Many settings in empirical economics involve estimation of a large number of parameters. In such settings, methods that combine regularized estimation and data-driven choices of regularization parameters are useful. We provide guidance to applied researchers on the choice between regularized estimators and data-driven selection of regularization parameters. We characterize the risk and relative performance of regularized estimators as a function of the data-generating process and show that data-driven choices of regularization parameters yield estimators with risk uniformly close to the risk attained under the optimal (unfeasible) choice of regularization parameters. We illustrate using examples from empirical economics.

Some empirical results are more likely to be published than others. Selective publication leads to biased estimates and distorted inference. We propose two approaches for identifying the conditional probability of publication as a function of a study’s results, the first based on systematic replication studies and the second on meta-studies. For known conditional publication probabilities, we propose bias-corrected estimators and confidence sets. We apply our methods to recent replication studies in experimental economics and psychology, and to a meta-study on the effect of the minimum wage. When replication and meta-study data are available, we find similar results from both.

Standard experimental designs are geared toward point estimation and hypothesis testing, while bandit algorithms are geared toward in‐sample outcomes. Here, we instead consider treatment assignment in an experiment with several waves for choosing the best among a set of possible policies (treatments) at the end of the experiment. We propose a computationally tractable assignment algorithm that we call “exploration sampling,” where assignment probabilities in each wave are an increasing concave function of the posterior probabilities that each treatment is optimal. We prove an asymptotic optimality result for this algorithm and demonstrate improvements in welfare in calibrated simulations over both non‐adaptive designs and bandit algorithms. An application to selecting between six different recruitment strategies for an agricultural extension service in India demonstrates practical feasibility.

We consider the problem of repeatedly choosing policies to maximize social welfare. Welfare is a weighted sum of private utility and public revenue. Earlier outcomes inform later policies. Utility is not observed, but indirectly inferred. Response functions are learned through experimentation. We derive a lower bound on regret, and a matching adversarial upper bound for a variant of the Exp3 algorithm. Cumulative regret grows at a rate of T 2/3 . This implies that (i) welfare maximization is harder than the multiarmed bandit problem (with a rate of T 1/2 for finite policy sets), and (ii) our algorithm achieves the optimal rate. For the stochastic setting, if social welfare is concave, we can achieve a rate of T 1/2 (for continuous policy sets), using a dyadic search algorithm. We analyze an extension to nonlinear income taxation, and sketch an extension to commodity taxation. We compare our setting to monopoly pricing (which is easier), and price setting for bilateral trade (which is harder).