There are many situations in financial research where it is the explained variable rather than one or more of the explanatory variables that is qualitative. The qualitative information would then be coded as a dummy variable and the situation would be referred to as a limited dependent variable and needs to be treated differently. The term refers to any problem where the values that the dependent variables may take are limited to certain integers (e.g. 0, 1, 2, 3, 4) or even where it is a binary number (only 0 or 1).

The linear probability model (LPM) is by far the simplest way of dealing with binary dependent variables, and it is based on an assumption that the probability of an event occurring is linearly related to a set of explanatory variables. The actual probabilities cannot be observed, so we would estimate a model where the outcomes, yi (the series of zeros and ones), would be the dependent variable. This is then a linear regression model and would be estimated by OLS. The set of explanatory variables could include either quantitative variables or dummies or both. The fitted values from this regression are the estimated probabilities that yi = 1 for each observation i.

The linear probability model has many important flaws and consequently the logit and probit approaches are used instead. Both models are able to overcome the limitation of the LPM that it can produce estimated probabilities that are negative or greater than one.