Semiparametric Approach to Estimation of Marginal and Quantile Effects

TL;DR

This paper introduces a semiparametric estimation method for marginal and quantile effects within generalized linear models, demonstrating theoretical properties and practical performance through simulations and real data analysis.

Contribution

It proposes an approximate maximum likelihood estimator with proven consistency, asymptotic normality, and efficiency for both effect types in semiparametric models.

Findings

Estimator is consistent and asymptotically normal.

Simulation studies show good finite sample performance.

Application reveals a new predictor in income data.

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.