The first two chapters of this thesis develop a new methodology in the Generalized Method of Moments. Typically, researchers assume that the data come from an unknown ideal distribution. In the first two chapters, we relax this assumption by assuming shrinking neighborhoods of this ideal distribution. We show the conditions that are needed for GMM estimators to have a stable behaviour in these neighborhoods and propose a robust GMM estimator based on these conditions. Finally, we show how to perform Moment and Model Selection based on the robust GMM estimators. The third chapter is an extension of the framework introduced by J. Taylor in 1993. We propose a more flexible setting that can capture asymmetric preferences of the Central Bank between the macroeconomic fundamentals as well as a possibly nonlinear economy.