Bayesian Estimation of DSGE Models: An Update

This chapter surveys Bayesian methods for estimating dynamic stochastic general equilibrium (DSGE) models. We focus on New Keynesian (NK)DSGE models because of the ongoing interest shown in this class of models by economists in academic and policy-making institutions. Their interest stems from the ability of this class of DSGE model to transmit monetary policy shocks into endogenous fluctuations at business cycle frequencies. Intuition about this propagation mechanism is developed by reviewing the structure of a canonical NKDSGE model. Estimation and evaluation of the NKDSGE model rests on detrending its optimality and equilibrium conditions to construct a linear approximation of the model from which we solve for its linear decision rules. This solution is mapped into a linear state space model. It allows us to run the Kalman filter generating predictions and updates of the detrended state and control variables and the predictive likelihood of the linear approximate NKDSGE model. The predictions, updates, and likelihood are inputs needed to operate the Metropolis-Hastings Markov chain Monte Carlo sampler from which we draw the posterior distribution of the NKDSGE model. The sampler also requires the analyst to pick priors for the NKDSGE model parameters and initial conditions to start the sampler. We review pseudo-code that implements this sampler before reporting estimates of a canonical NKDSGE model across samples that begin in 1982Q1 and end in 2019Q4, 2020Q4, 2021Q4, and 2022Q4. The estimates are compared across the four samples. This survey also gives a short history of DSGE model estimation as well as pointing to issues that are at the frontier of this research agenda.