Time-varying Individual Effects in a Panel Data Probit Model with an Application to Female Labor Force Participation

Abstract In this article, we study a panel data probit model with time-varying individual effects. Under a Gaussian assumption on the error term, we show the common slope coefficients and time factors can be identified up to scale. We propose for the identified parameters a multi-stage estimation procedure. The proposed estimators have a closed form expression, thus are very convenient to compute even in large samples. We establish the root-n consistency as well as asymptotically normality for these estimators. Using a German socioeconomic panel dataset, we estimate the labor supply function for married women. We find that the unobserved skill premium is positive and shows an upward trend during 2008-2012, in support of the biased technological progress hypothesis.