UC San Diego

This dissertation contributes to the analysis of the unconditional effects of counterfactual policies that manipulate the distribution of covariates. By unconditional effects we mean the effects on any functional of the unconditional distribution of the outcome. Chapter 1 focuses on the effect on the unconditional quantiles of the outcome. We first show how to achieve identification under unconfoundedness. Then, we characterize the asymptotic bias of the unconditional regression estimator that ignores the endogeneity and elaborate on the channels that the endogeneity can render the unconditional regressor estimator inconsistent. We show that even if the treatment status is exogenous, the unconditional regression estimator can still be inconsistent when there are common covariates affecting both the treatment status and the outcome variable. Chapter 2 provides identification and estimation results for the case of an endogenous binary variable. We introduce a new class of marginal treatment effects (MTE) based on the influence function of the functional underlying the policy target. We show that an unconditional policy effect can be represented as a weighted average of the newly defined MTEs over the individuals at the margin of indifference. Point identification is achieved using the local instrumental variable approach. Furthermore, the unconditional policy effects are shown to include the marginal policy-relevant treatment effect in the literature as a special case. Methods of estimation and inference for the unconditional policy effects are provided. In the empirical application, we estimate the effect of changing college enrollment status, induced by higher tuition subsidy, on the quantiles of the wage distribution. Chapter 3 proposes a framework to analyze the effects of counterfactual policies when neither unconfoundedness holds nor an instrumental variable is available. For a given counterfactual policy, we obtain identified sets for the effect of both marginal and global changes in the proportion of treated individuals. To conduct a sensitivity analysis, we introduce the quantile breakdown frontier, a curve that quantifies the maximum amount of selection bias consistent with a given conclusion. To illustrate our method, we perform a sensitivity analysis on the effect of unionizing low income workers on the quantiles of the distribution of wages.