科学研究

Professor Myoung-jae Lee is an econometrician/statistician in Korea University. He held regular positions in many universities around the world, including Penn State, Tilburg University, Chinese University of Hong Kong, and Australian National University. He published six single-authored books on micro-econometrics and treatment effect analysis, and more than 90 papers in SCI/SSCI-listed journals on economics, statistics, transportation, medicine, sociology and political science.

For multiple treatments D=0,1,...,J, covariates X and outcome Y, the ordinary least squares estimator (OLS) of Y on {D(1),...,D(j),X} is widely applied to a constant-effect linear model, where D(j) is the dummy variable for D=j. However, the treatment effects are almost always X-heterogeneous in reality, or Y is noncontinuous, to invalidate such a linear model. The blind hope of practitioners is that the OLS "somehow" estimates a sensible average of the unknown X-heterogeneous effects. This paper shows that, unfortunately, the OLS is inconsistent unless all treatment effects are constant, because the estimand of the D(d)-slope involves the X-heterogeneous effects of all treatments, not just D(d). One way to overcome this "contamination" problem is the OLS of Y on D(d)-E{D(d)|X, D=0,d} using only the subsample D=0,d, and this paper proposes a modified version of the subsample OLS that is robust to misspecifications of E{D(d)|X, D=0,d}. The robustified subsample OLS is proven to be consistent for an "overlap weight" average of the X-heterogeneous effect of D(d) for any form of Y (continuous, binary, count, ...).