Essays in econometrics

This thesis presents three essays in econometrics that develop methods for experiment design, policy learning, and auction estimation. The first essay develops an adaptive sequential experiment framework for efficient estimation of causal parameters from a broad class of estimands, including average and quantile treatment effects, tail means, and inequality measures. The optimal randomization scheme for each parameter is characterized through Riesz representers, and nonparametric estimators are proposed that consistently estimate the conditional variances needed to guide the experiment toward the optimal scheme. The resulting estimators achieve oracle efficiency, and an accompanying bootstrap procedure provides valid inference. Simulation evidence calibrated to the Oregon Health Experiment illustrates the efficiency gains. The second essay studies optimal policy learning in a transfer setting, where a policymaker uses experimental data from a source population to design treatment assignments for a target population under a budget constraint. Because participation incentives may differ across populations, the policymaker faces uncertainty about compliance behavior. The problem is addressed through a maximin approach and reformulated using Almost First-Order Stochastic Dominance constraints. The resulting optimal policy has an explicit form. It prioritizes individuals expected to comply who have the highest returns to treatment relative to cost. An estimator of the optimal policy is proposed and shown to be consistent. An empirical application to the National Supported Work program illustrates the approach under three social objectives. The third essay studies the two-stage kernel estimator of Guerre et al. (2000) for valuation densities in first-price auctions, where existing asymptotic results assume both bandwidths decay at a common rate. This essay establishes asymptotic normality under unequal rates and, from a pointwise mean squared error perspective, shows through a surrogate criterion that the optimal bandwidth ratio should converge to zero. However, remainder terms in the stochastic expansion prevent a precise characterization. Monte Carlo simulations confirm that the minimizing ratio decreases with sample size, but also that pushing it too low causes a sharp increase in MSE.