Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression

Abstract

The phrase business cycle is usually used for short term fluctuations in macroeconomic time series. In this paper we focus on the estimation of business cycles in a bivariate manner by fitting two series simultaneously. The underlying model is thereby nonparametric in that no functional form is prespecified but smoothness of the functions are assumed. The functions are then estimated using penalized spline estimation. The bivariate approach will allow to compare business cycles, check and compare phase lengths and visualize this in forms of loops in a bivariate way. Moreover, the focus is on separation of long and short phase fluctuation, where only the latter is the classical business cycle while the first is better known as Friedman or Goodwin cycle, respectively. Again, we use nonparametric models and fit the functional shape with penalized splines. For the separation of long and short phase components we employ an Akaike criterion.

Multiplicity of time scales in climate, matter, life, and economy

“…An economy with rapid shifts between regulation and de-regulation. In [63], Kauermann, Teuber and Flaschel found that the corresponding time series of the US economy for the period 1955-2005 yield a different Fig. 17: The long-phase wave in (c) seems to dipsy-doodle and lacks any remembrance of a cycle, presumably due to the state interventions of price and wage-stops of the Nixon administration and the abolition of union influence by the Reagan administration.…”

“…3) shows the evolution of the employment rate of workers in the sphere of production e(t) and its consequences for the income distribution between capital and labor v(t) over longer periods. To explore the emergence of two characteristic time scales in these two variables, we refer to [63]: they assume that y(t) := (e(t), v(t)) follows a long term trend c(t) = (c 1 (t), c 2 (t)) and a business cycle fluctuation g(t) = (g 1 (t), g 2 (t)), and model y(t) = c(t) + g(t) + ε(t) with an error term ε(t). In that way, the data can point to two essential aspects of economic crises in capitalism that otherwise are nowadays disguised behind GDP data, namely…”

“…Our Fig. 16 was found by exploring the German data with bivariate loops using penalized spline regression, as explained in [63]. It is based on data provided by C. Groth and J.B. Madsen, Copenhagen, see also [64].…”

“…Plot a and b show the time series wage share y 1 (t) and employment rate y 2 (t), with long-phase estimate (solid line) and final estimation (bold solid line). Plot c shows the observation cloud with the estimated zigzag line instead of an expected long-phase cycle and d shows the de-trended time series with estimated short-phase business cycle (solid line) and its confidence region (grey shaded area).Reprinted from[63, Fig. 4]…”

Some new insights on the empirics of Goodwin's growth-cycle model

“…On the other hand, scholars such as Goldstein (1999), Barbosa-Filho and Taylor (2006), Moura Jr. and Ribeiro (2013), Basu et al (2013), Kiefer and Rada (2015), Barbosa-Filho (2016), and more recently Grasselli and Maheshwari (2018) provided parametric quantitative evidence. Non-parametric treatments have also received some attention by Kauermann et al (2012). Furthermore, Barrales and von Arnim (2017), using quarterly data for the United States, have decomposed employment, utilisation, and income distribution time series into wavelets of varying periodicity and showed the existence of cycles a la Goodwin.…”