Invalidity of the Bootstrap and the m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities

This paper analyzes the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n bootstrap is valid in finite samples or in a uniform asymptotic sense in general when applied directly to construct CI endpoints. In contrast, other results in the literature show that other ways of applying the bootstrap, m out of n bootstrap, and subsampling do lead to uniformly asymptotically valid confidence sets in moment inequality models. Thus, the uniform asymptotic validity of resampling methods in moment inequality models depends on the way in which the resampling methods are employed.Bootstrap, Coverage probability, m out of n bootstrap, Moment inequality model, Partial identification, Subsampling

Sharp Bounds on Treatment Effects for Policy Evaluation

For counterfactual policy evaluation, it is important to ensure that treatment parameters are relevant to the policies in question. This is especially challenging under unobserved heterogeneity, as is well featured in the definition of the local average treatment effect (LATE). Being intrinsically local, the LATE is known to lack external validity in counterfactual environments. This paper investigates the possibility of extrapolating local treatment effects to different counterfactual settings when instrumental variables are only binary. We propose a novel framework to systematically calculate sharp nonparametric bounds on various policy-relevant treatment parameters that are defined as weighted averages of the marginal treatment effect (MTE). Our framework is flexible enough to incorporate a large menu of identifying assumptions beyond the shape restrictions on the MTE that have been considered in prior studies. We apply our method to understand the effects of medical insurance policies on the use of medical services

Inference for Interval-Identified Parameters Selected from an Estimated Set

Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of individuals' treatment uptake. In this setting, a treatment or policy will typically become an object of interest to the researcher when it is either selected from the estimated set of best-performers or arises from a data-dependent selection rule. In this paper, we develop new inference tools for interval-identified parameters chosen via these forms of selection. We develop three types of confidence intervals for data-dependent and interval-identified parameters, discuss how they apply to several examples of interest and prove their uniform asymptotic validity under weak assumptions

On Quantile Treatment Effects, Rank Similarity, and Variation of Instrumental Variables

This paper investigates how certain relationship between observed and counterfactual distributions serves as an identifying condition for treatment effects when the treatment is endogenous, and shows that this condition holds in a range of nonparametric models for treatment effects. To this end, we first provide a novel characterization of the prevalent assumption restricting treatment heterogeneity in the literature, namely rank similarity. Our characterization demonstrates the stringency of this assumption and allows us to relax it in an economically meaningful way, resulting in our identifying condition. It also justifies the quest of richer exogenous variations in the data (e.g., multi-valued or multiple instrumental variables) in exchange for weaker identifying conditions. The primary goal of this investigation is to provide empirical researchers with tools that are robust and easy to implement but still yield tight policy evaluations

Censored quantile instrumental variable estimation with Stata

Many applications involve a censored dependent variable and an endogenous independent variable. Chernozhukov, Fernandez-Val, and Kowalski (2015) introduced a censored quantile instrumental variable estimator (CQIV) for use in those applications, which has been applied by Kowalski (2016), among others. In this article, we introduce a Stata command, cqiv, that simplifes application of the CQIV estimator in Stata. We summarize the CQIV estimator and algorithm, we describe the use of the cqiv command, and we provide empirical examples.https://arxiv.org/abs/1801.05305First author draf

Bootstrap for Interval Endpoints Defined by Moment Inequalities

This paper analyzes the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n bootstrap is valid in finite samples or in a uniform asymptotic sense in general when applied directly to construct CI endpoints. In contrast, other results in the literature show that other ways of applying the bootstrap, m out of n bootstrap, and subsampling do lead to uniformly asymptotically valid confidence sets in moment inequality models. Thus, the uniform asymptotic validity of resampling methods in moment inequality models depends on the way in which the resampling methods are employed