Panel Least Squares estimation method Nonlinear optimization algorithm

[acemi]

Hello,

I am estimating a non linear model via a panel data set in eviews9. Since model spec is nonlinear, I enter the equation directly in specification tab and selecting the default LS- Least Squares method, selecting "None" from Panel Options Tab > Cross section and Weights dropdown lists. One estimation result report shows eviews used Panel Least Squares Method.

1-What optimization algorithm does eviews use in Panel Least Squares Method ? (i.e. standard iterative algorithms like newton-raphson, Marquardt etc)
2- When my data is panel I cannot see or choose the method from equation estimation tab. How can I see or choose the algorithm ?

PS. I searched eviews guide and forum, couldnt find any info on this.

Would appreciate any info on this.
Thank you in advance

[acemi]

Still not a clue on this issue.. I guess it must be either a concept so well known that nobody comments even the moderators..

All the best.

[EViews Glenn]

Sorry, didn't see this.

The panel NLS uses Gauss-Newton (the panel engine hasn't yet been revised to allow for all of the options available for standard single equation estimation).

[acemi]

Thank you.

[acemi]

Hello,

I ran through Eviews help files and could not find how panel nonlinear least squares method(Gauss Newton Algorithm) differs from nonlinear least squares method(Gauss Newton Algorithm) for reference purposes. Would appreciate if anyone can refer to a resource or comment on it.
Many thanks in advance.
acemi

[EViews Glenn]

I am not sure what you mean by differs. It's the same algorithm applied to a different objective function.

[acemi]

Dear Eviews Glenn,

Sorry for the confusion, I am trying to explicitly state objective function to be minimized for Panel Nonlinear Least Squares. I couldn't find it Eviews help files, or on the internet, or missed out. Would appreciate if you can provide any reference on this.
Best regards
acemi

[EViews Glenn]

It depends on what model you are estimating, though at heart it's some variant on a sum-of-squares.

[acemi]

Dear Glenn,

I understand but isnt it possible to write it out in shorthand ? If I'm not mistaken at heart we should be approximating the SSR (objective function to be minized) with quadratic taylor series.Then applying GNA for iterations. But how this works out for panel setting I cant figure it out. Would be grateful if you can comment.
PS : I'm also attaching NLS specification
BR
acemi

[EViews Glenn]

I don't see your specification. That said, the Gauss-Newton methods use first derivatives in the optimization. The Newton-Raphson uses the second derivatives. There's nothing different about the panel algorithms than the algorithms discussed for the standard NLLS. The only difference is that the SSRs are obtained after stacking the cross-sections and applying transformations and weighting as necessary for the estimator in question.

As in

http://www.eviews.com/help/helpintro.ht ... ect_header

The only difference is that the objective is slightly more complex.

[acemi]

When I try to add the spec via word, error parsing server response is given. So pasting it in text below sorry for the messy look.

ln⁡〖y_it 〗={(1⁡〖-e^(-βt) 〗 )α(1-θ) ln⁡〖s_it 〗+(1⁡〖-e^(-βt) 〗 )β1 ln⁡〖L_it 〗+(1⁡〖-e^(-βt) 〗 )ϕ ln⁡〖〖FI〗_it 〗+(1⁡〖-e^(-βt) 〗 )ln[γ+(1-α)β1n_it ]+(1⁡〖-e^(-βt) 〗 )α(1-θ) ln⁡[(n_it+δ)+β1n_it ] }+e^(-βt) ln⁡〖y_(it-1) 〗+u_it

[EViews Glenn]

What is it that you put into EViews?

[acemi]

nls object within the attached wf has the specification.
a valid starting point for c vector is : 0.010000 0.200000 0.200000 0.000000 0.400000
best regards

[EViews Glenn]

As you have experienced, that specification can't really be estimated with these data. I've played around with it a bit and it looks as though there's an identification problem as the C(3) coefficient wants to go off to infinity.

Our older panel code only supports one type of nonlinear estimation technique (in contrast to the newer standard equation nonlinear estimation implementation) so I've converted your problem into a non-panel workfile (by generating a YLAG and TREND variable in the panel, then unstructuring), and then running a modified equation on an unstructured workfile. I can get convergence with BFGS, but the standard errors and gradients suggest that the model isn't estimated with any precision.

In short, I think the parameters of the model are not well identified (collinearity in a nonlinear setting).

One last comment. I can't really read your Word specification so I'm not certain that the EViews spec you are estimating matches what you have there. You should probably double check that just to be sure.

[acemi]

Understood, my sincere thanks for your elaborate effort and explanations. At least we now know there exists collinearity.

About your last comment : 1) specification was uploaded in workfile in my previous post within nls equation object.

2) I ran a comprehensive simulation via program and for these starting values the algorithm converged c(1)-c(5) : 0.01, 1.8, 0.1, 0.7, 0.4
I'm attaching workfile having converged results in eqn object eq01. Not all coeff are significant but two are and additional one more is very close.
The reason I was checking for collinearity was that very few convergence existed and most of them are out of range for theory.

BR
acemi