“…The major concern of applying TS2SLS is how to obtain the asymptotic covariance matrix of the second stage estimator to estimate standard errors. There are two commonly used methods to address this issue -Inoue and Solon(2010)'s method which originates from Murphy and Topel's (1986) two step estimator(e.g., Currie and Yelowitz, 2001;Berg,Pinger, and Schoch, 2016), and a bootstrap method (e.g., Bjorklund&Jantti, 1997;Anderson, 2011;Olivetti and Paserman, 2015). In this paper, we follow Inoue and Solon (2010)'s approach, a simple version of the method is expressed as follows:…”