Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review

This paper provides a review of methodological advancements in the evaluation of heterogeneous treatment effect models based on instrumental variable (IV) methods. We focus on models that achieve identification through a monotonicity assumption on the selection equation and analyze local average and quantile treatment effects for the subpopulation of compliers. We start with a comprehensive discussion of the binary treatment and binary instrument case which is relevant for instance in randomized experiments with imperfect compliance. We then review extensions to identification and estimation with covariates, multi-valued and multiple treatments and instruments, outcome attrition and measurement error, and the identification of direct and indirect treatment effects, among others. We also discuss testable implications and possible relaxations of the IV assumptions, approaches to extrapolate from local to global treatment effects, and the relationship to other IV approaches

Generic inference on quantile and quantile effect functions for discrete outcomes

Quantile and quantile effect functions are important tools for descriptive and inferential analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This paper offers a simple, practical construction of simultaneous confidence bands for quantile and quantile effect functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling strategies and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. Our analysis generates new, interesting empirical findings, and complements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering existing inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.https://arxiv.org/abs/1608.05142First author draf

Distributional conformal prediction

We propose a robust method for constructing conditionally valid prediction intervals based on regression models for conditional distributions such as quantile and distribution regression. Our approach exploits the probability integral transform and relies on permuting estimated ``ranks'' instead of regression residuals. Unlike residuals, these ranks are independent of the covariates, which allows us to establish the conditional validity of the resulting prediction intervals under consistent estimation of the conditional distributions. We also establish theoretical performance guarantees under arbitrary model misspecification. The usefulness of the proposed method is illustrated based on two applications. First, we study the problem of predicting daily returns using realized volatility. Second, we consider a synthetic control setting where the goal is to predict a country's counterfactual GDP growth rate based on the contemporaneous GDP growth rates of other countries

Selection and parallel trends

One of the perceived advantages of difference-in-differences (DiD) methods is that they do not explicitly restrict how units select into treatment. However, when justifying DiD, researchers often argue that the treatment is "quasi-randomly" assigned. We investigate what selection mechanisms are compatible with the parallel trends assumptions underlying DiD. We derive necessary conditions for parallel trends that clarify whether and how selection can depend on time-invariant and time-varying unobservables. Motivated by these necessary conditions, we suggest a menu of interpretable sufficient conditions for parallel trends, thereby providing the formal underpinnings for justifying DiD based on contextual information about selection into treatment. We provide results for both separable and nonseparable outcome models and show that this distinction has implications for the use of covariates in DiD analyses

Set Identification of Generalized Linear Predictors in the Presence of Non-Classical Measurement Errors

This paper studies the identification of coefficients in generalized linear predictors where the outcome variable suffers from non-classical measurement errors. Combining a mixture model of data errors with the bounding procedure proposed by Stoye (2007), I derive bounds on the coefficient vector under different non-parametric assumptions about the structure of the measurement error. The method is illustrated by analyzing a simple earnings equation

A Comparison of two Qantile Models with Endogeneity

This paper analyzes estimators based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2004, 2005, 2006) under the local quantile treatment effects (LQTE) framework (Abadie et al., 2002). I show that the quantile treatment effect (QTE) estimators in the IVQR model are equivalent to LQTE for the compliers at transformed quantile levels. This transformation adjusts for differences between the subpopulation-specific potential outcome distributions that are identified in the LQTE model. Moreover, the IVQR estimator of the average treatment effect (ATE) corresponds to a convex combination of the local average treatment effect (LATE) and a weighted average of LQTE for the compliers. I extend the analysis to more general setups that allow for partial failures of the LQTE assumptions, non-binary instruments, and covariates. The results are illustrated with two empirical applications

Semiparametric estimation of quantile treatment effects with endogeneity

This paper studies estimation of conditional and unconditional quantile treatment effects based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2004, 2005, 2006). I introduce a class of semiparametric plug-in estimators based on closed form solutions derived from the IVQR moment conditions. These estimators do not rely on separability of the structural quantile function, while retaining computational tractability and root-n-consistency. Functional central limit theorems and bootstrap validity results for the estimators of the quantile treatment effects and other functionals are provided. I apply my method to reanalyze the effect of 401(k) plans on individual savings behavior

Evaluating pay-as-you-go social security systems

This paper proposes a new method for welfare analysis of unfunded social security systems. Based on an overlapping generations model with endogenous labor supply, we derive a formula for the evaluation of existing pay-as-you-go social security systems that depends on impulse response functions and projected growth rates only. We propose an implementation strategy based on reduced form estimates of a VAR model that is valid under weak assumptions about the deep structure of the model. Our method is related to the sufficient statistic approach (Chetty, 2009). For the current system in the United States, we find that a transitory increase in the payroll tax rate along with higher pension benefits leads to a welfare increase mainly due to welfare gains of today’s retirees. A scenario analysis demonstrates the robustness of this result

Evaluating pay-as-you-go social security systems

This paper proposes a method for the welfare analysis of pay-as-you-go social security systems. We derive a formula for the welfare consequences of a permanent marginal change in the payroll tax rate that is valid under weak assumptions about the deep structure of the economy. Our approach requires neither a full specification of preferences and technology, nor knowledge of the individual savings behavior. Instead of parameterizing and calibrating the deep model structure, we implement our formula based on reduced form estimates of a VAR model. We apply our method to evaluate the social security system in the United States