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Complexity and economics1
Victor A. Beker
Introduction
This chapter provides an overview of the main ideas that comprise the complexity approach in economics.
There is no doubt that the economy is a very complex system. The traditional approach to understanding it has been to reduce complexities to simple rules and behaviours, abstracting many features of the real economy.
The key issue in this reductionist approach is what features of the real world are kept in the theoretical model and what features are disposed of. What one keeps in and what one gets rid of makes the main difference between orthodoxy and heterodoxy in economics.
In the orthodox approach, simplification is often done in order to make it mathematically tractable, at the expense of the modelsâ ability to capture relevant phenomena. Therefore, in many cases, mainstream economists conclude with models which exclude most of the features which may be of interest for policy making.
An alternative to reductionism consists of studying economic systems with a complexity approach. The complexity approachâs point of departure is that reductionism is not suitable for studying systems with many parts that interact to produce global behaviour. This behaviour goes far beyond what can be explained in terms of interactions between the individual constituent elements: the behaviour of the whole is much more complex than the behaviour of the parts. From the interaction of the parts, new behaviours or new phenomena emerge. The study of these newly emergent behaviours and phenomena is the object of study of the complexity approach.
Is there any definition for âcomplexityâ? The physicist Seth Miller has gathered at least 45 different definitions of âcomplexity.â However, many of these are not appropriate for economics.
The economist Richard Day (1994) defined complexity in economics in terms of dynamic outcomes. An economic system is dynamically complex if its deterministic endogenous processes do not lead it asymptotically to a fixed point, a limit cycle or an explosion.
Yoguel and Robert (2013) propose the following five dimensions to synthesise the 15 elements they find in the different definitions of complexity: (1) heterogeneity, (2) disequilibrium and divergence, (3) interactions and partial information, (4) network architecture and (5) emergent properties.
The complexity approach changes not only the answers but also the questions to which economics has to respond.
For instance, the ArrowâDebreu general equilibrium model is concerned with the static, timeless allocation of resources. Its dynamics just have to do with the existence, stability and uniqueness of the equilibrium.
On the contrary, the complexity approach focuses on processes, pointing out the evolution of the economic system over time, including out-of-equilibrium dynamics.
The complexity perspective implies a rejection of mainstream conceptual categories and tools, including economic methodology. While the received theory is based on deductive formal proofs of theorems that seek to derive broadly applicable general solutions, the complexity perspective relies on computer simulations and experimental methods to inductively determine possible outcomes and ranges of solutions.
According to Brian Arthur (2014), âcomplexity economics got its start in 1987 when a now-famous conference of scientists and economists convened by physicist Philip Anderson and economist Kenneth Arrow met to discuss the economy as an evolving complex system.â
Complexity economics has focused on economic phenomena like business cycle, crises and other out-of-equilibrium behaviour. On the contrary, the main interest of mainstream economics has been to show that the economic system converges on a stable equilibrium. Economic fluctuations are modelled as stochastic shocks attached to low order linear difference equations. The fact that economic fluctuations appear as a sole product of exogenous shocks is in line with the mainstream equilibrium approach in economic thought. In the absence of such shocks, the system would tend to a steady state, as different versions of the neoclassical model of optimal growth predict. âEverything is for the best in the best of all possible worldsâ is the Panglossian neoclassical conclusion.
The orthodox approach to economic phenomena has little to do with empirical reality. Economic data provide little â if any â evidence of linear, simple dynamics or of lasting convergence to stationary states or regular cyclical behaviour. Irregular frequencies and amplitudes of economic fluctuations are persistent and do not show clear convergence or steady oscillations.
Orthodoxy developed a theory which excluded the possibility that a catastrophic crisis could ever happen. It assumes not only that the economy tends towards equilibrium but also that that equilibrium is a stable one. Therefore, economists enrolled in this line of thought not only did not foresee the 2007â2008 financial crisis but also did not even consider it possible. Consequently, they were absolutely unable and unprepared to deal with it.
Alternative approaches to the fairy tale that neoclassical economics tells us came back to the fore after the crisis. One of them is the complexity approach to economic phenomena. Its use of nonlinear models offers the advantage that the same model allows us to describe stable as well as unstable and even chaotic behaviours.
The non-linearity assumption and its implications
Once non-linearity is admitted, we are in the presence of positive feedback or increasing returns. Mainstream economic theory removed the assumption of increasing returns from most of its areas because of its tendency to generate the existence of multiple equilibria. Convexity was a necessary assumption to warrant uniqueness of equilibrium.
However, the existence of non-convexities and increasing returns are widely used assumptions in some areas of economic analysis. International trade theory, macroeconomics, economic growth, industrial organisation, regional economics and economics of technology are examples. Multiple equilibria are also a widespread result in game theory.
The multiplicity of equilibria means that there are many possible worlds. Which of these worlds finally resulted is the product of history: it is history dependent. Another dynamic trajectory might have led to another result. If the equilibrium is unique, history does not matter: sooner or later, the system will arrive at that unique equilibrium. The process is ergodic: whatever the sequence of events, the outcome is always the same. On the other hand, if the process is non-ergodic, the path defines the result. From this perspective, the economy can be seen as a process of self-organisation: the system âchoosesâ between the different options that are presented to it.
Non-linearity, attractors and chaos
The equilibrium approach in economics2 is interested in only one type of attractor: fixed-point attractors. Most efforts are devoted to finding out the conditions under which a unique and stable equilibrium exists. In fact, linear systems either converge on a fixed point or explode.
Nonlinear dynamic systems may evolve towards other types of attractors, such as limit cycle or periodic attractors, quasiperiodic attractors and chaotic attractors.
The equilibrium approach, as Samuelson (1983: 21) points out, has been taken from equilibrium thermodynamics, which is based on linear relationships. It was the introduction of nonlinear relationships which allowed the development of non-equilibrium thermodynamics.
Since sensitive dependence on initial conditions is the main feature of chaotic dynamics, the measure of chaos is provided by the Lyapunov exponent, and more precisely by the largest positive Lyapunov exponent. Lyapunov exponents (L) measure how quickly nearby orbits diverge in phase space. Unpredictability is an intrinsic feature of chaotic systems. Chaos implies the existence of a temporal horizon â defined by the Lyapunov time3 â beyond which predictions lose any reliability.
The paradox of chaos is that we are in the presence of unpredictable behaviour that is generated by a completely deterministic process.
Economistsâ interest in non-linearity emerges from its potential aptitude to model fluctuations in the economy and in financial markets. It offers more options beyond the linear modelâs binary alternative between a stable and an explosive path.
Non-linearities in the financial markets
The traditional approach in the literature on finance has been based on the efficient-market hypothesis, which argues that the price of financial assets reflects all available information. If so, there is no opportunity for persistent speculative profits, because any news is immediately reflected in prices. However, the view that emerges from this traditional approach contrasts with the widespread perception that financial markets offer opportunities for speculative profits.
An alternative approach is based on the distinction between chartists â also called noise-traders â and fundamentalists. While the first extrapolate past trends, the latter are investors governed by the fundamentals of the market. The fact that these models are very successful in replicating the stylised facts of financial markets is seen as a kind of empirical validation.
Altavilla and De Grauwe (2010) developed a simple theoretical model in which chartists and fundamentalists interact. The model predicts the existence of different regimes, and thus non-linearities in the link between the exchange rate and its fundamentals. The results suggest the presence of nonlinear mean reversion in the nominal exchange rate process. Traditional linear rational expectations models cannot account for this except by introducing exogenous changes in regimes â that is, by leaving these switches unexplained. The most striking finding is that there appear to be two regimes: one in which the exchange rate follows the fundamental exchange rate quite closely and another in which the fundamentals do not seem to play any role in determining the exchange rate. Both regimes alternate in unpredictable ways; there are frequent switches between fundamental and non-fundamental regimes. As a result, the relation between the exchange rate and the fundamentals is an unstable one.
These results are in line with other empirical studies that have so frequently found a disconnection between macroeconomic fundamentals and the exchange rate. They corroborate the advantages of using a nonlinear approach which allows for the existence of more than one state to be detected. The switching nature of the exchange rate process is inconsistent with a linear representation of the relation between the exchange rate and its fundamentals.
In a more recent paper, De Grauwe and Rovira Kaltwasser (2012) introduce a distinction between optimist and pessimist fundamentalist traders, respectively referring to traders that systematically overestimate or underestimate the fundamental rate. They show that, even in the absence of chartists, chaos can govern asset price dynamics. Furthermore, chaos can indeed be triggered by the presence of biased fundamentalist traders alone as well as by the interaction between biased and unbiased fundamentalist traders. The model is extended, introducing unbiased fundamentalists and chartists. The latter prove to have a destabilising influence: the larger the coefficient expressing the degree with which they extrapolate the past change in the exchange rate, the stronger their destabilisation power. The system exhibits a NeimarkâSacker bifurcation of the steady state that leads to a stable limit cycle of the market exchange rate. Increasing the value of the chartistsâ extrapolation coefficient eventually leads to a break of the limit cycle; the exchange rate is governed by a chaotic attractor. This feature of the model is a common result obtained in the literature of heterogeneous agent models in finance, where the interaction between fundamentalists and chartists is analysed and the chartists act as a destabilising force in the market.
Finally, the authors perform a Monte Carlo simulation. The model replicates the widely observed phenomenon that exchange rate returns are not normally distributed but, on the contrary, exhibit fat tails.
It is clear that once the Holy Trinity of the unbounded rational representative agent, efficient markets and linearity hypotheses is put aside, new illuminating results are obtained.
Several models have been introduced where markets are viewed as evolutionary adaptive systems with heterogeneous boundedly rational interacting agents. They match important stylised facts in financial time series such as fat tails and long memory in the returns distribution and clustered volatility. They exhibit interesting dynamics characterised by temporary bubbles and crashes (see Hommes and Wagener, 2008).
Chaos and economics
The detection of...
