Advanced Econometrics Takeshi Amemiya
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,
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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.
