Essays in econometrics

Gu, Xinchen
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This dissertation consists of three chapters with a focus on the identification and estimation of causal effects. We consider various empirical strategies that are commonly used in the field of social sciences in general, and in the field of economics in particular.

The first chapter considers estimating heterogeneous causal effects in regression discontinuity designs. We take advantage of recent development in random forest based estimation methods (e.g. Athey and Wager 2018) to non-parametrically estimate heterogeneous treatment effects. A forest based algorithm is used to generate weights for each observation taking into account their similarity in treatment response. A local linear regression is subsequently run on the weighted sample. We show that the estimation procedure is able to select neighbor with higher "quality" as sample size grows, thus consistently recover heterogeneous treatment effects. We provide simulation evidence that the proposed method performs better than alternative approaches such as kernel estimation especially when the dimension of covariates is not small. We apply the method to study the effects of a Head Start assistance program on child mortality and find significant level of heterogeneity across counties.

In the second chapter, we investigate partial identification of treatment effects under several classes of assumptions. Under binary treatment and finite support of the potential outcomes, we introduce a transition matrix representation of the potential outcome pair. We show that it can be used to characterize the identified region of the joint distribution for the potential outcomes, which in turn generates the identified region of both the marginal distributions and the average treatment effect. We apply the matrix framework to support restrictions such as monotone treatment response and self-selection type assumptions. We then provide general partial identification results when support restrictions are combined with binary instrumental variables.

The third chapter 3 takes a structural view and analyzes the identification of signaling games. We extend the literature by allowing players to hold private information. Under the new information structure, we characterize the equilibrium of the game and propose smoothing procedure to ensure its existence. We propose a Jacobian-based characterization to determine regions in the support of covariates that generate unique equilibrium. We provide sufficient conditions under which the model parameters are identified.