ESSAYS ON ECONOMETRICS: SPARSITY, DURATION, AND BINOMIAL PANEL DATA MODELS

Abstract

This dissertation consists of three chapters on econometrics. The first chapter, coauthored with Michal Kolesár and Ulrich K. Müller, documents that linear regression estimates which rely on an assumption of sparsity are fragile. First, we show that different choices of the regressor matrix that do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates by two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. Across the three applications we find many rejections of the sparsity assumptions using these tests. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust inference at little efficiency cost. The second chapter generalizes the canonical proportional hazards model to allow for two-way unobserved heterogeneity. The duration models of interest are those generated by a match between entities from two distinct groups, so the focus is on bipartite graphs. Identification of the coefficient on the explanatory variables and the difference of intra-group baseline hazards is proven when baseline hazard rates are “double-stratified.” In the special case where at least one group has time-invariant heterogeneity, we provide a consistent and asymptotically normal estimator of the coefficient vector when both groups grow at the same rate. The final chapter, coauthored with Bo E. Honoré, generalizes recent developments for binary outcome panel data models with fixed effects to models with binomial outcomes. We first consider models where the outcome is the sum of conditionally independent and identically distributed “logit” Bernoulli random variables. We show that results from the binary outcome literature concerning the existence of sufficient statistics carry over. In cases where a sufficient statistic does not exist, we find moment conditions. We then relax the assumption on identical distributions and show that certain results extend to the resulting “Poisson-Binomial” models. Finally, we connect the models analyzed to those in the literature on entry games.