osterbias: Calculate Unobserved Selection Bias

In KatoPachi/Rkato: My R functions

Description

We calculate an effect of selection on unobservables on estiamted coefficient of treatment. This method is presented by Oster (2019, Journal of Business & Economic Statistics). Let b0 and r0 be the coefficient of treatment and R-squared resulting from the regression of outcome on treatment. Let b1 and r1 be the coefficient of treatment and R-squared resulting from the regression of outcome on treatment and observed covariates. Let rmax be the R-squared resulting from the hypothetical regression of outcome on treatment, observed covairates, and unobserved covariates. The value rmax depends on researchers. Oster' suggestion is rmax = r1 * 1.3 (See a paper for detailed discussion). Define b^ = b1 - (b0 - b1)*(rmax - r1)/(r1 - r0). Under the following assumpetions, the value b^ converges to a true b in probability one. Assumption 1 is that covariates are orthogonal to unobservables. Assumption 2 is that the unobservable and observables are equally related to the treatment. Assumption 3 is that the coefficient of covariates on treatment is same as the coefficient of covairates on outcome. These assumptions are not precise. See a paper for detailed discussion.

Usage

osterbias(x, r_max = NULL, r_multiply = 1.3)

Arguments

x	an object whose class is RCT.
r_max	a numerical value of rmax. Default is null.
r_multiply	a numerical value of multiple of r1. Default is 1.3.

Value

a numeric vector whose class is RCT and OsterBias.

KatoPachi/Rkato documentation built on Dec. 18, 2021, 2:42 a.m.