This dissertation consists of three chapters. The first and second chapters develop new estimation methods for multiple fractional response variables with endogeneity. Multiple fractional response variables have two features. Each response is between zero and one, and the sum of the responses for a unit is one. The first chapter proposes an estimation method accounting for these features when there is a continuous endogenous explanatory variable (EEV). It is a two step estimation method combining a control function approach. The first step generates a control function using a linear regression, and the second step maximizes a multinomial log likelihood function with a multinomial logit conditional mean which depends on the control function generated in the first step. Monte Carlo simulations examine the performance of the estimation method when the conditional mean in the second step is misspecified. The simulation results provide evidence that the method's average partial effect (APE) estimates approximate well true APEs as long as an instrument is not weak and that the method's approximation outperforms an alternative linear method's. We apply the proposed two step estimation method to Michigan's fourth grade math test data to estimate the average partial effects of spending on student performance. The second chapter develops and evaluates an estimation method allowing for the discrete nature of an EEV. We modify the two step estimation method proposed in the first chapter by following Wooldridge (2014); instead of unstandardized residual, we use the generalized residuals as control functions The Monte Carlo simulation demonstrate that although the two step estimation method cannot provide consistent estimators for the mean parameters and average partial effects under the conditional mean misspecification, it yields a decent approximation to average partial effects. In the third chapter, we clarify some issues in computing average partial (or marginal) effects in models that have been estimated using control function or correlated random effects approaches (or some combination). In particular, we show that a common method of estimating average partial effects, where the averaging is done across all variables and across the entire sample, estimates an interesting parameter. Nevertheless, the method differs from averaging across the observed covariates the partial effects obtained via the average structural function. In the special case where unobservables are independent of the observed covariates the two methods are identical.
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