Robust Priors in Non-Linear Panel Data Models – Estimating Average Marginal Effects
Abstract
In a seminal paper, Arellano and Bonhomme (“Robust priors in nonlinear panel data models,” Econometrica, 2009) propose priors to simultaneously reduce the bias for estimating the common parameters (theta_0) and the average marginal effects (M) in non-linear panel data models with fixed effects. However, we show that the Arellano-Bonhomme (AB) priors are not simultaneously bias reducing by proving mathematically that although the AB priors always reduce the bias for estimating theta_0, they do not always reduce the bias for estimating M. E.g., in the static panel probit model or, generally, for dynamic panel data models, the AB priors only reduce the bias for estimating theta_0 but not for estimating M, whereas in the static panel logit and Poisson models the AB priors simultaneously reduce the bias for estimating theta_0 and M. Furthermore, we construct priors that we prove are simultaneously bias reducing for general non-linear panel data models including panel probit, and show numerically in a simulation study that the AB priors for a panel probit model do not reduce the bias for estimating M — the bias of the estimator of M based on the AB priors remains comparable to the bias of the maximum likelihood estimator of M even when the panel is long — whereas the priors that we construct do.
This is joint work with my supervisors, Gautam Tripathi and Martin Schumann. It appears in part in print in the forthcoming (Arellano, M., Bonhomme, S., Borodich Suarez, S., Schumann, M., Shi, X., and Tripathi, G. (2025): “Erratum to “Robust Priors in Nonlinear Panel Data Models”,” Econometrica, 93, 3 , doi: 10.3982/ECTA23441, in production).
Language
English