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{{merge to|Maximum likelihood estimation|date=October 2017}}
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Partial (pooled) likelihood estimation for [[panel data]] assumes that density of ''y<sub>it</sub>'' given ''x<sub>it</sub>'' is correctly specified for each time period but it allows for misspecification in the conditional density of ''y<sub>i</sub>≔(y<sub>i1</sub>,…,y<sub>iT</sub>) given x<sub>i</sub>≔(x<sub>i1</sub>,…,x<sub>iT</sub>)''.
==Description== Concretely, partial likelihood estimation uses the product of conditional densities as the density of the joint conditional distribution. This generality facilitates [[maximum likelihood]] methods in panel data setting because fully specifying conditional distribution of ''y<sub>i</sub>'' can be computationally demanding.<ref name= "Woolridge">Wooldridge, J.M., Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.</ref> On the other hand, allowing for misspecification generally results in violation of information equality and thus requires robust [[standard error estimator]] for inference. In the following exposition, we follow the treatment in Wooldridge.<ref name= "Woolridge" /> Particularly, the asymptotic derivation is done under fixed-T, growing-N setting.
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