Structural change methods for common breaks and quantile regression

Structural breaks and quantile regression have recently been active research areas in econometrics. Over the last fifteen years, growing attention has been paid to estimating and testing for multiple structural changes with unknown change points in both theoretical and applied research. Also, estimation and inference for quantile regression have received increasing attention. In this dissertation, I make further theoretical contributions in these areas and present empirical applications.;In chapter one, I address the issue of testing for common breaks across or within equations. The null hypothesis the chapter focuses on is that some subsets of parameters share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test considered is the quasi-likelihood ratio test assuming normal errors, though, as usual, the limit distribution of the test remains valid with non-normal errors.;In chapter two, I consider the estimation of multiple structural changes occurring at unknown dates in one or multiple quantiles. The analysis covers time series models as well as models with both time series and cross-sectional observations. The estimates are obtained by minimizing the check function over permissible break dates. The limiting distributions are derived under mild conditions. The paper also discusses a procedure to estimate the number of changes as well as two empirical applications.;In chapter three, I propose a nonparametric estimation method for conditional quantile functions when these functions contain multiple discontinuities at unknown locations but are otherwise smooth. Estimators of the jump locations and sizes are based on comparisons of one-sided local linear quantile estimators. This method captures the change in the whole conditional distribution under a flexible functional form assumption. The proposed jump location estimator avoids a mis-specification problem while maintaining the parametric convergence rate. I provide the limiting distribution of the discontinuous jump locations and their sizes.