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Abstract The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently in the absence of treatment, namely if the parallel trends assumption is violated. We propose a general identification strategy that leverages two groups of control units whose outcomes relative to the treated units exhibit a negative correlation, and achieves partial identification of the average treatment effect for the treated. The identified set is of a union bounds form that involves the minimum and maximum operators, which makes the canonical bootstrap generally inconsistent and naive methods overly conservative. By using the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we theoretically establish the asymptotic validity of the proposed method. We develop a simple falsification test and sensitivity analysis. We apply the proposed strategy for bracketing to study whether minimum wage laws affect employment levels. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We investigate the efficacy of surgical versus nonsurgical management for two gastrointestinal conditions, colitis and diverticulitis, using observational data. We deploy an instrumental variable design with surgeons' tendencies to operate as an instrument. Assuming instrument validity, we find that nonsurgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for nonseptic patients. The validity of our instrument is plausible but not ironclad, necessitating a sensitivity analysis. Existing sensitivity analyses for IV designs assume effect homogeneity, unlikely to hold here because of patient-specific physiology. We develop a new sensitivity analysis that accommodates arbitrary effect heterogeneity and exploits components explainable by observed features. We find that the results for nonseptic patients prove more robust to hidden bias despite having smaller estimated effects. For nonseptic patients, two individuals with identical observed characteristics would have to differ in their odds of assignment to a high tendency to operate surgeon by a factor of 2.34 to overturn our finding of a benefit for nonsurgical management in reducing length of stay. For septic patients, this value is only 1.64. Simulations illustrate that this phenomenon may be explained by differences in within-group heterogeneity. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Pretreatment selection or censoring ("selection on treatment") can occur when two treatment levels are compared ignoring the third option of neither treatment, in "censoring by death" settings where treatment is only defined for those who survive long enough to receive it, or in general in studies where the treatment is only defined for a subset of the population. Unfortunately, the standard instrumental variable (IV) estimand is not defined in the presence of such selection, so we consider estimating a new survivor-complier causal effect. Although this effect is generally not identified under standard IV assumptions, it is possible to construct sharp bounds. We derive these bounds and give a corresponding data-driven sensitivity analysis, along with nonparametric yet efficient estimation methods. Importantly, our approach allows for high-dimensional confounding adjustment, and valid inference even after employing machine learning. Incorporating covariates can tighten bounds dramatically, especially when they are strong predictors of the selection process. We apply the methods in a UK cohort study of critical care patients to examine the mortality effects of prompt admission to the intensive care unit, using ICU bed availability as an instrument. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In policy evaluations, interest may focus on why a particular treatment works. One tool for understanding why treatments work is causal mediation analysis. In this essay, I focus on the assumptions needed to estimate mediation effects. I show that there is no “gold standard” method for the identification of causal mediation effects. In particular, mediation effects will always have the character of estimates from observational data since they are generally subject to a specific form of confounding. Additionally, I demonstrate how randomization of the mediator and instrumental variables methods lead to fundamentally different quantities than causal mediation analyses. I also review recent work that discusses how the assumptions of mediation analyses differ when there is treatment noncompliance or when there are multiple mediators. Throughout, I motivate concepts using path diagrams and an example of a classroom intervention designed to increase test scores. [ABSTRACT FROM AUTHOR]

Causal analysis in program evaluation has primarily focused on the question about whether or not a program, or package of policies, has an impact on the targeted outcome of interest. However, it is often of scientific and practical importance to also explain why such impacts occur. In this paper, we introduce causal mediation analysis, a statistical framework for analyzing causal mechanisms that has become increasingly popular in social and medical sciences in recent years. The framework enables us to show exactly what assumptions are sufficient for identifying causal mediation effects for the mechanisms of interest, derive a general algorithm for estimating such mechanism-specific effects, and formulate a sensitivity analysis for the violation of those identification assumptions. We also discuss an extension of the framework to analyze causal mechanisms in the presence of treatment noncompliance, a common problem in randomized evaluation studies. The methods are illustrated via applications to two intervention studies on pre-school classes and job-training workshops. [ABSTRACT FROM AUTHOR]

Mediation analysis has been extensively applied in psychological and other social science research. A number of methodologists have recently developed a formal theoretical framework for mediation analysis from a modem causal inference perspective. In Imai, Keele, and Tingley (2010), we have offered such an approach to causal mediation analysis that formalizes identification, estimation, and sensitivity analysis in a single framework. This approach has been used by a number of substantive researchers, and in subsequent work we have also further extended it to more complex settings and developed new research designs. In an insightful article, Pearl (2014) proposed an alternative approach that is based on a set of assumptions weaker than ours. In this comment, we demonstrate that the theoretical differences between our identification assumptions and his alternative conditions are likely to be of little practical relevance in the substantive research settings faced by most psychologists and other social scientists. We also show that our proposed estimation algorithms can be easily applied in the situations discussed in Pearl (2014). The methods discussed in this comment and many more are implemented via mediation, an open-source software (Tingley, Yamamoto, Hirose, Keele, & Imai, 2013). [ABSTRACT FROM AUTHOR]

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the inability to specify the key identification assumption, and the difficulty of extending the framework to nonlinear models. In this article, we propose an alternative approach that overcomes these limitations. Our approach is general because it offers the definition, identification, estimation, and sensitivity analysis of causal mediation effects without reference to any specific statistical model. Further, our approach explicitly links these 4 elements closely together within a single framework. As a result, the proposed framework can accommodate linear and nonlinear relationships, parametric and nonparametric models, continuous and discrete mediators, and various types of outcome variables. The general definition and identification result also allow us to develop sensitivity analysis in the context of commonly used models, which enables applied researchers to formally assess the robustness of their empirical conclusions to violations of the key assumption. We illustrate our approach by applying it to the Job Search Intervention Study. We also offer easy-to-use software that implements all our proposed methods. [ABSTRACT FROM AUTHOR]