Hamilton Versus Hamilton: Spurious Nonlinearities

Abstract

Using Monte Carlo simulations, this paper evaluates the ability of the trend-cycle decomposition approach of Hamilton (2018) to adequately identify asymmetries in business cycles fluctuations. By considering different specifications of linear and asymmetric processes consistent with previous estimates, the results indicate that the approach of Hamilton (2018) is unable to preserve true asymmetric behavior nor reproduce U.S. business cycles features, especially in highly persistent or mildly asymmetric processes, or in small samples. The findings are robust to the presence of a time-varying drift, the complexity of the autoregressive dynamics and symmetric nonlinearity. Furthermore, the approach of Hamilton (2018) generates spurious expansionary periods when none exist in the data-generating process. Interestingly, they occur, exclusively, in the case of Markov-switching models of the type introduced by Hamilton (1989), but not for other nonlinear models. Meanwhile, the distortions are also present in the case of symmetric nonlinearity. Based on these findings, caution is called into question when the approach is applied to processes that are thought to behave nonlinearly.