The roads not taken: Graph theory and macroeconomic regimes in stock-flow consistent modeling

Standard presentations of stock-flow consistent modeling use specific Post Keynesian closures, even though a given stock-flow accounting structure supports various different economic dynamics. In this paper we separate the dynamic closure from the accounting constraints and cast the latter in the language of graph theory. The graph formulation provides (1) a representation of an economy as a collection of cash flows on a network and (2) a collection of algebraic techniques to identify independent versus 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 within this framework. We illustrate the graph tools through application of the simple stock-flow consistent model, or "SIM model," found in Godley and Lavoie (2007). In this model there are eight different possible dynamic closures of the same underlying accounting structure. We classify the possible closures and discuss three of them in detail: the 'standard' Godley-Lavoie closure, where government spending is the key policy lever; an "austerity" regime, where government spending adjusts to taxes that depend on private sector decisions; and a "colonial" regime, which is driven by taxation.