Semiparametric Approach to Estimation of Marginal and Quantile Effects

Abstract: We consider a semiparametric generalized linear model and study estimation of both marginal and quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal effect and the quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze a Swiss non-labor income data and discover a new interesting predictor.