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But, it is not assumed that the joint conditional density is correctly specified. Under some regularity conditions, partial MLE is consistent and asymptotically normal.
By the usual argument for [[M-estimator]]s (details in Wooldridge <ref name= "Woolridge" />), the asymptotic variance of {{radic|''N''}} ''(θ<sub>MLE</sub>- θ<sub>0</sub>) is A<sup>−1</sup> BA<sup>−1</sup>'' where ''A<sup>−1</sup> = E[ ∑<sub>t</sub>∇<sup>2</sup><sub>θ</sub> logf<sub>t</sub> (y<sub>it</sub>│x<sub>it</sub> ; θ)]<sup>−1</sup> and B=E[( ∑<sub>t</sub>∇<sub>θ</sub> logf<sub>t</sub> (y<sub>it</sub>│x<sub>it</sub> ; θ) ) ( ∑<sub>t</sub>∇<sub>θ</sub> logf<sub>t</sub> (y<sub>it</sub>│x<sub>it</sub>; θ ) )<sup>T</sup>]''. If the joint conditional density of y<sub>i</sub> given x<sub>i</sub> is correctly specified, the above formula for asymptotic variance simplifies because information equality says ''B=A''. Yet, except for special circumstances, the [[joint probability distribution#Joint density function or mass function|joint density]] modeled by partial MLE is not correct. Therefore, for valid inference, the above formula for asymptotic variance should be used. For information equality to hold, one sufficient condition is that scores of the densities for each time period are uncorrelated. In dynamically complete models, the condition holds and thus simplified asymptotic variance is valid.<ref name= "Woolridge" />
==References==
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