Bayesian multivariate Beveridge–Nelson decomposition of I(1) and I(2) series with cointegration

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.