This dissertation contains three self-contained chapters. The first two are related in their analysis of California's Quality Education Investment Act (QEIA), with the former estimating its effect on student achievement and the latter exploiting an aspect of the law to estimate district preferences for resource allocation over low-performing schools. The final chapter considers the distributions of quantile regressors under complex random sampling. Beginning in the 2007-08 school year, California's QEIA required schools selected via lottery to institute reforms including class size reduction, increased average teacher experience, and extra professional training. The act provided additional per-pupil funding for schools to meet these requirements. Conditional on known probabilities of selection, which differed across schools, treatment is uncorrelated with potential outcomes, allowing for non-parametric identification of the causal effect by inverse probability weighting. In the first fully-funded year of the program, math scores in 4th grade increased by 0.32 SD in the population of California school-grade averages, and by the second fully-funded year 5th grade math scores improved by 0.37 SD. By the third fully-funded year of the program, math scores in 2nd grade were 0.30 SD higher in the distribution of California school-grade averages, and 0.29 SD higher in 3rd grade. Selected schools did not increase teacher experience, and had 4.4 to 4.8 fewer students in the first fully-funded year in 4th and 5th grade. In kindergarten through 3rd grade class sizes were reduced later and less dramatically, by 3 to 4.2 students by the third fully-funded year, due primarily to unselected schools exiting California's previous class size reduction program. The timing of class size reductions and student achievement gains suggests class size was the driving factor. This novel intervention also required school districts to rank their low-performing schools, the analysis of which constitutes my second chapter. Districts understood that higher ranked schools would be more likely to receive significant increases in funding to implement QEIA reforms. These rankings provide a unique revelation of district preferences for resource allocation across low-performing schools. Using a discrete-choice model, I estimate the school characteristics that districts ranked highly. I find descriptive evidence that districts were more likely to rank highly schools with a high percentage of students eligible for Free and Reduced Price Lunch, and which were repeatedly sanctioned under No Child Left Behind for failing to make Adequate Yearly Progress. I also find some evidence that districts ranked highly high schools that applied for an alternative program, in which they crafted their own reforms. The final chapter, coauthored with Ot\'{a}vio Bartalotti, extends previous work that developed the asymptotic properties of quantile regression estimators under Standard Stratified sampling, to Variable Probability sampling. Formulas for the asymptotic variance and feasible estimators are provided. Simulation results are provided for both Standard Stratified and Variable Probability sampling. Simulation results confirm econometric theory by demonstrating that under exogenous stratification unweighted estimates preform well and are more efficient than weighted estimates. Under endogenous stratification and SS sampling, no estimate of standard errors performs best across coefficients, quantiles, and sample sizes. Under endogenous stratification and VP sampling, however, bootstrapped standard errors consistently perform well.
Read
