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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.

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I was told that for the model with the dummy variable I simply have to show that $[X'X]^{-1}$ exist...meaning that the determinants of this matrix is not equal to 0. Correct? – CharlesM Oct 4 '12 at 3:09
I also posted question on math exchange and nothing.... – CharlesM Oct 5 '12 at 0:31
Does this help or just more of what you already know? UChicago course notes – kirk May 6 '13 at 8:48

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