Chapter 20: Generalized Method of Moments estimation of DSGE models
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This chapter examines the application of the Generalized Method of Moments (GMM) to the estimation of dynamic stochastic general equilibrium (DSGE) models. The goal is to present the use of GMM in a pedagogical manner and to provide evidence on its small sample properties. The version of GMM where the moment conditions are computed via simulation – that is, the Simulated Method of Moments (SMM) – is examined in this chapter as well. The use of the method of moments for the estimation of DSGE models is attractive for several reasons. First, it delivers consistent and asymptotically normal parameter estimates under the hypothesis that the model is correctly specified. Of course, other estimators (for example, Maximum Likelihood (ML)) have these properties and, thus, the difference between them is statistical efficiency and computational ease. Second, GMM is relatively fast because the evaluation of the statistical objective function is cheap. Ruge-Murcia (2007) compares the computing time required by different methods used for the estimation of DSGE models and finds that GMM is the fastest, followed, in that order, by ML, SMM and indirect inference. Third, the method of moments is more robust than ML to the stochastic singularity of DSGE models. DSGE models are stochastically singular because they generate implications about a large number of observable variables using as input a relatively small number of structural shocks.

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