19 results in Agent-Based Models in Economics
6 - Interaction
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- By Alberto Russo, Università Politecnica delle Marche, Ancona, Gabriele Tedeschi, Giorgio Fagiolo, Sant'Anna School of Advanced Studies
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
It is a fact of life that the preferences, information, and choices – hence the behavior – of an agent affect and are affected by the behavior of the agents she interacts with. In fact, there is a two-way feedback between individual and aggregate behavior: agents’ interaction affects the evolution of the system as a whole; at the same time, the collective dynamics that shape the social structure of the economy affect individual behavior.
For example, consider the case of the adoption of a new technology by initially uninformed consumers. Each agent, based on her preferences, may have some ex-ante evaluation about the quality of new products introduced in the market. However, by interacting with their peers, agents may gather fresh information about the new product and, eventually, they may decide whether to buy it or not. This influences the adoption rate of the product, which can be in turn exploited by other consumers as a parameter to be employed when subsequently considering whether to buy the product or not. Therefore, individual decisions may be affected by agent interactions, then impact on the aggregate state of the system, which can in turn feed back to individual behaviors.
Traditionally, economic theory has largely overlooked the importance of interactions among economic agents. In standard economic theory, interactions are treated as externalities or spillovers. In general equilibrium theory (GET), the presence of externalities is often treated as a pathology of the model, leading to possible nonexistence of equilibria. Therefore, in the model it is often assumed that externalities do not simply exist – i.e., that agents only interact indirectly through a nonagent – that is prices, whose role is to aggregate individual information. Hence, in GET, agents are totally disconnected, dots living in a vacuum without any connections (links) between them.
To appreciate the importance of externalities in mainstream economics, one has to resort to game theoretic models. In this setup, agents interact directly with all the other agents in the game. Interactions are captured via strategic complementarities: the payoff of any single agent depends directly on the choices made in the game by all the N − 1 other agents. This configures a scenario completely at odds with the one portrayed in GET, namely one where agents live in a fully connected world, where they are linked with anyone else.
3 - Agent-Based Models as Recursive Systems
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- By Matteo Richiardi, University of Oxford
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
A rather common misunderstanding about simulations is that they are not as sound as mathematical models. Computer simulations are, according to a popular view, characterised by an intermediate level of abstraction: they are more abstract than verbal descriptions but less abstract than ‘pure’ mathematics. This is nonsense. Simulations do consist of a well-defined (although not concise) set of functions, which relate inputs to outputs. These functions describe a fully recursive system and unambiguously define its macro dynamics. In this respect, AB models are no different from any other model: they are logical theorems saying that, given the environment and the rules described by the model, outputs necessarily follow from inputs. As in any other model, they provide sufficiency theorems: the environment and the rules are sufficient conditions to obtain the results, given the inputs. The resort to computer simulations is only an efficient way – given some conditions – to obtain the results.
In this chapter we offer a characterisation of AB models as recursive models. The chapter has a simple structure: Section 3.2 places AB modelling in the wider context of simulation models; Section 3.3 introduces the notation and the key concepts; finally, Section 3.4 concludes elaborating on what constitutes a proof in an AB setting.
Discrete-Event vs. Continuous Simulations and the Management of Time
Computer-based simulations face the problem of reproducing real-life phenomena, many of which are temporally continuous processes, using discrete microprocessors. The abstract representation of a continuous phenomenon in a simulation model requires that all events be presented in discrete terms. However, there are different ways of simulating a discrete system.
In Discrete Event Simulations (DES) entities are thought of as moving between different states as time passes. The entities enter the system and visit some of the states (not necessarily only once) before leaving the system. This can be contrasted with System Dynamics (SD), or continuous simulation modelling, a technique created during the mid-1950s by Jay Forrester at the Massachusetts Institute of Technology (Forrester, 1971), which characterises a system in terms of ordinary differential equations (ODEs). SD takes a slightly different approach to DES, focusing more on flows around networks than on the individual behaviour of entities. In SD, three main objects are considered: stocks, flows and delays. Stocks are basic stores of objects, as the number of unemployed workers.
4 - Rationality, Behavior, and Expectations
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- By Domenico Delli Gatti, Catholic University, Milan
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
In order to achieve her goals, an agent must decide a line of action (a behavioral rule). Mental representations of the environment and of the behavior of other agents are key in taking this decision. The availability of an adequate and appropriate information set and of cognitive capabilities to process information, in turn, are key in forming these mental models. In a context characterized by uncertainty, one of the most important cognitive process is expectation formation. In this chapter we overview the way in which rationality, behavioral rules and expectation formation are connected in modern macroeconomics.
In Section 4.2 we set the stage by discussing (optimal) decision-making in an environment of full rationality and certainty. From Section 4.3 on, we discuss the consequences of uncertainty – in its wide range of specifications – and expectation on individual decision making and on macroeconomic performance.
Section 4.3 is devoted to the theory of choice in the presence of measurable uncertainty (risk). Uncertainty is measurable when agents are able to attach probabilities to uncertain events. In this setting the probability distribution of the variable of interest replaces the true value of the variable (which is available only in the case of certainty) in the information set of the agent. We will provide simple examples of choice in the case of risk neutrality (Subsection 4.3.1) and risk aversion (Subsection 4.3.2). Moreover, we will discuss choice in a multi-period setting (Subsection 4.3.3).
We will show that it is straightforward, and extremely useful, to extend the notion of measurable uncertainty discussed in Subsections 4.3.1 and 4.3.2 to the multi-period setting. Also in a multi-period context, in fact, the true values of the variables of interest are replaced by probability distributions.
The Rational approach to Expectation formation (RE) is the natural candidate to model expectations in such a setting. In fact we introduce a Linear Stochastic Difference Equation at this early stage of the analysis.
We illustrate its solution by means of a graphical tool which exploits the two-way relationship between current and expected value of a variable of interest. The true (or actual or current) value of variable x is a function of the expectation of the same variable xe, in symbols x = f (xe) (represented by the True Value, or TV, schedule).
List of Contributors
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10 - Epilogue
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Summary
The economic crisis the world has experienced in 2007, and is still ongoing in some parts of the globe, has been also a crisis of the economic profession. “Over the past three decades, economists have largely developed and come to rely on models that disregard key factors – including heterogeneity of decision rules, revisions of forecasting strategies, and changes in the social context – that drive outcomes in asset and other markets. It is obvious, even to the casual observer that these models fail to account for the actual evolution of the realworld economy… In our hour of greatest need, societies around the world are left to grope in the dark without a theory” (Colander et al., 2009).
This predicament was not new. Back in 1995, Frank Hahn and Robert Solow fiercefully argued against the new classical basic methodological principle according to which “the only appropriate micro model is Walrasian … based exclusively on inter-temporal utility maximization subject to budget and technological constraints … [This model] proposes that the actual economy can be read as it is … approximating the infinite time discounted utility maximizing program of a single immortal representative agent … There is simply no possibility of coordination failures … Of course that is the economy of Dr. Pangloss and it bears little relation to the world” (Hahn, 1995, p.2). Since then, some developments of economic thought have gone in the right direction, but overall their criticisms have gone largely unnoticed. The straight jacket of axiomatic Walrasian micro-foundations has limited the scope of the research for alternatives.
Walrasian micro-foundations should be considered the wrong answer to a right research question, the most stimulating question since the very beginning of economic thought: How does a completely decentralized economy composed of myriads of self-interested agents manages to coordinate individual actions?
Agent-based models provide a promising tentative answer to this question. There is still a long way to go, but the path has been traced. These elements present and discuss the basic toolkit for researchers interested in building ABMs.
If the reader arrives so far in this book, we will be happy. If, from now on, it is we who will follow the reader's progress, we will be blissfully happy.
9 - Estimation of Agent-Based Models
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- By Matteo Richiardi, University of Oxford
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
‘How absurdly simple!’ I cried.
‘Quite so!’ said he, a little nettled.
‘Every problem becomes very childish when once it is explained to you.’
Arthur Conan Doyle. The Adventure of the Dancing Men.Introduction
The ultimate test of a theory is its empirical validity, so the question whether a model ‘fits the data well’ is crucial. In the last chapter, we introduced some of the many issues involved in model evaluation. Here, we dig into the problem of tuning the values of the parameters. Moreover, we are also interested in the values of the estimated parameters for interpreting the model behaviour and to perform what-if type counterfactual (e.g., policy) evaluation exercises. Agent-based (AB) models are in general complex non-linear models, and can therefore display many different behaviours depending on the region of the parameter space being sampled. Assessing the performances of the model in the right region of the parameter space is therefore important for model evaluation. Once this region has been identified and the model deemed appropriate for its scopes, lessons can be learned about what might happen in the real world if some of the parameters changed, either as a consequence of some unforeseen developments (scenario analysis) or due to some specific actions purposefully implemented (policy analysis).
Our goal, broadly speaking, is comparing (possibly an infinite number of) instances of the model with different parameter values and select those that fits the data better.
Before going on, a first remark is necessary. Generally, we do not aim at calibrating or estimating a model by getting to a single optimal choice for all the parameters. In a frequentist approach, we rather look at confidence intervals – that is, ranges where the ‘true’ value of the parameters, assuming the model is correctly specified, is likely to lie – while in a Bayesian approach we focus on the posterior probability distributions for the parameters – reflecting our uncertainty about the parameters values given our prior knowledge and the information contained in the data. In this chapter we will provide examples of both approaches.
8 - Empirical Validation of Agent-Based Models
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- By Giorgio Fagiolo, Sant'Anna School of Advanced Studies, Matteo Richiardi, University of Oxford
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
Generally speaking, validation involves a judgment over the quality of a model. How good is model A is? Is it better or worse than model B? A model can be good from a certain point of view and bad, or inadequate, from another one. Also, validation is not necessarily a 0–1 pass test: the criteria can be continuous.
The validity of a model can be defined as the degree of homomorphism between a certain system (the model) and another system that it purportedly represents (the real-world system).
Model validation can be defined along different dimensions.
First of all, no model exists without an underlying theory. A first dimension of validation therefore is concept validation, i.e., the validation of the model relative to the theory: is the model consistent with the theory on which it is based? This is common to both analytical and computational models. The latter, however, need an additional level of validation (Stanislaw, 1986): program validation, i.e., the validation of the simulator (the code that simulates the model) relative to the model itself.
Second, models can be evaluated against real data. This is empirical validation. The aim of this chapter is to introduce the reader to the techniques of empirical validation of ABMs in economics. It requires (i) the choice of the relevant empirical indicators (so that the theoretical framework can be validated relative to its indicators) and (ii) the validation of the empirical true value relative to its indicator.
Empirical validation is often the basis for theory validation – the validation of the theory relative to the simuland (the real-world system).
Empirically validating an ABM means, broadly speaking, “taking the model to the data,” in the form of empirical and/or experimental data, historical evidence or even anecdotal knowledge.
Empirical validation may concern the model inputs and/or outputs. Input validation refers to the realism of the assumptions. There are two classes of inputs of an ABM. The first one consists of structural assumptions concerning the behavior of the agents or the pattern of their interactions. Examples include a particular bounded-rationality rule that we assume agents follow (e.g., a mark-up price-setting rule), or a peculiar type of network (for instance, a small-world) governing the interactions among agents.
Index
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Frontmatter
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List of Figures
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Contents
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1 - Introduction
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- By Domenico Delli Gatti, Catholic University, Milan, Mauro Gallegati, Università Politecnica delle Marche, Ancona
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Hard Times for Dr Pangloss
High and persistent unemployment, over-indebtedness and financial instability, bankruptcies, domino effects and the spreading of systemic risk: these phenomena have taken center stage in light of the Global Financial Crisis.
By construction, the Neoclassical approach is much better suited to study the features of the world of Dr Pangloss (Buiter, 1980) than the intricacies of a complex, financially sophisticated economy. This point is well taken in the introduction of a seminal paper by Bernanke, Gertler and Gilchrist published well before the Global Financial Crisis: ‘How does one go about incorporating financial distress and similar concepts into macroeconomics? While it seems that there has always been an empirical case for including credit-market factors in the mainstream model, early writers found it difficult to bring such apparently diverse and chaotic phenomena into their formal analyses. As a result, advocacy of a role for these factors in aggregate dynamics fell for the most part to economists outside the US academic mainstream, such as Hyman Minsky, and to some forecasters and financial market practitioners.’ (Bernanke et al., 1999, p. 1344).
This candid admission by three of the most distinguished macroeconomics (one of them destined to be Chairman of the Federal Reserve for eight long and turbulent years) – which, incidentally, provides a long overdue implicit tribute to Hyman Minsky – also provides the research question for a model of the financial accelerator which has started a non-negligible body of literature in contemporary macroeconomics.
In order to put this development in macroeconomic thinking into context, it is necessary to recall that any mainstream macroeconomic model is based on a Dynamic Stochastic General Equilibrium (DSGE) skeleton, which can support either a Real Business Cycle (RBC) model or a New Keynesian (NK) model.
The latter differs from the former because of the presence of imperfections, the most important being imperfect competition and nominal rigidity. The structural form of the standard NK-DSGE framework boils down to a threeequation model consisting of an optimising IS equation, an NK Phillips curve and a monetary policy rule based on changes in the interest rate.
The NK-DSGE framework is, of course, too simple and therefore inadequate to analyse the emergence of a financial crisis and a major recession for the very good reason that neither asset prices nor measures of agents, financial fragility show up anywhere in the model.
5 - Agents’ Behavior and Learning
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- By Alberto Russo, Università Politecnica delle Marche, Ancona, Domenico Delli Gatti, Catholic University, Milan, Saul Desiderio, Ivo Vlaev
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
The fundamental building blocks of every agent-based model are agents. From a general point of view, in order to build an agent-based model, four main issues need to be addressed: (i) the nature of the agents; (ii) the list of variables describing their state; (iii) the list of the actions the agents can perform; (iv) the structure of their interaction with other agents. In what follows, we will discuss the first three points, while the last will be deeply analyzed in Chapter 6.
A peculiar feature differentiating agents in agent-based models from those of mainstream models is their autonomy of action. Indeed, agents in a rationalexpectations- cum-equilibrium model behave according to rules that are not independent of what the others are doing: in any situation, their actions depend on some variable that is determined by the behavior of the entire system. In a typical market model, for instance, a firm must know the actual market price (i.e., market-clearing price) in order to decide its production level, and this price is determined by the interplay of all the agents populating the economy. Hence, agents’ actions are mutually dependent through the equilibrium state or, differently stated, the actual implementation of actions depends on the outcome of actions (outcome ⇒ actions). As this simple but representative example clarifies, mainstream models are dynamically incomplete since no mechanism for out-of-equilibrium dynamics is provided. Thus, the central problem characterizing a decentralized market economy – i.e., the coordination problem – is left aside. On the contrary, the character of autonomy in an agentbased model consists in the existence of a set of behavioral rules allowing agents to take decisions in any situation, independently from what the others are doing and without a central Auctioneer, intervenes as a deus ex machina in determining some sort of equilibrium state. The implementation of actions is not dependent of the outcome of actions. Of course, the final outcome generally will depend on the whole system of interactions among the agents, implying the possibility of individual rationing in case of coordination failures, but this is not an obstacle to the implementation of autonomous decisionmaking. In fact, what makes this possible is that agents’ actions directly influence only other agents’ variables, and not also their own variables. To clarify the point, let us imagine a consumer wanting to buy a good from a shop.
7 - The Agent-Based Experiment
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- By Jakob Grazzini, Matteo Richiardi, University of Oxford, Lisa Sella
- Edited by Domenico Delli Gatti, Università Cattolica del Sacro Cuore, Milano, Giorgio Fagiolo, Mauro Gallegati, Matteo Richiardi, Università degli Studi di Torino, Italy, Alberto Russo
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Summary
Introduction
This chapter deals with the problem of analysing the behaviour of an agentbased (AB) model. The problem is similar to the one faced by any modelling methodology: the researcher sets up the rules of the game, but does not know in advance the implications of those rules. Actually, it is in this a priori uncertainty about the model outcomes, and the relationship between the model outputs and the model inputs, that rests the value of developing a model. However, the techniques to gain understanding about the model behaviour differ substantially across modelling methodologies, and they remain quite underexplored in the AB literature. In a simulation model, only inductive knowledge about its behaviour can be gained by repeatedly running the model under different samples from the parameter space.
The analysis of this inductive evidence has to confront with the a priori unknown stochastic properties of the model. The easiest case is when, for any values of the parameters, the model is stationary and ergodic: in these circumstances it is generally possible, with a reasonable number of experiments, to characterise both the equilibrium properties of the model and the adjustment dynamics to the equilibria. On the other hand, non-stationarity renders the analytical concepts of equilibrium and adjustment dynamics inapplicable, while non-ergodicity might hinder the same possibility of fully describing the behaviour of the model. A preliminary analysis to discriminate between these cases is therefore necessary, and it can only be done by statistical testing. In this chapter, we will provide examples of the tests that can be used to detect both stationarity and ergodicity.
These properties in turn affect the types of subsequent analyses that can be performed, and the interpretation of the results. The techniques that are used to describe the relationships between the different variables of the model are referred to in general terms as sensitivity analysis (SA). Although a complete survey of these techniques is outside the scope of this chapter, we briefly describe them and offer an example of how they can be applied to a specific AB model.
The chapter is structured as follows. Section 7.2 introduces the notion of statistical equilibria, and discusses the effects of non-stationarity.
List of Tables
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Dedication
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2 - Agent-Based Computational Economics: What, Why, When
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- By Matteo Richiardi, University of Oxford
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Summary
Introduction
What are agent-based (AB) models? In a nutshell, they are models (i.e., abstract representations of the reality) in which (i) a multitude of objects interact with each other and with the environment, (ii) the objects are autonomous (i.e., there is no central, or “top-down,” control over their behavior and, more generally, on the dynamics of the system), and (iii) the outcome of their interaction is numerically computed. Since the objects are autonomous, they are called agents. The application of agent-based modeling to economics is called Agent-Based Computational Economics (ACE). As Leigh Tesfatsion – one of the leading researchers in the field and the “mother” of the ACE acronym – defines it, ACE is
the computational study of economic processes modeled as dynamic systems of interacting agents (Tesfatsion, 2006).
In other terms, AB models are the tool traditionally employed by ACE researchers to study economies as complex evolving systems, that is systems composed by many interacting units evolving through time.
None of the features above, in isolation, define the methodology: the microperspective implied by (i) and (ii) is roughly the same as the one adopted, for instance, by game theory, where strategic interaction is investigated analytically (though in game theory the number of individuals who populate the models is generally very small). The computational approach, instead, is typical of Computational General Equilibrium or Stock-Flow Consistent models, which are, however, based on aggregate representations of the system.
In this introductory chapter we describe the features of AB models (Section 2.2), offering an overview of their historical development (Section 2.3), discussing when they can be fruitfully employed and how they can be combined with more traditional approaches (Section 2.4). As an example, we describe one of the first and most prominent AB models, Thomas Schelling's Segregation model (Section 2.5). Conclusions follow.
Features of Agent-Based Models
The basic units of AB models are the “agents.” In economics, agents can be anything from individuals to social groups – like families or firms. They may also be more complicated organizations (banks for instance), or even industries or countries. Agents can be composed by other agents: the only requirement being that they are perceived as a unit from the outside, and that they do something – that is they have the ability to act – and possibly react to external stimuli and interact with the environment and with other agents.
Bibliography
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Preface
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Summary
As Schumpeter pointed out long ago, conceptual frameworks, models and policy prescriptions are embedded in the economist's ‘preanalytic vision’ of the economy. And preanalytic visions have been, and still are, very different in the profession.
Nowadays the majority of the profession embraces the neoclassical approach to economic behaviour, according to which agents are endowed with substantial rationality, adopt optimal rules and interact indirectly through the price vector on markets which are continuously in equilibrium. This approach has been extraordinarily fruitful, as it has allowed economists to build models that can be solved analytically and yield clear-cut policy implications. The obvious case in point is Walras's theory of General Equilibrium, beautifully outlined in his Elements d'Economie Politique, and elegantly extended and refined by Arrow and Debreu. Moreover, the approach has been remarkably flexible. Appropriately designed variants of the neoclassical approach have been applied to economies characterised by imperfect competition, imperfect information, strategic interaction, and heterogeneous agents. The most insightful of these theoretical developments have been incorporated in microfounded macroeconomic models of the New Neoclassical Synthesis that have been all the rage during the years of the Great Moderation.
However, the capability of the neoclassical approach to encompass and explain all the complex details of economic life has reached a limit. For instance, it is now abundantly clear that the neoclassical approach is not wellsuited to describe the Global Financial Crisis and the Great Recession. In models that follow the New Neoclassical Synthesis, in fact, a great recession may be explained only by a large aggregate negative shock, whose probability is extremely low (i.e., it is an extreme and rare event). This mechanism does not clarify much of the crisis and does not help to devise appropriate remedies.
The current predicament, both in the real world and in the public debate, resembles the early 1930s. The way out of the Great Depression required a new economic theory and the Second World War.1 Luckily, in order to escape the current predicament, we can dispense at least with the latter. We still need, however, to reshape the way in which we think about the economy.
For several years now, a complexity approach has been developed which conceives the economy as a complex system of heterogeneous interacting agents characterised by limited information and bounded rationality. In this view, a ‘crisis’ is a macroscopic phenomenon which spontaneously emerges from the web of microscopic interactions.
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