Exponential Panel Models with Coefficient Heterogeneity

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 difficulty. 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.