The Stochastic actor-oriented model (SAO) is a statistical model for longitudinal network data. The most often used procedure for the estimation of the parameter of the SAO model is the Method of Moments (MoM), which estimates the parameters using one observed statistic for each estimated parameter. A new set of statistics is defined taking into account the different ways of creating and deleting ties to which a certain effect can contribute. This definition leads to having more than one statistic for a single parameter, i.e. to an over-determined system of equations. Thus, the ordinary MoM cannot be applied. A suitable method then is the Generalized Method of Moments (GMM), an estimation technique mainly used in econometrics, and potentially more efficient than the MoM. Like the regular MoM, the GMM is based on the differences between the expected values of the statistics and their sample counterparts, but the GMM involves the minimization of a quadratic function of these differences rather than setting all differences to 0. This means that an extra problem arises: the determination of a matrix of weights reflecting the different importance and correlations of the statistics involved. An optimization-simulation algorithm is used, following the approach suggested by Gelman (1995) and based on the Newton-Raphson algorithm, to compare the estimators deriving from the MoM and the GMM. Simulation results suggest that the new set of statistics performs better when network observations are close. In fact, in this context the standard errors of the GMM estimators are lower than those of the MoM.