If heterogeneous slopes are ignored in exponential panel models, fixed effects Poisson may not estimate any quantity of interest. Existing estimation methods often involve treating only a small subset of the slopes as "random effects" and integrating from the likelihood, increasing computational diffculty. I propose a test to detect slope heterogeneity that, unlike the traditional approach, does not amount to testing for information matrix equality. Additionally, I present a correlated random coefficients approach to identification which allows for estimation of the coefficient means and average partial effects. I test these proposed methods using a Monte Carlo experiment and apply them to the patent-R&D relationship for U.S. manufacturing firms.