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st: structural estimation of exponential model with foc using gmm


From   "Mani, Vidya (Kenan-Flagler)" <Vidya_Mani@unc.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: structural estimation of exponential model with foc using gmm
Date   Mon, 8 Mar 2010 21:18:08 -0500

 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

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