Distribution-free estimation of some nonlinear panel data models

This paper studies distribution-free estimation of some multiplicative unobserved components panel data models. One class of estimators requires only specification of the conditional mean; in particular, the multinomial quasi-conditional maximum likelihood estimator is shown to be consistent when only the conditional mean in the unobserved effects model is correctly specified. Additional orthogonality conditions can be used in a method of moments framework. A second class of problems specifies the conditional mean, conditional variances, and conditional covariances. Using the notion of a conditional linear predictor, it is shown that specification of conditional second moments implies further orthogonality conditions in the observable data that can be exploited for efficiency gains. This has applications to both count and gamma-type panel data regression models.