科学研究

Myoung-jae Lee is an econometrician/statistician in the Department of Economics, Korea University. He held regular positions in many countries and regions around the world. He published more than 90 SSCI/SCI-listed papers on limited dependent variables, panel data and treatment effect analysis.

For a binary treatment D, an outcome Y and covariates X, a linear model with a constant treatment effect is widely used, but the linear model is untenable if Y is a limited dependent variable (LDV) and there is a continuous covariate. Despite this problem, motivations to use a linear model are strong when D is endogenous, because dealing with a binary endogenous D and a LDV Y is particularly difficult unless a fully parametric approach is adopted. Hence, practitioners often apply instrumental variable estimator (IVE) to a linear model with a LDV Y. In this paper, firstly, we show that IVE with a binary instrument Z for D estimates a `weighted average of X-heterogeneous effects on compliers' plus a bias term, where the bias is not zero in general unless a restrictive condition is met. Secondly, the bias can be reduced much by specifying the X-part in the linear model such that the X-part explains Z well, not just Y. Thirdly, a modified IVE using the `instrument residual' instead of Z has zero bias without the restrictive condition. An empirical analysis is provided to demonstrate these points.