Using generalized estimating equations to estimate nonlinear models with spatial data

We study the estimation of nonlinear models with cross-sectional data using two-step generalized estimating equations within the quasi-maximum likelihood estimation framework. To improve efficiency, we propose a grouped estimator that accounts for potential spatial correlation in the underlying innovations of nonlinear models. Under mild weak dependence assumptions, we provide results on estimation consistency and asymptotic normality. Monte Carlo simulations demonstrate the efficiency gain of our approach compared to various estimation methods. Finally, we apply the proposed approach to examine the role of cultural distance in an extended gravity equation using international trade data from China. Compared to existing methods, our approach yields estimates with smaller standard errors and reinforces the hypothesis that both cultural and geographical distances significantly negatively influence international trade.