Fitting and interpreting Cragg's tobit alternative using Stata

Abstract

In this article, I introduce the user-written command craggit, which simultaneously fits both tiers of Cragg's (1971, Econometrica 39: 829-844) "two-tier" (sometimes called "two-stage" or "double-hurdle" ) alternative to tobit for corner-solution models. A key limitation to the tobit model is that the probability of a positive value and the actual value, given that it is positive, are determined by the same underlying process (i.e., the same parameters). Cragg proposed a more flexible alternative that allows these outcomes to be determined by separate processes through the incorporation of a probit model in the first tier and a truncated normal model in the second. Also, tobit is nested in craggit, making the latter a popular choice among "two-tier" models. In the article, I also present postestimation syntax to facilitate the understanding and interpretation of results. © 2009 StataCorp LP.