Endogeneity in a Binomial Model

A characterization of endogeneity in the binomial regression model is given. The relationship to a model subject to selection is indicated. Maximum likelihood and nonlinear instrumental variable estimators are obtained and evaluated in a Monte Carlo study. A new LM test and a Hausman test against endogeneity are also evaluated. Maximum likelihood estimation based on an instrumental variable and the LM test are found to perform well. An illustration based on choice set sizes for Swedish unemployed is included.