Semiparametrically Efficient Estimation of the Average Linear Regression Function / Bryan S. Graham, Cristine Campos de Xavier Pinto.

Format:

Book

Author/Creator:

Graham, Bryan S.

Contributor:

National Bureau of Economic Research.

Campos de Xavier Pinto, Cristine.

Series:

Working Paper Series (National Bureau of Economic Research) no. w25234.

NBER working paper series no. w25234

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2018.

Summary:

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).

Notes:

Print version record

November 2018.