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

The consumption Euler equation implies that the output growth rate and the real interest rate are of the same order of integration; thus 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 multivariate Beveridge--Nelson decomposition to such a case, and develops a Bayesian method to obtain error bands. 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 all gaps.