st: structural estimation of exponential model with foc using gmm

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

Dear All,
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  (equation 2, 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 estimate 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

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