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We can use structural causal models (SCMs) to help us evaluate the consequences of actions given data. SCMs identify actions with structural interventions. A careful decision maker may wonder whether this identification is justified. We seek such a justification. We begin with decision models , which map actions to distributions over outcomes but avoid additional causal assumptions. We then examine assumptions that could justify causal interventions, with a focus on symmetry. First, we introduce conditionally independent and identical responses (CIIR), a generalisation of the IID assumption to decision models. CIIR justifies identifying actions with interventions, but is often an implausible assumption. We consider an alternative: precedent is the assumption that “what I can do has been done before, and its consequences observed,” and is generally more plausible than CIIR. We show that precedent together with independence of causal mechanisms (ICM) and an observed conditional independence can justify identifying actions with causal interventions. ICM has been proposed as an alternative foundation for causal modelling, but this work suggests that it may in fact justify the interventional interpretation of causal models.

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this article, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves (EICs) of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox.

Time-dependent coarse structural nested mean models (coarse SNMMs) were developed to estimate treatment effects from longitudinal observational data. Coarse SNMMs estimate the combined effect of multiple treatment dosages and are thus useful to estimate the effect of treatments that are initiated and then never stopped. Coarse SNMMs lead to a large class of estimators, with widely varying estimates and standard errors. To optimize precision, we derive an explicit solution for the optimal coarse SNMM estimator. We apply our methods by estimating how the effect on immune reconstitution of initiating 1 year of ART depends on the time between HIV infection and ART initiation, in the early stages of HIV infection. The CDC and the WHO are encouraging HIV testing, leading to earlier HIV diagnoses. Thus, more treatment decisions need to be made in early and acute infection. However, evidence is lacking about the clinical benefits of initiating ART in early and acute HIV infection, with guidelines developed mostly from analyzing patients with chronic infection. In the simulations and our motivating HIV application, naive coarse SNMM estimators render useless inference, whereas our new fitting methods render informative analyses. We thus hope that this article leads to broader applicability of SNMMs.

The Oaxaca-Blinder (OB) decomposition is a widely used method to explain social disparities. However, assigning causal meaning to its estimated components requires strong assumptions that often lack explicit justification. This article emphasizes the importance of clearly defined estimands and their identification when targeting mediating mechanisms of social disparities. Three approaches are distinguished on the basis of their scientific questions and assumptions: a mediation approach and two interventional approaches. The OB decomposition and Monte Carlo simulation-based g-computation are discussed for estimation in relation to these approaches. The latter method is used in an interventional effects analysis of the observed gender pay gap in Western Germany, using data from the 2017 German Socio-Economic Panel. Ten mediators are considered, including indicators of human capital and job characteristics. Key findings indicate that the gender pay gap in log hourly wages could be reduced by up to 86% if these mediators were equally distributed between women and men. Substantial reductions could be achieved by aligning full-time employment and work experience.

In an observational study, it is common to leverage known null effects to detect bias. One such strategy is to set aside a placebo sample – a subset of data immune from the hypothesized cause-and-effect relationship. Existence of an effect in the placebo sample raises concerns about unmeasured confounding bias while the absence of it helps corroborate the causal conclusion. This article describes a framework for using a placebo sample to detect and remove bias. We state the identification assumptions and develop estimation and inference methods based on outcome regression, inverse probability weighting, and doubly robust approaches. Simulation studies investigate the finite-sample performance of the proposed methods. We illustrate the methods using an empirical study of the effect of the earned income tax credit on infant health.

Combining observational and experimental data for causal inference can improve treatment effect estimation. However, many observational datasets cannot be released due to data privacy considerations, so one researcher may not have access to both experimental and observational data. Nonetheless, a small amount of risk of disclosing sensitive information might be tolerable to organizations that house confidential data. In these cases, organizations can employ data privacy techniques, which decrease disclosure risk, potentially at the expense of data utility. In this study, we explore disclosure limiting transformations of observational data, which can be combined with experimental data to estimate the sample and population average treatment effects. We consider leveraging observational data to improve generalizability of treatment effect estimates, when a randomized controlled trial (RCT) is not representative of the population of interest, and to increase precision of treatment effect estimates. Through simulation studies, we illustrate the trade-off between privacy and utility when employing different disclosure limiting transformations. We find that leveraging transformed observational data in treatment effect estimation can still improve estimation over only using data from an RCT.

Confounding bias and selection bias bring two significant challenges to the validity of conclusions drawn from applied causal inference. The latter can stem from informative missingness, such as in cases of attrition. We introduce the sequential adjustment criteria , which extend available graphical conditions for recovering causal effects from confounding and attrition using sequential regressions, allowing for the inclusion of postexposure and forbidden variables in the adjustment sets. We propose an estimator for the recovered average treatment effect based on targeted minimum-loss estimation , which exhibits multiple robustness under certain technical conditions. This approach ensures consistency even in scenarios where the double inverse probability weighting and the naïve plug-in sequential regressions approaches fall short. Through a simulation study, we assess the performance of the proposed estimator against alternative methods across different graph setups and model specification scenarios. As a motivating application, we examine the effect of pharmacological treatment for attention-deficit/hyperactivity disorder upon the scores obtained by diagnosed Norwegian schoolchildren in national tests using observational data ( n = 9,352 n=\hspace{0.1em}\text{9,352}\hspace{0.1em} ). Our findings align with the accumulated clinical evidence, affirming a positive but small impact of medication on academic achievement.

In causal inference, the joint law of a set of counterfactual random variables is generally not identified. But many interesting quantities are functions of the joint distribution. For example, the individual treatment effect is a difference of counterfactuals and any functional of this difference such as the variance, the quantiles and density, all depend on this joint distribution. For binary treatments, many researchers have found identifiable bounds on these quantities. We extend this idea to continuous treatments. We show that a conservative version of the joint law – corresponding to the smallest treatment effect – is identified. The notion of “conservative” depends on how we choose to measure the causal effect and we consider a few such measures. Finding this law uses recent results from optimal transport theory. Under this conservative law we can bound causal effects and we may construct inferences for each individual’s counterfactual dose-response curve. Intuitively, this is the flattest counterfactual curve for each subject that is consistent with the distribution of the observables. If the outcome is univariate then, under mild conditions, this curve is simply the quantile function of the counterfactual distribution that passes through the observed point. This curve corresponds to a nonparametric rank preserving structural model.

Causal inference methods for treatment effect estimation usually assume independent units. However, this assumption is often questionable because units may interact, resulting in spillover effects between them. We develop augmented inverse probability weighting (AIPW) for estimation and inference of the expected average treatment effect (EATE) with observational data from a single (social) network with spillover effects. In contrast to overall effects such as the global average treatment effect, the EATE measures, in expectation and on average over all units, how the outcome of a unit is causally affected by its own treatment, marginalizing over the spillover effects from other units. We develop cross-fitting theory with plugin machine learning to obtain a semiparametric treatment effect estimator that converges at the parametric rate and asymptotically follows a Gaussian distribution. The asymptotics are developed using the dependency graph rather than the network graph, which makes explicit that we allow for spillover effects beyond immediate neighbors in the network. We apply our AIPW method to the Swiss StudentLife Study data to investigate the effect of hours spent studying on exam performance accounting for the students’ social network.

We consider the problem of learning a directed graph G ⋆ {G}^{\star } from observational data. We assume that the distribution that gives rise to the samples is Markov and faithful to the graph G ⋆ {G}^{\star } and that there are no unobserved variables. We do not rely on any further assumptions regarding the graph or the distribution of the variables. Particularly, we allow for directed cycles in G ⋆ {G}^{\star } and work in the fully nonparametric setting. Given the set of conditional independence statements satisfied by the distribution, we aim to find a directed graph, which satisfies the same d d -separation statements as G ⋆ {G}^{\star } . We propose a hybrid approach consisting of two steps. We first find a partially ordered partition of the vertices of G ⋆ {G}^{\star } by optimizing a certain score in a greedy fashion. We prove that any optimal partition uniquely characterizes the Markov equivalence class of G ⋆ {G}^{\star } . Given an optimal partition, we propose an algorithm for constructing a graph in the Markov equivalence class of G ⋆ {G}^{\star } whose strongly connected components correspond to the elements of the partition, and which are partially ordered according to the partial order of the partition. Our algorithm comes in two versions – one that is provably correct and another one that performs fast in practice.

We propose a set of causal estimands that we call “the mediated probabilities of causation.” These estimands quantify the probabilities that an observed negative outcome was induced via a mediating pathway versus a direct pathway in a stylized setting involving a binary exposure or intervention, a single binary mediator, and a binary outcome. We outline a set of conditions sufficient to identify these effects given observed data and propose a doubly robust projection-based estimation strategy that allows for the use of flexible nonparametric and machine learning methods for estimation. We argue that these effects may be more relevant than the probability of causation, particularly in settings where we observe both some negative outcome and negative mediating event, and we wish to distinguish between settings where the outcome was induced via the exposure inducing the mediator versus the exposure inducing the outcome directly. We motivate these estimands by discussing applications to legal and medical questions of causal attribution.

In recent years, the field of causal inference from observational data has emerged rapidly. The literature has focused on (conditional) average causal effect estimation. When (remaining) variability of individual causal effects (ICEs) is considerable, average effects may be uninformative for an individual. The fundamental problem of causal inference precludes estimating the joint distribution of potential outcomes without making assumptions. In this work, we show that the ICE distribution is identifiable under (conditional) independence of the individual effect and the potential outcome under no exposure, in addition to the common assumptions of consistency, positivity, and conditional exchangeability. Moreover, we present a family of flexible latent variable models that can be used to study individual effect modification and estimate the ICE distribution from cross-sectional data. How such latent variable models can be applied and validated in practice is illustrated in a case study on the effect of hepatic steatosis on a clinical precursor to heart failure. Under the assumptions presented, we estimate that 20.6% (95% Bayesian credible interval: 8.9%, 33.6%) of the population has a harmful effect greater than twice the average causal effect.

Marine conservation preserves fish biodiversity, protects marine and coastal ecosystems, and supports climate resilience and adaptation. Despite the importance of establishing marine protected areas (MPAs), research on the effectiveness of MPAs with different conservation policies is limited due to the lack of quantitative MPA information. In this article, by leveraging a global MPA database, we investigate the causal impact of MPA policies on fish biodiversity. To address challenges posed by this clustered and confounded observational study, we construct a bias-corrected matching estimator of the average treatment effect assuming treatment is assigned at the cluster level and a cluster-weighted bootstrap method for variance estimation. We establish the theoretical guarantees of the matching estimator and its variance estimator. Under our proposed matching framework, we recommend matching on both cluster-level and unit-level covariates to achieve efficiency. The simulation study results demonstrate that our matching strategy minimizes the bias and achieves the nominal confidence interval coverage. Applying our proposed matching method to compare different MPA policies reveals that the no-take policy is more effective than the multi-use policy in preserving fish biodiversity.

We present a new method for causal discovery in linear structural vector autoregressive models. We adapt an idea designed for independent observations to the case of time series while retaining its favorable properties, i.e., explicit error control for false causal discovery, at least asymptotically. We apply our method to several real-world bivariate time series datasets and discuss its findings that mostly agree with common understanding. The arrow of time in a model can be interpreted as background knowledge on possible causal mechanisms. Hence, our ideas could be extended to incorporating different background knowledge, even for independent observations.

Synthetic control methods are widely used to estimate the treatment effect on a single treated unit in time-series settings. A common approach to estimate synthetic control weights is to regress the treated unit’s pretreatment outcome and covariates’ time series measurements on those of untreated units via ordinary least squares. However, this approach can perform poorly if the pretreatment fit is not near perfect, whether the weights are normalized. In this article, we introduce a single proxy synthetic control approach, which views the outcomes of untreated units as proxies of the treatment-free potential outcome of the treated unit, a perspective we leverage to construct a valid synthetic control. Under this framework, we establish an alternative identification strategy and corresponding estimation methods for synthetic controls and the treatment effect on the treated unit. Notably, unlike existing proximal synthetic control methods, which require two types of proxies for identification, ours relies on a single type of proxy, thus facilitating its practical relevance. ∣In addition, we adapt a conformal inference approach to perform inference about the treatment effect, obviating the need for a large number of posttreatment observations. Finally, our framework can accommodate time-varying covariates and nonlinear models. We demonstrate the proposed approach in a simulation study and a real-world application.

Fixed effects estimation, with linear controls for stratum membership, is often used to estimate treatment effects when assignment propensities differ across strata. In the presence of heterogeneity in treatment effects across strata, this estimator does not target the average treatment effect, however. Indeed, the implied estimand can range anywhere from the lowest to the highest stratum-level average effect. To facilitate the interpretation of results using this approach, I establish that if stratum-level average effects are monotonic in the shares assigned to treatment, then the fixed effects estimand lies between the average treatment effect for the treated and the average treatment effect for the controls.

Randomized controlled trials (RCTs) are the gold standard for evaluating the causal effect of a treatment; however, they often have limited sample sizes and sometimes poor generalizability. On the other hand, non-randomized, observational data derived from large administrative databases have massive sample sizes and better generalizability, but are prone to unmeasured confounding bias. It is thus of considerable interest to reconcile effect estimates obtained from RCTs and observational studies investigating the same intervention, potentially harvesting the best from both realms. In this article, we theoretically characterize the potential efficiency gain from integrating observational data into the RCT-based analysis from a minimax perspective. For estimation, we derive the minimax rate of convergence for the mean-squared error and propose adaptive estimators that attain the optimal rate up to poly-log factors. For inference, we characterize the minimax rate for the length of confidence intervals and show that adaptation (to unknown confounding bias) is in general impossible. A curious phenomenon thus emerges: for estimation, the efficiency gain from data integration can be achieved without prior knowledge of the magnitude of the confounding bias; for inference, the same task becomes information theoretically impossible in general. We corroborate our theoretical findings using simulations and a real data example from the RCT DUPLICATE initiative.

The estimation of conditional average treatment effects (CATEs) is an important problem in many applications. Many machine learning-based frameworks for such estimation have been proposed, including meta-learning, causal trees, and causal forests. However, few of these methods are interpretable, while those that do emphasize interpretability often suffer in terms of performance. Here, we propose several methods that build on existing meta-learning algorithms to produce CATE estimates that can be represented as trees. We also describe new methods for the estimation of optimal treatment policies (OTPs), an area where interpretable, auditable treatment decision rules are often desirable. We introduce this method for settings with an arbitrary number of treatment arms. We provide regret rates for the proposed methods and show that they outperform popular methods, both interpretable and not. Finally, we demonstrate the use of our method on both simulated and real data from the Antibiotics for Children with severe Diarrhea trial to create OTPs for antibiotic treatment.

Most of the scientific literature on causal modeling considers the structural framework of Pearl and the potential-outcome framework of Rubin to be formally equivalent and therefore interchangeably uses do-interventions and the potential-outcome framework to define counterfactual outcomes. In this article, we agnostically superimpose a structural causal model and a Rubin causal model compatible with the same observations to specify the mathematical conditions under which counterfactual outcomes obtained via do-interventions and potential outcomes need to, do not need to, can, or cannot be equal (almost surely or in law). Our comparison builds upon the fact that such causal models do not have to produce the same counterfactual outcomes and highlights real-world problems where they generally cannot correspond under classical causal-inference assumptions. Then, we examine common claims and practices from the causality literature in the light of this comparison. In doing so, we aim at clarifying the links between the two causal frameworks and the interpretation of their respective counterfactuals.

Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data-generating processes when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These methods typically require that all the confounders are observed to ensure identification of the effects. We contribute by showing how valid semiparametric inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We propose uncertainty intervals that allow for unobserved confounding, and show that the resulting inference is valid when the amount of unobserved confounding is not arbitrarily large; the latter is formalized in terms of convergence rates. Simulation experiments illustrate the finite sample properties of the proposed intervals. Finally, a case study on the effect of smoking during pregnancy on birth weight is used to illustrate the use of the methods introduced to perform an informed sensitivity analysis to the presence of unobserved confounding.

Synthetic control (SC) models are widely used to estimate causal effects in settings with observational time-series data. To identify the causal effect on a target unit, SC requires the existence of additional units that are not impacted by the intervention. Given one of these potential donor units, how can we decide whether it is in fact a valid donor – that is, one not subject to spillover effects from the intervention? Such a decision typically requires appealing to strong a priori domain knowledge specifying the units, which becomes infeasible in situations with large pools of potential donors. In this article, we introduce a practical, theoretically grounded donor selection procedure, aiming to weaken this domain knowledge requirement. Our main result is a theorem that yields the assumptions required to identify donor values at post-intervention time points using only pre-intervention data. We show how this theorem – and the assumptions underpinning it – can be turned into a practical method for detecting potential spillover effects and excluding invalid donors when constructing SCs. Importantly, we employ sensitivity analysis to formally bound the bias in our SC causal estimate in situations where an excluded donor was indeed valid, or where a selected donor was invalid. Using ideas from the proximal causal inference and instrumental variables literature, we show that the excluded donors can nevertheless be leveraged to further debias causal effect estimates. Finally, we illustrate our donor selection procedure on both simulated and real-world datasets.

A fully nonparametric approach to learning causal structures from observational data is proposed. The method is described in the setting of additive structural equation models with a link to causal inference. The estimation procedure of the additive structural equation functions is based on a novel application of the smooth backfitting (SBF) approach. The flexibility of the nonparametric procedure results in strong theoretical properties in the estimation of the variable ordering. It is shown that under mild conditions, the ordering estimate is consistent. Through simulations, it is demonstrated that our method is superior to the state-of-the-art approaches to causal learning. In particular, the SBF approach shows robustness when the noise is heteroscedastic.

Augmenting a randomized controlled trial (RCT) with external data may increase power at the risk of introducing bias. To select and analyze the experiment (RCT alone or combined with external data) with the optimal bias-variance tradeoff, we develop a novel experiment-selector cross-validated targeted maximum likelihood estimator for randomized-external data studies (ES-CVTMLE). This estimator utilizes two estimates of bias to determine whether to integrate external data based on (1) a function of the difference in conditional mean outcome under control between the RCT and combined experiments and (2) an estimate of the average treatment effect on a negative control outcome. We define the asymptotic distribution of the ES-CVTMLE under varying magnitudes of bias and construct confidence intervals by Monte Carlo simulation. We evaluate ES-CVTMLE compared to three other data fusion estimators in simulations and demonstrate the ability of ES-CVTMLE to distinguish biased from unbiased external controls in a real data analysis of the effect of liraglutide on glycemic control from the LEADER trial. The ES-CVTMLE has the potential to improve power while providing relatively robust inference for future hybrid RCT-external data studies.

The Causal Roadmap is a formal framework for causal and statistical inference that supports clear specification of the causal question, interpretable and transparent statement of required causal assumptions, robust inference, and optimal precision. The Roadmap is thus particularly well suited to evaluating longitudinal causal effects using large-scale registries; however, application of the Roadmap to registry data also introduces particular challenges. In this article, we provide a detailed case study of the longitudinal Causal Roadmap applied to the Danish National Registry to evaluate the comparative effectiveness of second-line diabetes drugs on dementia risk. Specifically, we evaluate the difference in counterfactual 5-year cumulative risk of dementia if a target population of adults with type 2 diabetes had initiated and remained on glucagon-like peptide-1 receptor agonists (GLP1-RA) (a second-line diabetes drug) compared to a range of active comparator protocols. Time-dependent confounding is accounted for through use of the iterated conditional expectation representation of the longitudinal g-formula as a statistical estimand. Statistical estimation uses longitudinal targeted maximum likelihood, incorporating machine learning. We provide practical guidance on the implementation of the Roadmap using registry data and highlight how rare exposures and outcomes over long-term follow-up can raise challenges for flexible and robust estimators, even in the context of the large sample sizes provided by the registry. We demonstrate how simulations can be used to help address these challenges by supporting careful estimator pre-specification. We find a protective effect of GLP-1RAs compared to some but not all other second-line treatments.

Orthogonal meta-learners, such as DR-learner (Kennedy EH. Towards optimal doubly robust estimation of heterogeneous causal effects. arXiv preprint arXiv:2004.14497 2020), R-learner (Nie X, Wager S. Quasi-oracle estimation of heterogeneous treatment effects. Biometrika 2021;108:299–319) and IF-learner (Curth A, Alaa AM, van der Schaar M. Estimating structural target functions using machine learning and influence functions. arXiv preprint arXiv:2008.06461 2020), are increasingly used to estimate conditional average treatment effects. They are hoped to improve convergence rates relative to naïve meta-learners (e.g., T-, S- and X-learner (Künzel SR, Sekhon JS, Bickel PJ, Yu B. Metalearners for estimating heterogeneous treatment effects using machine learning. Proc Natl Acad Sci 2019;116:4156–65)) through de-biasing procedures that involve applying standard learners to specifically transformed outcome data. This leads them to disregard the possibly constrained outcome space, which can be particularly problematic for dichotomous outcomes: these typically get transformed to values that are no longer constrained to the unit interval, which may cause instability and makes it difficult for standard learners to guarantee predictions within the unit interval. To address this, we construct a non-orthogonal imputation-learner and an orthogonal ‘i-learner’ for the prediction of counterfactual outcomes, which respect the outcome space. These are more generally expected to outperform existing learners, even when the outcome is unconstrained, as we confirm empirically in simulation studies and an analysis of critical care data. Our development also sheds broader light onto the construction of orthogonal learners for other estimands.

Causal random forests provide efficient estimates of heterogeneous treatment effects. However, forest algorithms are also well-known for their black-box nature, and therefore, do not characterize how input variables are involved in treatment effect heterogeneity, which is a strong practical limitation. In this article, we develop a new importance variable algorithm for causal forests, to quantify the impact of each input on the heterogeneity of treatment effects. The proposed approach is inspired from the drop and relearn principle, widely used for regression problems. Importantly, we show how to handle the case where the forest is retrained without a confounding variable. If the confounder is not involved in the treatment effect heterogeneity, the local centering step enforces consistency of the importance measure. Otherwise, when a confounder also impacts heterogeneity, we introduce a corrective term in the retrained causal forest to recover consistency. Additionally, experiments on simulated, semi-synthetic, and real data show the good performance of our importance measure, which outperforms competitors on several test cases. Experiments also show that our approach can be efficiently extended to groups of variables, providing key insights in practice.

The COVID-19 pandemic presents challenges to both public health and the economy. Our objective is to examine how household expenditure, a significant component of private demand, reacts to changes in mobility. This investigation is crucial for developing policies that balance public health and the economic and social impacts. We utilize extensive scanner data from a major retail chain in India and Google mobility data to address this important question. However, there are a few challenges, including outcomes with excessive zeros and complicated correlations, time-varying confounding, and irregular observation times. We propose incorporating a multiplicative structural nested mean model with inverse intensity weighting techniques to tackle these challenges. Our framework allows semiparametric/nonparametric estimation for nuisance functions. The resulting rate doubly robust estimator enables the use of a conventional sandwich variance estimator without taking into account the variability introduced by these flexible estimation methods. We demonstrate the properties of our method theoretically and further validate it through simulation studies. Using the Indian consumer spending data and Google mobility data, our method reveals that the substantial reduction in mobility has a significant impact on consumers’ fresh food expenditure.

The weighted average treatment effect (WATE) defines a versatile class of causal estimands for populations characterized by propensity score weights, including the average treatment effect (ATE), treatment effect on the treated (ATT), on controls (ATC), and for the overlap population (ATO). WATE has broad applicability in social and medical research, as many datasets from these fields align with its framework. However, the literature lacks a systematic investigation into the robustness and efficiency conditions for WATE estimation. Although doubly robust (DR) estimators are well-studied for ATE, their applicability to other WATEs remains uncertain. This paper investigates whether widely used WATEs admit DR or rate doubly robust (RDR) estimators and assesses the role of nuisance function accuracy, particularly with machine learning. Using semiparametric efficient influence function (EIF) theory and double/debiased machine learning (DML), we propose three RDR estimators under specific rate and regularity conditions and evaluate their performance via Monte Carlo simulations. Applications to NHANES data on smoking and blood lead levels, and SIPP data on 401(k) eligibility, demonstrate the methods’ practical relevance in medical and social sciences.

Symbolic nonparametric bounds for partial identification of causal effects now have a long history in the causal literature. Sharp bounds, bounds that use all available information to make the range of values as narrow as possible, are often the goal. For this reason, many publications have focused on deriving sharp bounds, but the concept of sharp bounds is nuanced and can be misleading. In settings with ancillary covariates, the situation becomes more complex. We provide clear definitions for pointwise and uniform sharpness of covariate-conditional bounds, that we then use to prove some general and some specific to the instrumental variable (IV) setting results about the relationship between these two concepts. As we demonstrate, general conditions are much more difficult to determine and thus, we urge authors to be clear when including ancillary covariates in bounds via conditioning about the setting of interest and the assumptions made.

The Credibility Revolution advances internally valid research designs intended to identify causal effects from quantitative data. The ensuing emphasis on internal validity, however, has enabled a neglect of construct and external validity. We show that ignoring construct and external validity within identification strategies undermines the Credibility Revolution’s own goal of understanding causality deductively. Without assumptions regarding construct validity, one cannot accurately label the cause or outcome. Without assumptions regarding external validity, one cannot label the conditions enabling the cause to have an effect. If any of the assumptions regarding internal, construct, and external validity are missing, the claim is not deductively supported. The critical role of theoretical and substantive knowledge in deductive causal inference is illuminated by making such assumptions explicit. This article critically reviews approaches to identification in causal inference while developing a framework called causal specification . Causal specification augments existing identification strategies to enable and justify deductive, generalized claims about causes and effects. In the process, we review a variety of developments in the philosophy of science and causality and interdisciplinary social science methodology.