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Dear Colleagues:
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!
Apologies for cross-postings.
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
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<title>Kenneth Benoit</title>
Kenneth Benoit<br>
<tt>[EMAIL PROTECTED]</tt><br>
Nov 26, 1999
<p>
<b>Consider a system where:</b>
<p>
<centEr><table border=0 align=center><tr><td>
<Table align=left><tr><td nowrap align=center>
</td><td nowrap align=center>
<TaBle>
<tr><td align="center"><TablE border=0><tr><td nowrap align=center>
Y<sub>1</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
= </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
X<sub>0</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
(1<font face=symbol>-</font
><font face=symbol>g</font
><sub>11</sub>)<font face=symbol>b</font
><sub>1</sub> X<sub>1</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>21</sub><font face=symbol>b</font
><sub>2</sub>X<sub>2</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>31</sub><font face=symbol>b</font
><sub>3</sub>X<sub>3</sub> </td></TABle></td>
<tr><td align="center"><TablE border=0><tr><td nowrap align=center>
Y<sub>2</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
= </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
X<sub>4</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>12</sub><font face=symbol>b</font
><sub>1</sub> X<sub>1</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
(1<font face=symbol>-</font
><font face=symbol>g</font
><sub>22</sub>)<font face=symbol>b</font
><sub>2</sub>X<sub>2</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>32</sub><font face=symbol>b</font
><sub>3</sub>X<sub>3</sub> </td></TABle></td>
<tr><td align="center"><TablE border=0><tr><td nowrap align=center>
Y<sub>3</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
= </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
</td></TABle></td><td align="center"><TablE border=0><tr><td nowrap align=center>
X<sub>5</sub> </td></TABle></td><td align="center"><TablE border=0><tr><td nowrap
align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>13</sub><font face=symbol>b</font
><sub>1</sub> X<sub>1</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
<font face=symbol>g</font
><sub>23</sub><font face=symbol>b</font
><sub>2</sub>X<sub>2</sub> </td></TABle></td><td align="center"><TablE
>border=0><tr><td nowrap align=center>
+ </td></TABle></td><td align="right"><TablE border=0><tr><td nowrap align=center>
(1<font face=symbol>-</font
><font face=symbol>g</font
><sub>33</sub>)<font face=symbol>b</font
><sub>3</sub>X<sub>3</sub> </td></TABle></td></TaBle>
</td><td nowrap align=center>
</td></Table>
</td></table></centEr>
<p>
and:
<p>
1 = Y<sub>1</sub> + Y<sub>2</sub> + Y<sub>3</sub>, 0 <font face=symbol>³</font
> Y<sub>i</sub> <font face=symbol>³</font
> 1.0 <font face=symbol>"</font
>i<br>
1 = X<sub>0</sub> + X<sub>4</sub> + X<sub>5</sub>, 0 <font face=symbol>³</font
> X<sub>i</sub> <font face=symbol>³</font
> 1.0 <font face=symbol>"</font
>i<br>
1 = <font face=symbol>g</font
><sub>11</sub> + <font face=symbol>g</font
><sub>12</sub> + <font face=symbol>g</font
><sub>13</sub>, 0 <font face=symbol>³</font
> <font face=symbol>g</font
><sub>ij</sub> <font face=symbol>³</font
> 1.0 <font face=symbol>"</font
>i,j <br>
1 = <font face=symbol>g</font
><sub>21</sub> + <font face=symbol>g</font
><sub>22</sub> + <font face=symbol>g</font
><sub>33</sub> <br>
1 = <font face=symbol>g</font
><sub>31</sub> + <font face=symbol>g</font
><sub>32</sub> + <font face=symbol>g</font
><sub>33</sub> <br>
<p>
<b>GOAL:</b> To estimate <font face=symbol>g</font
>'s and <font face=symbol>b</font
>'s. Problems:
overidentification; effects of the data items and some of the
parameters summing to 1 which I still don't fully understand.
<p>
<b>Background:</b> This is for a voting transition study in Italy,
where the <font face=symbol>b</font
>'s represent a the proportion of voters following a
rational proximity model, and the <font face=symbol>g</font
>'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). I have data for all of the Y's and
X's, which are proportions.
<p>
Possible ways to simplify:
<UL>
<p>
<li> Set <font face=symbol>g</font
><sub>ij</sub>'s to constants before estimation.
<li> Set <font face=symbol>g</font
><sub>ij</sub> = <font face=symbol>g</font
><sup>*</sup> <font face=symbol>"</font
> i,j.
<li> Set <font face=symbol>b</font
><sub>3</sub> = 1.
<li> Set <font face=symbol>b</font
><sub>1</sub> = <font face=symbol>b</font
><sub>2</sub>.
</UL>
<p>
<p><hr><small>File translated fromT<sub><font size="-1">E</font></sub>Xby <a
href="http://hutchinson.belmont.ma.us/tth/">T<sub><font
size="-1">T</font></sub>H</a>,version 2.56.<br>On 26 Nov 1999, 14:00.</small>
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