Should we use IV to estimate dynamic linear probability models with fixed effects?

Assistant Professor at Wang Yanan Institute for Studies in Economics (WISE) and Department of Statistics, School of Economics, Xiamen University

Researchers have applied linear panel data methods to estimate binary choice models while allowing for individual-specific unobserved heterogeneity and dynamics either to provide empirical findings or to demonstrate the robustness of their empirical results. This leads to IV/GMM/OLS estimation of a dynamic linear probability model (LPM) with fixed effects. In this paper, I give a set of pros and cons of this procedure using explicit analytical results, some simulations, and an empirical application. I find that this procedure should be treated with caution, especially in fixed- T settings. In large-T settings, existing procedures cannot be directly applied. As a consequence, I give guidance as to what choices researchers should make in both these settings.