Do long swings in the business cycle lead to strong persistence in output?

This paper investigates how the occasional long swing in the business cycle can produce long-memory behavior in US output. To prove this theoretical relationship, we extend the Hamilton Markov chain regime switching model of real aggregate output to include the occasional long regime. We do this by modeling the duration length of the expansion and recession regimes as draws from a fat-tailed distribution with realized durations that are high in variability and occasionally extreme in value. Empirically, we find that the tail indices for the length of US economic booms and busts correspond with the long-memory parameter estimates of Diebold and Rudebusch [1989. Long memory and persistence in aggregate output. Journal of Monetary Economics 24, 189–209] and Sowell [1992a. Modeling long-run behavior with the fractional ARIMA model. Journal of Monetary Economics 29, 277–302] for real US output. Estimates of our extended regime switching model produce better short- and long-run forecasts of output in comparison to forecasts with a fractionally integrated model. Furthermore, our estimated regime-switching model finds US expansions to be fragile during their infancy, but become more and more likely to continue after surviving the first seven quarters.