Non Linear Economic Time Series as a Testbed for Dynamic Macro Models

Abstract

This is a short exercise in using nonlinear time series analysis (NLTS) to assess the fit of a dynamic nonlinear macro economic process, the Goodwin model, against “realworld” nonlinear time series. The methodology follows the approach developed by Huffaker (2015 and variously) 1 After simulating the Goodwin model and generating plausible time series and an attractor a topologically equivalent attractor is extracted from a single dimension (unemployment) from the Goodwin model. Real US unemployment data is then subjected to SSA analysis to extract a signal from any background “noise” and this signal is then subject to time delay embedding. The attractor resulting from the SSA/Takens process to US unemployment data is topologically equivalent to the attractor from the Goodwin / Predator Prey phase portrait. This primae facie, suggests that the (assumed “black box”) nonlinear economic process which generated these statistics could well have had Goodwin characteristics. The solution is both a limit cycle but also the amplitude (ratio of profitability and unemployment) suddenly increases. This probably reflects that the time series covers the “great moderation” and the subsequent 07/08 crash. This is also a characteristic of more complex nonlinear models like Keen (1997) and suggests that a similar exercise with Keens model and private debt statistics would be interesting.