Marginal treatment effects in the absence of instrumental variables
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We propose a method for defining, identifying, and estimating the marginal treatment effect (MTE) without imposing the instrumental variable (IV) assumptions of independence, exclusion, and separability (or monotonicity). Under a new definition of the MTE based on reduced-form treatment error that is statistically independent of the covariates, we find that the relationship between the MTE and standard treatment parameters holds in the absence of IVs. We provide a set of sufficient conditions ensuring the identification of the defined MTE in an environment of essential heterogeneity. The key conditions include a linear restriction on potential outcome regression functions, a nonlinear restriction on the propensity score, and a conditional mean independence restriction that will lead to additive separability. We prove this identification using the notion of semiparametric identification based on functional form. And we provide an empirical application for the Head Start program to illustrate the usefulness of the proposed method in analyzing heterogenous causal effects when IVs are elusive.
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Instrumental variables (IVs) are widely used to estimate causal effects from non-randomized data. A canonical example is a randomized trial with noncompliance, in which the randomized treatment assignment serves as an IV for the non-ignorable treatment received. Under a monotonicity assumption, a valid IV nonparametrically identifies the average treatment effect among a latent complier subgroup, whose generalizability is often under debate. In many studies, there exist…
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In observational time series, statistical inference for dynamic causal effects of a one-time intervention across horizons is complicated by high-dimensional observed pre-treatment information, unmeasured confounding, and serial dependence. To address these challenges, we develop a semiparametric framework for inference from a single serially dependent time series, integrating debiased machine learning with instrumental variables through buffered block cross-fitting. Under…
乘法工具变量模型
Summary The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a homogeneity condition such as monotonicity or no unmeasured common effect modifier between the additive effect of the treatment on the outcome, and that of the IV on the treatment. In this work, we introduce the Multiplicative…
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Instrumental variable (IV) methods address treatment endogeneity, but with non-compliance and heterogeneous treatment effects a binary instrument generally identifies the local average treatment effect (LATE) among compliers rather than the population average treatment effect (ATE). When treatment effects and compliance probabilities are heterogeneous and dependent through latent factors, the ATE need not be identified by IV variation alone. We develop a proximal…
审查员工具变量设计的局部稳健半参数方法
I propose a locally robust semiparametric framework for estimating causal effects using examiner IV designs when adjustment for many or continuous covariates makes saturation infeasible or produces sparse cells. The key ingredient of this approach is an orthogonal moment function that removes the first-order effect of estimation errors in the two treatment regressions defining the examiner IV. I derive the orthogonal moment function and show that it remains valid under…