This paper focuses on the estimation of fiscal response functions for advanced economies and on the performance of alternative specifications of the Generalized Method of Moments (GMM) estimator for the rule's parameters. We first estimate the parameters on simulated data through Monte Carlo experiments; we then run an empirical test on data for the European Monetary Union (EMU). We estimate both the Cyclicallyadjusted primary balance (CAPB) and the Primary balance (PB) models, and check the robustness of the estimates to different specifications of the GMM estimator and to alternative settings of the parameters. We also compare alternative instrument reduction strategies in a context where several endogenous variables enter the model. We find that the system GMM estimator is the best-performing in this framework and the high instrument count comes out not to be problematic. We also make the algebraic links between the parameters in the CAPB and in the PB models explicit, suggesting an effective strategy to estimate the discretionary fiscal response from the coefficients of the PB model. In the empirical application on a dataset for EMU Countries, we find that the evidence of a-cyclicality of discretionary policies is robust to all the specifications of the GMM estimator.