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.
Even though all ABM do not verify stock-flow consistency, it is an hypothesis used by several authors @cite_57 @cite_40 @cite_29 @cite_37 @cite_27 . ABM are praised for their flexibility, their ability to study large populations of heterogeneous and learning agents that interact in possibly non-linear ways. However, ABM need computer intensive simulations and face the problem of being over-parametrized. Calibration is thus difficult and unstable, all the more since empirical studies and reliable data are not abundant compared to the dimension of the parameter space. Recent works tackle the issue of an efficient exploration of the parameter space @cite_31 .The issue of comparing a model to experimental data is another problem posed to practitioners, that has been addressed by different methods @cite_47 . Under simplifying assumptions such as the aggregation of a subset of agents, theoretical results concerning some macro-economic ABM were recently obtained in a stock-flow-consistent framework, and phase diagrams established, for specific dynamic rules @cite_18 @cite_44 .
@cite_37 @cite_47 @cite_18 @cite_29 @cite_57 @cite_44 @cite_27 @cite_40 @cite_31
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We model a macroeconomy with stock-flow consistent national accounts built from the local interactions of heterogenous agents (households, firms, bankers, and a government) through product, labor, and money markets in discrete time. We use this model to show that, without any restrictions on the type of interactions agents can make, and with asymmetric information on the part of firms and households in this economy, power-law dynamics with respect to firm size and firm age, income distribution, skill set choice, returns to innovation, and earnings can emerge from multiplicative processes originating in the labor market. This paper proposes a new method for empirically validate simulation models that generate artificial time series data comparable with real-world data. The approach is based on comparing structures of vector autoregression models which are estimated from both artificial and real-world data by means of causal search algorithms. This relatively simple procedure is able to tackle both the problem of confronting theoretical simulation models with the data and the problem of comparing different models in terms of their empirical reliability. Moreover the paper provides an application of the validation procedure to the (2015) macro-model. The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABMs) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its “phase diagram” in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the “Mark I” ABM devised by Delli Gatti and collaborators. In this regard, our major finding is the generic existence of a phase transition between a “good economy” where unemployment is low, and a “bad economy” where unemployment is high. We then introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-to-sales ratio. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the “good” phase) or deflation (in the “bad” phase), but leaves the overall phase diagram of the model essentially unchanged. We have also explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models. We present a model of a dynamic and complex economy in which the creation and the destruction of money result from interactions between multiple and heterogeneous agents. In the baseline scenario, we observe the stabilization of the income distribution between wages and profits. We then alter the model by increasing the flexibility of wages. This change leads to the formation of a deflationary spiral. Aggregate activity decreases and the unemployment increases. The macroeconomic stability of the model is affected and eventually a systemic crisis arises. Finally, we show that the introduction of a minimum wage would have allowed the aggregate demand to be boosted and to avoid this crisis. Given the economy's complex behavior and sudden transitions as evidenced in the 2007–08 crisis, agent-based models are widely considered a promising alternative to current macroeconomic practice dominated by DSGE models. Their failure is commonly interpreted as a failure to incorporate heterogeneous interacting agents. This paper explains that complex behavior and sudden transitions also arise from the economy's financial structure as reflected in its balance sheets, not just from heterogeneous interacting agents. It introduces "flow-of-funds" and "accounting" models, which were preeminent in successful anticipations of the recent crisis. In illustration, a simple balance-sheet model of the economy is developed to demonstrate that nonlinear behavior and sudden transition may arise from the economy’s balance-sheet structure, even without any microfoundations. The paper concludes by discussing one recent example of combining flow-of-funds and agent-based models. This appears a promising avenue for future research. Extensive exploration of simulation models comes at a high computational cost, all the more when the model involves a lot of parameters. Economists usually rely on random explorations, such as Monte Carlo simulations, and basic econometric modeling to approximate the properties of computational models. This paper aims to provide guidelines for the use of a much more efficient method that combines a parsimonious sampling of the parameter space using a specific design of experiments (DoE), with a well-suited metamodeling method first developed in geostatistics: kriging. We illustrate these guidelines by following them in the analysis of two simple and well known economic models: Nelson and Winter's industrial dynamics model, and Cournot oligopoly with learning firms. In each case, we show that our DoE experiments can catch the main effects of the parameters on the models' dynamics with a much lower number of simulations than the Monte-Carlo sampling (e.g. 85 simulations instead of 2,000 in the first case). In the analysis of the second model, we also introduce supplementary numerical tools that may be combined with this method, for characterizing configurations complying with a specific criterion (social optimal, replication of stylized facts, etc.). Our appendix gives an example of the R-project code that can be used to apply this method on other models, in order to encourage other researchers to quickly test this approach on their models.