Essays in Econometrics

Abstract

This thesis consists of three chapters on the development and analysis of methods in econometrics. In the first two chapters I consider the use of jackknife bias correction techniques to deal with the incidental parameters bias that arises from including fixed effect parameters in nonlinear models. The final chapter deals with the properties of common linear instrumental variables methods in the presence of many endogenous regressors.

Chapter 1 considers estimation of a directed network model in which outcomes are driven by dyad-specific variables (such as measures of homophily) as well as unobserved agent-specific parameters that capture degree heterogeneity. I develop a jackknife bias correction to deal with the incidental parameters problem that arises from fixed effect estimation of the model. In contrast to previous proposals, the jackknife approach is easily adaptable to different models and allows for non-binary outcome variables. Additionally, since the jackknife estimates all parameters in the model, including fixed effects, it allows researchers to construct estimates of average effects and counterfactual outcomes. I also show how the jackknife can be used to bias-correct fixed effect averages over functions that depend on multiple nodes, e.g. triads or tetrads in the network. As an example, I implement specification tests for dependence across dyads, such as reciprocity or transitivity. Finally, I demonstrate the usefulness of the estimator in an application to a gravity model for import/export relationships across countries.

In Chapter 2, joint with Jinyong Hahn, I compare the properties of two bias correction methods, the leave-one-out jackknife and the split-sample jackknife, in a nonlinear panel data model with individual fixed effects. Since both estimators are asymptotically unbiased with equal asymptotic variances, we derive higher-order bias and variance expressions for both bias corrections, and show that the split-sample jackknife has larger higher-order variance. This difference in higher-order variances can be important in practice, particularly in settings where the time-series dimension 𝑇 is not large. In addition, the remaining bias (after bias correction) is larger for the split-sample estimator. Simulations confirm these findings, and show significant distortions in coverage when the asymptotic distribution is used for inference on the split-sample jackknife estimator.

Chapter 3 considers the properties of linear IV estimators when used to estimate models in which there are many potentially endogenous regressors. One common setting in which many endogenous regressors naturally arise, is the interaction of endogenous treatment variables with exogenous covariates in models that aim to capture heterogeneity in treatment effects. I extend existing results on linear IV estimation by considering asymptotics under which the number of endogenous regressors is allowed to grow with the sample size, and derive consistency and asymptotic normality results for the jackknife IV estimator (JIVE), as well as the heteroskedasticity robust k-class style estimators (including the HLIM and HFUL). In simulations, the HFUL estimator is shown to outperform others in models with both many endogenous regressors and many instruments.