Inference on time-invariant variables using panel data: A pretest estimator

Abstract

For static panel data models that include endogenous time-invariant variables correlated with individual effects, exogenous averages over time of time-varying variables can be internal instruments. To pretest their exogeneity, we first estimate a random effects model that includes all averages over time of time-varying variables (Mundlak, 1978; Krishnakumar, 2006). Internal instruments are then selected if their parameter is statistically different from zero (Mundlak, 1978; Hausman and Taylor, 1981). Finally, we estimate a Hausman-Taylor (1981) model using these internal instruments. We then evaluate the biases of currently used alternative estimators in a Monte-Carlo simulation: repeated between, ordinary least squares, two-stage restricted between, Oaxaca-Geisler estimator, fixed effect vector decomposition, and random effects (restricted generalized least squares).