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1. Constructing multiple, independent analyses in the regression discontinuity design with multiple cutoffs

   https://doi.org/10.1353/obs.2024.a946585  

   Lee, Youjin; Tan, Chichun; Karmakar, Bikram (January 2024, Observational Studies)

   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. 

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2. When can we ignore measurement error in the running variable?

   https://doi.org/10.1002/jae.2974  

   Dong, Yingying; Kolesár, Michal (March 2023, Journal of Applied Econometrics)

   Summary In many applications of regression discontinuity designs, the running variable used to assign treatment is only observed with error. We show that, provided the observed running variable (i) correctly classifies treatment assignment and (ii) affects the conditional means of potential outcomes smoothly, ignoring the measurement error nonetheless yields an estimate with a causal interpretation: the average treatment effect for units whose observed running variable equals the cutoff. Possibly after doughnut trimming, these assumptions accommodate a variety of settings where support of the measurement error is not too wide. An empirical application illustrates the results for both sharp and fuzzy designs. 

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3. Propensity Score Weighting for Causal Inference with Clustered Data

   https://doi.org/10.1515/jci-2017-0027  

   Yang, Shu (September 2018, Journal of Causal Inference)

   Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania. 

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4. Double Machine Learning Density Estimation for Local Treatment Effects with Instruments

   Jung, Y.; Tian, J.; Bareinboim, E. (January 2021, Advances in neural information processing systems)

   It is common to quantify causal effects with mean values, which, however, may fail to capture significant distribution differences of the outcome under different treatments. We study the problem of estimating the density of the causal effect of a binary treatment on a continuous outcome given a binary instrumental variable in the presence of covariates. Specifically, we consider the local treatment effect, which measures the effect of treatment among those who comply with the assignment under the assumption of monotonicity (only the ones who were offered the treatment take it). We develop two families of methods for this task, kernel-smoothing and model-based approximations -- the former smoothes the density by convoluting with a smooth kernel function; the latter projects the density onto a finite-dimensional density class. For both approaches, we derive double/debiased machine learning (DML) based estimators. We study the asymptotic convergence rates of the estimators and show that they are robust to the biases in nuisance function estimation. We illustrate the proposed methods on synthetic data and a real dataset called 401(k). 

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5. Estimating the total treatment effect in randomized experiments with unknown network structure

   https://doi.org/10.1073/pnas.2208975119  

   Yu, Christina Lee; Airoldi, Edoardo M.; Borgs, Christian; Chayes, Jennifer T. (November 2022, Proceedings of the National Academy of Sciences)

   Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, and from public policy to the technology industry. Here we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact its neighbors’ outcomes, an issue referred to as network interference or as nonindividualized treatment response. A key challenge in these situations is that the network is often unknown and difficult or costly to measure. We assume a potential outcomes model with heterogeneous additive network effects, encompassing a broad class of network interference sources, including spillover, peer effects, and contagion. First, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference. By contrast, we subsequently develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance in situations where one is given access to average historical baseline measurements prior to the experiment. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. Due to their ease of interpretation and implementation, and their theoretical guarantees, we believe our results will have significant impact on the design of randomized experiments. 

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