Essays on Policy Learning and Network Econometrics

Abstract

This dissertation consists of three chapters: the first two develop methods for policylearning, and the third studies a framework for incorporating network data as proxy controls for unobserved heterogeneity in economic models. In the first chapter, coauthored with Yanqin Fan and Yuan Qi, we propose an optimal policy that targets the average welfare of the worst-off α-fraction of the post- treatment outcome distribution. We refer to this policy as the α-Expected Welfare Maximization (α-EWM) rule, where α∈(0,1] denotes the size of the subpopulation of interest. The α-EWM rule interpolates between the expected welfare (α= 1) and the Rawlsian welfare (α →0). For α ∈(0,1), an α-EWM rule can be interpreted as a distributionally robust EWM rule that allows the target population to have a different distribution than the study population. Using the dual formulation of our α-expected welfare function, we propose a debiased estimator for the optimal policy and establish its asymptotic upper regret bounds. In addition, we develop asymptotically valid inference for the optimal welfare based on the proposed debi- ased estimator. We examine the finite sample performance of the debiased estimator and inference via both real and synthetic data. In the second chapter, coauthored with Zequn Jin, Xi Zheng and Yahong Zhou,we develop a robust and efficient method for policy learning from observational data in the presence of unobserved confounding, complementing existing instrumental variable based approaches. We employ the marginal sensitivity model (MSM) to re- lax the commonly used yet restrictive unconfoundedness assumption by introducing a sensitivity parameter that captures the extent of selection bias induced by unob- served confounders. Building on this framework, we consider two distributionally robust welfare criteria, defined as the worst-case welfare and policy improvement functions, evaluated over an uncertainty set of counterfactual distributions charac- terized by the MSM. Closed-form expressions for both welfare criteria are derived. Leveraging these identification results, we construct doubly robust scores and es- timate the robust policies by maximizing the proposed criteria. Our approach ac- commodates flexible machine learning methods for estimating nuisance components, even when these converge at a moderately slow rate. We establish asymptotic re- gret bounds for the resulting policies, providing a robust guarantee against the most adversarial confounding scenario. The proposed method is evaluated through ex- tensive simulation studies and empirical applications to the JTPA study and Head Start program. In the third chapter, I study a nonparametric model where a latent variable cre-ates endogeneity by affecting both network formation and an outcome of interest. I generalize the existing network control function approach to nonparametric outcome models, using individuals’ link functions to account for the unobserved heterogene- ity. My identification is a form of matching on unobservables: I conceptually match individuals based on their latent link functions. To implement this strategy, I first estimate the distances or dissimilarities between the latent link functions using net- work data. Second, I apply a functional kernel smoothing over these distances to estimate the structural parameter. My asymptotic analysis reveals a fundamental trade-off: the robustness gained from this approach comes at the unavoidable cost of a slow convergence rate, driven by the difficulty of matching on latent objects. I characterize this statistical cost by deriving a minimax lower bound.