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In this paper, we review some estimators of count regression (Poisson and negative binomial) models in panel data modeling. These estimators based on the type of the panel data model (the model with fixed or random effects). Moreover, we study and compare the performance of these estimators based on a real dataset application. In our application, we study the effect of some economic variables on the number of patents for seventeen high-income countries in the world over the period from 2005 to 2016. The results indicate that the negative binomial model with fixed effects is the better and suitable for data, and the important (statistically significant) variables that effect on the number of patents in high-income countries are research and development (R&D) expenditures and gross domestic product (GDP) per capita.
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