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The Estimation of Time-Invariant Variables in Panel Analyses with Unit Fixed Effects Pluemper, Thomas Troeger, Vera E. Uploaded 07-23-2004 Keywords Time Invariant Variables Unit effects Monte Carlo Hausman-Taylor Abstract 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 unit-effects 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.

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Fitting Multilevel Models When Predictors and Group Effects Correlate Bafumi, Joseph Uploaded 04-27-2006 Keywords Multilevel models random effects fixed effects unit effects group effects Gauss-Markov Abstract Random effects models (that is, regressions with varying intercepts that are modeled with error) are avoided by some social scientists because of potential issues with bias and uncertainty estimates. Particularly, when one or more predictors correlate with the group or unit effects, a key Gauss-Markov assumption is violated and estimates are compromised. However, this problem can easily be solved by including the average of each individual-level predictors in the group-level regression. We explain the solution, demonstrate its effectiveness using simulations, show how it can be applied in some commonly-used statistical software, and discuss its potential for substantive modeling.