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ABSTRACT Researchers commonly use difference-in-differences (DiD) designs to evaluate public policy interventions. While methods exist for estimating effects in the context of binary interventions, policies often result in varied exposures across regions implementing the policy. Yet, existing approaches for incorporating continuous exposures face substantial limitations in addressing confounding variables associated with intervention status, exposure levels, and outcome trends. These limitations significantly constrain policymakers’ ability to fully comprehend policy impacts and design future interventions. In this work, we propose new estimators for causal effect curves within the DiD framework, accounting for multiple sources of confounding. Our approach accommodates misspecification of a subset of intervention, exposure, and outcome models while avoiding any parametric assumptions on the effect curve. We present the statistical properties of the proposed methods and illustrate their application through simulations and a study investigating the heterogeneous effects of a nutritional excise tax under different levels of accessibility to cross-border shopping. 

Abstract Policy interventions can spill over to units of a population that is not directly exposed to the policy but are geographically close to the units receiving the intervention. In recent work, investigations of spillover effects on neighbouring regions have focused on estimating the average treatment effect of a particular policy in an observed setting. Our research question broadens this scope by asking what policy consequences would the treated units have experienced under counterfactual exposure settings. When we only observe treated unit(s) surrounded by controls—as is common when a policy intervention is implemented in a single city or state—this effect inquires about the policy effects under a counterfactual neighbourhood policy status that we do not, in actuality, observe. In this work, we extend difference-in-differences approaches to spillover settings and develop identification conditions required to evaluate policy effects in counterfactual treatment scenarios. These causal quantities are policy-relevant for designing effective policies for populations subject to various neighbourhood statuses. We develop several estimators that have desirable properties. We provide an illustrative data application to the Philadelphia beverage tax study. 

Abstract To comprehensively evaluate a public policy intervention, researchers must consider the effects of the policy not just on the implementing region, but also nearby, indirectly affected regions. For example, an excise tax on sweetened beverages in Philadelphia, Pennsylvania was shown to not only be associated with a decrease in volume sales of taxed beverages in Philadelphia, but also an increase in sales in nontaxed bordering counties. The latter association may be explained by cross-border shopping behaviours of Philadelphia residents and indicate a causal effect of the tax on nearby regions, which may drastically offset the total effect of the intervention. In this paper, we adapt doubly robust difference-in-differences methodology to estimate distinct causal effects on the implementing and neighbouring control regions when they are geographically separable and data exists from an unaffected control region. Our approach adjusts for potential confounding in quasi-experimental evaluations and relaxes standard assumptions on model specification while accounting for geographically separable interference, repeated observations, spatial correlation, and unknown effect heterogeneity. We apply these methods to evaluate the effect of the Philadelphia beverage tax on taxed beverage sales in 231 Philadelphia and bordering county stores. We also use our methods to explore effect heterogeneity across geographical features. 

Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of K asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of K candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the K proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study. 

Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study. 

Abstract: The regression discontinuity (RD) design is a commonly used non-experimental approach for evaluating policy or program effects. However, this approach heavily relies on the untestable assumption that distribution of confounders or average potential outcomes near or at the cutoff are comparable. When there are multiple cutoffs that create several discontinuities in the treatment assignments, factors that can lead this assumption to the failure at one cutoff may overlap with those at other cutoffs, invalidating the causal effects from each cutoff. In this study, we propose a novel approach for testing the causal hypothesis of no RD treatment effect that can remain valid even when the assumption commonly considered in the RD design does not hold. We propose leveraging variations in multiple available cutoffs and constructing a set of instrumental variables (IVs). We then combine the evidence from multiple IVs with a direct comparison under the local randomization framework. This reinforced design that combines multiple factors from a single data can produce several, nearly independent inferential results that depend on very different assumptions with each other. Our proposed approach can be extended to a fuzzy RD design. We apply our method to evaluate the effect of having access to higher achievement schools on students' academic performances in Romania. 

Summary Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic under mild distributional assumptions on the graph structure, and demonstrate that it is able to efficiently identify the most informative graph embedding with respect to the diffusion time. The methodology is illustrated on both simulated and real data. 

Abstract Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well‐known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals outperform traditional instrumental variable confidence intervals when invalid instruments are present and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low‐density lipoprotein on globulin levels.