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Re: st: RE: Nonlinear least squares restrictions


From   "G. Anderson" <ga274@cam.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Nonlinear least squares restrictions
Date   06 Jun 2013 09:29:28 +0100

Hi Tim, Thanks a lot for getting back to me. Unfortunately I'm not sure standard OLS will work here- I want to constrain the relative responses in the vector B to be constant over time- and the estimate both the dummy scalar b (for each year) and the vector B.

Will give the stuff on dummy variables a read - looks like it could prove useful.

Many thanks,

Gareth


On Jun 6 2013, tshmak wrote:

Hi Gareth, I think this is a linear regression rather than a nonlinear regression problem.

Naively, we can just create a variable called year, run:
reg y i.year##X, nocons

This would result in a different intercept and slope for each year. To make the average of b = 1, simply divide the year-specific slopes by the average of the slopes, the average being your estimate of B.

The only problem of this approach is that your slopes across years would not meet at the boundary. To constraint the slopes to meet, you need to use splines. The best place to start is probably Roger Newson's -bspline- package. Dr. Newson has also written a few informative articles explaining their use in Stata Journal.

HTH, Tim

ps. I think the reason -nl- fails on this problem is that the problem is not identified unless you can somehow constraint the b to average 1, and I'm not sure you can do that in -nl-.



-----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of G. Anderson Sent: 05 June 2013 19:24 To: statalist@hsphsun2.harvard.edu Subject: st: Nonlinear least squares restrictions

Hi,

Using daily data, I am trying to estimate a relationship of the form y=a +bBX +u

Where a is a scalar which can vary across years, b is a scalar which can vary across years, X is a vector of data and B is a vector of parameters which is fixed across years.

Therefore I am trying to estimate a, b and B. I want to normalise b so that on average it is equal to 1 across years.

I have tried experimenting using the nonlinear regression function but so far to no avail- is this type of restriction possible in Stata?

Many Thanks, Gareth
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