Essays on Bayesian estimation of dynamic economies

This dissertation investigates questions that arise when we estimate the dynamic stochastic general equilibrium (DSGE) models. Chapter 1 proposes a model-based approach of estimating the capital stock. We specify a dynamic stochastic general equilibrium (DSGE) model with capital utilization to incorporate time-varying aspects of depreciation rate. The log-linearized model is estimated by Bayesian methods with the quarterly data and the per capita capital series is generated with confidence bands using the Kalman smoother. The implied capital stock is compared to the annual official capital stock series. Moreover, we proceed to accommodate the annual series into estimation by considering the estimation of a state space model with missing observations. Chapter 2 investigates the general framework to estimate higher-order approximations of DSGE models and the impact of the new method on welfare evaluations. It is by now commonly practiced to estimate log-linearized DSGE models with Bayesian methods. While log-linear approximations are sufficiently accurate in many applications, the recent literature on the welfare analysis shows that comparisons based on first-order approximations can be misleading. In many cases, second-order perturbation methods provide much more accurate approximations of model dynamics and welfare measures. Up to now, second-order approximated DSGE models have not been estimated with likelihood-based methods because of computational difficulties. Instead, researchers have taken the following short cut: first, estimate the log-linearized economy and, second, plug the estimates into the second-order approximation. Can this practice be misleading? To answer this question, we use a particle filter to construct the likelihood of a second-order approximated DSGE model. We apply our approach to a new Keynesian monetary model, which is widely used to examine the welfare effects of monetary policies.