This dissertation consists of three distinct papers. The first chapter estimates the effect of local labor market opportunities on crime among individuals exiting prison in California. The second chapter studies the behavior of the cluster robust variance estimator, commonly used in empirical research, when standard assumptions regarding the structure of observations across groups are relaxed. Finally, the third chapter estimates a compensating differential for fatality risk for workers in Mexico. An abstract for each chapter is provided below.

Chapter 1 Abstract: Identifying a causal effect of labor market opportunities on criminal behavior is difficult given (a) an endogenous relationship between labor markets and crime and (b) the challenge of using aggregate measures to capture employment opportunities for individuals on the margin of criminal activity. The institutional structure of the California criminal justice system as well as location-, skill-, and industry-specific employment measures provide a unique framework to identify a causal effect. I find that a one-standard-deviation increase in the prevalence of relevant employment opportunities is associated with a 1 to 2 percent decrease in the probability released offenders return to prison.

Chapter 2 Abstract: We study the behavior of a cluster-robust t statistic and make two principle contributions. First, we relax the restriction of previous asymptotic theory that clusters have identical size, and establish that the cluster-robust t statistic continues to have a Gaussian asymptotic null distribution. Second, we determine how variation in cluster sizes, together with other sources of cluster heterogeneity, affect the behavior of the test statistic. To do so, we determine the sample specific measure of cluster heterogeneity that governs this behavior and show that the measure depends on how three quantities vary over clusters: cluster size, the cluster specific error covariance matrix and the actual value of the covariates. Because, in the absence of a fixed design, the third quantity will always vary over clusters, the vast majority of empirical analyses have test statistics whose finite sample behavior is impacted by cluster heterogeneity. To capture this impact, we develop the effective number of clusters, which scales down the actual number of clusters by the measure of cluster heterogeneity. Through simulation we demonstrate this effect and find rejection rates as high as 30 percent for a nominal size of 5 percent. We then apply our measure of cluster heterogeneity in several empirical settings to show how observable variation over clusters impacts the performance of a cluster-robust test.

Chapter 3 Abstract: The escalation in violence in recent years resulting from the Mexican government's war on drug trafficking has caused a large and unprecedented increase in workplace fatality risk for workers in Mexico. We exploit this increase to estimate a compensating differential for fatality risk using panel data constructed from a national employment and occupation survey. We also provide estimates of the value of a statistical life (VSL) in Mexico. Our results imply a VSL between $160,000 and $350,000 U.S dollars for a nationally representative sample of Mexican workers. This is well below the range of estimates typically found in developed countries, which is consistent with the notion that health and safety are normal goods.