arXiv subjects

Max Rubinstein

Publications and source records attributed to Max Rubinstein.

10 recordsLinked to original sources

arXiv2026

State policy heterogeneity analyses: considerations and proposals

State-level policy studies often conduct heterogeneity analyses that quantify how treatment effects vary across state characteristics. These analyses may be used to inform state-specific policy decisions, or to infer how the effect of a policy changes in combination with other state characteristics. However, in state-level settings with varied contexts and policy landscapes, multiple versions of similar policies, and differential policy implementation, the causal quantities targeted by these analyses may not align with the inferential goals. This paper clarifies these issues by distinguishing several causal estimands relevant to heterogeneity analyses in state-policy settings, including state-specific treatment effects (ITE), conditional average treatment effects (CATE), and controlled direct effects (CDE). We argue that the CATE is often the easiest to identify and estimate, but may not be the most policy relevant target of inference. Moreover, the widespread practice of coarsening distinct policies or implementations into a single indicator further complicates the interpretation of these analyses. Motivated by these limitations, we propose bounding ITEs as an alternative inferential goal, yielding ranges for each state's policy effect under explicit assumptions that quantify deviations from the ideal identifying conditions. These bounds target a well-defined and policy-relevant quantity, the effect for specific states. We develop this approach within a difference-in-differences framework and discuss how sensitivity parameters may be informed using pre-treatment data. Through simulations we demonstrate that bounding state-specific effects can more reliably determine the sign of the ITEs than CATE estimates. We then illustrate this method to examine the effect of the Affordable Care Act Medicaid expansion on high-volume buprenorphine prescribing.

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arXiv2025

Choosing an analytic approach: Key study design considerations in state policy evaluation

This paper reviews and details methods for state policy evaluation to guide selection of a research approach based on evaluation setting and available data. We highlight key design considerations for an analysis, including treatment and control group selection, timing of policy adoption, expected effect heterogeneity, and data considerations. We then provide an overview of analytic approaches and differentiate between methods based on evaluation context, such as settings with no control units, a single treated unit, multiple treated units, or with multiple treatment cohorts. Methods discussed include interrupted time series models, difference-in-differences estimators, autoregressive models, and synthetic control methods, along with method extensions which address issues like staggered policy adoption and heterogenous treatment effects. We end with an illustrative example, applying the developed framework to evaluate the impacts of state-level naloxone standing order policies on overdose rates. Overall, we provide researchers with an approach for deciding on methods for state policy evaluations, which can be used to select study designs and inform methodological choices.

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arXiv2025

Assessing Bias and Precision in State Policy Evaluations: A Comparative Analysis of Time-Varying Estimators Using Policy Simulations

Using state-level opioid overdose mortality data from 1999-2016, we simulated four time-varying treatment scenarios, which correspond to real-world policy dynamics (ramp up, ramp down, temporary and inconsistent). We then evaluated seven commonly used policy evaluation methods: two-way fixed effects event study, debiased autoregressive model, augmented synthetic control, difference-in-differences with staggered adoption, event study with heterogeneous treatment, two-stage differences-in-differences and differences-in-differences imputation. Statistical performance was assessed by comparing bias, standard errors, coverage, and root mean squared error over 1,000 simulations. Results Our findings indicate that estimator performance varied across policy scenarios. In settings where policy effectiveness diminished over time, synthetic control methods recovered effects with lower bias and higher variance. Difference-in-difference approaches, while offering reasonable coverage under some scenarios, struggled when effects were non-monotonic. Autoregressive methods, although demonstrating lower variability, underestimated uncertainty. Overall, a clear bias-variance tradeoff emerged, underscoring that no single method uniformly excelled across scenarios. Conclusions This study highlights the importance of tailoring the choice of estimator to the expected trajectory of policy effects. In dynamic time-varying settings, particularly when a policy has an anticipated diminishing impact, methods like augmented synthetic controls may offer advantages despite reduced precision. Researchers should carefully consider these tradeoffs to ensure robust and credible state-policy evaluations.

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arXiv2024

Bounding causal effects with an unknown mixture of informative and non-informative missingness

In experimental and observational data settings, researchers often have limited knowledge of the reasons for missing outcomes. To address this uncertainty, we propose bounds on causal effects for missing outcomes, accommodating the scenario where missingness is an unobserved mixture of informative and non-informative components. Within this mixed missingness framework, we explore several assumptions to derive bounds on causal effects, including bounds expressed as a function of user-specified sensitivity parameters. We develop influence-function based estimators of these bounds to enable flexible, non-parametric, and machine learning based estimation, achieving root-n convergence rates and asymptotic normality under relatively mild conditions. We further consider the identification and estimation of bounds for other causal quantities that remain meaningful when informative missingness reflects a competing outcome, such as death. We conduct simulation studies and illustrate our methodology with a study on the causal effect of antipsychotic drugs on diabetes risk using a health insurance dataset.

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arXiv2024

Autoregressive models for panel data causal inference with application to state-level opioid policies

Motivated by the study of state opioid policies, we propose a novel approach that uses autoregressive models for causal effect estimation in settings with panel data and staggered treatment adoption. Specifically, we seek to estimate the impact of key opioid-related policies by quantifying the effects of must access prescription drug monitoring programs (PDMPs), naloxone access laws (NALs), and medical marijuana laws on opioid prescribing. Existing methods, such as differences-in-differences and synthetic controls, are challenging to apply in these types of dynamic policy landscapes where multiple policies are implemented over time and sample sizes are small. Autoregressive models are an alternative strategy that have been used to estimate policy effects in similar settings, but until this paper have lacked formal justification. We outline a set of assumptions that tie these models to causal effects, and we study biases of estimates based on this approach when key causal assumptions are violated. In a set of simulation studies that mirror the structure of our application, we show that our proposed estimators frequently outperform existing estimators. In short, we justify the use of autoregressive models to evaluate the effectiveness of four state policies in combating the opioid crisis.

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arXiv2024

Mediated probabilities of causation

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 non-parametric 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.

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arXiv2023

Generalized difference-in-differences

We propose a new method for estimating causal effects in longitudinal/panel data settings that we call generalized difference-in-differences. Our approach unifies two alternative approaches in these settings: ignorability estimators (e.g., synthetic controls) and difference-in-differences (DiD) estimators. We propose a new identifying assumption -- a stable bias assumption -- which generalizes the conditional parallel trends assumption in DiD, leading to the proposed generalized DiD framework. This change gives generalized DiD estimators the flexibility of ignorability estimators while maintaining the robustness to unobserved confounding of DiD. We also show how ignorability and DiD estimators are special cases of generalized DiD. We then propose influence-function based estimators of the observed data functional, allowing the use of double/debiased machine learning for estimation. We also show how generalized DiD easily extends to include clustered treatment assignment and staggered adoption settings, and we discuss how the framework can facilitate estimation of other treatment effects beyond the average treatment effect on the treated. Finally, we provide simulations which show that generalized DiD outperforms ignorability and DiD estimators when their identifying assumptions are not met, while being competitive with these special cases when their identifying assumptions are met.

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arXiv2022

Heterogeneous interventional indirect effects with multiple mediators: non-parametric and semi-parametric approaches

We propose semi- and non-parametric methods to estimate conditional interventional effects in the setting of two discrete mediators whose causal ordering is unknown. Average interventional indirect effects have been shown to decompose an average treatment effect into a direct effect and interventional indirect effects that quantify effects of hypothetical interventions on mediator distributions. Yet these effects may be heterogeneous across the covariate distribution. We consider the problem of estimating these effects at particular points. We propose an influence-function based estimator of the projection of the conditional effects onto a working model, and show under some conditions that we can achieve root-n consistent and asymptotically normal estimates. Second, we propose a fully non-parametric approach to estimation and show the conditions where this approach can achieve oracle rates of convergence. Finally, we propose a sensitivity analysis for the conditional effects in the presence of mediator-outcome confounding. We propose estimating bounds on the conditional effects using these same methods, and show that these results easily extend to allow for influence-function based estimates of the bounds on the average effects. We conclude examining heterogeneous effects with respect to the effect of COVID-19 vaccinations on depression during February 2021.

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arXiv2021

The effect of COVID-19 vaccinations on self-reported depression and anxiety during February 2021

Using the COVID-19 Trends and Impact survey, we find that COVID-19 vaccinations reduced the prevalence of self-reported feelings of depression and anxiety, isolation, and worries about health among vaccine-accepting respondents in February 2021 by 3.7, 3.3, and 4.3 percentage points, respectively, with particularly large reductions among respondents aged 18 and 24 years old. We show that interventions targeting social isolation account for 39.1\% of the total effect of COVID-19 vaccinations on depression, while interventions targeting worries about health can account for 8.3\%. This suggests that social isolation is a stronger mediator of the effect of COVID-19 vaccinations on depression than worries about health. We caution that these causal interpretations rely on strong assumptions.

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arXiv2021

Balancing weights for region-level analysis: the effect of Medicaid Expansion on the uninsurance rate among states that did not expand Medicaid

We predict the average effect of Medicaid expansion on the non-elderly adult uninsurance rate among states that did not expand Medicaid in 2014 as if they had expanded their Medicaid eligibility requirements. Using American Community Survey data aggregated to the region level, we estimate this effect by finding weights that approximately reweights the expansion regions to match the covariate distribution of the non-expansion regions. Existing methods to estimate balancing weights often assume that the covariates are measured without error and do not account for dependencies in the outcome model. Our covariates have random noise that is uncorrelated with the outcome errors and our outcome model has state-level random effects inducing dependence between regions. To correct for the bias induced by the measurement error, we propose generating our weights on a linear approximation to the true covariates, using an idea from measurement error literature known as "regression-calibration" (see, e.g., Carroll (2006)). This requires auxiliary data to estimate the variability of the measurement error. We also modify the Stable Balancing Weights objective proposed by Zubizaretta (2015)) to reduce the variance of our estimator when the model errors follow our assumed correlation structure. We show that these approaches outperform existing methods when attempting to predict observed outcomes during the pre-treatment period. Using this method we estimate that Medicaid expansion would have caused a -2.33 (-3.54, -1.11) percentage point change in the adult uninsurance rate among states that did not expand Medicaid.

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