Download This PaperOn the Local Power of Some Tests of Strict Exogeneity in Linear Fixed Effects Models
Econometrics and Statistics
57 Pages Posted: 26 Apr 2016 Last revised: 22 Apr 2022
Date Written: November 30, 2016
Abstract
The local asymptotic power of a variable addition test for strict exogeneity in a linear panel model is derived under near epoch dependence and the maintained assumption of contemporaneously exogenous regressors. The test, which generalizes an idea of Wooldridge (2010), is an F-statistic equipped with the clustered variance-covariance matrix estimator for the exclusion restriction pertaining to leads and lags in an auxiliary fixed effects regression. Local power is found to depend non-trivially on the relative size of the panel, on the width of the local neighbourhood, as well as on the maintained notion of exogeneity under the alternative. Under the maintained assumption of weak exogeneity, the test can be performed along the lines of Sims's (1972) causality test, and, for conditionally homoskedastic and uncorrelated innovations, is shown to be asymptotically equivalent to an incremental Sargan (1958) test based on a double-filter argument of Hayakawa et al. (2019). Further(dis)similarities between the variable addition test and Hausman (1978)-type tests are explored and asymptotic equivalencies established. It is shown that the latter test, albeit having inferior power, is able to consistently ascertain the validity of the fixed effects estimator if the time-series dimension is moderately large. Monte Carlo evidence confirms the accuracy of the asymptotic theory as a description of the finite sample behaviour.
Keywords: strict exogeneity, variable-addition test, incremental Sargan test, Hausman test, local power, near-epoch dependence
JEL Classification: C12, C22, C23
Suggested Citation: Suggested Citation