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Semiparametrically efficient estimation of the average linear regression function
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DOI：10.1016/j.jeconom.2021.07.008.png)
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Abstract
En 中文
Let Y be an outcome of interest, X a vector of treatment measures, and W a vector of pretreatment control variables. Here X may include (combinations of) continuous, discrete, or non-mutually exclusive treatments. Consider the linear regression of Y onto X in a subpopulation homogeneous in W = w (formally a conditional linear predictor). Let b(0) (w) be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average beta(0) = E [b(0) (W)]. When X is binary-valued (multi-valued) our procedure recovers the (a vector of) average treatment effect(s). When X is continuously-valued, or consists of multiple non-exclusive treatments, our estimand coincides with the average partial effect (APE) of X on Y when the underlying potential response function is linear in X, but otherwise heterogeneous across agents. When the potential response function takes a general nonlinear/heterogeneous form, and X is continuously-valued, our procedure recovers a weighted average of the gradient of this response across individuals and values of X. We provide a simple, and semiparametrically efficient, method of covariate adjustment for settings with complicated treatment regimes. Our method generalizes familiar methods of covariate adjustment used for program evaluation as well as methods of semiparametric regression (e.g., the partially linear regression model). (C) 2021 Elsevier B.V. All rights reserved.
Keywords:
Conditional linear predictor
Causal inference
Average treatment effect
Propensity score
Semiparametric efficiency
Semiparametric regression
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