The macrodynamics of household debt, growth, and inequality

How do inequality and growth evolve in the long run and why? We address this question by analyzing the interplay between household debt, growth and inequality within a monetary, stock-flow consistent framework. We first consider a Goodwin-Keen model where household consumption, rather than investment by firms, is the key behavioural driver for the dynamics of the economy. Whenever consumption exceeds current income, households can borrow from the banking sector. The resulting three dimensional dynamical system for wage share, employment rate, and household debt exhibits the characteristic asymptotic equilibria of the original Keen model, namely the analogue of Solovian balanced growth path with a stable NAIRU in addition to deflationary equilibria with explosive debt and collapsing employment. We then extend this set-up by separating the household sector into workers and investors, obtaining a four-dimensional system with analogous types of asymptotic behaviour. Our main result is that long-run increasing in quality between these two classes of households occurs if and only if the system approaches one of the equilibria with unbounded debt ratios. More specifically, we find that one essential channel of increased inequality is the wealth transfer from workers to investors due to interest paid on debt from the former to the latter. Finally, when properly rewritten, the celebrated inequality r > g turns out to be a necessary condition for the asymptotic stability of long-run debt-deflation. Our findings shed new light on the relationships between fairness and efficiency, and have implications for public economic policy.