Essays on the Theory and Application of Post-Regularization Inference and Selection Correction in Censored and Distribution Regression Models

Abstract

This dissertation explores the integration of modern machine learning techniques into classical econometric frameworks, with a focus on enhancing inference in models subject to outcome censoring or distributional heterogeneity. By bridging these domains, the thesis contributes both theoretical advances and empirical applications that demonstrate the added value of high-dimensional methods in addressing long-standing challenges in applied econometrics. The first essay develops a framework for post-selection inference in high-dimensional Tobit mo-dels. By combining maximum likelihood estimation with double machine learning and Neyman orthogonalization, it establishes asymptotically valid inference in settings with censored outco-mes. Simulations confirm its robustness, and an empirical application to HIV drug resistance data illustrates its practical relevance. This chapter demonstrates how regularization techniques can be successfully adapted to classical econometric models. The second essay investigates the effects of Germany’s statutory minimum wage using a post-double selection logistic distribution regression model. This high-dimensional approach allows for consistent inference across entire outcome distributions, eliminating reliance on ad hoc variable selection. Results show that the reform raised hourly wages at the bottom of the distribution wit-hout significant adverse effects on working hours, while effects on monthly earnings were more nuanced. The findings reconcile earlier mixed evidence and underscore the value of machine learning methods for labor market applications. The third essay applies a distribution regression model with sample selection correction to analy-ze the evolution of the gender wage inequality in Germany. The approach uncovers heterogene-ous patterns of unobserved selectivity across both full-time and part-time employment. Results indicate that the narrowing of the full-time gender wage gap over time is largely explained by changes in selectivity patterns and improvements in women’s characteristics, while part-time employment continues to exhibit pronounced gender differences, albeit with signs of conver-gence. Together, these essays demonstrate that incorporating machine learning into econometric analy-sis improves inference, reduces reliance on restrictive assumptions, and broadens the scope of research questions that can be rigorously addressed. The dissertation discusses and applies new tools for handling non-random sample selection and heterogeneous effects, and points toward a fruitful future agenda at the intersection of econometrics and statistical learning.