Censored regression analysis in large samples with many zero observations

With the advent of improved data collection techniques, the applied econometrician can nowadays have access to very large data bases. Sometimes, however, these can have fairly low informational content. For example, a typical response rate in direct mailings is below 1%. Given the small fraction of respondents, one could be tempted to omit the larger part of the nonrespondents from the analysis. If so, one should adapt the statistical analysis to this new situation. We put forward such an adaptation for the censored regression model. This model is often used in marketing research, for example, to analyze the amount of money spent on new products offered in a direct mailing campaign. We discuss how the likelihood function should be modified to obtain proper maximum likelihood [ML] estimates. Our empirical illustration concerns a data set of about 300000 observations. We show that our modified ML method yields the appropriate estimates, and that the loss of efficiency is not large.