Type 5 Tobit Model: P(yі < 0, ya) • P(y, > 0, ya)

10.10.1 Definition and Estimation

The Type 5 Tobit model is obtained from the Type 4 model (10.9.1) by omitting the equation for yu. We merely observe the sign of yf,. Thus the model is defined by

Уи = *иРі + Щі (10.10.1)

У*і = XliPl + m2i У *t = x’uPi + m3(

Угі = У *1 if У и > 0

= 0 if yf, ё 0

Ун = У it if Уи = о

= 0 if y*>0, і = 1, 2, . . . , п,

image769

where (uu, u2i, u3i} are i. i.d. drawings from a trivariate normal distribution. The likelihood function of the model is

where f3 and are as defined in (10.9.2). Because this model is somewhat

simpler than Type 4, the estimation methods discussed in the preceding section apply to this model a fortiori. Hence, we shall go immediately into the discussion of applications.

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