Binary regression quantiles

This dissertation considers the extension of binary and smoothed binary quantile regression to quantiles other the median. In Chapter 1 it is argued that although discrete choice models with unobserved heterogeneity have important theoretical and policy implications, the existing literature focuses exclusively on parametric representations of heterogeneity, thus introducing strict assumptions that are impossible to verify. It is therefore important to explore the possibility of estimating such models under weaker semiparametric assumptions that can adequately model unobserved heterogeneity without imposing arbitrary structure on the data.;Chapter 2 reviews some of the literature regarding identification and estimation of parametric binary response models and explores biases resulting from misspecification. Binary regression quantiles are then introduced and matters pertaining to the identification, estimation and interpretation of these estimates are addressed. In Chapter 3, smoothed binary regression quantiles are shown to be consistent and asymptotically normally distributed, while consistent estimators of the mean and covariance of the joint asymptotic distribution of several of smoothed quantiles are provided. The problem of efficiently combining several regression quantiles under i.i.d. errors is addressed, and tests of homoskedasticity and conditional symmetry of the underlying error distribution are developed.;An empirical application of the proposed estimators to a model of labor force participation of married women in the U.S. is presented in Chapter 4. Both parametric as well as semiparametric models are estimated. These models reveal a rich structure in the data with significant taste variation. In order to investigate the appropriateness of both the parametric and semiparametric models, nonparametric specifications tests are proposed, while the problem of estimating participation probabilities semiparametrically is also addressed.;Binary regression quantiles are solutions to difficult optimization problems that requires the use of a global optimizer. Chapter 5 reviews some of the literature on simulated annealing, a method widely used in a diverse array of fields to solve demanding optimization problems.