Evaluation of the efficacy of an intervention is often complicated because the intervention is not randomly assigned. Usually, interventions in marketing, such as coupons or retention campaigns, are directed at customers because their spending is below some threshold or because the customers themselves make a purchase decision. The presence of nonrandom assignment of the stimulus can lead to over- or underestimating the value of the intervention. This can cause future campaigns to be directed at the wrong customers or cause the impacts of these effects to be over- or understated.
This paper by Gunce Walton and Kenneth Sanford gives a brief overview of selection bias, demonstrates how selection in the data can be modeled, and shows how to apply some of the important consistent methods of estimating selection models, including Heckman’s two-step procedure, in an empirical example. Sample code is provided in an appendix.