NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
loading...

Semiparametrically Efficient Estimation of the Average Linear Regression Function

Bryan S. Graham, Cristine Campos de Xavier Pinto

NBER Working Paper No. 25234
Issued in November 2018
NBER Program(s):Development Economics, Labor Studies, Public Economics, Technical Working Papers

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 β0 = Ε[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).

You may purchase this paper on-line in .pdf format from SSRN.com ($5) for electronic delivery.

Access to NBER Papers

You are eligible for a free download if you are a subscriber, a corporate associate of the NBER, a journalist, an employee of the U.S. federal government with a ".GOV" domain name, or a resident of nearly any developing country or transition economy.

If you usually get free papers at work/university but do not at home, you can either connect to your work VPN or proxy (if any) or elect to have a link to the paper emailed to your work email address below. The email address must be connected to a subscribing college, university, or other subscribing institution. Gmail and other free email addresses will not have access.

E-mail:

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w25234

 
Publications
Activities
Meetings
NBER Videos
Themes
Data
People
About

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email: info@nber.org

Contact Us