The Roads Not Taken: Graph Theory and Macroeconomic Regimes in Stock-Flow Consistent Modelling

Abstract

Standard presentations of stock-flow consistent modelling use specific Post-Keynesian closures, even though a given stock-flow accounting structure supports various different economic dynamics. We separate the dynamic closure from the accounting constraints, and cast the latter in the language of graph theory. The graph formulation provides: a representation of an economy as a collection of cash flows on a network, and a collection of algebraic techniques to identify independent vs. dependent cash flow variables and solve the accounting constraints. The separation into independent and dependent variables is not unique, and we argue that each such separation can be interpreted as an institutional structure or policy regime. Questions about macroeconomic regime change can thus be addressed in this framework.

We illustrate the graph tools by application to the simplest "model SIM" of Godley and Lavoie (2007). In the case of model SIM there are eight different possible dynamic closures of the same underlying accounting structure. We classify the possible closures and discuss in detail three of them: the "standard" Godley-Lavoie closure where government spending is the key policy lever, an "austerity" regime where government spending adjusts to taxes which depend on private sector decisions, and a "colonial" regime which is driven by taxation.

Keywords: stock-flow consistent models, closures, graph theory, macroeconomic regimes, methodology

JEL Classification: E16, E17