Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model

Abstract

We show that a steady-state stock-flow consistent macro-economic model can be represented as a Constraint Satisfaction Problem (CSP). The set of solutions is a polytope, which volume depends on the constraints applied and reveals the potential fragility of the economic circuit, with no need to study the dynamics. Several methods to compute the volume are compared, inspired by operations research methods and the analysis of metabolic networks, both exact and approximate. We also introduce a random transaction matrix, and study the particular case of linear flows with respect to money stocks.In this article we propose an approach to macro-economic modeling inspired by stock-flow consistent (SFC) models [1] and statistical physics, solving a Constraint Satisfaction Problem (CSP) in a way similar to recent works in the field of metabolic networks [2]. The SFC framework provides accounting identities ensuring that "everything comes from somewhere and everything goes some where"[1, p.38], thanks to budget constraints and behavioral constraints. The formalism of DSGE (Dynamic Stochastic General Equilibrium) is dominant today in macro-economics, partly because the corresponding models can be written in the form of state-space models and estimated in a well-studied statistical framework 1 . Their usefulness has been widely debated among economists [4,5] and physicists [6] because of their inability to predict crises. Many of their hypotheses have been criticized, such as representative rational agents, exogeneity of financial factors, clearing markets where offer always meet demand, etc. . . Moreover, DSGE models usually do not implement SFC accounting identities.Most SFC works take place at the macroeconomic aggregate level. Various assets (loans, equities, bonds, . . . ) and sectors (households, firms, banks, states,. . . ) have been considered in the litterature [7]. Models can be more or less detailed, depending on the focus of the study (for example, the production sector can be aggregated or multi-sectoral). The issue of the micro-foundations of SFC models has been tackled with the combination of SFC and agent-based models (ABM). ABM [8,9] can represent large populations of heterogeneous agents, to explore the influence of networks effects, coordination, bounded rationality and learning. However, they do not usually implement stock-flow consistency. Recent works combine SFC and ABM [10,11,12], providing micro-foundations to SFC models, and imposing macro constraints to ABMs. Nevertheless, the computational cost of ABM simulations is high, and theoretical understanding is limited so far. Calibration and validation are known to be difficult problems.We consider a simplified stock-flow consistent model developed by macro-economists, where the state of the economy is the set of all stocks and flows of money. It is shown that one can compute the set of admissible steady-state configurations of this simple model. In this steady-state solution space, all configurations are equally weighted, thus allowing unusual states of ...

Stock-flow consistent macroeconomic model with nonuniform distributional constraint

“…This last feature can be thought of as expressing the fact that the distribution of wealth or income are exogenous, as the result of an evolving balance of power between capital and workforce. This improves over [8] where an SFC model was seen as a Constraint Satisfaction Problem, but without a priori constraint on distributions.…”

“…Several works in the field of metabolic networks research use HR, to sample feasible metabolic flows in a uniform [23,24] or possibly non-uniform way [25]. SFC macro models were also studied with this algorithm in [8].…”

“…The particular model is a partially aggregated BMW model, with private money, no state nor central bank, where agents are grouped by sector (firms, banks, households). More detail can be found in [4,7], and a fully disaggregated version is discussed in [8]. It follows from this simplified setup that the stock of capital K, the stock of loans L, and the sum of deposits M i are equal.…”

“…an analytic expression can be found for the stationary state (if any) and for time-dependent transients [4] of aggregated models. In [8], the stationary state of a particular, fully-disaggregated SFC model with random connectivity, was seen as a Constraint Satisfaction Problem (CSP), with solutions lying inside a random convex polytope. Marginal pdf of money stocks and flows were numerically estimated, and the effect of various flow knockouts was evaluated in the case of a BMW model [4,7] which describes an economy where private banks create money through loans.…”

Plotting the Words of Econophysics

“…Consistently with these macro developments, the fourth is also the subarea comprising topics such as monetary and banking relationships, an operational field that, until then, has played a marginal role in econophysics [44].…”