On dynamics in a Keynesian model of monetary and fiscal stabilization policy mix with twin debt accumulation

Abstract

In this paper, a six‐dimensional model of flexible prices with the monetary and fiscal policy mix, describing the development of the firms’ private debt, the output, the expected rate of inflation, the rate of interest, government expenditure, and government bonds are analyzed. The stress put on the “twin debt accumulation” means that in our model both private debt accumulation and the public debt (government bond) accumulation are explicitly introduced. Questions concerning the existence of limit cycles around its normal equilibrium point are investigated. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. Numerical example illustrating the results attained is presented by means of numerical simulations.

Financial structure, cycle, and instability

“…Ninomiya and Tokuda (2017) contended that their investigation may support this argument. 3 See, for example, Keen (1995), Asada (2001Asada ( , 2006, Ninomiya (2006), Hein (2007), Charles (2008a), Sasaki and Fujita (2014), Ninomiya (2018), and Asada et al (2019). 4 Nishi (2012a) investigated the dynamic relationships among income distribution, debt ratio, and capital accumulation in the Japanese economy.…”

On dynamics in a medium-term Keynesian model

“…1 Taking this approach, a number of studies have demonstrated the presence of business cycles. 2 As is well known, limit cycles can be stable or unstable; stable limit cycles have inner and outer attracting domains, while unstable limit cycles have inner and outer repelling domains. In the theory of economic dynamics, both of them have important implications; it is indicated by the former that the state of an economy converges to persistent business cycles while by the latter that a stable region associated with "corridor stability" may exist.…”

“…4 For recent exceptional investigations of the stability of periodic orbits in high-dimensional dynamic models (with dimensionality of three or more) in economics, see Asada et al [1,2] and Murakami and Zimka [30]. 5 Murakami [21] established the existence of stable limit cycles in the two-dimensional model but not in the three-or four-dimensional model.…”

A three-country Kaldorian business cycle model with fixed exchange rates: A continuous time analysis

“…Typical examples of such 'Keynesian' macrodynamic models are Kaldor [23], Kalecki [24] and Goodwin [20]. Later examples of models in this tradition include Torre [47], Semmler [45], Dohtani, Misawa, Inaba, Yokoo and Owase [16], Asada, Chiarella, Flaschel and Franke [4], and Asada, Demetrian and Zimka [5], [6].…”

“…For detailed examples of how Liu's criterion can be satisfied in a high-dimensional nonlinear dynamical system, see Maličký and Zimka[32],[33], or Asada et al[5],[6].…”