Abstract: Simultaneous equation models play an important role in making economic policies,analyzing economic structure and economic forecasting.This paper presents local linear estimators by GMM for every structural equation in nonparametric simultaneous equation models in the random design case that all variables in model are stochastic.We prove its consistency and asymptotic normality in interior by using laws of large numbers and central limit theorems in probability.Its rates of convergence in interior points equal the optimal rate of convergence for estimating nonparametric function.

Key words: Nonparmetric simultaneous equation, local linear estimation, GMM, consistency, asymptotic normality, rate of convergence