Personalized Subsidy Rules
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Subsidies are commonly used to encourage behaviors that can lead to short- or long-term benefits. Typical examples include subsidized job training programs and provisions of preventive health products, in which both behavioral responses and associated gains can exhibit heterogeneity. This study uses the marginal treatment effect (MTE) framework to study personalized assignments of subsidies based on individual characteristics. First, we derive the optimality condition for a welfare-maximizing subsidy rule by showing that the welfare can be represented as a function of the MTE. Next, we show that subsidies generally result in better welfare than directly mandating the encouraged behavior because subsidy rules implicitly target individuals through unobserved heterogeneity in the behavioral response. When there is positive selection, that is, when individuals with higher returns are more likely to select the encouraged behavior, the optimal subsidy rule achieves the first-best welfare, which is the optimal welfare if a policy-maker can observe individuals' private information. We then provide methods to (partially) identify the optimal subsidy rule when the MTE is identified and unidentified. Particularly, positive selection allows for the point identification of the optimal subsidy rule even when the MTE curve is not. As an empirical application, we study the optimal wage subsidy using the experimental data from the Jordan New Opportunities for Women pilot study.
Mendelian randomization (MR) infers causal effects of exposures on outcomes using genetic variants as instrumental variables, but existing methods remain vulnerable to bias and loss of power when instruments are invalid. We hypothesize that closely related outcome traits share a large overlap in their valid instruments for a given exposure, so that borrowing instruments across such traits can yield more robust MR inference. To operationalize this, we introduce a novel…
Principal stratification (PS) is a commonly used approach for understanding the mechanisms through which a treatment affects an outcome. The goal of this work is to extend the PS framework to studies with continuous treatments, which introduces a number of both challenges and opportunities in terms of defining causal effects and performing inference. This manuscript provides multiple key methodological contributions: 1) we introduce principal causal estimands for continuous…
Background: Generalized Odds (Gen Odds) provide summaries for ordinal outcomes without requiring the proportional odds assumption. However, conventional Gen Odds compares independently drawn treatment and control outcomes and targets a population-level contrast rather than an individual-level contrast. We developed an individual-level causal formulation of Gen Odds and examined its identification. Methods: We defined the Causal Gen Odds using the joint distribution of…
We develop a semiparametric continuous time inferential framework for testing cumulative treatment effects, including both immediate and carryover effects. The latent state process is modeled by an ordinary differential equation (ODE) whose drift depends on state and treatment, while the observed data are noisy measurements of this latent state at irregular, multi resolution time points. We define the average treatment effect (ATE) as the difference of expected cumulative…
We study inference for continuous linear functionals of solutions to ill-posed inverse problems, including Euclidean parameters arising in nonparametric instrumental variables, proximal causal inference, and shadow-variable models. Although pointwise root-$n$ inference is possible under standard conditions, we show that this need not translate into locally reliable inference. Under a model imposing only minimal regularity conditions, the target is Hellinger discontinuous…
Motivation: Mediation analysis is an important tool for elucidating causal mechanisms in biomedical research and has recently gained increasing attention in microbiome studies. Motivated by a microbiome study of acute myeloid leukemia (AML) patients, we investigate whether the effect of induction chemotherapy intensity on infection status is mediated through gut microbial taxa. This problem poses substantial methodological challenges due to the high dimensionality, zero…