In this dissertation, I develop two semiparametric estimators and consider a variation on an existing semiparametric estimator in the third chapter. In Chapter 1, I develop a model and an estimator for a panel data setting with multiple fractional response variables with a binary endogenous co- variate. I develop a two-step technique to obtain consistent estimates of the average partial effects. Then, I provide a variable addition test for endogeneity. I demonstrate using simulations that if the chosen conditional mean function is incorrect, it is still possible to obtain estimates of the average partial effects that are close to the true values. Data from the NLSY97 survey is used to estimate the average partial effect of marriage on how individuals allocate their time within a year. In Chapter 2, I develop a doubly-robust estimator of the quantile treatment effect on the treated (QTT). This estimator can obtain consistent estimates of the QTT using either the propensity score or the conditional cdf of the first-differenced untreated outcomes. Aside from the benefits of obtaining consistent estimates of a QTT when a nuisance function is misspecified, there are also efficiency gains. In addition, assumptions on the smoothness of the nuisance parameters can be relaxed when the estimator is doubly-robust. I also show that asymptotically valid confidence intervals can be constructed using the empirical bootstrap. Then, I demonstrate via simulations that my estimator can produce a sharply lower root mean square error compared to other estimators. I apply my estimator to estimate the effect of increasing the minimum wage on county-level unemployment rates, where I show significant and varied quantile treatment effects. In Chapter 3, I consider whether a modification of the parametric estimators of the nuisance functions described in Chapter 2 will lead to an improved performance compared to existing estimators. In particular, an additional moment will be included to estimate the parameters of the nuisance functions, but only one of those nuisance functions will be used to estimate the quantile treatment effect on the treated (QTT). I show that even if this additional moment is applied, the small-sample performance of the estimator is not improved over the doubly-robust estimator in Chapter 2. This is true regardless of which nuisance function is misspecified.
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