Variable Selection for Structural Equation with Endogeneity

This paper studies variable selection problem in structural equation of a two-stage least squares (2SLS) model in presence of endogeneity which is commonly encountered in empirical economic studies. Model uncertainty and variable selection in the structural equation is an important issue as described in Andrews and Lu (2001) and Caner (2009). The authors propose an adaptive Lasso 2SLS estimator for linear structural equation with endogeneity and show that it enjoys the oracle properties, i.e., the consistency in both estimation and model selection. In Monte Carlo simulations, the authors demonstrate that the proposed estimator has smaller bias and MSE compared with the bridge-type GMM estimator (Caner, 2009). In a case study, the authors revisit the classic returns to education problem (Angrist and Krueger, 1991) using the China Population census data. The authors find that the education level not only has strong effects on income but also shows heterogeneity in different age cohorts.