A Generalized Poisson-Pseudo Maximum Likelihood Estimator

We examine the Constant Variance to Mean Ratio (CVMR) assumption—a key condition to make PPML an efficient estimator—and propose Generalized Poisson-Pseudo Maximum Likelihood (G-PPML) as a complementary estimator. We estimate the conditional variance of the dependent variable using an iterated GMM, thereby providing a specification test for the CVMR assumption. The proposed G-PPML estimator, which capitalizes on conditional variance estimates, is more efficient than existing PML estimators. After establishing the asymptotic properties of the G-PPML estimator, we verify that it performs well under fairly general assumptions about the conditional variance. Our empirical application to trade flows data demonstrates that the CVMR assumption is satisfied in most but not all cases. The standard errors of G-PPML are approximately 20% smaller than those of PPML, demonstrating its improved estimation efficiency.