Date of Award

Spring 2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Economics

First Advisor

Vytlacil, Edward

Abstract

In this dissertation, I discuss identification problems with two sources of endogeneity. In both chapters, one source of endogeneity is self-selection into treatment. To address this problem, I use the Marginal Treatment Effect framework developed by Heckman and Vytlacil (2009). In the first chapter, I partially identify the marginal treatment effect (MTE) function when the treatment variable is misclassified. To do so, I explore three sets of restrictions on the relationship between the instrument, the misclassified treatment and the correctly measured treatment, allowing for dependence between the instrument and the misclassification decision. If the signs of the derivatives of the correctly measured propensity score and the mismeasured one are the same, I identify the sign of the MTE function at every point in the instrument's support. If those derivatives are close to each other, I bound the MTE function. Finally, by imposing a functional restriction between those two propensity scores, I derive sharp bounds around the MTE function and any weighted average of the MTE function. To illustrate the usefulness of my partial identification method, I analyze the impact of alternative sentences --- e.g., fines or community services --- on recidivism using random assignment of judges within Brazilian court districts. In this context, misclassification is an issue when the researcher measures the treatment based solely on trial judge's rulings, ignoring that the Appeals Court may reverse sentences. I show that, when I use the trial judge's rulings as my misclassified treatment variable, the misclassification bias may be as large as 10\% of the MTE function, which can be estimated using the final ruling in each case as my correctly measured treatment variable. Moreover, I show that the proposed bounds contain the MTE function in this empirical example. In the second chapter, my coauthors and I present identification results for the marginal treatment effect (MTE) when there is sample selection. We show that the MTE is partially identified for individuals who are always observed regardless of treatment, and derive uniformly sharp bounds on this parameter under three increasingly restrictive sets of assumptions. The first result imposes standard MTE assumptions with an unrestricted sample selection mechanism. The second set of conditions imposes monotonicity of the sample selection variable with respect to treatment, considerably shrinking the identified set. Finally, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Our analysis extends to discrete instruments. The results rely on a mixture reformulation of the problem where the mixture weights are identified, extending Lee's (2009) trimming procedure to the MTE context. We propose estimators for the bounds derived and use data made available by Deb et al. (2006) to empirically illustrate the usefulness of our approach.

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