Journal of Evolutionary Economics

, Volume 29, Issue 1, pp 299–335 | Cite as

Is the market really a good teacher?

Market selection, collective adaptation and financial instability
  • Pascal SeppecherEmail author
  • Isabelle Salle
  • Dany Lang
Regular Article


This paper proposes to model market mechanisms as a collective learning process for firms in a complex adaptive system, namely Jamel, an agent-based, stock-flow consistent macroeconomic model. Inspired by Alchian’s (J Polit Econ: 5(3):211–221, 1950) “blanketing shotgun process” idea, our learning model is an ever-adapting process that puts a significant weight on exploration vis-à-vis exploitation. We show that decentralized market selection allows firms collectively to adapt their overall debt strategies to the changes in the macroeconomic environment so that the system sustains itself, but at the cost of recurrent deep downturns. We conclude that, in complex evolving economies, market processes do not lead to the selection of optimal behaviors, as the characterization of successful behaviors itself constantly evolves as a result of the market conditions that these behaviors contribute to shaping. Heterogeneity in behavior remains essential to adaptation. We come to an evolutionary characterization of a crisis, as the point where the evolution of the macroeconomic system becomes faster than the adaptation capabilities of the agents that populate it.


Evolutionary economics Learning Firms’ adaptation Business cycles 

JEL Classification

B52 C63 D21 D83 E32 

1 Introduction

A market operates on a decentralized ground: it is a place where a collection of heterogeneous agents locally and constantly interact, without seeing the resulting whole picture. This property poses a challenge to the use of a representative agent with rational expectations, and raises the question of how to model agents’ behaviors and learning in market economies. This paper proposes a decentralized adaptation model rooted in the functioning of the market itself: the selection mechanism operates through market competition, as firms that use non performing strategies are driven out of the market by bankruptcy.

The idea that market mechanisms determine the aggregate behavior of the system, by selecting appropriate behaviors and discarding inappropriate ones, without the need to model any rationality or foresight of adaptive behavior from the individual agents is originally due to Alchian (1950). Alchian (1950, p. 219) calls such a process the “blanketing shotgun process” (BSP hereafter): a multitude of agents randomly select strategies, without assuming any intentional decision making at the individual level, and the market selects the best-performing behaviors by excluding the unsuccessful ones. This process requires individual heterogeneity and market interactions, and postulates that the collective adaptation force of the system is superior to the one of the individual agents. This process also puts more emphasis on the exploration for potential strategies than on the exploitation of already discovered strategies. The BSP therefore appears particularly well-suited to represent adaptation of a population in an ever-changing environment. We believe that all these features, rather than referring to the principle of the survival of the fittest as a defense of profit maximization, bring simple but relevant principles that are reconcilable with, and even precursory of, both the theory of bounded rationality (Simon 1961) and evolutionary economics (Nelson and Winter 1982), and may be useful for modeling behavior in macro ABMs. Besides, our approach shares affinities with early evolutionary growth models in the way learning and adaptation are modeled (Silverberg and Verspagen 1994a, 1994b).

In this paper, we introduce investment and capital depreciation in the Jamel model,1 along with refinements in the banking sector. Investment dynamics brings instability into the macroeconomic dynamics of the model compared to previous versions, and reinforces market competition. We then apply the principles of the BSP to the determination of firms’ leverage strategies. We choose this model as a playground because it is simple enough to get a grip on the emerging dynamics, while allowing for rich monetary and real interactions between agents, and especially between firms, in a fully stock-flow consistent (SFC) framework.2 We choose the leverage strategies for testing the BSP because this decision is in several ways particularly challenging from the firms’ perspective. Leverage decisions amount specifically to solving a “growth-safety trade-off”, i.e. a trade-off between a continuous, debt-financed increase in market capacities and financial safety that preserves a low debt level, but at the risk of losing productive capital, if investment is insufficient to renew depreciating capital, and market shares (Crotty 1990, 1992a, 1992b, 1993). The debt behaviors of firms in turn collectively contribute to shape the macroeconomic environment, so that the environment constantly changes, and complex dynamics emerge. In such an hostile and selective environment, not even the modeler would be able to identify an “optimal” solution. We therefore let the leverage strategies of a collection of competing firms evolve on a completely random basis, and the only selection pressure comes from bankruptcies.

With the Jamel model as a playground, we perform a theoretical exercise that aims to assess to what extent the process of “natural” market selection constitutes a suitable adaptation model for agents in a complex system. This amounts to characterizing the dynamics that emerge from ever-adapting individual behaviors under the sole selection pressure of market conditions that they in turn contribute to shaping: Can the system settle down on an “equilibrium”? Otherwise, what are the emerging dynamics? Admittedly, the use of evolutionary learning mechanisms to model firms’ adaptation under market competition is not new, especially in the AB literature. Our implementation differs, though, along a number of dimensions, that makes our algorithm a very parsimonious and effective way of addressing the so-called “wilderness of bounded rationality”, as explained in Section 2. More importantly, the novelty of our paper is a formal and detailed analysis of those evolutionary mechanisms. We shed light on their implications on the micro and the macro dynamics, while those mechanisms have been embedded into ABMs in a mostly implicit way, without being the focus of the analysis.

Our results are as follows. Decentralized market selection allows the firms collectively to adapt the overall leverage level to the changes in the macro environment in a way that the system can sustain itself. However, this regulation comes at the price of wild fluctuations and deep downturns. This emerging macro dynamics are caused by a clear alternating pattern between a sustained rise in indebtedness along the boom phase that feeds back into the goods demand, and brutal deleveraging movements along the busts, once the financial fragility of firms, combined with increased interest rates and excess production capacities, increases to the point where insolvency and bankruptcies are unavoidable. We conclude that, even if the “natural” market selection process allows for a certain resilience and adaptability of the system, it does not result in collective optimization or convergence toward an “optimal” equilibrium. Our conclusion stands in sharp contrast to the view, dating back to Friedman (1953), that systematically advocates market selection to justify full rationality assumptions and equilibrium reasoning.

We then make the point that heterogeneity of behaviors is essential to the adaptation process of a population in an unstable and quickly evolving environment. The BSP allows us to make this heterogeneity endogenous and dynamic: it combines converging forces (market selection and imitation) with diverging forces (exploration), so that behaviors co-evolve with the macroeconomic dynamics that they contribute to shaping. This property makes the BSP an appealing candidate to model learning and adaptation in complex adaptive systems. We show that, while individual and aggregate behaviors appear to commonly self-reinforce each other, they can suddenly disconnect from each other. This observation leads us to suggest an evolutionary characterization of a crisis, as the point where the evolution of the macro system becomes faster than the adaptation capabilities of the agents that populate it.

The rest of the paper is organized as follows. Section 2 discusses the non-trivial problem of modeling individual behaviors in complex systems and details our implementation of the BSP, Section 3 details the Jamel model, Section 4 presents the results from the numerical simulations, and Section 5 discusses the results and concludes with the characterization of a crisis in the model.

2 Modeling individual behavior in macro ABMs: learning and adaptation

This section paves the way to the introduction of the adaptation process based on the BSP in the Jamel model. We first discuss the challenges posed by the modeling of agents’ behavior in macro ABMs. We then define the concepts of adaptation and learning and stress their importance in this type of models. We finally contrast individual versus social learning by focusing on evolutionary models and discuss their limitations.

2.1 Particularities and challenges

The “wilderness of bounded rationality”

The functioning of ABMs is rooted in a multitude of heterogeneous agents who repeatedly interact in a decentralized way. Those interactions generate complexity, in the sense that even the perfect knowledge of individual behavior is not enough to anticipate the resulting macroeconomic outcomes. In such a complex world, uncertainty is both strategic and radical: there is no trivial probabilistic mapping between the entire set of possible actions of an agent and the resulting states of the world and associated pay-off. Neither the agents nor the modeler may be able to define the fully rational/optimal decision (Dosi et al. 2003b). As a consequence, the use of the standard microeconomic maximization tools is not suited in ABMs; agents’ rationality can only be bounded, in the sense of Simon (1955), i.e. procedural and adaptive. The challenge is how to model this boundedly rational behavior. This is a challenge because the modeler has to cope with the so-called “wilderness of bounded rationality” (Sims 1980): while there is one single way of solving an optimization program, there are many ways of being boundedly rational, and the question is how to discriminate between the multitude of alternative behavioral rules. This is a crucial question as the dynamics of the ABM, and the conclusions drawn from the analysis, are likely to depend on the behavioral rules that have been incorporated into it.

Empirical observations as the main guideline

We argue that what we can observe from real-life behavior should be the main ground for modeling agents’ behavior in artificial economies (Cohen 1960; Farmer and Foley 2009a). The growing amount of experimental evidence from controlled lab environments with human subjects in economics, sociology and psychology, as well as the increasing availability of survey data has fueled our knowledge of how agents actually behave under alternative environments. However, this collection of empirical evidence comes with limitations. Individual behaviors do not always find a clear-cut interpretation; they can be highly heterogeneous and can vary from one period to the next.3 In other words, real agents’ behaviors are unstable, and any attempt to summarize agents’ reactions by a fixed behavioral rule derived from a sample of empirical observations may pose a problem of realism. Such an attempt could be acceptable if the model were only aimed at the analysis of very short-run dynamics, over which we can consider that agents’ behavior is fixed. However, when it comes to the analysis of longer-run dynamics, this modeling strategy introduces an ad-hoc, exogenous stickiness in the model that may distort the conclusions. When it comes to policy analysis and the comparison of different model scenarios, this strategy does not allow us to address the so-called Lucas critique: fixing behavioral rules amounts to performing ceteris paribus analysis, and ignoring that policy changes are likely to affect, in turn, micro behavior. This was also the criticism made by Keynes to Tinbergen’s macroeconometric models (Keuzenkamp 1995). What is more, we argue that this is a gross contradiction with the decentralized and autonomous nature of ABMs (Gaffeo et al. 2008; Delli Gatti et al. 2010).

Modeling adaptation and learning

The alternative to the use of a fixed set of behavioral rules is to endow agents with a genuine ability to adapt or, in other words, to learn (Farmer and Geanakoplos 2009b). Modeling learning shall be understood as designing behaviors that agents constantly and endogenously adapt as a reaction to the feedback they receive from their environment. Modeling learning can combine heuristics based on empirical observations and adaptation (Delli Gatti et al. 2010). This idea is also at the root of the heterogeneous agent literature in which agents endogenously switch between a fixed (Brock and Hommes 1997) or evolving (Anufriev et al. 2015) set of heuristics according to their relative pay-off performances.

By inducing an intricate co-evolution between the micro and the macro dynamics, learning introduces an additional layer of complexity to the model (Winter 1971). On the one hand, agents adapt their behavior as aresult of the macro environment, so that the macro level feeds back into the micro level. On the other, there is an interdependence between individual learning behavior. This is precisely what (March 1991, p. 81) defines as an “ecology of competition”. As aresult of this ecology of competition, the environment in which agents interact cannot be considered as exogenous and is, on the contrary, ever-changing (Dosi et al. 2003b). This idea is acrucial component of complex adaptive systems as discussed by Holland (1992). Because the environment is constantly changing, this type of systems cannot be comprehended in terms of fixed point analysis, in which the equilibrium of the system is the fixed point of the mapping between beliefs and realizations, as is the case for rational expectations macro models. On the contrary, in such acontext, learning goes hand-to-hand with adaptation.This point had been made already by Alchian (1950), and this is the reason why this contribution is the starting point of our modeling strategy:

In astatic environment, if one improves his position relative to his former position, then the action taken is better than the former one, and presumably one could continue by small increments to advance to alocal optimum. … [in achanging environment] there can be no observable comparison of the result of an action with any other. Comparability of resulting situations is destroyed by the changing environment … the possibility of an individual’s converging to the optimum activity via atrial-and-error process disappears. Alchian (1950, p. 219)

2.2 Why social learning in ABMs?

Learning can be modeled at the individual level or the social level (Vriend 2000). Individual learning assumes that each agent is endowed with an evolving set of strategies that can be interpreted as his search capacities. Social learning envisions each agent as a single strategy and adaptation intervenes at the population level.

Individual learning can be understood as atrial-and-error process. On its own, it is certainly slow, as atime step is necessary to evaluate one strategy (unless the agent makes use of some foregone/“what-if” pay-off functions). By contrast, social learning allows the agents to parallelize the evaluation of the available strategies, so that the larger the population, the quicker the evaluation process.4 A quick adaptation process is most valuable if the environment is itself ever-changing, as argued above in acomplex adaptive system. For this reason, we use social learning, which has to be understood in abroad sense:

Social learning means all kinds of processes, where agents learn from one another. Examples for social learning are learning by imitation or learning by communication. Riechmann (2002, p. 46)

Social learning in market economies is derived from the “Darwinian” archetype (Dosi et al. 2003b, p. 62). This is also the “as if” interpretation of rational behavior (Friedman 1953): selection between individual strategies operates according to the principle of the survival of the fittest, so that the least performing strategies in terms of pay-off are eliminated from the population, and replaced by the best performing ones. Because of this Darwinian analogy, social learning in a decentralized economy is often represented by the means of evolutionary algorithms, such as genetic algorithms (GAs hereafter) – see Arifovic (2000) for a survey of GA in stylized macro models. GA learning dynamics is driven by two main forces: innovation that constantly introduces new behaviors in the system, and selection pressure that duplicates the best performing ones at the expense of the other.

However, GAs are not exempt from limitations. Their operators do not always find an easy economic interpretation (Chattoe 1998; Salle and Seppecher 2016). Most importantly, because they have been initially developed to find optima in complicated static problems (Holland 1975), they have been used in economics as a way for agents to learn how to maximize their profits or utility functions, and the focus has been put on the conditions under which agents end up coordinating on the optimal state of the model under GA learning (Arifovic 1990). In these set-ups, the mapping between strategies and pay-off is supposed to be time-invariant. In face of perpetually evolving environment, GAs perform badly because they assimilate adaptation with convergence on an equilibrium and individual coordination (which implies a progressive loss of diversity in the strategy population). This is even sometimes obtained at the price of ad-hoc mechanisms such as an exogenous decrease in the innovation force of the algorithm (Arifovic et al. 2013).5 We believe that this is a major flaw of the macroeconomic learning literature: the neoclassical paradigm has contributed to reduce learning to convergence on a fixed optimum. In ABMs however, decentralized learning mechanisms and market selection can be represented without the use of GAs, precisely because ABMs allow us to model directly these mechanisms in a simpler and more realistic way.6 The purpose of this paper is to provide such a proof-of-concept.

2.3 The “blanketing shotgun process” (BSP)

We now develop a learning model based on the “blanketing shotgun process” of Alchian (1950, p. 219) because the BSP consists precisely in constantly and randomly covering the space of strategies, instead of modeling learning as an individual converging search. We support the idea that Alchian (1950) can be considered as a major precursor of the evolutionist/post-Schumpeterian school of thought because he provided a precise description of the co-evolution between market selection and behavior adaptation.

Three operators

The BSP encompasses three operators, all inspired by the biological, Darwinian metaphor (Alchian 1950). First, profits stand for the natural selection process: firms with positive profits are considered successful and survive, while those with losses go bankrupt and disappear. We notice that Alchian stresses that positive, not maximal profits, are the success criterion, in tune already with the satisfycing principle àla Simon (1955):

Adaptive, imitative, and trial-and-error behavior in the pursuit of “positive profits” is utilized rather than its sharp contrast, the pursuit of “maximized profits.” Alchian 1950, p. 211).

Second, innovation (or mutation or individual experimentation) intervenes at any time, even in case of positive profits, during a“trial-and-error” process. We follow here Alchian’s “extreme” hypothesis by modeling “trial-and-error” as acompletely random, blind and unintended model of exploration (Alchian 1950, p. 211). We do not claim that deliberate individual learning plays no role in the real world but, following Alchian, we wish to abstract from it in this paper in order to focus on social learning stemming from regulation by market competition. Therefore, at most, we model individual learning as blind individual experimentation (“random mutations”) that is, on average, ineffective (i.e. the average change in strategies is zero at the population level); see Section 3.2.6 for details. Trial-and-error processes may, for instance, represent internal organizational changes, whether voluntary or not. They may happen even if the firm is making profits (Winter 1964). This type of innovation maintains the diversity of the population of strategies. We also refer here to the concept of “persistent search” in Winter (1971):

By “persistent search” is meant asearch process that continues indefinitely, regardless of how satisfactory or unsatisfactory performance may be — although the search may be slow, sporadic, or both. Winter (1971, p. 247)

Those innovations constantly introduce heterogeneity in the firms’ debt strategies, which allows for exploration. This heterogeneity is counteracted by the third operator, imitation, that stands for heredity: operating characteristics (or “routines” in the terminology of Nelson and Winter 1982) of successful firms are copied by non-successful firms, i.e. firms that go bankrupt. The copy of the firm’s strategies is not exact though, so that innovation is also introduced at that stage.7 Imitation provides the endogenous selection process that allows for exploitation.

BSP versus GA

Even if, at first glance, the three operators of the BSP seem to have a lot in common with those of a GA, there are important differences. In a GA, changes in behavior are triggered by exogenously fixed probabilities. By contrast, in our implementation of the BSP, the imitation process is endogenously triggered by market selection pressure in the event of a firm’s bankruptcy. Indeed, the occurrence of imitation is endogenous, because a firm will only imitate another firm’s strategy if it goes bankrupt. In the event of bankruptcy, a firm is taken over by a new management team, its operating characteristics (in this paper, its leverage strategy) disappear and are replaced by the ones of a randomly chosen firm in the population of surviving firms. Moreover, in GA, the imitated agents are selected in relation to their relative performances, e.g. through a tournament or roulette-wheel selection process. By contrast, under the BSP, a bankrupted firm imitates the strategy of any surviving firm, randomly drawn among the population, independently from its relative level of profits.

Furthermore, the BSP and GAs differ in the relative weight that they give to exploration versus exploitation. A weak selective pressure favors exploration and allows for the survival of poor-performing strategies. Such systems may end of with “many undeveloped new ideas and too little distinctive competence” (March 1991, p. 1971). Conversely, a strong selection process exposes the system to the risk of a premature loss of diversity and homogenization of the strategies on poor ones. The adaptive process is then potentially self-destructive (March 1991, p. 85). Consequently, the ability of a system to adapt and survive relies heavily on the balance between exploitation and exploration. As GA-based learning algorithms have been primarily designed to coordinate individual behaviors on a fixed optimal strategy, they requires a progressive homogenization of the strategy population and emphasize adaptation, i.e. exploitation over exploration. By contrast, the BSP favors exploration, by keeping a perpetual dispersion of the strategies, and therefore reinforces the adaptability of the system. We argue that this feature is most convincing in a dynamic market environment in which firms have to compete without being able to derive an optimal strategy. In Section 4.2.1, we show that this dimension turns out to be crucial in shaping the emerging macroeconomic dynamics. We now apply the BSP learning algorithm in a simple macro ABM – Jamel – and raise the question whether “the market is indeed a good teacher” (Day 1967, p. 303).

3 Learning and adaptation in a simple macro ABM

The first innovation of this paper is to model the firms’ leverage strategies through the BSP. We therefore introduce capital accumulation and depreciation in the Jamel model. The size of the firms evolves endogenously as a result of their investment decisions. We also refine the specification of the banking sector. We intend to provide here a self-contained presentation of Jamel, and we pay specific attention to the description and the explanation of the new features that this paper introduces. We refer the interested reader to Seppecher and Salle (2015) for an exhaustive discussion and justification of the rest of the assumptions of the model. Appendix A provides the pseudo-code of the model that makes the timing of events together with each equation explicit, and defines each variable and each parameter. We refer the reader to this appendix for the detail of the model design. The open source code (in Java) as well as an executable demo are available on the corresponding author’s website at, as we believe this is a necessary step for the transparency and credibility of the simulation results.

3.1 The main features of Jamel

Jamel exhibits two essential features: full decentralization and stock-flow consistency. Decentralization ensures that aggregates, such as prices and wages, stem from the local interactions in the markets: there is no planner, no auctioneer and all interactions are direct and individual. The resulting emerging patterns, such as income distribution, are therefore endogenous. Stock-flow consistency links all agents’ balance sheets together and guarantees that micro behaviors are correctly aggregated (Godley and Lavoie 2007). In Appendix C, we provide the relevant transactions and balance sheet matrices.

The economy is populated by h heterogeneous households (indexed by i = 1,...,h), f heterogeneous firms (indexed by j, j = 1,...,f) and one bank (indexed by b). The firms produce homogeneous goods by using labor, supplied by households, and fixed capital, resulting from their investment decisions. Labor and capital are complementary production factors. Capital depreciates: one unit of fixed capital lasts for an exogenous and stochastic number of periods. In other words, machines break down at some point and become irreversibly unproductive. Both households, for consumption purposes, and firms, for investment purposes, purchase the goods. There is a capital accumulation dynamics through investment, but no technical progress, as the productivity of capital (parameter prk hereafter) remains fixed and common to all firms. The bank provides loans to the firms to finance their production (wage bill and capital investment). The firms and the bank are assumed to be owned by households, who then receive dividends. One time step t may be understood as a month.

3.2 The firms

3.2.1 Production process

Each firm j is endowed with an integer kj,t of fixed capital that can be understood as its number of machines. Each machine can be used in combination with at most one unit of labor (one worker) in every period. One unit of labor increments the production process of the machine by one step in each period. Each machine needs dp time steps to deliver an output and, after completion, this output represents dpprk units of goods, and adds to the firm’s inventory level, denoted by inj,t.

3.2.2 Quantity decisions

We assume that each firm maintains a fraction 1 − μF of its inventories inj,t as a buffer to cope with unexpected variations of its demand, and puts in the goods market the fraction μF. We also assume that the maximum market capacity of each firm is equal to dm months of production at full capacity: dmprkkj,t. Hence, in each period t, each firm j’s goods supply is given by: max(μFinj,t,dmprkkj,t)

For the sake of parsimony, the maximum market capacity is also the targeted level of inventories of each firm, i.e \({{in}^T_{j,t}} = {d^{m}} \cdot {{pr}^k} \cdot {k_{j,t}} \). The firms use the changes in their inventories as a proxy for the variations in their goods demand: lower-than-targeted (resp. higher-than-targeted) inventories signal excess demand (resp. lack of demand), and firms are likely to increase (resp. decrease) their production, and hence their labor demand \({n^T_{j,t}}\). The firms then proceed by small, stochastic adjustments in the corresponding direction.

3.2.3 Price setting

Each firm increases (resp. decreases) its price in case of lower-than-targeted (resp. higher-than-targeted) level of inventories and if it was (resp. was not) able to sell all its supply during the last period. Each firm proceeds by tâtonnement, and keeps track of a floor price \({\underline {P}_{j,t}}\) (that can be understood as a a price thought to be lower than the market price), and a ceiling price \({\overline {P}_{j,t}}\) (a price thought to be higher than the market price). The floor and the ceiling prices constitute the search area for the suitable price \([{\underline {P}_{j,t}}, {\overline {P}_{j,t}}]\) in case of price adjustment. This search area is dynamically updated so that it increases when the firm keeps on adjusting its price in the same direction, and decreases when the firm reverts its price trend. Therefore, in a strong inflationary environment (resp. deflationary environment), the firm can quickly increase (resp. decrease) its price, and adapt in order to “catch-up” with the price level in the economy.

3.2.4 Wage setting

The wage setting procedure encompasses two routines, so as to account for both an adjustment component to labor market tightness and an “institutional” component that undoubtedly plays an essential role in the determination of wage levels. Large firms tend to be wage makers and follow the first routine, which is essentially the same mechanism as the price updating process just described. They adjust their wage offer according to their observed level of vacancies compared to their targeted one and their past wage levels.

However, the vacancy level is indicative only if the firm’s size is large enough, but is of little informational content for a small firm. For instance, in the case of a single employee, this information is binary: either 0 or 100% of vacancies. Moreover, such a routine is easy to implement in the case of prices, as firms interact with consumers and/or investors in the goods market in every period. However, firms go to the labor market only in periods when they need to renew a contract or increase their workforce, so that the information that they collect by interacting with households is fragmented, and may be insufficient to set wages that are compatible with market conditions. We therefore introduce a second wage setting routine that is akin to a convention or a norm: small firms tend to be wage takers, and simply use the wage levels prevailing in larger firms of their sector. Copying another firm’s wage offer can be easily justified as every machine, and hence every worker has exactly the same productivity. The duration of an offered contract is set to a maximum of dw > 1 periods, and the wage remains fixed for this whole period.

We shall stress that these pricing rules imply flexible and independently-fixed prices and wages. The only rigidity stems from the dependence on the previous price and wage levels. For the purpose of this paper, it appears to us important not to impose exogenous constraints such as menu costs, or fixed pricing rules, such as a mark-up procedure, on the firms, in order to let the market exert the only pressure on the firms.

3.2.5 Financial decisions and investment

Payment of dividends

At the beginning of each period, the firm distributes to its owners a share of its equities Ej,t as a dividend.


The firm may have to obtain loans from the bank. There are four types of loans. Short-run (non-amortized) loans allow the firm to finance wages if its available cash-on-hand is not enough to cover fully its expected wage bill. Short-run (amortized) loans partly finance its investment (see below), and investment is primary financed with (amortized) long-run loans. The bank also grants short-run loans as overdraft facility in the case where a firm does not have enough cash-on-hand to cover its monthly repayments, (See Sub-Section 3.3.2 how the loans are granted.)

Investment decisions

Each firm has a targeted level of equity \({E^T_{j,t}} \equiv (1 - {\ell ^T_{j,t}}){A_{j,t}}\), where Aj,t denotes the total assets of the firm j in time t, and \({\ell ^T_{j,t}} \in [0,1]\) its target debt ratio. Its equity target is the amount of its assets that the firm is not willing to finance by debt. Each firm compares its equity target to its actual level Ej,t. Only if \({E_{j,t}} > {E^T_{j,t}}\) will the firm consider to invest.8 If so, the firm computes the size of its investment by applying an expansion factor, or “greediness” factor β > 1, to its average past sales (in quantities). Note that this investment objective includes de facto both the renewing of obsolete, aging machines and the purchase of new ones.

The firms willing to invest buy and transform the homogeneous goods into machines. Firms need vk goods to deliver a machine. Once purchased, we assume that those goods are transformed into machines immediately and at no cost.9 We assume that each firm uses the net present value (NPV) analysis to choose the number of machines to purchase.10 The firm randomly samples g sellers in the goods market to estimate the price of the investment. The discount factor is taken to be equal to the risk-free interest rate of the bank (see below) discounted by average past inflation; the expected cash-flow of the project is computed using the firm’s current price and wage, within the limit of its maximum market capacity.11 The firms reviews the possible investment projects by starting from m = 0 (i.e. buying 0 machine), then m = 1, etc. until the NPV of the project m + 1 is less than the NPV of the project m previously considered. The firm then chooses the project m, and buys m machines.

As an illustration, Fig. 1a shows the pace of investment decisions for an arbitrary chosen firm in the baseline simulation: only when the effective level of debt lies below its target can investment be performed, but this is not a sufficient condition. The NPV also integrates expected demand, real interest rates and profitability considerations.

Once the firm decides to purchase m new machines, it computes the share \({\ell ^T_{j,t}}\) of the total price of the investment Im that is to be financed using a long-run, amortized loan. For simplification, we assume that the length of a long-run loan equals the average expected lifetime of the machines dk. If the firm’s cash-on-hand is not enough to cover the share \(1- {\ell ^T_{j,t}}\) of the investment, the firm uses an amortized short-run loan. This procedure ensures that the firm is never constrained by insufficient cash-on-hand whenever it has decided to invest. The firm’s debt may temporary exceed its debt objective due to the additional short-run loan, but the gap progressively closes, as illustrated in Fig. 1b for the same, arbitrary chosen firm in the baseline simulation.

Each new machine adds to the firm’s assets Aj,t at its purchasing price and is uniformly depreciated by a fraction \(\frac {1}{{d^k}}\) of its initial value in every period, unless it breaks down before dk periods, and its value then falls to zero. The fixed capital depreciation on the asset side of the balance sheet, together with the long run loan amortization on the liability side, allow the firms roughly to maintain the ratio between long run loans and fixed assets in line with their debt objective throughout the life of the machines (see Fig. 1b).
Fig. 1

An individual example of a firm’s investment and financing behaviors from the baseline simulation: periods 750–1250

3.2.6 Firms’ adaptation through the BSP

Firms adapt their indebtedness strategy \({\ell ^T_{j,t}}\) through the BSP, because it summarizes the “growth-safety trade-off” in our model: the higher the debt target, the more likely the investment to be realized and the quicker the market expansion, because the firm needs less of its own equity to finance it. But this involves a higher risk of insolvency and bankruptcy.


The permanent trial-and-error innovation process is completely random, blind and unintended: in each period, with a given probability pbBSP, firms perturb their debt objective \({\ell ^T_{j,t}}\) by a Gaussian noise, with the same standard deviation σBSP as the one applied during the imitation process (see hereafter).

Bankruptcy and imitation

Firms can go out of business in two ways: bankruptcy by insolvency (when negative profits exhaust their equity, i.e. when their liabilities exceed their assets), and the loss of productive capacities (in the case where they do not succeed in investing to renew their aging machines). We simplify here the entry-exit process of firms and assume that the failed firm does not disappear: the firm is bailed out by the bank, its ownership is changed, its management team is fired, and replaced by another team coming from a more successful firm. Concretely, its debt objective \({\ell ^T_{j,t}}\) is copied on a randomly chosen surviving firm. The copy is not exact though, as a (small) Gaussian noise is introduced (with the same standard deviation σBSP).

3.3 The rest of the model

3.3.1 The households

In the labor market, each household i is endowed with a constant one-unit labor supply and a reservation wage. If employed, the reservation wage is his current wage. If unemployed, the reservation wage is adjusted downward as a function of his unemployment duration.

Regarding consumption decisions, the households follow a buffer-stock rule à la (Allen and Carroll 2001) to smooth their consumption in face of unanticipated income variations by building precautionary savings as deposits at the bank. Households cannot borrow and consumption is budget-constrained in every period.

3.3.2 The bank

The functioning of the banking system is very stylized. The bank hosts firm and household deposits at a zero-interest rate, and grants to firms short-run and long-run credits for exogenously fixed duration, common across firms. For simplification, we assume that the interest rate is the same for the two types of loans and is equivalent to the risk-free interest rate. The risk-free interest rate is set by a central bank according to a most simplified Taylor rule that aims to stabilize inflation and takes into account the zero-lower bound.

At a first step, the bank is fully accommodating, and satisfies all the credit demands. However, when a firm is not able to pay off a loan in due terms, the firm receives an overdraft facility at a higher interest rate it + rp. Parameter rp > 0 translates a risk premium and is assumed to be the same for all firms. If a firm j becomes insolvent, it goes bankrupt and the bank starts a foreclosure procedure. The bank first recapitalizes the failed firm: it computes the targeted value of the failed firm, \({E^T_{j,t}} = {\kappa _ s} {A_{j,t}}\) and then erases the corresponding amount of debt: \({L_{j,t}} - {A_{j,t}} + {E^T_{j,t}}\), absorbing this loss through its own resources. Then the bank attempts to resell the restructured firm at its new book value \({E_{j,t}}={E^T_{j,t}}\), by soliciting households that hold more than a threshold fraction of the restructured firm value in cash-on-hand, and progressively decreasing this threshold if not enough funds can be raised. In the case where the capital of the bank is not enough to recapitalize the bankrupted firm, the bank goes bankrupt and the simulation breaks off.12

The bank also distributes dividends to its owners. We assume that it simply distributes its excess net worth, if any, compared to its targeted one.

3.3.3 Markets and aggregation

The markets operate through decentralized interactions based on a standard tournament selection procedure. In the labor market, each firm posts its job offers, and each unemployed household consults g job offers and selects the one with the highest wage, provided that this wage is at least as high as its reservation wage. Otherwise, it stays unemployed.

In the goods market, each firm j posts \({s^T_{j,t}}\) goods at a price Pj,t, each household i enters with its desired level of consumption expenditures, and each investing firm enters with an investment budget. Firms first meet investor-firms, and then interact with households.13 Each household selects a subset of g firms, and chooses to buy from the cheapest one. These processes are repeated until one side of the markets is exhausted.

As usual in ABMs, aggregate variables are computed as a straightforward summation of individual ones.

3.4 Simulation protocol

We use a baseline scenario of the model derived from the empirical validation exercise performed in Seppecher and Salle (2015), but we do not attempt statistically to match empirical micro- or macroeconomic regularities in this paper.14 We use the model as a virtual macroeconomic playground to test the simple idea of adaptation through the BSP learning model. This playground is nevertheless qualitatively realistic in the following important dimensions for the purpose of our study: it is a complex, monetary and stock-flow consistent market economy. Regarding the new parameters that have been introduced, the lifetime dk of the machines is a random draw in \(\mathcal {N}(120,15)\), and we set vk = 500, where vk represents the real cost of an investment/machine. This positive cost of capital shall be counter-balanced by a moderate length of production of a machine, to maintain a similar profit share; see Seppecher (2014) for further discussion. We then set dp = 4. We set the firms’ greediness at β = 1.2, which translates into a intended 20% increase in productive capacities. This could appear ambitious at a first glance, but it is actually rather conservative: recall that this investment objective includes both the renewing of aging machines and the purchase of new ones. Highest values of this parameter only slightly accentuate the cycles, which is quite expected given the importance of the investment multiplier in our model. We fix the individual experimentation parameters of the BSP to small values (pbBSP = σBSP = 0.05), as usual in the learning literature discussed in Section 2. We set the parameters of the Taylor rule to standard values (ϕπ = 2 and πT = 2%). We set δP = 0.04 and δW = 0.02, which implies more flexible prices than wages. This relative wage rigidity is necessary to dampen, and even interrupt deflationary dynamics along the bust dynamics, so that the single bank does not go bankrupt (see Seppecher and Salle (2015) for more detail).15 The risk premium rp on doubtful debt is set to 4% (monthly) and the recapitalization rate in case of bankruptcy is κs = 20%. The number of wage observations is set to g = 3. However, the qualitative dynamics of the simulation does not seem sensitive to these three specific values. Appendix A lists all parameter values used in the sequel, and the initialization of the model is described in Appendix B.

4 Numerical results

We now give a broad description of the cyclical dynamics that comes out as a robust pattern of the simulations, and then zoom on one cycle to highlight the mechanisms at play.

4.1 Overview of the macroeconomic dynamics

Figure 2 reports typical time series of one run of the baseline scenario: demand and supply in the goods and the labor markets, the corresponding (downward sloping) Phillips and Beveridge curves, nominal and real interest rates, firm debt, the number of firm bankruptcies as well as financial fragility.16 We measure financial fragility by the ratio between the aggregate debt level and the aggregate net profits (i.e. the firms’ profits minus the interests). It is clear from the dynamics of all aggregate variables displayed that the macroeconomic dynamics of the model is characterized by a cyclical pattern, with alternating periods of booms and busts. Figure 2g already reveals the engine of those cycles: a pro-cyclical leverage. We stress that this is an endogenous product of the adaptation process, not an ingredient of the model. This explains why financial fragility and potential output (as measured by the total amount of goods that can be produced by all the machines in the economy) interact along a strongly circular dynamics (Fig. 2h). Along a business cycle, the simulations show that the economy follows an anti-clockwise motion in the output/fragility diagram, which indicates that output peaks before financial fragility; see Stockhammer and Michell (2014) for a detailed discussion. Moreover, Fig 2i proves that the building up and the collapse of assets of non-financial businesses (firms) is the main force driving the adaptation of the system as a whole: debt ratios of firms are leading GDP, high debt ratios in the past are associated with high present GDP. In the sequel, we discuss those dynamics in detail.
Fig. 2

Baseline simulation

Giving a closer look at the emerging cycles, we notice that the boom and the bust phases differ in terms of both length and magnitude throughout the same simulations. For instance, in Fig. 2, the recession around period 800 is the deepest in this simulation, while fluctuations between periods 1400 and 1800 are the most dampened. This reflects the complex nature of the ABM. The timing as well as the size of the downturns are an endogenous product of the model, and result from the intricate relations between the collective adaptive behavior of firms and market selection. In the following section, we unpack the underlying mechanisms.

Before we do so, we shall stress that the observed cycles are a robust feature of our model that we observed in all simulations we have run, albeit irregular and of various amplitudes.17 In order to show so, Table 1 presents descriptive statistics of the model outcomes over 30 replications of the baseline scenario with different seeds of the RNG. The similarity between the replications of the baseline scenario is clear from the low values of the standard deviations between runs, for all macroeconomic indicators that we report (see all numbers in brackets). As for the cyclical pattern, it is reflected by the particularly high values of the standard deviation of these indicators compared to their average values. For instance, on average between all runs, the GDP growth rate is 0.2%,18 but with a standard deviation of 0.065. This clearly depicts a strong macroeconomic volatility.
Table 1

Average (and standard deviation between brackets) computed over all periods (discarding the first 500 periods) over 30 replications of the baseline scenario



std. dev.



GDP growth rate










Inflation rate










Bankruptcy rate










Financial fragility










Firms’ leverage










Investment growth rate










The main conclusion that we can draw from our observations is that there seems to be no such thing as equilibrium or collective optimization. Nevertheless, the system exhibits some regularities and is sustainable. There is no explosive dynamics. The macroeconomic system survives and reproduces itself but at the price of a strong volatility. Market pressure does work as a selection device between a multitude of randomly generated firms’ behaviors, but the market discipline is “brutal”, not stabilizing, as reflected by the pace of bankruptcies (Fig. 2e).

4.2 Analysis of a typical cycle

In this section, we zoom on a typical cycle (between periods 750 and 1250) of the baseline simulation displayed in Fig. 2.

4.2.1 Firms’ adaptation

We show that the very core mechanism at play in generating the cycles is the alternating of two phenomena: a sustained increase trend in firms’ indebtedness, followed by a brutal correction through a chain of bankruptcies. This is particularly clear from the evolution of the targeted debt ratio of firms weighted by their assets (blue curve in Fig. 2g). To provide further insights into firm behavior over a business cycle, Fig. 3 reports the debt objectives \({\ell ^T_{}}\) versus the sizes of the firms (in number of machines) at six different phases of a cycle, in the following order: the start of the downturn, the bust, the bottom of the bust, the beginning of the recovery, the boom and the top of the boom.

Figure 3 sheds light on the growth-safety trade-off that the firms face: the higher the financial risk (the further on the right side on the scatterplots of Fig. 3), the quicker the expansion of the firms (the further up on these same graphs). As a consequence, in the boom dynamics (Figs. 3e-f), we observe a dispersion toward the top-right corner of the scatterplots (heavy debt and big size). This evolution is progressive, as a result of the small random but perpetual innovations in the adaptation process that determine the investment behavior of the firms. The “skittish” behaviors that correspond to low debt strategies run the risk of being eliminated if they are not enough to even renew the aging and obsolete machines, which would then drive the productive capacities to zero (i.e. toward the origin on the scatterplots). In this case, the firms go bankrupt and imitate another surviving firm. However, the top right corners of those plots are not densely populated because this area is competitive and represents risky behaviors: only a few firms will end up cornering the market, but they all run the risk of unsold production, which would lead to a drop in profits and a risk of insolvency. The riskiness of this behavior is clear from the proportion of speculative, and even Ponzi firms in the top right corner of the figures. This risk is also illustrated by the evolution of firms’ positions on the scatterplots throughout the cycles. Once the downturn starts, we observe a clear contraction of the firms toward the bottom of the scatterplot (see Figs. 3a-c). This tightening phenomenon is the result of a twofold motion: the bankruptcies of the most indebted firms that massively and brutally drive out non-cautious high debt strategies (movements toward the left of the plot); and the decrease in capital due to the non-renewal of depreciating productive capacities (movement toward the bottom). As is clear by comparing Figs. 3f and c, economic crises endogenously produce a homogenization of firm behavior because they first affect the few, but biggest firms that grew by heavily indebtedness. (See how the population of speculative firms starts growing among the biggest firms first in Fig. 3a.) In the wake of the bust, the speculative, and even Ponzi-types of financing seem to affect every firm, not only the biggest ones (Fig. 3b). Once the recovery starts (Fig. 3d), indebtedness starts increasing again, and few firms start growing and cornering the market again (Fig. 3e). This process repeats itself along each cycle. (To see this, notice the striking similarity between Figs. 3a and e.)
Fig. 3

Firms’ size distribution against debt behavior in six phases of a business cycle. Scatterplots report, ∀j, \({\ell ^T_{j}}\) (debt target, x-axis) versus kj (size as the number of machines, y-axis). Colors denote income-debt relations, according to the classification and terminology of Minsky (1986): blue for hedge, yellow for speculative, red for Ponzi-financing firms

Importantly, the market selection through bankruptcies along the bust dynamics is brutal (movements toward the bottom left of the scatterplots), and much quicker than the pace of the small-step innovations that progressively drive the system toward an increasing financial fragility along the boom dynamics (i.e. movements toward the top right). This difference explains why recoveries are slow and crises are severe. Deep crises as abrutal disciplining device have been part of the evolutionary economics ideas for along time:

Severe depression eliminates large numbers of firms from the economy, but behavior patterns that would be viable under more normal conditions may be disproportionately represented in the casualty list. At the same time, behavior patterns that were in the process of disappearing under more normal conditions may suddenly prove viable… (Winter 1964, p. 266)

Our ABM allows for a detailed and formal analysis of this mechanism in a micro-founded macro model.
As a final exercise on the firm side, we verify the robustness of those observations across different cycles of the baseline simulation. We use the slope of the regression line in the scatterplots of Fig. 3 (sizes vis-à-vis debt targets) and its dynamics over the cycles as a synthetic indicator.19 Figure 4 indicates a strongly pro-cyclical and coincident pattern: the slope is high at the top of the bubbles, then decreasing during the bust and finally increasing up to the top of the boom.
Fig. 4

Robustness check of the pattern in Fig. 3 along different cycles

From these observations, we draw the following conclusions. The adaptive model provided by the BSP collectively solves the growth-safety trade-off faced by the firms by eliminating the investment behaviors that are incompatible with current market conditions. The BSP ever creates heterogeneity in behaviors, with a strong emphasis on exploration. This heterogeneity is not random but is characterized by a salient emerging and recurring structure. This structure is endogenous, relatively stable from one cycle to the next, but, importantly, dynamic: market conditions evolve along the cycle, and behaviors that were judged virtuous in a given phase of the cycle (audacious behavior in the boom) turn out to be vicious in another (during a bust). This heterogeneity provides to the system as a whole its ability to react and adapt. This simple simulation exercise shows that there is no such thing as an efficient or optimal behavior in this complex adaptive system, but the characterization of successful behaviors itself constantly evolves as a result of the market conditions that these behaviors contribute to shaping.20 We now focus on those aggregate market conditions.

4.2.2 Macroeconomic dynamics

Figure 5 zooms on the cycle between period 750 and 1250 of the baseline simulation. On Fig. 5d, the blue curve that depicts the average debt ratio weighted by assets moves faster than the red one that reports the simple arithmetic average over firms. This reflects the fact that during a boom, the aggregate amount of debt grows mostly as a result of few, big firms with high leverage strategies. We now explain how this financial instability interacts with the goods demand, and provokes the boom and bust cycles.
Fig. 5

Zoom on one cycle of the baseline simulation: periods 750–1250

Along the boom phase of the cycle, investment feeds the demand for goods, which calls in turn for more expansion in market capacities (Fig. 5a). This optimistic outlook of firms is self-reinforcing because it is followed by the bank, which is fully accommodating in our model. However, the balance sheet of the firms also becomes more fragile (Fig. 5d), and the lending interest rates rise in the boom phase21 (Figure 5c). This rise generates a negative feedback between firms’ financial fragility, investment and goods demand that puts an end to this boom dynamics. Larger and larger shares of firms’ cash-flow are absorbed by debt services, especially for the biggest, and therefore more indebted, firms. At some point, this mechanism leads to a drop in profits and investment (see the evolution of potential output on Fig. 5b), a rise in bankruptcies (Fig. 5b) and a rise in unemployment results (Fig. 5a). A series of bankruptcies accelerates the imitation process through the BSP, bankrupted firms imitate the debt strategies of surviving firms. Those strategies correspond to more cautious debt behavior, as explained in Section 4.2.1. However, a phenomenon akin to a Fischerian debt-deflation sets in: we observe a sharp increase in indebtedness precisely when firms choose to deleverage (Fig. 5d).22

We can also look at the building up and collapse of assets and the interaction with the goods demand through the balance sheets of the agents. Along the bust phase, firms’ fixed capital drops, which reflects the drop in productive capacities stemming from the non-renewal of depreciated capital (Fig. 5a). However, firms’ circulating capital (which consists of the sum of finished and unfinished goods, and therefore measures firms’ inventories) only drops with a lag and less dramatically than fixed capital, which indicates excess inventories. Figure 5e also illustrates the liabilities side of firms’ balance sheets along the bust dynamics: the dramatic increase in inventories translates into firms’ financial difficulties, and a strong rise in overdraft facilities/short-run loans (even above the amount of circulating capital). Figure 5f synthesizes the categorization of firms into the three Minskian financing types (hedge, speculative and Ponzi; see the blue curve that represents the ratio of revenues over debt services), and indicates the degradation of firms’ solvency at the macroeconomic level.

Tables 2 and 3 allow for a similar reading. Those tables report the balance sheet matrix just before (in period t = 1000) and right after (t = 1050) the downturn (see Appendix C how these matrices are constructed). Within these 50 periods, the overall value of the net worth (i.e. the sum of deposits and equities held by households) has lost 30% of its real value. This loss stems from the collapse in investment, which implies that depreciated capital is not replaced: the firms’ capital represent almost half of the overall net worth before the downturn, and but only account for a quarter 50 periods later. By contrast, on the asset side of the firms, inventories represent 25% of the overall net worth in t = 1000, and more than 40% in t = 1050, which reflects the drop in goods demand and firms’ sales. On the liabilities side of the firms, the drop in investment shows up in the drop of long-run loans (i.e. the loans that are only intended to finance investment), from 28 to 14% of the overall net worth. By contrast, the share of the short-run loans increases from 54 to more than 70%, which translates the firms’ liquidity problems as a result of the drop in their sales. This simple exercise stresses the usefulness of stock-flow consistency for macroeconomic modeling. SFC modeling provides both a disciplinary device in the design of the financial behaviors and accounting relations between sectors, and an analytic tool to dissect dynamics emerging from the simulations.
Table 2

Balance sheet matrix, period 1000 (in real terms)






Work In Process










Fixed Capital








− 2,268,873.31


Short Term Loans


− 1,672,184.92



Long Term Loans


− 875,731.31





− 1,429,162.72

− 279,042.92







Table 3

Balance sheet matrix, period 1050 (in real terms)






Work In Process










Fixed Capital








− 1,643,209.89


Short Term Loans


− 1,529,421.24



Long Term Loans


− 312,271.74





− 926,605.22

− 198,483.09







We conclude that, in our ABM, the process of collective adaptation through the market selection pressure yields cyclical macroeconomic dynamics that look more in line with the “financial instability” hypothesis (Minsky 1986) than with the “as-if” hypothesis (Friedman 1953), which predicts a stabilization of the system around a socially desirable steady state by driving out inefficient behaviors.

5 Conclusions

Our model touches upon two, somehow distinct, research areas – learning and agent-based modeling. This section first makes the point that these areas should be more closely linked together in order to improve macroeconomic modeling and our understanding of macroeconomic dynamics.

Our exercise shows the interest of modeling learning, not as a process intended to converge toward a particular steady state, but as an ever-changing, ever-adapting process. In an adaptive complex environment, such as the simple macroeconomy modeled in Section 3, and probably the real world, there is no such thing as an “optimal” or efficient behavior. On the contrary, the characterization of successful behaviors itself constantly evolves as a result of the market conditions that these behaviors contribute to shaping. To put our results in parallel with a quote from March (1991, p. 73), in our model, there is not a single efficient way for the firms of addressing the growth-safety trade-off:
  • “What is good in the long run is not always good in the short run”: a cautious financial strategy (limiting the indebtedness of the firm) is desirable in a long-run perspective because these firms are more resilient to severe downturns, but impeding in the short-run, because it restrains their expansion and make them lose market shares in favor of more audacious firms.

  • “What is good at a particular historical moment is not always good at another time”: high leverage strategies allow a virtuous expansion circle to set in in periods of output growth, while they turn into a vicious circle in downturns, when firms unsuccessfully try to deleverage.23

  • “What is good for one part of an organization is not always good for another part”: while the fast growth of capital is desirable from the production division viewpoint, it puts the financial department at risk by deteriorating the capital ratio of the firm.

  • “What is good for an organization is not always good for a larger social system of which it is a part.”: in the wake of a downturn, bankrupted firms tend to imitate deleveraging strategies, hence downsizing their investment to improve their financial situation and avoid insolvency, but this behavior has, in turn, dramatic effects on the macroeconomic system as a whole because it amplifies and deepens the recession.

We conclude our formal and detailed analysis of learning and adaptation mechanisms with a conceptual definition of an economic crisis. Our model shows how an economic downturn or crisis endogenously stems from the adaptation and the failure of adaptation of the agents in the system.24 As shown by our model, a crisis corresponds to the moment when behaviors that were judged by the market successful and compatible with the environment suddenly appear unsuited and unsustainable from the firms’ financial perspective, and for the financial system as a whole. In other words, a crisis is the moment when individual behaviors suddenly turn out to be incompatible with the macroeconomic environment, while the two had been reinforcing each other previously. Stated differently, a crisis arises when the pace of change of the economic context becomes faster than the adaptation capacities of the agents that populate it.

The interpretation of crises as brutal disconnections between individual behaviors and aggregate outcomes and reversal between what used to appear virtuous and what used to be considered as vicious have recently found some revival interests, in the wake of the Great Recession (Eggertsson and Krugman 2012; Blanchard 2014; Battiston et al. 2016). Modeling such a transition is a challenge, though, and our paper shows how ABM can provide a micro-founded, fully decentralized, stock-flow consistent and endogenous approach to this question. The general interdependence of agents’ balance-sheets and the interconnection between the financial and the real sectors provided by the stock-flow consistency constitute an essential channel through which imbalances can propagate and crises can emerge as contagion phenomena. Genuine behavioral heterogeneity, together with full decentralization, produces the resulting co-evolution between micro behaviors and macro outcomes, and the endogenous emergence of this type of crises.

Finally, we conclude this paper by pointing toward an interesting extension of our work. In our model, the BSP mechanism only operates on the demand side of the credit market. Banks are actually subject to the same type of trade-off as the firms: a too prudent strategy can lead the bank to lose customers and profit opportunities along the boom, whereas a too aggressive strategy may expose the bank to undue risks. In a version of Jamel where the banking sector is disaggregated, credit supply strategies could also evolve under a BSP mechanism. The concomitant selection processes operating on the demand and supply side of the credit market may reinforce the boom and bust dynamics explained in this paper, but they might also dampen it. This is a promising research question that we leave for future work.


  1. 1.

    Jamel stands for Java Agent-based MacroEconomic Laboratory; see Seppecher (2012a, 2012b) and Seppecher and Salle (2015).

  2. 2.

    Following Cincotti et al. (2010), Kinsella et al. (2011) and Seppecher (2012a), a growing literature has emphasized the interest of combining SFC and ABM principles; see Caverzasi and Godin (2015). A non-exhaustive list of SFC-AB models, besides Jamel, includes Raberto et al. (2012), Caiani et al. (2016), Riccetti et al. (2014), Russo et al. (2016).

  3. 3.

    For instance, Lainé (2016) shows the challenge posed by the heterogeneity of the observed investment behavior of firms if one seeks to derive a model of investment decisions.

  4. 4.

    Allen and Carroll (2001) and Palmer (2012) illustrate this difference within the simple framework of the buffer-stock consumption rule; see also Salle and Seppecher (2016).

  5. 5.

    Admittedly, several modifications have been proposed to make GA more suited to ever-changing environments (see, e.g., Cobb and Grefenstette 1993). Classifier systems which combine GA with features taken from other types of expert systems, such as Artificial Neural Networks, are also somehow effective in changing environments. However, those algorithms are often complicated and computationally quite costly. By contrast, the BSP used in this paper is simple, parsimonious, and while being flexible in its implementation, finds an intuitive interpretation and involves a low computational burden.

  6. 6.

    As stressed by Dosi and Winter (2003a, p. 396), nor are necessary aggregate/centralized interaction models such as the replicator dynamics. We could make a similar point for the heuristic switching model à la Brock and Hommes (1997).

  7. 7.

    This can be because the firm’s operating characteristics are not perfectly observable by its competitors, or because the firm’s routines cannot be exactly transferred to another firm, or because of control error in the implementation of the new routine. Alchian (1950, pp. 218-219) uses the concept of “rough-and-ready imitative rules”.

  8. 8.

    See e.g. Kalecki (2010), who stresses that the amount of the entrepreneurial equity is the main limitation to the expansion of a firm.

  9. 9.

    This simplifying assumption avoids complicating the model by introducing a second industrial sector. An upcoming version of the model does encompass a capital good sector.

  10. 10.

    This is a quite standard procedure in corporate finance. However, other types of investment functions could be easily envisioned, and will be considered in further developments of the model.

  11. 11.

    The price and wage could be computed in a more complicated way, such as a trend projection of past values over the next window periods. However, this would complicated the decision making of firms, without adding much to the qualitative simulation results.

  12. 12.

    We document the frequency of this event in the simulations in Section 4; see Footnote 17. This is due to the very simplistic design of the banking sector in Jamel, a feature that is intended to be abandoned in future versions of the model.

  13. 13.

    This matching order ensures that the biggest purchasers first enter the market, which appears reasonable. However, this order does not matter as all simulations show that households’ rationing in the goods market remains a rare and negligible event, which would not be realistic otherwise.

  14. 14.

    However, we have checked that our model is able to reproduce the empirical macro regularities of Seppecher and Salle (2015). This is indeed the case, along with few more stylized facts that we can seek to reproduce now that our model incorporates investment, e.g. more volatile investment than GDP, and strong positive correlation between firms’ debt.

  15. 15.

    This, first, comes from our very stylized banking system and the absence of government intervention besides the Taylor rule that is ineffective in deflationary downturns.

  16. 16.

    The contribution of each figure to our argumentation will be presented throughout the whole section.

  17. 17.

    Because the model is randomly initialized and the single bank bears alone all the costs of firms’ losses (see Appendix A), the required adjustments may be too drastic for the single bank to absorb firms’ losses, and the simulation may break off at the beginning. We observe that this is the case in roughly 15% of the simulations. We do not report those runs in Table 1. However, once the economy survives this take-off period, we always observed the same cyclical aggregate pattern.

  18. 18.

    Recall that the model does not encompass any technological progress nor population changes. An average growth rate close to zero is therefore an expected outcome.

  19. 19.

    We are grateful to an anonymous referee for suggesting this exercise.

  20. 20.

    Brock and Hommes (1998) make a similar point by showing that “non-rational”, trend-chasing traders are not driven out by fundamental ones in a financial market model but their relative shares co-evolve in a non-linear way with the dynamics of the market that can display, as a result, very complicated, and even chaotic dynamics. See also Hommes (2006) for a related discussion.

  21. 21.

    In our model, this raise stems from the Taylor rule that increases nominal rates along the boom. Another explanation is the increase in the bank’s risk premium in an attempt to control for the increasing borrowers’ financial fragility (Stockhammer and Michell 2014). For simplicity, we abstract here from modeling endogenous risk premiums.

  22. 22.

    As explained in Seppecher and Salle (2015), the relative wage rigidity that we assume, see Section 3.4, is the driving force that brings back the system on an increasing trend.

  23. 23.

    On the deleveraging crisis and debt-deflation phenomenon, see notably Eggertsson and Krugman (2012). See Seppecher and Salle (2015) for an analysis within a simpler version of the Jamel model.

  24. 24.

    On the phenomenon of economic crises as coordination failures, see also Clower (1965), Cooper and John (1988), Howitt (2001), Gaffeo et al. (2008), Delli Gatti et al. (2008, 2010).



The authors would like to thank the two anonymous referees for their most useful comments and suggestions. They also wish to thank the guest editors of this issue and the participants of the symposia and seminars in which previous versions of this paper have been presented, namely: the 2nd Workshop on Modeling and Analysis of Complex Monetary Economies; the first Grenoble Post-Keynesian Conference; the 26th “Journée évolution artificielle Thématique”; the 22nd International Conference on Computing in Economics and Finance; the 6th annual congress of the French association for political economy; the 20th Conference of the Research Network Macroeconomics and Macroeconomic Policies; the 3rd Bordeaux Workshop on Agent-Based Macroeconomics; the seminar of the LEMNA; the seminar of the GREDEG.

Funding Information

This research was partly founded by the EU FP7 project MACFINROBODS, grant agreement No. 612796, as well as by the ‘Lavoie Chair’, Sorbonne Paris Cité.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CEPN (Centre d’Economie de Paris Nord), UMR CNRS 7234Université Paris 13VilletaneuseFrance
  2. 2.Utrecht UniversityTC UtrechtThe Netherlands

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