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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" />
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Pooled QMLE is a technique that allows estimating parameters when [[panel data]] is available with Poisson outcomes. For instance, one might have information on the number of patents files by a number of different firms over time. Pooled QMLE does not necessarily contain [[unobserved effects]] (which can be either [[random effects]] or [[fixed effects]]), and the estimation method is mainly proposed for these purposes. The computational requirements are less stringent, especially compared to [[fixed-effect Poisson model]]s, but the trade off is the possibly strong assumption of no [[unobserved heterogeneity]]. Pooled refers to pooling the data over the different time periods ''T'', while QMLE refers to the quasi-maximum likelihood technique.
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