Nonlinear GMM estimation in dynamic panels with serially correlated unobservables

This article proposes a nonlinear generalized method of moments (GMM) estimator for dynamic panels with serially correlated unobservables. We demonstrate that our method helps mitigate the weak identification problem in the practically important scenarios where (i) the autoregressive parameter is close to the unit circle and (ii) the ratio of variances of individual heterogeneity and idiosyncratic errors diverges to infinity. We further derive analytical expressions for the bias term of the conventional linear GMM estimators and the nonlinear GMM estimator and show that the use of nonlinear moments results in smaller bias. Specification tests for the structure of serial correlation are also provided. In simulation studies, the nonlinear GMM estimator performs favorably relative to the linear alternatives. Finally, we illustrate our approach by revisiting the income-democracy relationship and estimating a Cobb-Douglas production function. Compared to traditional GMM procedures, our method delivers more accurate estimates of autoregressive parameters in both observables and unobservables when the data exhibit high persistence and measurement error.