Joint Distribution Of Potential Outcomes Research Articles

Nonparametric identification and estimation of the extended Roy model

We propose a new identification method for the extended Roy model, in which the agents maximize their utility rather than just their outcome. We nonparametrically identify the joint distribution of potential outcomes, which is of great importance in causal inference. We exploit the extended Roy model structure and the monotonicity assumption but do not require any functional form assumption nor any support assumption. The identification is achieved by matching the indifferent agents across choices, who are identified by the local instrumental variable method. Based on the identification result, we propose an easy-to-implement nonparametric simulation-based estimator and derive its convergence rate. An empirical illustration on Malawian farmers’ hybrid maize adoption is provided.

Partial identification of the distribution of treatment effects with an application to the Knowledge is Power Program (KIPP)

We bound the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are mutually stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The resulting bounds substantially sharpen bounds based on classical inequalities. We apply our method to estimate bounds on the distribution of effects of attending a Knowledge is Power Program (KIPP) charter school on student achievement, and find that a substantial majority of students' math achievement benefited from attendance, especially those who would have fared poorly in a traditional classroom.

Bounds on distributional treatment effect parameters using panel data with an application on job displacement

This paper develops new techniques to bound distributional treatment effect parameters that depend on the joint distribution of potential outcomes — an object not identified by standard identifying assumptions such as selection on observables or even when treatment is randomly assigned. I show that panel data and an additional assumption on the dependence between untreated potential outcomes for the treated group over time (i) provide more identifying power for distributional treatment effect parameters than existing bounds and (ii) provide a more plausible set of conditions than existing methods that obtain point identification. I apply these bounds to study heterogeneity in the effect of job displacement during the Great Recession. Using standard techniques, I find that workers who were displaced during the Great Recession lost on average 34% of their earnings relative to their counterfactual earnings had they not been displaced. Using the methods developed in the current paper, I also show that the average effect masks substantial heterogeneity across workers.

Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects

This article proposes an identification and estimation method that allows researchers to bound continuous functionals of the joint distribution of potential outcomes from the literature on treatment effects. The focus is on a model where no restrictions are imposed on treatment selection. The method can sharply bound interesting parameters when analytical bounds are difficult to derive, can be used in settings in which instruments are available, and can easily accommodate additional model constraints. However, computational considerations for the method are found to be important and are discussed in detail. Supplementary materials for this article are available online.

Job Displacement during the Great Recession: Tight Bounds on Distributional Treatment Effect Parameters Using Panel Data

This paper develops new techniques to bound distributional treatment effect parameters that depend on the joint distribution of potential outcomes -- an object not identified by standard identifying assumptions such as selection on observables or even when treatment is randomly assigned. I show that panel data and an additional assumption on the dependence between untreated potential outcomes for the treated group over time (i) provide more identifying power for distributional treatment effect parameters than existing bounds and (ii) provide a more plausible set of conditions than existing methods that obtain point identification. I apply these bounds to study heterogeneity in the effect of job displacement during the Great Recession. Using standard techniques, I find that workers who were displaced during the Great Recession lost on average 34% of their earnings relative to their counterfactual earnings had they not been displaced. Using the methods developed in the current paper, I also show that the average effect masks substantial heterogeneity across workers.

A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models

The usual decomposition of effects in corner solution models into extensive and intensive margins is generally incompatible with a causal interpretation. This paper proposes a decomposition based on the joint distribution of potential outcomes which is meaningful in a causal sense. The difference between decompositions can be substantial and yield diametrically opposed results, as shown in a standard Tobit model example. In a generalized Tobit application exploring the effect of reducing firm entry regulation on bilateral trade flows between countries, estimates suggest that using the usual decomposition would overstate the contribution of the extensive margin by around 15%.

Semiparametric Bayesian Estimation for Marginal Parametric Potential Outcome Modeling: Application to Causal Inference

We propose a new semiparametric Bayesian model for causal inference in which assignment to treatment depends on potential outcomes. The model uses the probit stick-breaking process mixture proposed by Chung and Dunson (2009), a variant of the Dirichlet process mixture modeling. In contrast to previous Bayesian models, the proposed model directly estimates the parameters of the marginal parametric model of potential outcomes, while it relaxes the strong ignorability assumption, and requires no parametric model assumption for the assignment model and conditional distribution of the covariate vector. The proposed estimation method is more robust than maximum likelihood estimation, in that it does not require knowledge of the full joint distribution of potential outcomes, covariates, and assignments. In addition, the method is more efficient than fully nonparametric Bayes methods. We apply this model to infer the differential effects of cognitive and noncognitive skills on the wages of production and nonproduction workers using panel data from the National Longitudinal Survey of Youth in 1979. The study also presents the causal effect of online word-of-mouth on Web site browsing behavior. Supplementary materials for this article are available online.

Assessing the heterogeneity of treatment effects via potential outcomes of individual patients.

There is growing interest in understanding the heterogeneity of treatment effects (HTE), which has important implications in treatment evaluation and selection. The standard approach to assessing HTE (i.e. subgroup analyses based on known effect modifiers) is informative about the heterogeneity between subpopulations but not within. It is arguably more informative to assess HTE in terms of individual treatment effects, which can be defined by using potential outcomes. However, estimation of HTE based on potential outcomes is challenged by the lack of complete identifiability. The paper proposes methods to deal with the identifiability problem by using relevant information in baseline covariates and repeated measurements. If a set of covariates is sufficient for explaining the dependence between potential outcomes, the joint distribution of potential outcomes and hence all measures of HTE will then be identified under a conditional independence assumption. Possible violations of this assumption can be addressed by including a random effect to account for residual dependence or by specifying the conditional dependence structure directly. The methods proposed are shown to reduce effectively the uncertainty about HTE in a trial of human immunodeficiency virus.

Interval Estimation of Treatment Effects In Randomized Trials: When do Confidence Intervals Have Nominal Coverage?

SummaryIn the classical theory of randomized trials (RTs), the treatment effect is defined as a mean difference of potential outcomes. To achieve nominal coverage probability for confidence intervals (CIs) on treatment effects in RTs, certain assumptions are necessary. Specifically, one must either make assumptions about the joint distribution of potential outcomes or enroll subjects in the trial by random sampling of the target population on which the treatment effect is defined. In practice, no such sampling usually takes place and assumptions about the joint distribution of potential outcomes cannot be verified based on observed data. Furthermore, the most common of these assumptions, such as treatment‐unit additivity (TUA) or independence are biologically implausible in most RTs involving human subjects. Hence, it is not usually possible to construct CIs on treatment effects with nominal coverage probability. However, for any joint distribution of potential outcomes, the standard estimator of the variance of the difference of two independent sample means produces CIs with asymptotic coverage at least at the nominal level. This interpretation of CIs as conservative bounds may not always hold in conventional regression models applied to RT data.

Sharp Bounds and Testability of a Roy Model of STEM Major Choices

We analyze the empirical content of the Roy model, stripped down to sector-specific unobserved heterogeneity and self-selection on the basis of potential outcomes. We characterize sharp bounds on the joint distribution of potential outcomes and testable implications of the Roy model. We apply these bounds to derive a measure of departure from Roy self-selection, so as to identify prime targets for intervention. Special emphasis is put on the case of binary outcomes. We analyze a Roy model of college major choice in Canada and Germany and take a new look at the underrepresentation of women in science, technology, engineering, and mathematics.

Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regime models with normal mean-variance mixture errors and in the semi-parametric switching regime models of Heckman (1990). Our results for parametric switching regime models with normal mean-variance mixture errors extend some existing results for the Gaussian switching regime model and our results for semi-parametric switching regime models supplement the point identification results of Heckman (1990). Compared with the corresponding sharp bounds when selection is random, we observe that self-selection tightens the bounds on the joint distribution of the potential outcomes and the distribution of treatment effects. These bounds depend on the identified model parameters only and can be easily estimated once the identified model parameters are estimated. The important issue of inference is briefly discussed.

Analysis of treatment response data without the joint distribution of potential outcomes

In this paper we show how it is possible to develop a Bayesian framework for analyzing structural models for treatment response data without the joint distribution of the potential outcomes. That this is possible has not been noticed in the literature. We also discuss the computation of the model marginal likelihood and present recipes for finding relevant treatment effects, averaged over both parameters and covariates. As compared to an approach in which the counterfactuals are part of the prior-posterior analysis (as in the work to date), the approach we suggest is simpler in terms of the required prior inputs, computational burden and extensibility to more complex settings.