Essays on econometrics and economic theory

Abstract

This thesis consists of three chapters. The first chapter extends the recent result of Athey and Wager on the asymptotic normality of random forest estimators to a multivariate setting; in particular, we examine stability properties and bounds for certain classes of tree estimators, and provide guidance and heuristics that make our results useful for practitioners. The second chapter studies a continuous-time principal-agent model for risky projects in which success is binary and not quantifiable. We consider optimal incentive contracts which feature two components: a flow payment that is paid out at each moment and a lump-sum bonus that is paid on project success. We characterize the optimal solution and calibrate our model to data on executive compensation. The final chapter studies speed and competition in trading venues, in particular those for illiquid markets. We show that differences in trading speeds among different venues lead to endogenous market segmentation, thus increasing trading volume and overall liquidity. We also examine equilibria and various notions of welfare in an entry game in which an entrant has the option to create a faster trading venue and compete against an incumbent.