Quantile regression and the duration of unemployment

Abstract

Powell (1986) proposed a quantile regression estimator for censored regression models on the basis of equivariance of quantiles to monotone transformations. In this thesis, censored quantile regression models are generalized using two-parameter Box-Cox transformation to relax the conventional linear specification of functional form, and the quantile regression estimator of the parameters of the transformed and censored regression models is presented. Both the N\sp{1/2}-consistency and the asymptotic normality of quantile estimator are derived for nonlinear regression models. The proof of asymptotic normality is based on the approach introduced by Pollard (1989) using maximal inequalities and quadratic approximation to the objective function, thus simplifying the argument and relaxing the need for convexity of the objective function in the parameter vector.From a practical point of view, this thesis proposes a new simple computational technique for nonlinear quantile regression estimation including Powell's piecewise linear censored regression quantile estimation. This algorithm is an extension of Meketon's (1985) idea for l\sb1 estimation of linear models using Karmarkar's interior point approach. It has remarkable advantages. It is computationally simple because the core of the algorithm is a standard least-squares computation. Numerical experience with a wide variety of test problems from the literature has shown it to perform quite satisfactorily.The final chapter of the thesis is devoted to applying the transformed and censored regression quantile model to the study of the duration of unemployment. The model is estimated using data from the Michigan Panel Study of Income Dynamics and Efron's (1979) bootstrap technique is taken to estimate the asymptotic covariance matrix. This empirical study clarifies the effect of education on unemployment duration particularly at the upper quantiles of the duration distribution. This is a new finding which has not been considered in past research, and is indicative of the value of the quantile regression approach.U of I OnlyETDs are only available to UIUC Users without author permissio