A note on Keen's model: The limits of Schumpeter's "Creative Destruction"

TL;DR

This paper analytically examines Keen's endogenous money creation model, revealing it admits only two long-term outcomes—either stable growth or collapse—and provides explicit formulas for key dynamical features.

Contribution

It offers a comprehensive analytical solution to Keen's model, clarifying the conditions for stability and collapse, and deriving explicit expressions for the period and growth rates.

Findings

Keen's model has only two long-term solutions: stable growth or collapse.

Collapse can occur immediately or after an exponential growth phase.

The period of oscillation is linked to roots of a specific polynomial.

Abstract

This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Moderation. It emerges that Keen's model has just two possible long term solutions: stable growth or terminal collapse. While collapse can come about immediately from economies that are nonviable by virtue of unsuitable parameters or initial conditions, in general the collapse is preceded by an interval of exponential growth. In first approximation, the duration of that exponential growth is half a period of a sinusoidal oscillation. The period is determined by reciprocal of the imaginary part of one root of a certain quintic polynomial. The real part of the same root determines the rate of growth of the economy. The coefficients of that polynomial depend in a complicated way upon the numerous parameters in the problem and so, therefore, the pattern of roots. For a favorable choice of parameters, the salient root is purely real. This is the circumstance that admits the second possible long term solution, that of indefinite stable growth, i.e. an infinite period.