Testing for Strict Exogeneity in Fixed-Effects Panel Models

Abstract

A generalization of a variable-addition test first mentioned in Wooldridge (2002) is proposed to validate the null hypothesis of strict exogeneity in a fixed-effects panel data model. The test is easily constructed by augmenting the within-groups (WG) regression with leads and lags. As this paper demonstrates, the approach can be motivated by its asymptotic equivalence with a refined version of the incremental Sargan (1958) test for overidentifying restrictions based on a suitably transformed set of internal instruments. The equivalence is shown to break down when the number of tested restrictions diverges. Specifically, utilizing the many-restrictions framework proposed by Anatolyev and Gospodinov (2011), the variable-addition test is shown to over-reject while the incremental test is overly conservative when the number of tested moment conditions diverges at the same rate as the time-series dimension and n is fixed. Both test statistics are correctly sized when also the cross-sectional dimension diverges. It is shwon that the variable-addition test statistic can handle heteroskedasticity irrespective of the expansion path of (n,T) when equipped with Stock and Watson's (2008) bias-corrected variance-covariance estimator. The paper demonstrates furthermore that Hausman (1978)-type tests based on the WG estimator are likely to lack power when the time-series dimension is large. The variable-addition test possesses non-trivial local power, while Hausman (1978) type tests enjoy local power only if the time-series dimension is much smaller than the cross-sectional dimension and the local alternatives are relatively far apart from the null. The theoretical results are complemented by finite sample Monte Carlo evidence.