Remeasuring and decomposing stochastic trends in business cycles

This paper is motivated by the fact that the standard deviation of cyclical TFP derived from the standard approach under the stochastic trend is not even close to the real-world data. The main part of the paper devotes to developing a new method to apply geometric Brownian motion to characterize TFP in continuous time and converting it to an estimated process of random walk with drift. As a result, the drift estimate together with the lagged TFP in the random walk process are the stochastic trend of TFP and the stochastic error term in the random walk with drift process is the cyclical component of TFP. I then have two findings: the first one is that the standard deviation of cyclical TFP derived from the new approach is much closer to the real-world data; the second one is that stochastic trend of TFP can be decomposed into three parts: an initial value, a deterministic trend, and a term involved with Weiner process. Moreover, this paper argues that, by recalculating the business cycle statistics based on a rational expectations model, if we remeasure the stochastic trend and cyclical component of TFP using the new approach, then the ability of real business cycle model to mimic real-world economic fluctuations will be significantly improved.