Parameter-Specific Bias Diagnostics in Random-Effects Panel Data Models

Abstract

The Hausman specification test assesses the random-effects specification by comparing random-effects and fixed-effects estimators. This note shows how a coefficient-specific diagnostic for linear mixed models can complement that comparison. The diagnostic measures alignment between fitted random effects and the weights used to estimate a coefficient or contrast. It is an internal sensitivity summary, not an estimate of every contribution to finite-sample bias: response-dependent covariance estimates introduce an additional weighted-error term. We explain this distinction, describe simulations that refit the covariance parameters and retain both contributions, and illustrate the calculations with gasoline-demand data and a multiple-membership value-added model. A covariance-scale analysis of the gasoline example connects the local diagnostic to movement toward the fixed-effects estimate. We also discuss how conditioning on stochastic regressors extends the interpretation, and what further assumptions would be needed for calibrated inference.

arXiv comment17 pages, 2 figures, 3 tables. Corrected bias decomposition and diagnostic interpretation; gasoline and CP value-added conditional response-refit simulations, and covariance-scale sensitivity paths. Focused reproduction/simulation scripts, public data and aggregate results included; R packages installed separately