| This dissertation considers three essays on quantile regression methods for panel data models. Chapter 1 investigates a class of penalized quantile regression estimators for panel data. Under plausible conditions, I obtain the minimum variance estimator in the class of penalized quantile regression estimators, the analog of the Gaussian random effects estimator in the class of penalized least squares estimators for panel data. Monte-Carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias. I then employ panel data quantile regression methods for analysing voucher programs that serve heterogeneous students.;Chapter 2 develops a fixed effects quantile regression application. Rouse (1998) analysis of the Milwaukee Parental Choice program suggests that students selected to attend the choice school had a positive linear gain in mathematics. We show that students' gains are more subtle in nature. Remarkably, while high attainment students had a positive, convexly increasing gain in mathematics, lower attainment students were actually adversely affected over time. However, the evidence suggests that the program prevented weak students from having an even bigger loss experienced by students in the comparison group.;Chapter 3 illustrates the use of the penalized quantile regression estimator. Angrist et al. (2002) points out that the primary incentive effect of the Colombia's voucher program should be on those who are near the margin for passing on to the next grade because vouchers were renewable as long as the students maintained good academic progress. Applying quantile regression, they report that increases in test scores are not observed in the lower quantiles of the conditional educational attainment distribution. They also estimate a classical Gaussian random effects model to account for individual heterogeneity, but this approach precludes estimating effects other than the mean. To get around the problem, we employ the quantile regression panel methods. The analysis shows that the program impact is largest in the lower tail of the conditional educational attainment distribution. This was conjectured by the original authors, but could not be confirmed empirically using conventional panel data methods that focused on the conditional mean. |
