This thesis contains three essays. The first essay develops methodology for detecting and measuring racial bias in police traffic searches. The second essay develops methodology for using instrumental variable strategies to extrapolate beyond complier subpopulations, and is coauthored with Alexander Torgovitsky. The third essay provides large sample distribution theory for support vector regression with l1-norm regularization, and is coauthored with Yuehao Bai, Hung Ho, and Guillaume Pouliot.