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== Example: pooled QMLE for Poisson models==
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.
The [[Poisson distribution]] of <math>y_i</math> given <math>x_i</math> is specified as follows:<ref name="CameronTrivedi">Cameron, C. A. and P. K. Trivedi (2015) Count Panel Data, Oxford Handbook of Panel Data, ed. by B. Baltagi, Oxford University Press, pp. 233–256</ref>
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A popular choice is <math>m=(x_t,b_0)=\exp(x_t b_0)</math>, as Poisson processes are defined over the positive real line.<ref name="Woolbridge2002"/> This reduces the conditional moment to an exponential index function, where <math>x_t b_0</math> is the linear index and exp is the link function.<ref>McCullagh, P. and J. A. Nelder (1989): Generalized Linear Models, CRC Monographs on Statistics and Applied Probability (Book 37), 2nd Edition, Chapman and Hall, London.</ref>
==References==
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