Dear all,

I have a question related to the estimation of the exponential model. This is related to this thread:
https://www.statalist.org/forums/for...sion-nl-vs-reg

The recommendation was to use the Poisson (or gamma quasi-MLEs). If I got it right, this is because of efficiency gains when estimating the parameters.

The issue is my model not fully multiplicative but it has a sum. There is an extra parameter "s" which mean I cannot just add the independent variables. A simplified version of my structural equation would be:

Y = [ X1^(s-1) X2^(s) + X3^(s-1) X4^(s) ]^b1 [ X1^(-s) X2^(s) + X3^(-s) X4^(s) ]^b2

I could give a try to calibrate "s" (then I can compute the sums) to use Poisson or gamma quasi-MLEs. However, it is not clear this is a superior approach just because there is a gain in efficiency. I would lose "s". I had a look to the commands -ppml and -glm and they cannot fit this equation.

Is there still an alternative to NLS to estimate my equation? Any feedback would be most welcomed.

Best,

Paulo

PS: A less simplified version of my equation is

Y_i = [ (p_ij)^(s-1) (q_j)^(s) + (p_ik)^(s-1) (q_k)^(s) ]^b1 [ (p_ij)^(-s) (q_j)^(s) + (p_ik)^(-s) (q_k)^(s) ]^b2

where i, j and K can be the three individuals in my model. I think renaiming these variables as X1-X4 does not change anything but just in case.