A. Colin Cameron and Per Johansson
"Count Data Regression Models using Series Expansions: with Applications"
Journal of Applied Econometrics, May 1997, Vol. 12, pp.203-223.
A new class of parametric regression models for both underdispersed and overdispersed count data is proposed. These models are based on squared polynomial expansions around a Poisson baseline density. The approach is similar to that for continuous data using squared Hermite polynomials proposed by Gallant and Nychka and applied to financial data by, amongst others, Gallant and Tauchen.
The count models are applied to underdispersed data on the number of takeover bids received by targeted firms, and to overdispersed data on number of visits to health practitioners. The models appear to be particularly useful for underdispersed count data.