Applying Bayesian methods for macroeconomic modeling of business cycle phases

Abstract

In the present research, the features of applying two models for estimating macroeconomic dynamic in the USA are investigated: Bayesian vector autoregression and Bayesian vector autoregression with Markov switching. The research goal is to identify periods, structure of fluctuations and the main directions of interaction of the variables (real US GDP and employment) using Bayesian vector autoregression models. Models with Markov chains include many equations (structures). The switching mechanisms between these structures are controlled by an unobservable variable that follows a first-order Markov process. The analyzed variables were taken from the first quarter of 1953 to the third quarter of 2015. The model parameters were estimated on the basis of a prior for the multivariate normal distribution — the inverse Wishart distribution (a generalization of the Minnesota a priori distribution). Basing on the results of the estimation of the two-dimensional model with Markov Switching the average GDP growth rate and expected duration of phases was calculated. The estimated model is acceptable for describing the US economy and with high accuracy describes the probability of being in a particular phase in different periods of time. On the basis of medium-term forecasts, root mean squared errors of the forecast are calculated and a conclusion is made about the most appropriate model. Within the framework of this paper, impulse response functions are built allowing to evaluate how variables in the model react on fluctuations, shocks.