Implementing the Heckman Treatment Estimate Approach
The Heckman Treatment Estimate addresses treatment choice (i.e., a binary predictor) with the assumption that a strong and valid instrument removes the endogenous part of the binary predictor (Heckmann 1979). Thus, the equation for the endogenous binary-treatment should include at least one strong and valid instrument.
The etregress command can be used to implement the Heckman Treatment Estimate with the following code in Stata (https://www.stata.com/manuals/causaletregress.pdf).
//estimate the parameters of the endogenous treatment-regression model
etregress Outcome Controls (treat = Predictor Instrument Controls)
The sampleSelection package can be used to implement the Heckman Treatment Estimate with the following code in R (https://cran.r-project.org/web/packages/sampleSelection/index.html).
#load the sampleSelection package
library (sampleSelection)
#outcome and treatment selection equations
model_HTE <- treatreg(
formula = Outcome ~ Controls,
treat.formula = Predictor ~ Instrument + Controls,
data = Dataset
)
#obtain the estimates
summary(model_HTE)
References
Heckman, James J. (1979), “Sample Selection Bias as a Specification Error,” Econometrica: Journal of the Econometric Society, 47, 153-161.