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st: Constrained regression question

From   "John Pfaff" <[email protected]>
To   <[email protected]>
Subject   st: Constrained regression question
Date   Tue, 27 Mar 2012 18:04:11 -0400

I am curious if it is possible to use Stata to estimate a set of weights. My basic problem is the following:
I have data on R_t for years t = 1988 to 2008
I have data on A_t for years t = 1977 to 2008
I want to see how well I can approximate R_t using 11 lagged years of A_t. In other words, I want to estimate the weights w_s in the following equation:
R_t = w0*A_t + w1*A_(t-1) + w2*A_(t-2) + ... + w11*A_(t-11)
The catch is that I have two sets of restrictions:
(1) For each w_s, 0 < w_s < 1.
(2) Also, w0 + w1 + ... + w11 = 0.95
Simply running a simple regression fails, since restriction (1) is violated numerous times (lots of negative weights).
I started at, which showed me how to satisfy restriction (1). But two problems arise:
* The non-linear regression dropped 7 of the 11 A variables.
* I do not see any obvious way to impose restriction (2) when using invlogit.
Is there a better way to accomplish this? Thank you for any assistance!

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