Identification and Extrapolation of Causal Effects with Instrumental Variables

2018 ◽  
Vol 10 (1) ◽  
pp. 577-613 ◽  
Author(s):  
Magne Mogstad ◽  
Alexander Torgovitsky
Keyword(s):  
Instrumental Variables ◽  
Policy Evaluation ◽  
General Framework ◽  
Unobserved Heterogeneity ◽  
Causal Effect ◽  
Partial Identification ◽  
Causal Effects ◽  
Average Causal Effect ◽  
Special Cases ◽  
Selection On Unobservables

Instrumental variables (IV) are widely used in economics to address selection on unobservables. Standard IV methods produce estimates of causal effects that are specific to individuals whose behavior can be manipulated by the instrument at hand. In many cases, these individuals are not the same as those who would be induced to treatment by an intervention or policy of interest to the researcher. The average causal effect for the two groups can differ significantly if the effect of the treatment varies systematically with unobserved factors that are correlated with treatment choice. We review the implications of this type of unobserved heterogeneity for the interpretation of standard IV methods and for their relevance to policy evaluation. We argue that making inferences about policy-relevant parameters typically requires extrapolating from the individuals affected by the instrument to the individuals who would be induced to treatment by the policy under consideration. We discuss a variety of alternatives to standard IV methods that can be used to rigorously perform this extrapolation. We show that many of these approaches can be nested as special cases of a general framework that embraces the possibility of partial identification.

Causal inference via string diagram surgery

2021 ◽  
pp. 1-22
Author(s):  
Bart Jacobs ◽  
Aleks Kissinger ◽  
Fabio Zanasi
Keyword(s):  
Causal Inference ◽  
Probabilistic Reasoning ◽  
Causal Effect ◽  
Sufficient Conditions ◽  
Causal Effects ◽  
Stochastic Matrices ◽  
Counterfactual Reasoning ◽  
Special Cases ◽  
String Diagram ◽  
Set Up

Abstract Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endo-functor which performs ‘string diagram surgery’ within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on two well-known toy examples: one where we predict the causal effect of smoking on cancer in the presence of a confounding common cause and where we show that this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature; the other one is an illustration of counterfactual reasoning where the same interventional techniques are used, but now in a ‘twinned’ set-up, with two version of the world – one factual and one counterfactual – joined together via exogenous variables that capture the uncertainties at hand.

Circulating adiponectin levels and systemic lupus erythematosus: a two-sample Mendelian randomization study

Rheumatology ◽  
2020 ◽  
Author(s):  
Yi-Lin Dan ◽  
Peng Wang ◽  
Zhongle Cheng ◽  
Qian Wu ◽  
Xue-Rong Wang ◽  
...  
Keyword(s):  
Single Nucleotide Polymorphisms ◽  
Instrumental Variables ◽  
Mendelian Randomization ◽  
Causal Effect ◽  
Causal Effects ◽  
European Ancestry ◽  
Nucleotide Polymorphisms ◽  
Single Nucleotide ◽  
Inverse Variance ◽  
Weighted Median

Abstract Objectives Several studies have reported increased serum/plasma adiponectin levels in SLE patients. This study was performed to estimate the causal effects of circulating adiponectin levels on SLE. Methods We selected nine independent single-nucleotide polymorphisms that were associated with circulating adiponectin levels (P < 5 × 10−8) as instrumental variables from a published genome-wide association study (GWAS) meta-analysis. The corresponding effects between instrumental variables and outcome (SLE) were obtained from an SLE GWAS analysis, including 7219 cases with 15 991 controls of European ancestry. Two-sample Mendelian randomization (MR) analyses with inverse-variance weighted, MR-Egger regression, weighted median and weight mode methods were used to evaluate the causal effects. Results The results of inverse-variance weighted methods showed no significantly causal associations of genetically predicted circulating adiponectin levels and the risk for SLE, with an odds ratio (OR) of 1.38 (95% CI 0.91, 1.35; P = 0.130). MR-Egger [OR 1.62 (95% CI 0.85, 1.54), P = 0.195], weighted median [OR 1.37 (95% CI 0.82, 1.35), P = 0.235) and weighted mode methods [OR 1.39 (95% CI 0.86, 1.38), P = 0.219] also supported no significant associations of circulating adiponectin levels and the risk for SLE. Furthermore, MR analyses in using SLE-associated single-nucleotide polymorphisms as an instrumental variable showed no associations of genetically predicted risk of SLE with circulating adiponectin levels. Conclusion Our study did not find evidence for a causal relationship between circulating adiponectin levels and the risk of SLE or of a causal effect of SLE on circulating adiponectin levels.

scholarly journals Data-Adaptive Causal Effects and Superefficiency

2016 ◽  
Vol 4 (2) ◽  
Author(s):  
Peter M. Aronow
Keyword(s):  
Causal Inference ◽  
Empirical Distribution ◽  
Causal Effect ◽  
Short Note ◽  
Causal Effects ◽  
Asymptotically Normal ◽  
Average Causal Effect ◽  
Population Average ◽  
Data Adaptive ◽  
Local Average

AbstractRecent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can potentially be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root-$n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect.

scholarly journals Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

2018 ◽  
Vol 43 (5) ◽  
pp. 540-567 ◽  
Author(s):  
Jiannan Lu ◽  
Peng Ding ◽  
Tirthankar Dasgupta
Keyword(s):  
Causal Effect ◽  
Real Life ◽  
Causal Effects ◽  
Potential Outcomes ◽  
Randomized Experiments ◽  
Sharp Bounds ◽  
Average Causal Effect ◽  
Behavioral Studies ◽  
And Control ◽  
Potential Outcomes Framework

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

Estimating Causal Effects From Multilevel Group-Allocation Data

2005 ◽  
Vol 30 (4) ◽  
pp. 397-412 ◽  
Author(s):  
Alix I. Gitelman
Keyword(s):  
Group Membership ◽  
Causal Effect ◽  
Hierarchical Linear Model ◽  
Dynamic Effect ◽  
Educational Interventions ◽  
Causal Effects ◽  
Group Dynamic ◽  
Average Causal Effect ◽  
Effect Of Treatment ◽  
Group Allocation

In group-allocation studies for comparing behavioral, social, or educational interventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are developed to provide a structure for specifying causal effects of treatment in the multilevel setting. An average causal effect of treatment cannot be specified, however, without a simplifying assumption of group-membership invariance (i.e., no group-dynamic effect). Under group-membership invariance and ignorability assumptions, the average causal effect is then connected to estimable quantities of the hierarchical linear model (HLM). Furthermore, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect.

The Causal Effect of Federal Work-Study Participation

2011 ◽  
Vol 33 (4) ◽  
pp. 506-527 ◽  
Author(s):  
Judith Scott-Clayton
Keyword(s):  
Instrumental Variables ◽  
Causal Effect ◽  
Causal Effects ◽  
Work Study ◽  
Study Participation ◽  
Negative Effects ◽  
Full Sample ◽  
Positive Effects ◽  
Quasi Experimental ◽  
Student Employees

Since 1964, the Federal Work-Study (FWS) program has provided funds to subsidize the wages of student employees, but it has never been studied directly. I use an instrumental variables difference-in-difference framework with administrative data from West Virginia to identify causal effects, comparing eligible and ineligible students across institutions with higher and lower FWS availability and using differences in FWS availability to instrument for actual FWS participation. I find no evidence that FWS participation improves academic outcomes for the full sample, but this masks significant negative effects for women and some significant positive effects for men. Although results should be interpreted cautiously given limitations of the sample, they represent the first direct, quasi-experimental evidence regarding the effect of the program.

scholarly journals Testing for the Unconfoundedness Assumption Using an Instrumental Assumption

2014 ◽  
Vol 2 (2) ◽  
pp. 187-199 ◽  
Author(s):  
Xavier de Luna ◽  
Per Johansson
Keyword(s):  
Simulation Study ◽  
Instrumental Variable ◽  
Observational Studies ◽  
Causal Effect ◽  
Causal Effects ◽  
Nonparametric Identification ◽  
Average Causal Effect

AbstractThe identification of average causal effects of a treatment in observational studies is typically based either on the unconfoundedness assumption (exogeneity of the treatment) or on the availability of an instrument. When available, instruments may also be used to test for the unconfoundedness assumption. In this paper, we present a set of assumptions on an instrumental variable which allows us to test for the unconfoundedness assumption, although they do not necessarily yield nonparametric identification of an average causal effect. We propose a test for the unconfoundedness assumption based on the instrumental assumptions introduced and give conditions under which the test has power. We perform a simulation study and apply the results to a case study where the interest lies in evaluating the effect of job practice on employment.

Heterogeneous Returns to Training

2006 ◽  
Vol 226 (1) ◽  
Author(s):  
Anja Kuckulenz ◽  
Michael Maier
Keyword(s):  
Instrumental Variables ◽  
Unobserved Heterogeneity ◽  
Empirical Work ◽  
Expected Return ◽  
Returns To Schooling ◽  
Recent Advances ◽  
Returns To Training ◽  
The Impact ◽  
Selection On Unobservables

SummaryEmpirical work on the wage impact of training has noted that unobserved heterogeneity of training participants should play a role. The expected return to training, which partly depends on unobservable characteristics, is likely to be a crucial criterion in the decision to take part in training or not. We try to account for this fact by using recent advances in estimating returns to schooling, which allow for selection on unobservables, and apply it to estimating the impact of training on earnings. Allowing heterogeneity to be unobserved by the econometrician, but assuming that individuals may act upon this heterogeneity, completely changes the interpretation and properties of commonly used estimators. Our results based on local instrumental variables suggest that traditional estimates of the wage impact of training overestimate this effect.

scholarly journals Asymptotic theory of rerandomization in treatment–control experiments

2018 ◽  
Vol 115 (37) ◽  
pp. 9157-9162 ◽  
Author(s):  
Xinran Li ◽  
Peng Ding ◽  
Donald B. Rubin
Keyword(s):  
Asymptotic Theory ◽  
Causal Effect ◽  
Random Variable ◽  
Causal Effects ◽  
Equal Treatment ◽  
Finite Sample ◽  
Previous Theory ◽  
Covariate Balance ◽  
Average Causal Effect ◽  
The Difference

Although complete randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.

scholarly journals Minimum Intervention Cover of a Causal Graph

2019 ◽  
Vol 33 ◽  
pp. 2876-2885
Author(s):  
Saravanan Kandasamy ◽  
Arnab Bhattacharyya ◽  
Vasant G. Honavar
Keyword(s):  
Artificial Intelligence ◽  
Computational Complexity ◽  
Causal Model ◽  
Causal Effect ◽  
Practical Interest ◽  
Causal Effects ◽  
Causal Graph ◽  
Special Cases

Eliciting causal effects from interventions and observations is one of the central concerns of science, and increasingly, artificial intelligence. We provide an algorithm that, given a causal graph G, determines MIC(G), a minimum intervention cover of G, i.e., a minimum set of interventions that suffices for identifying every causal effect that is identifiable in a causal model characterized by G. We establish the completeness of do-calculus for computing MIC(G). MIC(G) effectively offers an efficient compilation of all of the information obtainable from all possible interventions in a causal model characterized by G. Minimum intervention cover finds applications in a variety of contexts including counterfactual inference, and generalizing causal effects across experimental settings. We analyze the computational complexity of minimum intervention cover and identify some special cases of practical interest in which MIC(G) can be computed in time that is polynomial in the size of G.

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