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st: Inverse Mills


From   "Danny Yap" <dyap82@hotmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Inverse Mills
Date   Tue, 23 Sep 2003 15:59:35 +1000

Dear all,

I have the following model.

Y1 = b0 + a1Y1 + a3X3 + e1 (Y1 is binary)
Y2 = b1 + a2Y2 + a4X4 + e2 (Y2 is observed but its truncated at 0)

I want to estimate both equations simultaneously using probit for Y1 and OLS
for Y2. But because Y2 is truncated, it would not be consistent to use OLS.
I could use a Tobit for Y2 but it is very difficult to program. Morever I
have reason to believe that a two-stage estimator using the Cragg model is
more suitable for the data set that I have.

Hence I plan to do a Cragg Model where I do a probit on Y2* (where Y2*=0 if
Y2=0, Y2*=1 if Y2>0)

Y2* = b1 + a4X4 +e1 ->Save the inverse mills  (Y2* is binary)

Then delete all the observations where Y2 is equal to 0 and estimate the
following equation

Y1 = b0 + a1Y1 + a3X3 + e1 + inverse mills
Y2 = b1 + a2Y2 + a4X4 +e2 + inverse mills

The inverse mills is included to control for selectivity bias.

Thanks for reading this far. Thus my questions are

1. How do I calculate the inverse mills for the initial probit on Y2*. Is
the following correct?

After the probit for Y2*

predict fitted_name, xbs
gen invmill = normden(fitted_name)/norm(fitted_name)

2. Can anyone see anything fundamentally wrong with the model I am
estimating?

 I have seen similar models estimated using a double OLS in a few finance
papers. (See Barton, J., 2001, Does the use of financial derivatives affect
earnings management decisions? Accounting Review 76, 1-26 and Pincus, M. and
S. Rajgopal, 2002, The interaction of accounting policy choice and hedging:
Evidence from oil and gas firms, Accounting Review 77, 127-160)

Thanks again, I really appreciate any comments.

Danny Yap
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