In modeling claim count data in an insurance environment, I began with Poisson but then noticed overdispersion. A Quasi-Poisson better modeled the greater mean-variance relationship than the basic Poisson, but I noticed that the coefficients were identical in both Poisson and Quasi-Poisson models.

Is this an error? If it is an error, how might I resolve it? If it isn't an error, why might this be the result and what would be the benefit of using Quasi-Poisson over Poisson?

Things to note:

• I am using glm() with family = poisson or quasipoisson and a log link for code.
• I tested for overdispersion via dispersiontest in the AER package. My dispersion parameter was approximately 8.4, with p-value at the 10^-16 magnitude.
• When running the Poisson code, I come out with warnings of "In dpois(y, mu, log = TRUE) : non-integer x = ...".