st: structural estimation of exponential model with foc using gmm

["Mani, Vidya (Kenan-Flagler)" <Vidya_Mani@unc.edu>]

 Hi,

I had a question on structural estimation using GMM.

I have 2 equations:

1.       Sales equation: S = a*(N^b1)*exp(-b2/l)

2.       Profit equation: P = S - w*l

The parameters to be estimated are a, b1, b2 and w

The FOC wrt l  for the profit equation (by substituting the value of S) is

3.       a*(N^b1)*exp(-b2/l)*(b2/l^2) - w  = 0

Using GMM I would like to estimate equations 1 and 3  with instruments as N and l.

However, if I use equation 3 in its present form, I do not seem to get convergence even after trying different initial values, providing derivatives for parameters and using a log form.

I would like to know if I can substitute equation 3 with

4.       S*b2 - w*(l^2) = 0

Where I use the form of S from equation 1 and substitute back in 3. I now estimates equations 1 and 4 as the moment equations in GMM. Would it be possible to tell me if I am making a mistake while estimating the parameters a, b1, b2 and w using equations 1 and 4 instead of using equations 1 and 3?

Thank you for your help,

Vidya

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/