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I'm interested in potentially using Poisson panel Generalized Method of Moments to hopefully gain consistent estimates for my parameters of interest. However, I have an endogenous binary variable (a time varying dummy variable I suspect is correlated with other time varying unobservables).

Following this working paper here: GMM for panel count data models by Frank Windmeijer, section 3.3, I notice that the Wooldridge moment condition is conditioned based on a 2 period lag of instruments of interest?

Is this correct? Could I use further lags as well? Any help would be definitely appreciated. Thank you. Wooldridge's transformation for endogeneity

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