Limited Dependent Variables

In labor economics, one is faced with explaining the decision to participate in the labor force, the decision to join a union, or the decision to migrate from one region to the other. In finance, a consumer defaults on a loan or a credit card debt, or purchases a stock or an asset like a house or a car. In these examples, the dependent variable is usually a dummy variable with values 1 if the worker participates (or consumer defaults on a loan) and 0 if he or she does not participate (or default). We dealt with dummy variables as explanatory variables on the right hand side of the regression, but what additional problems arise when this dummy variable appears on the left hand side of the equation? As we have done in previous chapters, we first study its effects on the usual least squares estimator, and then consider alternative estimators that are more appropriate for models of this nature.