The 2008 financial crisis has highlighted the importance of nonlinear features of our economy including risks, uncertainty shocks, rare disasters, structural changes, zero-lower bound, and occasionally binding constraints. Macroeconomists have tried to build nonlinear models to analyze these interesting features and take the models to the data. Dynamic Stochastic General Equilibrium (DSGE) model that essentially takes into account dynamic optimal decision making of households, firms, and government is one of the useful tools to deal with these issues. In the model, there are various random shocks causing the macroeconomic variables such as GDP, consumption, and investment to fluctuate over time. Above all things, the nonlinear approximation of the model allows us to capture the impact of risk on decision making. The focus of this dissertation is to provide a novel Bayesian estimation procedure for the estimation of nonlinear DSGE model and apply the proposed methodologies to analyze some nonlinear issues related to DSGE models. ... In the third chapter, I investigate a real business cycle (RBC) model for a small open economy by estimating the model solved up to second order. The higher order approximation more closely approximates the original model than the linear approximation. In this study, I evaluate the likelihood of the nonlinear model using the Gaussian mixture a lter (GMF) and employ the GMF within the MCMC algorithm. From the estimation results of the quadratic approximation, I obtain the following implications for a small open economy: First, the quadratic RBC model with financial frictions does a good job at identifying the parameters of the nonstationary productivity shock process. Second, the observed data favor the quadratic benchmark RBC and financial-friction models over the linear models. Third, the quadratic RBC model with financial frictions does a better job at capturing serial correlations of the observed data than the linear model with financial frictions. Fourth, contrary to the linear model with financial frictions, a nonstationary productivity shock in the quadratic model plays an important role in explaining Argentine economic fluctuations.
Three essays on bayesian analysis of nonlinear DSGE models