Title: Solving the unobserved components puzzle: A fractional approach to measuring the business cycle
Authors: Tobias Hartl - University of Regensburg (Germany) [presenting]
Rolf Tschernig - Universitaet Regensburg (Germany)
Enzo Weber - University of Regensburg and Institute for Employment Research (Germany)
Abstract: Measures for the business cycle obtained from trend-cycle decompositions are puzzling, as they often are noisy, at odds with the NBER chronology, and not well in line with economic theory. We argue that these results are driven by the neglect of fractionally integrated trends in log US real GDP. To account for fractional integration, we develop a generalization of trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics and treats the integration order as a random variable. The integration order is jointly estimated with the other model parameters via a quasi maximum likelihood estimator that is shown to be consistent and asymptotically normal. In addition, single-step estimators for the latent components that are identical to the Kalman filter and smoother but computationally superior are derived. We find that log US real GDP is integrated of order around $1.3$, the resulting trend-cycle decomposition is in line with the NBER chronology, and the model well explains the puzzling results in the literature that result from model misspecification.