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Tobit Regression

Predicting nonpayment behavior is of considerable interest in the financial community - spanning industries such as banking, insurance, and retail. Corporations are interested in many issues surrounding nonpayment, ranging from various levels of delinquency all the way to write-offs. Typical solutions to forecasting this behavior involve the construction of credit scoring models using either standard linear regression and logistic regression which attempt to classify each individual in one of two categories. If the payment behavior was acceptable over a certain span of time, then the dependent variable in the model might take on a value of one. If behavior was unacceptable, the dependent variable would be assigned a zero value. The dependent variable is then measured against information from the credit bureau and / or the corporation to form a statistical profile to predict future delinquencies. These procedures often stop at the classification step.

Sometimes, as in the case of a mail order company wanting to forecast account write-offs for installment purchases, the classification process may need to go further. For example, a customer may pay 100% of the actual order, 75%, 25%, or default on the order in its entirety at some point in time. The forecast variable no longer is simply a dichotomous variable taking on values of zero or one, but a continuous variable. Furthermore, this variable will be bounded between zero and one hundred, often with many observations at one extreme. Because of the clustering problem around the limits, ordinary least square estimates are biased and would produce numerous negative predicted values. This bias can impact the examination of the true relationship between the nonpayment rate and the profile characteristics.

Tobit regression can be used as a tool to provide a more accurate estimation of nonpayment rates and provide benchmark comparisons using neural networks and ordinary least squares. In particular, it has found a home in telecommunications, banking and finance, and other industries where estimates need to be made on the amount of dollars recovered after an account goes into the write-off stage of the credit life cycle. In these applications, collection models are often built using tobit regression and used to help in the collection process.


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