Binary Response Models: Logits, Probits and

A binary response model is a regression model in which the dependentvariable Y is a binary random variable that takes on only the values zeroand one. In many economic applications of this model, an agent makes a choice between two alternatives: for example, a commuter chooses to drive a car to work or to take public transport. Another example is the choice of a worker between taking a job or not. Driving to work and taking a job are choices that correspond to Y 5 1, and taking public transport and not taking a job to Y 5 0. The model gives the probability that Y 5 1 is chosen conditional on a set of explanatory variables. In the transportation example, common explanatory variables include the time and the cost of travel; in the worker example, common explanatory variables include age, education and experience. The econometric problem is to estimate the conditional probability that Y 5 1 considered as a function of the explanatory variables. The most commonly used approach, notably logit and probit models, assumes that the functional form of the dependence on the explanatory variables is known. The logit and probit models have been used almost exclusively in econometric applications in the leading journals. However, the functional form is seldom known in practice. If the functional form is misspecified, then the estimates of the coefficients and the inferences based on them can be highly misleading. It is possible to relax the restrictive assumption that the functional form is known by using either semiparametric or nonparametric models. In these types of models, the functional form is unknown. The problems of estimating semiparametric and nonparametric binary response models hav