Critically assess the Linear Probability Model used in credit risk analysis.

Critically assess the Linear Probability Model used in credit risk analysis. 

Ans. Linear probability models are econometric models in which the dependent variable is a probability between zero and one. These are easier to estimate than probit or logit models but usually have the problem that some predictions will not be in the range of zero to one. The probability of observing a 0 or 1 in any one case is treated as depending on one or more explanatory variables. For the “linear probability model”, this relationship is a particularly simple one, and allows the model to be fitted by simple linear regression. The model assumes that, for a binary outcome (Bernoulli trial), Y, and its associated vector of explanatory variables, X, 

and hence the vector of parameters  can be estimated using least squares. This method of fitting would be inefficient This method of fitting can be improved by adopting an iterative scheme based on weighted least squares, in which the model from the previous iteration is used to supply estimates of the conditional variances, var (Y|X=x), which would vary between observations. This approach can be related to fitting the model by maximum likelihood. A drawback of this model for the parameter of the Bernoulli distribution is that, unless restrictions are placed on , the estimated coefficients can imply probabilities outside the unit interval.: [0, 1] For this reason, models such as the logit model or the probit model are more commonly used. The assumption that a probability model is linear in the independent variables is unrealistic in most cases. Further, if we incorrectly specify the model as linear, the statistical properties derived under the linearity assumption will not, in general, hold. (Indeed, the parameters being estimated may not even be relevant.)