Econometrics 2 Pr. Dr. S. Sperlich Assignment 4: Tobit Models ...

Econometrics 2
Pr. Dr. S. Sperlich
Assignment 4: Tobit Models Summer 2008
(c) Use the results from (b) to estimate the difference in expected pension benefits
for a white male and a nonwhite female, both of whom are 35 years old, single
with no dependents, have 16 years of education and 10 years of experience.
(d) Add union to the Tobit model and comment on its significance.
(e) Apply the Tobit model from part (d) but with peratio, the pension-earnings
ratio, as the dependent variable. (Notice that is a fraction between zero and one,
but, while it often takes on the value zero, it never gets close to being unity.
Thus, a Tobit model is fine as an approximation.) Does gender or race have an
effect on the pension-earnings ratio?
Exercise 4: Consider a double hurdle model of durable goods expenditure, where the purchase
decision is represented by
Y i1 = 1I Y ∗
i1 >0
but the actual amount purchased is represented by a censored regression model, thereby
avoiding negativity of Y i2 . In this case
Y i2 = Y i1 · max(0,Y ∗
i2).
One interpretation of this model is that observed demand Y i2 is zero either because
an individual genuinely does not consume the good (that is, Yi1 ∗ ≤ 0), or because
for some reason (infrequently of purchase, misreporting, etc.) zero expenditure was
recorded (that is, Yi2 ∗ ≤ 0).
(a) Determine P(Y i2 = 0) when Yi1 ∗ and Y i2 ∗ are independent.
(b) Specify the sample log–likelihood.
(c) What happens when P(Y i1 = 1) = 1 for all sample units?
(d) Which other than the ML–estimator could we use for estimation?
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