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st: joint estimation


From   bpersson@bu.edu
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: joint estimation
Date   Sat, 17 Sep 2005 16:51:32 -0400

Dear Stata list,

I would very much appreciate your help with the following estimation
problem. I am trying to estimate the three parameters a, b, and c in
the regression:

y(t) = a + b* sum(c^s*x(t-s)),  where s ranges from 0 to t.

That is, the three first terms in the regression are:

y(1) = a + b*x(1)

y(2) = a + b* [x(2)+c*x(1)]

y(3) = a + b* [x(3)+c*x(2)+c^2*x(1)]

Hence, there is an additional RHS term associated with each ascending
LHS variable, y(t).

I assume that the nl or ml Stata routines would be appropriate here
since this is a nonlinear problem, but I am not sure how to set up
the problem (so that the parameter b and the sum involving c could be
identified?).

Is it possible to estimate this jointly somehow, or do I have to run
the regression for various fixed c and then pick the one with the
best fit? If so, does anyone have a suggestion on how to do this in
an efficient way?

Thank you very much for your help
Bjorn


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