This dissertation is a collection of three essays in empirical microeconomics. In the first chapter, I (along with Amit Gandhi and Salvador Navarro) develop a methodology for estimating production functions that, in addition to addressing some of the problems in the production function estimation literature, allows for a greater amount of firm-level heterogeneity. The key to the method lies in using the firm's static input decision as a source of identifying information. In particular, we use the first order condition as a second structural equation that allows us to separate out the endogenous part of the error term in the production function.;In the second chapter, I provide evidence that, contrary to a common empirical finding in the international trade literature, exporting firms do not possess a productivity advantage relative to non-exporting firms. I recover productivity through the estimation of a gross output production function. Using the methodology developed in the first chapter, I am able to control for endogeneity caused by the correlation between inputs and both unobserved productivity and unobserved differences between firm-level prices and the deflator. I argue that the relative productivity of exporters is overestimated for two reasons. The first is the use of value-added as opposed to gross output production functions. The second is the fact that the price received by exporting firms is a mixture of the domestic and foreign prices. With these corrections, I find that the estimated productivity gap between exporting and non-exporting firms decreases to zero. This result is inconsistent with productivity being the main determinant of entry into export markets.;In the third chapter, I (along with Steven Durlauf and Salvador Navarro) provide a general description of the relationship between individual decision problems and aggregate crime regressions. The analysis is designed to elucidate the behavioral and statistical assumptions that are implicit in the use of aggregate crime regressions for both the analysis of crime determinants as well as in counterfactual policy evaluation. We apply our general arguments to the question of the deterrent effect of capital punishment and show how alternative assumptions affect estimates of the deterrent effect.
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