Essays on Measuring Monetary Policy Uncertainty and Forecasting Business Cycle

Abstract

Chapter 1 is a survey paper for economists new to the field of a Monte Carlo simulation based method: particle filter. Particle filter can be applied to many flexible state space models such as non-linear, non-Gaussian, stochastic volatility models or stochastic volatility models with zero lower bound. These models have become increasingly popular in macro-economics and finance. The stochastic volatility model with zero lower bound is designed for applying zero interest rate policy. The primary purpose of this paper is to provide particle filter algorithms for these models and make comparisons of the Kalman filter, extended Kalman filter and particle filter. In Chapter 2, we estimate a non-linear, non-Gaussian state space model for the short-term interest rate. The model features a potentially binding zero-lower bound constraint and stochastic volatility. We use the model to extract a measure of monetary policy uncertainty. We find that ignoring the zero-lower bound constraint on nominal interest rate leads to overestimation of the shadow rate and underestimation of the monetary policy uncertainty in recent periods. We find that the policy uncertainty is especially high at the beginning and the end of a quantitative easing episode. We also find a policy uncertainty shock lowers output growth and raises unemployment and seems to be a priced risk factor in the stock market. In Chapter 3, I build a probit model of yields and business cycles. The proposed model incorporates the interrelation of yields and a latent business cycle factor, which will be extracted from the joint model. Different to previous literature, this model allows for interactions of the latent business factor and a portfolio of yields. The parameters and the latent variable are estimated through likelihood maximization at one step. I use the fully adapted particle filter to generate the likelihood of the nonlinear model. I find that the model with the autocorrelated latent variable forecasts better than the model without autocorrelated latent variable in terms of in-sample and out-of-sample forecast. The model implied business cycle factor indicates all 7 recessions from 1969 to 2015.