The estimation uncertainty of permanent-transitory decompositions in co-integrated systems

The topic of this article is the estimation uncertainty of the Stock–Watson and Gonzalo–Granger permanent-transitory decompositions in the framework of the co-integrated vector autoregression. We suggest an approach to construct the confidence interval of the transitory component estimate in a given period (e.g., the latest observation) by conditioning on the observed data in that period. To calculate asymptotically valid confidence intervals, we use the delta method and two bootstrap variants. As an illustration, we analyze the uncertainty of (U.S.) output gap estimates in a system of output, consumption, and investment.