The Estimation of Time-Invariant Variables in Panel Analyses with Unit Fixed Effects

This paper analyzes the estimation of time-invariant variables in panel data models with unit-effects. We compare three procedures that have frequently been employed in comparative politics, namely pooled-OLS, random effects and the Hausman-Taylor model, to a vector decomposition procedure that allows estimating time-invariant variables in an augmented fixed effects approach. The procedure we suggest consists of three stages: the first stage runs a fixed-effects model without time-invariant variables, the second stage decomposes the uniteffects vector into a part explained by the time-invariant variables and an error term, and the third stage re-estimates the first stage by pooled-OLS including the time invariant variables plus the error term of stage 2. We use Monte Carlo simulations to demonstrate that this method works better than its alternatives in estimating typical models in comparative politics. Specifically, the unit fixed effects vector decomposition technique performs better than both pooled OLS and random effects in the estimation of time-invariant variables correlated with the unit effects and better than Hausman-Taylor in estimating the time-invariant variables correlated with the unit effects. Finally, we re-analyze recent work by Huber and Stephens (2001) as well as by Beramendi and Cusack (2004). These analyses seek to cope with the problem of time-invariant variables in panel data