Robust Poisson Regression

Abstract

It is well-known among applied researchers that the assumption of equality of conditional mean and variance in the Poisson model is rather restrictive, especially that there is a tendency for too low standard errors in case of overdispersion. Pre-tests or more general models have been proposed to solve the problem. Here, we suggest the use of robust standard errors and discuss two alternative asymptotically valid covariance matrices. Monte Carlo experiments show how well this method works even in medium sized samples and how poor the conventional Poisson standard errors perform. The importance of this methodology is then investigated for the firm size — invention activity debate in industrial organization using patent data.

The data set used in the empirical application was provided by Joachim Schwalbach. We thank Jan A. Nelder and Ludwig Fahrmeir for valuable comments.