Semiparametrically efficient estimation of the average linear regression function

Bryan S. Graham and Cristine Pinto

Journal of Econometrics, 2022, vol. 226, issue 1, 115-138

Abstract: Let Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment 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 b0w be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average β0=Eb0W. 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).

Keywords: Conditional linear predictor; Causal inference; Average treatment effect; Propensity score; Semiparametric efficiency; Semiparametric regression (search for similar items in EconPapers)
JEL-codes: C14 C21 C31 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Working Paper: Semiparametrically efficient estimation of the average linear regression function (2018)
Working Paper: Semiparametrically efficient estimation of the average linear regression function (2018)
Working Paper: Semiparametrically Efficient Estimation of the Average Linear Regression Function (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:226:y:2022:i:1:p:115-138

DOI: 10.1016/j.jeconom.2021.07.008

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