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This monograph presents the instrumental variable estimation of the Euler equation and the system of Euler equations from the basic Consumption - based Capital Asset Pricing Model (C-CAPM) using a large set of possible instruments. This large set of possible instruments is due to the Rational Expectation Hypothesis. The optimal GMM estimator, which is used in the estimation, has a finite sample bias proportional to the number of instruments. This means that there is a need of the efficient instrument dimension reduction method. The two different methods of such a reduction are compared: the FIV estimator and the optimal GMM estimator that uses preselected principal components (constructed from the large set of possible instruments) as instruments. Originally, the two methods were developed for linear models. The latter method is extended to non-linear models. The Euler equation is estimated in both nonlinear and linearized forms with different utility function specifications.