Introduction to Bayesian Econometrics

THIS CHAPTER CONCERNS 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. Three types of models are taken up 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 inmany clinical trials, the assignmentmay 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 is a choice made by the individual, and the choice 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. You 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. The problem may be less serious if individuals are randomly assigned to the training program, but there may still be confounding. For example, individuals assigned to the program may choose not to participate, and individuals not assigned to the program may find a way to participate.