Destabilizing a stable crisis: Employment persistence and government intervention in macroeconomics

The basic Keen model is a three-dimensional dynamical system describing the time evolution of the wage share, employment rate, and private debt in a closed economy. In the absence of government intervention this system admits, among others, two locally stable equilibria: one with a finite level of debt and nonzero wages and employment rate, and another characterized by infinite debt and vanishing wages and employment. We show how the addition of a government sector, modelled through appropriately selected functions describing spending and taxation, prevents the equilibrium with infinite debt. Specifically, we show that, by countering the fall in private profits with sufficiently high government spending at low employment, the extended system can be made uniformly weakly persistent with respect to the employment rate. In other words, the economy is guaranteed not to stay in a permanently depressed state with arbitrarily low employment rates.