Use of two-limit probit regression model. An analysis of lender response to loan requests

Research problems where the observed dependent variable is restricted to lie within an interval with massing of some of the observations at the limiting values of the interval are frequent in business research studies. This paper analyzes one such problem-that of lender response to a business loan application. The unique features of a regression model with a doubly limited dependent variable are explained and interpreted. Parameter estimation for such models is undertaken by maximum-likelihood techniques. In this paper maximum likelihood estimates are obtained for an empirical problem and compared with ordinary least-squares estimators. Results show substantial differences between least-squares and maximum-likelihood estimates, indicating a possibility for serious errors by using least-squares methods on models with a doubly limited dependent variable.