New robust estimators for the fixed effects negative binomial model: a simulation and real-world applications to European panel data

This study introduces a more flexible approach by employing the fixed effects negative binomial model to address challenges associated with outliers and dispersion. Unlike previous studies that focused on the robust estimation of the Poisson model with fixed effects, which assumes equidispersion and cannot handle dispersion in count panel data, we develop novel estimators specifically designed for the fixed effects negative binomial panel regression model in the presence of outliers, under-dispersion, and over-dispersion. The methodology is assessed through comprehensive simulation experiments across different scenarios. A comprehensive empirical analysis is conducted using updated and extended panel datasets on COVID-19 and patent applications in Europe. The results of both Monte Carlo simulation and the empirical studies indicate that the robust estimators: the robust fixed negative binomial Huber, fixed negative binomial Hampel, and fixed negative binomial Tukey estimators, outperform the classical non-robust fixed negative binomial estimator.