For example, y i could be the medal won by the ith Olympian. However, this is not typically a concern because interest usually only focuses on the coefficients of the regressors, namely γ in this formulation of the model. It follows that the original intercept b cannot be estimated unless the threshold c is known. Then, in this case the inequality condition in ( B), y i ⁎ ⩾ c would be b 0 + z i γ + η i ⩾ 0, where b 0 = ( b − c ). Clearly, if the purchase is not made y i = 0 as in ( C).Īs a technicality, given that the constant term is one of the regressors in x i, and for purposes of illustration, let x i β = b + z i γ where z i is an observed regressor vector. For instance, in the case of a durable good purchase, ( A) in (11.6.7) would relate to the extent of desired purchases, c in ( B) would be the least expensive of that durable good, and y i would indicate that the extent of the actual purchase, which would be equal to the desired purchase, y i ⁎, if the desired purchase is at least as high as the least expensive durable. Examples of Tobit models are durable good purchases, length of a worker's “down” time due to injury, length of unemployment, etc. Where y i ⁎ is a latent variable which is not observed, c is a constant threshold value which need not be known, and could be zero, x i is a row vector of regressors which includes the constant term. (11.6.7) ( A ) y i ⁎ = x i β + η i, ( B ) y i = y i ⁎ if y i ⁎ ⩾ c, ( C ) y i = 0 otherwise
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