Chapter 16: Bayesian methods
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The scope of this chapter is to introduce applied macroeconomists to the world of Bayesian estimation methods. Why would an empirical macroeconomist invest in learning Bayesian estimation after having invested hours learning estimation methods like maximum likelihood and generalized method of moments (see previous chapters)? Nowadays, with the advancement of computing power and the establishment of new simulation techniques, it is probably much easier to answer this question compared to, say, thirty years ago. First, Bayesian methods offer a wide range of estimation tools for macroeconomic models, ranging from simple time series models to structural macroeconometric models. When optimizing the likelihood function becomes a daunting task (due to its high dimensionality or multimodality, or due to underidentification of specific model parameters), Bayesian methods can prove more robust since they do not rely on using complex optimization techniques that might get stuck in local optima. Second, Bayesian methods allow the researcher to incorporate prior beliefs in her model. We argue in this chapter that such beliefs are not so difficult to formalize as one may fear a priori, and that they may help to get reasonable estimates and forecasts, for example through soft shrinkage constraints.

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