Specification Testing in Panel Data With Instrumental Variables

This paper shows a convenient way to test whether instrumental variables are correlated with individual effects in a panel data set. It shows that the correlated fixed effects specification tests developed by Hausman and Taylor (1981) extend in an analogous way to panel data sets with endogenous right hand side variables. In the panel data context, different sets of instrumental variables can be used to construct the test. Asymptotically, I show that the test in many cases is more efficient if an incomplete set of instruments is used. However, in small samples one is likely to do better using the complete set of instruments. Monte Carlo results demonstrate the likely gains for different assumptions about the degree of variance in the data across observations relative to variation across time.