Is the Macroeconomy Locally Unstable and Why Should We Care?

Abstract

In most modern macroeconomic models, the steady state (or balanced growth path) of the system is a local attractor, in the sense that, in the absence of shocks, the economy would converge to the steady state. In this paper, we examine whether the time series behavior of macroeconomic aggregates (especially labor market aggregates) is in fact supportive of this local-stability view of macroeconomic dynamics, or if it instead favors an alternative interpretation in which the macroeconomy may be better characterized as being locally unstable, with nonlinear deterministic forces capable of producing endogenous cyclical behavior. To do this, we extend a standard AR representation of the data to allow for smooth nonlinearities. Our main finding is that, even using a procedure that may have low power to detect local instability, the data provide intriguing support for the view that the macroeconomy may be locally unstable and involve limit-cycle forces. An interesting finding is that the degree of nonlinearity we detect in the data is small, but nevertheless enough to alter the description of macroeconomic behavior. We complete the paper with a discussion of the extent to which these two different views about the inherent dynamics of the macroeconomy may matter for policy.

Causes and Consequences of Hysteresis: Aggregate Demand, Productivity and Employment

“…-, without jeopardizing the underlying unique equilibrium assumption. The obvious dissatisfaction with the (linear) unit-root process approach is currently bringing a revival of the importance of the detection of nonlinearities in empirical macroeconomics: so, for example, Beaudry et al (2016) examining a few empirical time series, like unemployment and working hours, do find evidence of cyclical recurrent patterns not detectable when estimating auto-regressive linear stochastic models, therefore questioning the widespread use of such methods. However, the critique to the unit-root process approach is deeper and concerns the very underlying theory: as suggested by Piscitelli et al (2000), Hallett and Piscitelli (2002), Amable et al (2004) and Bassi and Lang (2016), genuine models of hysteresis should embed a nonlinear structure.…”

Testing fundamentalist–momentum trader financial cycles: An empirical analysis via the Kalman filter

“…Specifically, such a model could allow for an endogenous change of the share of fundamentalists and momentum traders conditional on their previous performance, (see e.g., Franke, 2008;Lux, 2018;Lux & Zwinkels, 2018;Ter Ellen & Verschoor, 2017). This would also help to overcome the issue that estimates from a linear model may bias the eigenvalues toward stability (see Beaudry et al, 2017). For this reason, using non-linear methods and higher frequency sampling will help to enrich the analysis for more complex dynamics such as limit cycles, quasi-periodic cycles or chaos.…”

On the long-run fluctuations of inheritance in two-sector OLG models

“…Here a two-sector optimal OLG growth problem with non-separable and strictly concave preferences is able to generate a Hopf bifurcation and quasi-periodic cycles taking some intermediate and plausible values for the elasticity of current consumption, the elasticity of intertemporal substitution and a upper threshold condition for the sectoral elasticities of capital-labor substitution. 12 Turning to the decentralized problem in the presence of altruistic parents, we show that the optimal conditions and thus the dynamical system characterizing the decentralized equilibrium are equivalent to those associated with the central planner problem described above as long as bequests are strictly positive. After providing conditions for the existence of strictly stationary bequests, we argue that the (sufficient) conditions for optimal periodic and quasi-periodic cycles derived for the central planner solution also hold in the presence of positive bequests.…”

“…pattern, especially when extracting its medium to long-run component. 4 In a broader perspective, this descriptive fact is to be reconciled with recent papers (e.g., Beaudry et al [11,12,13]; Growiec et al [32,33]) that challenge the seminal contributions of Granger [31] and Sargent [56]: macroeconomic variables do not display (very) pronounced peaks at business cycles frequencies and thus data are not supportive of strong internal boombust cycles. 5 For instance, Beaudry et al [11,13] show the existence of a recurrent peak in several spectral densities of US trendless macroeconomic data suggesting the presence of periodicities around 9 to 10 years irrespective of the exogenous cyclical forces.…”

“…Especially the seminal contributions of Benhabib and Nishimura [15,16] have shown that even in standard models featuring forward-looking agents and a competitive equilibrium structure, the steady state or balanced growth path was inherently unstable and thus deterministic (endogenous) fluctuations were easily obtained as soon as the fundamental nonlinear structure of the model was taken into account. More recently, Beaudry et al [11,12,13] have put forward the existence of endogenous stochastic limit cycles, i.e. a deterministic cycle where the stochastic component is essentially an i.i.d.…”