Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 6

(Requires calculus)

(i) Suppose in the Tobit model that x1 = log(z1), and this is the only place z1 appears in x. Show that

where ?1 is the coefficient on log(z1).

(ii) If x1 = z1, and x2 = zl, show that

where ?1 is the coefficient on z1 and ?2 is the coefficient on Z12

Step 1 of 3

(i)

Consider the Tobit model such that

This implies:

Now when is differentiated with respect to , such that:

The result is:

For the Tobit model,

Consider, then

Consider

In denominator it is cumulative density function.

Now, differentiate with respect to

The result is:

Since,