This paper provides a framework for identifying reasons for non-purchase of a commodity on statistical grounds without having explicit information about these reasons. The traditional corner solution has frequently been modeled in the literature using the Tobit model. Two generalizations of the Tobit model are the double-hurdle model and the purchase-infrequency model. This study proposes an integrated approach which nests both double-hurdle and purchase-infrequency as special cases, and hence enables a distinction between these reasons for non-purchase. Although previous studies have compared the performance of these models by a non-nested test, the integrated approach enables a simple and probably stronger nested test. A set of Monte-Carlo simulations shows that the integrated model is much more robust to mis-specification than any of the two simpler models, and that the non-nested test has relatively low power. In the empirical application, an Engel curve for tobacco is estimated using Israeli family expenditure data, utilizing all of the above methods. The results confirm the usefulness of the integrated approach: whereas both the double-hurdle and purchase-infrequency models were rejected in favor of the integrated model using the nested likelihood-ratio test, the non-nested test was not able to reject either one of the nested models in favor of the other. The findings show that 996 of the sample households are censored due to the second hurdle and another 7% due to infrequency of purchase. The conventional corner solution (Tobit-type censoring) occurs in 40% of the households. A total of 60% of the sample households did not purchase tobacco during the survey's 2-week period, and this was predicted correctly by the integrated model for 60% of these. The coefficients of log total expenditure in the tobacco-share equation estimated by the different models are all negative. However, relative to the integrated model, the Tobit coefficient is largely underestimated and the double-hurdle coefficient is largely overestimated (both in absolute values). Other socioeconomic explanatory variables are shown to affect the different equations (second-hurdle, purchase, and consumption) in different ways.