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I always struggle to get the true essence of identification in econometrics. I know that we state that a parameter (say $\hat{\theta}$) can be identified if by simply looking at its (joint) distribution we can infer the value of the parameter. In a simple case of $y=b_1X+u$, where $E[u]=0,E[u|x]=0$ we can state that $b_1$ is identified if we know that its variance $Var(\hat{b})>0$. But what if $E[u|X]=a$ where $a$ is an unknown parameter? Can $a$ and $b_1$ be identified?

If I expand the model to $Y=b_0+b_1X+b_2XD=u$ where $D\in\{0,1\}$ and $E[u|X,D]=0$, to show that $b_1,b_2,b_3$are identified, do I simply have to restate that the variance for all three parameters is greater than zero?

I appreciate all the help on clearing my mind concerning identification.


I asked the same question on Cross-Validated but yet no response...

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If you don't get an answer here, you can try CrossValidated, which is the stackexchange site for statistics. –  Gerry Myerson Oct 4 '12 at 3:52
    
@GerryMyerson I previously did but I don't any answer...simply votes! –  ChuckM Oct 4 '12 at 4:09
1  
If you posted this question to that site, you should edit a link to it in your question here. –  Gerry Myerson Oct 4 '12 at 5:56
    
done! thanks for the suggestion –  ChuckM Oct 4 '12 at 7:17
    
And of course vice versa (the point being to avoid unnecessary duplication of efforts). –  joriki Oct 4 '12 at 7:45

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