Cars H. Hommes

Heterogeneous beliefs and routes to chaos in a simple asset pricing model

This paper investigates the dynamics in the simple present discounted value asset pricing model with heterogeneous beliefs.

A rational route to randomness

Complex dynamics in economics arise from nonlinear systems that do not converge to a fixed point, a limit cycle, or explode or implode exponentially due to endogenous factors. They arise from cybernetics, catastrophe theory, chaos theory, or the varieties of modern complexity theory, including models with heterogeneous, interacting agents. This major three-volume collection presents the most important papers in the area of complexity in economics.

Heterogeneous Agent Models in Economics and Finance

This paper surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

Coordination of Expectations in Asset Pricing Experiments

An information display device wherein there is a base plate with information bearing face plates detachably mounted thereon by one or more spline elements that press-fit with formations on each of the opposing faces of the base and face plate. End caps are optional as are also separator strips between panels where there are a number of panels mounted on one base plate. Splines press-fit into grooves in each of the base plate and face plate. In one embodiment the spline is U-shaped receiving therein a rib on one member and projecting into a groove formed between two ribs on the other of the two plates.

Chapter 23 Heterogeneous Agent Models in Economics and Finance

Abstract This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand

The price-quantity dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand curves is analysed. We prove that chaotic dynamical behaviour can occur, even if both the supply and demand curves are monotonic. The introduction of adaptive expectations into the cobweb model leads to price-quantity fluctuations with a smaller amplitude. However, at the same time the price-quantity cycles may become unstable and chaotic oscillations may arise. We present a geometric explanation why chaos can occur for a large class of nonlinear, monotonic supply and demand curves.

On the consistency of backward-looking expectations: The case of the cobweb

In dynamic models of economic fluctuations backward-looking expectations with systematic forecasting errors are inconsistent with rational behaviour. In non-linear dynamic models exhibiting seemingly unpredictable, chaotic fluctuations, however, simple habitual ‘rule of thumb’ backward-looking expectation rules may yield non-zero but nevertheless non-systematic forecasting errors. In a chaotic model expectational forecasting errors may have zero autocorrelations at all lags. Even for rational agents patterns in these forecasting errors may be very difficult to detect, especially in the presence of (small) noise. Backward-looking expectations are then not necessarily inconsistent with rational behaviour. We investigate whether simple expectation schemes such as naive or adaptive expectations can be consistent with rational behaviour in the simplest of all non-linear dynamic economic models, the non-linear cobweb model.

ADAPTIVE LEARNING AND ROADS TO CHAOS - THE CASE OF THE COBWEB

Abstract We investigate the dynamics of the cobweb model with adaptive expectations, a linear demand curve, and a nonlinear, S-shaped, increasing supply curve. Both stable periodic and chaotic price behaviour can occur. We investigate, how the dynamics of the model depend on the parameters. Both infinitely many period doubling and period halving bifurcations can occur, when the demand curve is shifted upwards. The same result holds with respect to the expectations weight factor.

Complexity theory and financial regulation

Economic policy needs interdisciplinary network analysis and behavioral modeling Traditional economic theory could not explain, much less predict, the near collapse of the financial system and its long-lasting effects on the global economy. Since the 2008 crisis, there has been increasing interest in using ideas from complexity theory to make sense of economic and financial markets. Concepts, such as tipping points, networks, contagion, feedback, and resilience have entered the financial and regulatory lexicon, but actual use of complexity models and results remains at an early stage. Recent insights and techniques offer potential for better monitoring and management of highly interconnected economic and financial systems and, thus, may help anticipate and manage future crises.

Heterogeneous beliefs and the non-linear cobweb model.

Abstract This paper generalizes the evolutionary cobweb model with heterogeneous beliefs of Brock and Hommes (1997. Econometrica 65, 1059–1095), to the case of non-linear demand and supply. Agents choose between a simple, freely available prediction strategy such as naive expectations and a sophisticated, costly prediction strategy such as rational expectations, and update their beliefs according to an evolutionary ‘fitness’ measure such as past realized net profits. It is shown that, for generic non-linear, monotonic demand and supply curves, the evolutionary dynamics exhibits ‘rational routes to randomness’, that is, bifurcation routes to strange attractors occur when the traders’ sensitivity to differences in evolutionary fitness increases.