Comments embedded in original post...
> Kenneth Benoit wrote:
>
> Perhaps someone can help me with this problem. I am trying to solve for
> a number of parameters in three equations which are linked through
> composition of the data. each model yields different parameter
> estimates when estimated alone since the parameters are overidentified.
> I'd be happy for any advice on the problem!
>
> Ken Benoit
>
> ---------------------------------------------------------
> Kenneth Benoit http://benoit.tcd.ie
> Department of Political Science mailto:[EMAIL PROTECTED]
> Trinity College Tel: 353-1-608-2491
> Dublin 2, Ireland Fax: 353-1-677-0546
> Consider a system where:
>
> Y1 = X0 + (1-g11)b1 X1 + g21b2X2 + g31b3X3
>
> Y2 = X4 + g12b1 X1 + (1-g22)b2X2 + g32b3X3
>
> Y3 = X5 + g13b1 X1 + g23b2X2 + (1-g33)b3X3
It is not clear that this is possible. From the constraints below,
Y1 + Y2 + Y3 = X0 + X4 + X5 = 1; it follows that the other 9
terms must add to zero. But the gij are all nonnegative, and from the
description below so must be the bi; then can X1, X2, and/or X3 be
negative? If not, then every one of the 9 terms must equal zero.
> and: (I take it that ³ means < or =. and " means 'for all')
>
> 1 = Y1 + Y2 + Y3, 0 ³ Yi ³ 1.0 "i
> 1 = X0 + X4 + X5, 0 ³ Xi ³ 1.0 "i
> 1 = g11 + g12 + g13, 0 ³ gij ³ 1.0 "i,j
> 1 = g21 + g22 + g33
^^^ This should read g23 ?
> 1 = g31 + g32 + g33
>
> GOAL: To estimate g's and b's. Problems: overidentification; effects
> of the data items and some of the parameters summing to 1 which I
> still don't fully understand.
> Background: This is for a voting transition study in Italy, where the
> b's represent a the proportion of voters following a rational
> proximity model, and the g's represent the discrete probability
> distribution according to which non-rational voters distribute their
> votes to one of three electoral coalitions (corresponding to the Y's).
It is not clear to me why it is reasonable to multiply the g's by the
b's. Seems to be representing the proportion of (those voters who vote
rationally) who are voting non-rationally, which on the face of it would
seem to be a contradiction in terms.
> I have data for all of the Y's and X's, which are proportions.
>
> Possible ways to simplify:
>
> * Set gij's to constants before estimation.
> * Set gij = g* " i,j.
> * Set b3 = 1.
> * Set b1 = b2.
>
> -----------------------------------------------------------------------
> File translated fromTEXby TTH,version 2.56.
> On 26 Nov 1999, 14:00.
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