CENSORED OR TRUNCATED REGRESSION MODEL (TOBIT MODEL)
Tobin (1958) proposed 
the following important model: 

(13.6.1) 
yf = Хг’р + Ui 

and 

(13.6.2) 
Уі = x’p + и{ 
if yf > о 
= 0 
if yf >0, і = 1, 2…………………. n, 
where (wj are assumed to be i. i.d. N(0, cr2) and хг is a known nonstochastic vector. It is assumed that {yj and (x,) are observed for all i, but {y*} are unobserved if y* < 0. This model is called the censored regression model or the Tobit model (after Tobin, in analogy to probit). If the observations corresponding to y* < 0 are totally lost, that is, if {x,} are not observed whenever y* < 0, and if the researcher does not know how many observations exist for which y* < 0, the model is called the truncated regression model.
Tobin used this model to explain a household’s expenditure (y) on a ...
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