Inside money in a Kaldor-Kalecki-Steindl fiscal policy model: The unit of account, inflation, leverage, and financial fragility

We hope to model financial fragility and money in a way that captures much of what is crucial in Hyman Minsky's financial fragility hypothesis. This approach to modeling Minsky may be unique in the formal Minskyan literature. Namely, we adopt a model in which a psychological variable we call financial prudence (P) declines over time following a financial crash, driving a cyclical buildup of leverage in household balance sheets. High leverage or a low safe-asset ratio in turn induces high financial fragility (FF). In turn, the pathways of FF and capacity utilization (u) determine the probabilistic risk of a crash in any time interval. When they occur, these crashes entail discrete downward jumps in stock prices and financial sector assets and liabilities. To the endogenous government liabilities in Hannsgen (2014), we add common stock and bank loans and deposits. In two alternative versions of the wage-price module in the model (wage-Phillips curve and chartalist, respectively), the rate of wage inflation depends on either unemployment or the wage-setting policies of the government sector. At any given time t, goods prices also depend on endogenous markup and labor productivity variables. Goods inflation affects aggregate demand through its impact on the value of assets and debts. Bank rates depend on an endogenous markup of their own. Furthermore, in light of the limited carbon budget of humankind over a 50-year horizon, goods production in this model consumes fossil fuels and generates greenhouse gases. The government produces at a rate given by a reaction function that pulls government activity toward levels prescribed by a fiscal policy rule. Subcategories of government spending affect the pace of technical progress and prudence in lending practices. The intended ultimate purpose of the model is to examine the effects of fiscal policy reaction functions, including one with dual unemployment rate and public production targets, testing their effects on numerically computed solution pathways. Analytical results in the penultimate section show that (1) the model has no equilibrium (steady state) for reasons related to Minsky's argument that modern capitalist economies possess a property that he called "the instability of stability," and (2) solution pathways exist and are unique, given vectors of initial conditions and parameter values and realizations of the Poisson model of financial crises.