More efficient estimation of multiplicative panel data models in the presence of serial correlation

We provide a systematic approach in obtaining an estimator asymptotically more efficient than the popular fixed effects Poisson (FEP) estimator for panel data models with multiplicative heterogeneity in the conditional mean. In particular, we derive the optimal instrumental variables under appealing "working" second moment assumptions that allow underdispersion, overdispersion, and general patterns of serial correlation. Because parameters in the optimal instruments must be estimated, we argue for combining our new moment conditions with those that define the FEP estimator to obtain a generalized method of moments (GMM) estimator no less efficient than the FEP estimator and the estimator using the new instruments. A simulation study shows that the overidentfied GMM estimator behaves well in terms of bias and it often delivers nontrivial efficiency gains - even when the working second-moment assumptions fail. We apply the new estimator to modeling firm patent filings and spending on R&D, and find nontrivial reductions in standard errors using the new estimator.