THIS CHAPTER IS CONCERNED with data sets for which the assumption made about the exogeneity of covariates in Chapter 4 and subsequent chapters is untenable. Covariates that are correlated with the disturbance term are called endogenous variables in the econometrics literature. We take up three types of models in which endogeneity may be present: treatment models, unobserved covariates, and sample selection subject to incidental truncation.

Treatment Models

Treatment models are used to compare responses of individuals who belong either to a treatment or a control group. If the assignment to a group is random, as in many of the clinical trials that arise in biostatistical applications, the assignment may be regarded as independent of any characteristics of the individual. But in many economic applications and in clinical trials in which compliance is not guaranteed, whether an individual is in the treatment or control group may depend on unobserved covariates that are correlated with the response variable. Such unobserved covariates are called confounders in the statistical literature; in the econometrics literature, the treatment assignment is called endogenous when it is not independent of the response variable. As an example, let the response variable be wages and the treatment be participation in a job training program. We might expect that people with sufficient motivation to participate in training would earn higher wages, even without participating in the program, than those with less motivation.