This paper develops a specification test for instrument validity in the heterogeneous treatment effect model with a binary treatment and a discrete instrument. The strongest testable implication for instrument validity is given by the condition for nonnegativity of point‐identifiable compliers' outcome densities. Our specification test infers this testable implication using a variance‐weighted Kolmogorov–Smirnov test statistic. The test can be applied to both discrete and continuous outcome cases, and an extension of the test to settings with conditioning covariates is provided.

Abstract Policy makers, firms, and researchers often choose among multiple options based on estimates. Sampling error in the estimates used to guide choice leads to a winner’s curse, since we are more likely to select a given option precisely when we overestimate its effectiveness. This winner’s curse biases our estimates for selected options upward and can invalidate conventional confidence intervals. This article develops estimators and confidence intervals that eliminate this winner’s curse. We illustrate our results by studying selection of job-training programs based on estimated earnings effects and selection of neighborhoods based on estimated economic opportunity. We find that our winner’s curse corrections can make an economically significant difference to conclusions but still allow informative inference.

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set‐identified models by adopting a multiple‐prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set‐identified models and show that they have a well‐defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reduced‐form parameter. The corresponding class of posteriors can be summarized by reporting the ‘posterior lower and upper probabilities’ of a given event and/or the ‘set of posterior means’ and the associated ‘robust credible region’. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulse‐response analysis in set‐identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior.

One of the main objectives of empirical analysis of experiments and quasi‐experiments is to inform policy decisions that determine the allocation of treatments to individuals with different observable covariates. We study the properties and implementation of the Empirical Welfare Maximization (EWM) method, which estimates a treatment assignment policy by maximizing the sample analog of average social welfare over a class of candidate treatment policies. The EWM approach is attractive in terms of both statistical performance and practical implementation in realistic settings of policy design. Common features of these settings include: (i) feasible treatment assignment rules are constrained exogenously for ethical, legislative, or political reasons, (ii) a policy maker wants a simple treatment assignment rule based on one or more eligibility scores in order to reduce the dimensionality of individual observable characteristics, and/or (iii) the proportion of individuals who can receive the treatment is a priori limited due to a budget or a capacity constraint. We show that when the propensity score is known, the average social welfare attained by EWM rules converges at least at n−1/2 rate to the maximum obtainable welfare uniformly over a minimally constrained class of data distributions, and this uniform convergence rate is minimax optimal. We examine how the uniform convergence rate depends on the richness of the class of candidate decision rules, the distribution of conditional treatment effects, and the lack of knowledge of the propensity score. We offer easily implementable algorithms for computing the EWM rule and an application using experimental data from the National JTPA Study.

We develop an optimal policy assignment rule that integrates two distinctive approaches commonly used in economics—targeting by observables and targeting through self‐selection . Our method can be used with experimental or quasi‐experimental data to identify who should be treated, be untreated, and self‐select to achieve a policymaker's objective. Applying this method to a randomized controlled trial on a residential energy rebate program, we find that targeting that optimally exploits both observable data and self‐selection outperforms conventional targeting. We use the Local Average Treatment Effect (LATE) framework (Imbens and Angrist (1994)) to investigate the mechanism in our approach. By estimating several key LATEs based on the random variation created by our experiment, we demonstrate how our method allows policymakers to identify whose self‐selection would be valuable and harmful to social welfare.

Abstract We estimate the impact of piped water and sewers on property values in late 19th century Chicago. The cost of sewer construction depends sensitively on imperceptible variation in elevation, and such variation delays water and sewer service to part of the city. This delay provides quasi-random variation for causal estimates. We extrapolate ate estimates from our natural experiment to the area treated with water and sewer service during 1874-1880 using a new estimator. Water and sewer access increases property values by a factor of about 2.8. This suggests that benefits are large relative to: the value of the value of averted mortality, many other infrastructure projects, and construction costs.