Mark,
Thanks for your input. Greene's series of papers on nonlinear models and fixed effects is certainly helpful. I'll have to go over the paper more carefully, but initially it seems I may be OK in terms of consistency since the data covers a larger number of time periods. It seems that these models generally get better as T increases (but that is just a first guess). Greene certainly seems to be optimistic that panel data and nonlinear models can coexist.
As far as the other issues goes, de-meaning would seem to give me more flexibility. Maybe I could wipe out the fixed effects and then use the -nlfcns- to estimate the nonlinear model. -cnsreg- is close to what I need but it only accepts linear constraints and I would like to add a nonlinear one.
Thanks again,
Larry Chavis
Ph.D. Student
Stanford Graduate School of Business
[email protected]
(650)724-4909
-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Mark Schaffer
Sent: Tuesday, April 20, 2004 8:10 AM
To: [email protected]
Subject: Re: Nonlinear Least Squares and Fixed Effects
Larry,
Is your estimation going to be consistent? Sometimes, with fixed
effects models, the incidental parameters problem makes the estimator
inconsistent.
Bill Greene has a short paper about this on his website that also has
some useful reading:
http://www.stern.nyu.edu/~wgreene/fixedeffects.doc
In your first example, it looks like you might be able to de-mean the
data by hand to wipe out the fixed effects and then do a constrained
linear estimation with -cnsreg-.
Hope this helps.
--Mark
Subject: st: Nonlinear Least Squares and Fixed Effects
Date sent: Mon, 19 Apr 2004 13:28:34 -0700
From: "Chavis, Larry Wilson" <[email protected]>
To: <[email protected]>
Send reply to: [email protected]
>
>
> Hi,
>
> I am working with panel data and I am trying to impose some nonlinear constraints on an equation with a large number of fixed effects. So far I have been unsuccessful and I have a couple of questions in this regard. Any advice you could provide would be greatly appreciated.
>
>
> 1) For one specification I have run the following linear regression -xtreg lnunit dummy1 dummy2 dummy3 week2-week104, fe i(id)-. Basically I have about 8,000 products (id's) that I have data on for 104 weeks. I would also like to estimate this while constraining the coefficients on dummy1
dummy2 and dummy3 in a nonlinear fashion (i.e. _b[dummy1] = (_b[dummy2]^2) / _b[dummy3]. I am able to test the restriction post-estimation using -testnl-, but I would like to incorporate the restrictions into the regression. Any ideas?
>
>
> 2) Similarly I could aggregate the data by country so that the panel data now represents 43 countries over 104 weeks. Now the data is a manageable size to use the -nl- command and set up the regression using -nlfcns-. The only problem is that I am not sure how to set up the fixed effects
dummies in the equation. The only thing I can think of is to us the brute force method and just type in something like - '1' = $B1 * week1 + $B2 * week2 + $B3 week3 + ......-. This seems a little cumbersome since I have over 140 fixed effect dummies. I would also have to type a similarly long
list to declare and initialize the parameters. I thought of using -for num- to declare and initialize the sequence of variables, but I am still stuck when it comes to the actual equation. Is there something akin to a summation sign that I could use in this situation?
>
>
> Thanks,
> Larry Chavis
>
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
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