the cross section dimension N -> infinite). The second is to design a formal test to assess the admissibility of the AFV restriction and to evaluate the small sample properties of the test by undertaking Monte Carlo experiments. Finally, we illustrate an application in the context of the current account empirical literature where the AFV restriction is rejected.