A Simple Interactive Fixed Effects Estimator for Short Panels

We study the interactive effects (IE) model as an extension of the conventional additive effects (AE) model. For the AE model, the fixed effects estimator can be obtained by applying least squares to a regression that adds a linear projection of the fixed effect on the explanatory variables (Mundlak, 1978; Chamberlain, 1984). In this paper, we develop a novel estimator -- the projection-based IE (PIE) estimator -- for the IE model that is based on a similar approach. We show that, for the IE model, fixed effects estimators that have appeared in the literature are not equivalent to our PIE estimator, though both can be expressed as a generalized within estimator. Unlike the fixed effects estimators for the IE model, the PIE estimator is consistent for a fixed number of time periods with no restrictions on serial correlation or conditional heteroskedasticity in the errors. We also derive a statistic for testing the consistency of the two-way fixed effects estimator in the possible presence of iterative effects. Moreover, although the PIE estimator is the solution to a high-dimensional nonlinear least squares problem, we show that it can be computed by iterating between two steps, both of which have simple analytical solutions. The computational simplicity is an important advantage relative to other strategies that have been proposed for estimating the IE model for short panels. Finally, we compare the finite sample performance of IE estimators through simulations.