Abstract
Abstract The dynamic IS equation implies that if the real interest rate is I(1), then so is the output growth rate with possible cointegration, and log output is I(2). This paper extends the Beveridge–Nelson decomposition to such a case, and develops a Bayesian method to obtain error bands. The method is valid whether log output is I(1) or I(2). The paper applies the method to US data to estimate the natural rates (or their permanent components) and gaps of output, inflation, interest, and unemployment jointly, and finds that allowing for cointegration gives much bigger estimates of the gaps for all variables.
Highlights
Distinguishing between growth and cycles is fundamental in macroeconomics
This paper focuses on the multivariate Beveridge–Nelson (B–N) decomposition, which decomposes a multivariate I(1) or CI(1,1) series into a random walk permanent component and an I(0) transitory component, assuming a linear time series model such as a VAR model or a vector error-correction model (VECM) for the differenced series
We extend the multivariate B–N decomposition to such a case, and apply Bayesian analysis to obtain error bands for the components
Summary
Distinguishing between growth and cycles is fundamental in macroeconomics. One can define growth as the time-varying steady state, or the permanent component, and cycles as deviations from the steady state, or the transitory component. As Murasawa (2015) shows, for non-US data, the B–N decomposition assuming I(1) log output often gives an unreasonable estimate of the output gap, perhaps because of possible structural breaks in the mean output growth rate; see Figure 1. Murasawa: Bayesian multivariate Beveridge–Nelson decomposition | 3 state form of a VECM Since some hyperparameters such as the tightness (shrinkage) hyperparameter on the VAR coefficients are difficult to choose, Giannone, Lenza, and Primiceri (2015) use a hierarchical prior. To apply the Bayesian multivariate B–N decomposition of I(1) and I(2) series with cointegration, we assume a four-variate VAR model for the output growth rate, the CPI inflation rate, the short-term interest rate, and the unemployment rate, and estimate it in the VECM form. We use the notation proposed by Abadir and Magnus (2002)
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