Essays in Econometrics of Networks and Models with Errors-in-Variables

Abstract

Latent variables such as fixed effects or measurement errors are pervasive in economics. Unless properly accounted for, their impact may lead to inconsistent estimators and erroneous inference. This dissertation studies some of these issues and develops a number of estimation and inference techniques that account for the presence of such latent variables.

In Chapter 1, I demonstrate the importance of allowing for a flexible form of interactive unobserved heterogeneity in network models: the agents’ unobserved characteristics (fixed effects) are likely to affect the outcomes of their interactions, potentially in a complicated way. To address this concern, I consider a network model with nonparametric unobserved heterogeneity, leaving the role of the fixed effects and the nature of their interaction unspecified. I show that all policy relevant features of the model can be identified and estimated even though the form of the fixed effects interactions is unrestricted. I construct several estimators of the parameters of interest, establish their rates of convergence, and illustrate their usefulness in a Monte-Carlo experiment.

In Chapters 2 and 3, which are coauthored with Professor Kirill S. Evdokimov, we study estimation and inference in nonlinear models with Errors-In-Variables (EIV).

In Chapter 2, we propose a simple and practical approach to estimation of general moment conditions models with EIV. For any initial moment conditions, our approach provides corrected moment conditions that do not suffer from the EIV bias. The EIV-robust estimator is then computed as a standard GMM estimator with the corrected moment conditions. We show that our estimator is asymptotically normal and unbiased, and the usual tests provide valid inference, even when the “naive” tests falsely reject the true null hypothesis 100% of the time.

In Chapter 3, we document an important and previously unrecognized pitfall in the existing EIV literature: the features of the measurement error distribution may be weakly or not identified even when the instruments are strong. As a result, commonly employed EIV estimators generally are not asymptotically normal and the standard tests and confidence sets are invalid. To address this issue, we develop simple novel approaches to uniformly valid yet powerful inference.