Semiparametrically efficient estimation of the average linear regression function

Bryan Graham and Cristine Pinto

No CWP62/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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, and/or non-mutually exclusive “treatments”. Consider the linear regression of Y onto X in a subpopulation homogenous in W = w (formally a conditional linear predictor). Let b0 (w) be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average ß0 = E [b0 (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 heterogenous across agents. When the potential response function takes a general nonlinear/heterogenous 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: 2018-11-07
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
https://www.ifs.org.uk/uploads/cemmap/wps/CWP621818.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.ifs.org.uk/uploads/cemmap/wps/CWP621818.pdf [302 Found]--> https://ifs.org.uk/uploads/cemmap/wps/CWP621818.pdf)

Related works:
Journal Article: Semiparametrically efficient estimation of the average linear regression function (2022)
Working Paper: Semiparametrically efficient estimation of the average linear regression function (2018)
Working Paper: Semiparametrically Efficient Estimation of the Average Linear Regression Function (2018)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:62/18

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().