A sample is censored in when is observed for all observations , but the true value of is known only for a restricted range of observations. If the sample is truncated, both and are only observed if falls in the restricted range. See Breen, Richard (1996). Regression Models : Censored, Samples Selected, or Truncated Data. Thousand Oaks: Sage. pp. 2–4. ISBN0-8039-5710-6.
doi.org
When asked why it was called the "tobit" model, instead of Tobin, James Tobin explained that this term was introduced by Arthur Goldberger, either as a portmanteau of "Tobin's probit", or as a reference to the novel The Caine Mutiny, a novel by Tobin's friend Herman Wouk, in which Tobin makes a cameo as "Mr Tobit". Tobin reports having actually asked Goldberger which it was, and the man refused to say. See Shiller, Robert J. (1999). "The ET Interview: Professor James Tobin". Econometric Theory. 15 (6): 867–900. doi:10.1017/S0266466699156056. S2CID122574727.
An almost identical model was independently suggested by Anders Hald in 1949, see Hald, A. (1949). "Maximum Likelihood Estimation of the Parameters of a Normal Distribution which is Truncated at a Known Point". Scandinavian Actuarial Journal. 49 (4): 119–134. doi:10.1080/03461238.1949.10419767.
Olsen, Randall J. (1978). "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model". Econometrica. 46 (5): 1211–1215. doi:10.2307/1911445. JSTOR1911445.
Orme, Chris (1989). "On the Uniqueness of the Maximum Likelihood Estimator in Truncated Regression Models". Econometric Reviews. 8 (2): 217–222. doi:10.1080/07474938908800171.
Olsen, Randall J. (1978). "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model". Econometrica. 46 (5): 1211–1215. doi:10.2307/1911445. JSTOR1911445.
When asked why it was called the "tobit" model, instead of Tobin, James Tobin explained that this term was introduced by Arthur Goldberger, either as a portmanteau of "Tobin's probit", or as a reference to the novel The Caine Mutiny, a novel by Tobin's friend Herman Wouk, in which Tobin makes a cameo as "Mr Tobit". Tobin reports having actually asked Goldberger which it was, and the man refused to say. See Shiller, Robert J. (1999). "The ET Interview: Professor James Tobin". Econometric Theory. 15 (6): 867–900. doi:10.1017/S0266466699156056. S2CID122574727.