Frank Westerhoff

University of Bamberg · Institut für Volkswirtschaftslehre

We utilize a chartist-fundamentalist model to examine the limits of informationally efficient stock markets. In our model, chartists are permanently active in the stock market, while fundamentalists trade only when their mispricing-dependent trading signals are strong. Our findings indicate the possible coexistence of two distinct regimes. Dependin...

We propose an evolutionary competition model to investigate the green transition of firms, highlighting the role of adjustment costs, dynamically adjusted transition risk, and green technology progress in this process. Firms base their decisions to adopt either green or brown technologies on relative performance. To incorporate the costs of switchi...

We propose a stock market model with chartists, fundamentalists and market makers. Chartists chase stock price trends, fundamentalists bet on mean reversion, and market makers adjust stock prices to reflect current excess demand. Fundamentalists’ perception of the stock market’s fundamental value is subject to animal spirits. As long as the stock m...

We explore the impact of fake news on asset price dynamics within the asset-pricing model of Brock and Hommes (Brock, W. A., and C. H. Hommes. 1998. “Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model.” Journal of Economic Dynamics and Control 22 (8): 1235–74). By polluting the information landscape, fake news interferes with...

We consider the bifurcations occurring in a two-dimensional piecewise-linear discontinuous map that describes the dynamics of a cobweb model in which firms rely on a regime-switching expectation rule. In three different partitions of the phase plane, separated by two discontinuity lines, the map is defined by linear functions with the same Jacobian...

We propose a simple agent-based version of Paul de Grauwe’s chaotic exchange rate model. In particular, we assume that each speculator follows his own technical and fundamental trading rule. Moreover, a speculator’s choice between these two trading philosophies depends on his individual assessment of current market circumstances. Our agent-based mo...

We consider the bifurcations occurring in a two-dimensional piecewise-linear discontinuous map that describes the dynamics of a cobweb model in which firms rely on a regime-switching expectation rule. In three different partitions of the phase plane, separated by two discontinuity lines, the map is defined by linear functions with the same Jacobian...

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment tra...

We develop a nonlinear duopoly model in which the heuristic expectation formation and learning behavior of two boundedly rational firms may engender complex dynamics. Most importantly, we assume that the firms employ different forecasting models to predict the behavior of their opponent. Moreover, the firms learn by leaning more strongly on forecas...

It takes time to produce commodities, and different production technologies may take different lengths of time. Suppose that firms may switch between different production technologies that take different lengths of time. A natural implication of such a scenario is that not all firms would then offer their commodities in every period, i.e. firms’ to...

Based on a behavioral exchange rate model, we show that a central bank that conducts competitive interventions to promote its economy may devalue its currency, albeit at the expense of creating heightened exchange rate volatility. However, currency manipulation may easily spark currency wars, i.e. rival central banks may retaliate by conducting com...

We develop a behavioral stock market model in which a market maker adjusts stock prices with respect to the orders of chartists, fundamentalists and sentiment traders. We analytically prove that the mere presence of sentiment traders, i.e. traders who optimistically buy stocks in rising markets and pessimistically sell stocks in falling markets, co...

Policymakers around the world impose some form of capital gains taxes to foster the stability of financial markets. Unfortunately, there is no clarity on the effects of capital gains taxes. Based on a stylized behavioral asset-pricing model highlighting the trading activity of extrapolating speculators, we show that policymakers may involuntary des...

We apply recent stability and bifurcation results to provide an analytical characterization of Paul de Grauwe’s chaotic exchange rate model. We prove that the model’s fundamental steady state becomes unstable due to a Neimark-Sacker bifurcation when chartists extrapolate past exchange rate trends too strongly, a phenomenon that gives rise to cyclic...

We develop a cobweb model in which firms, facing a two-period production delay, have access to a flexible (costly) and an inflexible (cheap) production technology. Moreover, firms select between production technologies depending on their evolutionary fitness, measured in terms of past realized profits. The dynamics of our cobweb model is driven by...

We propose an empirically motivated financial market model in which speculators rely on trend-following, contrarian and fundamental trading rules to determine their orders. Speculators’ probabilistic rule-selection behavior – the only type of intrinsic randomness in our model – depends on past and current performance indicators. Our model replicate...

Based on the seminal asset-pricing model by Brock and Hommes (J Econ Dyn Control 22:1235–1274, 1998), we analytically show that higher wealth taxes increase the risky asset’s fundamental value, enlarge its local stability domain, may prevent the birth of nonfundamental steady states and, if they exist, reduce the risky asset’s mispricing. We furthe...

We reconsider the well-known conditions which guarantee the roots of a third-degree polynomial to be inside the unit circle. These conditions are important in the stability analysis of equilibria and cycles of three-dimensional systems in discrete time. A simplified set of conditions determine the boundary of the stability region and we prove which...

We integrate a plausible expectation formation and learning scheme of boundedly rational investors into a standard user cost housing market model, involving a rental and a housing capital market. In particular, investors switch between heterogeneous expectation rules according to an evolutionary fitness measure, given by the rules’ past profitabili...

We propose a novel housing market model to explore the effectiveness of rent control. Our model reveals that the expectation formation and learning behavior of boundedly rational homebuyers, switching between extrapolative and regressive expectation rules subject to their past forecasting accuracy, may create endogenous housing market dynamics. We...

We study a simple financial market model with interacting chartists and fundamentalists that may give rise to multiband chaotic attractors. In particular, asset prices fluctuate erratically around their fundamental values, displaying a significant bull and bear market behavior. An in-depth analytical and numerical study of our model furthermore rev...

We propose a simple agent-based computational model in which speculators’ trading behavior may cause bubbles and crashes, excess volatility, serially uncorrelated returns, fat-tailed return distributions and volatility clustering, thereby replicating five important stylized facts of stock markets. Since each speculator bets on his own (technical an...

We first present a brief review of nonlinear asset-pricing models and contributions in which such models have been used as benchmarks to evaluate the effectiveness of a number of regulatory policy measures. We then illustrate the functioning of one particular asset-pricing model—the seminal framework by Brock and Hommes (J Econ Dyn Control 22:1235–...

We reconsider the well-known Schur/Samuelson conditions, which guarantee the roots of a third-degree polynomial to be inside the unit circle. These conditions are important in the stability analysis of equilibria and cycles of three-dimensional systems in discrete time. We derive a simplified set of conditions that determine the boundary of the sta...

Based on a behavioral stock-flow housing market model in which the expectation formation behavior of boundedly rational and heterogeneous investors may generate endogenous boom-bust cycles, we explore whether central banks can stabilize housing markets via the interest rate. Using a mix of analytical and numerical tools, we find that the ability of...

We propose an asset-pricing model in which investors switch between extrapolative and regressive expectation rules subject to an evolutionary fitness measure and show that central banks may tame endogenous expectations-driven boom-bust cycles by adjusting interest rates with a view to the market’s momentum.

We present analytical tools that may be useful in studying the behaviour of dynamic economic models formulated in discrete time. In particular, we provide a simplified set of conditions for the stability of fixed points of three-dimensional maps, and the bifurcation types associated with them.

Since the instability of housing markets may be quite harmful for the real economy, we explore whether public housing construction programs may tame housing market fluctuations. As a workhorse, we use a behavioral stock-flow housing market model in which the complex interplay between speculative and real forces triggers reasonable housing market dy...

We propose an elementary housing model that replicates the key properties of housing bubbles, namely short-run momentum, long-run mean reversion, and excess volatility. We analytically proof that such dynamics can only emerge if homebuyers place sufficient weight on extrapolative expectations.

We provide a full analytical treatment of a multi-asset market model in which speculators have the choice between two risky and one safe asset. As it turns out, the dynamics of our model is driven by a four-dimensional nonlinear map and may undergo a transcritical, flip or Neimark–Sacker bifurcation. While the first bifurcation is associated with a...

We develop a simple agent-based financial market model in which speculators’ market entry decisions are subject to herding behavior and market risk. In addition, speculators’ orders depend on price trends, market misalignments and fundamental news. Using a mix of analytical and numerical tools, we show that a herding-induced market entry wave may a...

In recent times a number of agent-based models have been put forward that specify an aggregate sentiment as the difference between optimists and pessimists and let the agents endogenously switch between the two attitudes. The present paper extends this stylized framework by adding a third category, which may be viewed as neutrality. On this basis i...

We develop a model in which investors can participate in stock, bond and housing markets. Investors’ market entry decisions are subject to herding effects and depend on the markets’ price trends and on their mispricings. The dynamics of our model is governed by a four-dimensional nonlinear map and its unique inner steady state is characterized by s...

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of...

This paper is a survey of the burgeoning literature that seeks to take the enigmatic concept of the animal spirits more seriously by building heterodox macro‐dynamic models that can capture some of its crucial aspects in a rigorous way. Two approaches are considered: the discrete choice and the transition probability approach, where individual agen...

Several economic surveys specify an aggregate sentiment as the difference between optimists and pessimists. This concept is also applied in agent-based modelling where, governed by endogenously determined transition probabilities , the individual agents switch between two attitudes. The present paper extends this stylized framework by adding a thir...

With the help of two examples, this chapter illustrates the usefulness of agent-based models as tools for economic policy design. The first example applies a financial market model in which the order flow of speculators, relying on technical and fundamental analysis, generates intricate price dynamics. The second example applies a Keynesian-type go...

We review a recent literature that shows that interactions between markets, created by the market entry and exit behavior of boundedly rational firms, may cause complex endogenous dynamics. In particular, these models predict that welfare decreases if firms rapidly switch between markets. Against this background, we show that policy makers have the...

We propose a novel agent-based financial market framework in which speculators usually follow their own individual technical and fundamental trading rules to determine their orders. However, there are also sunspot-initiated periods in which their trading behavior is correlated. We are able to convert our (very) simple large-scale agent-based model...

We develop a partial equilibrium model in which firms can locate in two separate regions. A firm's decision where to locate in a given period depends on the regions' relative profitability. If firms react strongly to the regions' relative profitability, their market switching behavior generates unstable dynamics. If the goal of policy makers is to...

This paper is a survey of the burgeoning literature that seeks to take the enigmatic concept of the animal spirits more seriously by building heterodox macro-dynamic models that can capture some of its crucial aspects in a rigorous way. Two approaches are considered: the discrete choice and the transition probability approach, where individual agen...

After showing that the distribution of the S&P 500’s distortion, i.e. the log difference between its real stock market index and its real fundamental value, is bimodal, we demonstrate that agent-based financial market models may explain this puzzling observation. Within these models, speculators apply technical and fundamental analysis to predict a...

We propose a financial market model in which speculators follow a linear mix of technical and fundamental trading rules to determine their orders. Volatility clustering arises in our model due to speculators’ herding behaviour. In case of heightened uncertainty, speculators observe other speculators’ actions more closely. Since speculators’ trading...

In order to demonstrate that nonlinear tax systems may have surprising and potentially undesirable side effects, we develop an evolutionary market entry model in which firms decide on the basis of past profit opportunities whether or not to enter a competitive market. Our main focus is on the case of a proportional tax on positive profits. Such a p...

The seminal cobweb model by Brock and Hommes reveals that fixed-point dynamics may turn into increasingly complex dynamics, as firms switch more quickly between competing expectation rules. While policy makers may be able to manage such rational routes to randomness by imposing a proportional profit tax, the stability-ensuring tax rate may cause a...

We develop a model in which stock market participation depends on current market movements and on the fundamental state of the market. Our model explains empirical and experimental evidence according to which increasing (decreasing) stock market participation amplifies bubbles (crashes).

The goal of this paper is to review some work on agent-based financial market models in which the dynamics is driven by piecewise-linear maps. As we will see, such models allow deep analytical insights into the functioning of financial markets, may give rise to unexpected dynamics effects, allow explaining a number of important stylized facts of fi...

We combine a standard stock-flow housing market model, incorporating explicit relationships between house prices, the housing stock, and the rent level, with a parsimonious expectation formation scheme of housing market investors, reflecting an evolving mix of extrapolative and regressive expectation rules. The model results in a two-dimensional di...

Within the seminal cobweb model of Brock and Hommes, firms adapt their price expectations by a profit-based switching behavior between free naïve expectations and costly rational expectations. Brock and Hommes demonstrate that fixed-point dynamics may turn into increasingly complex dynamics as the firms’ intensity of choice increases. We show that...

We combine a standard stock-flow housing market model, incorporating explicit relationships between house prices, the housing stock, and the rent level, with a parsimonious expectation formation scheme of housing market investors, reflecting an evolving mix of extrapolative and regressive expectation rules. The model results in a two-dimensional di...

We develop a simple agent-based financial market model in which heterogeneous speculators apply technical and fundamental analysis to trade in two different stock markets. Speculators’ strategy/market selections are repeated at each time step and depend on predisposition effects, herding behavior and market circumstances. Simulations reveal that ou...

We develop a simple two-region, cobweb-type dynamic partial equilibrium model to demonstrate the existence of optimal, possibly non-zero, trade barriers. A pure comparative statics analysis of our model suggests that a reduction of trade barriers, modeled as small but positive import tariffs, always enhances welfare. However, taking a dynamic persp...

We develop a simple financial market model with heterogeneous interacting speculators. The dynamics of our model is driven by a one-dimensional discontinuous piecewise linear map, having two discontinuity points and three linear branches. On the one hand, we study this map analytically and numerically to advance our knowledge about such dynamical s...

We develop a financial market model with interacting chartists and fundamentalists that embeds the famous bull and bear market model of Huang and Day as a special case. Their model is given by a one-dimensional continuous piecewise-linear map. Our model, on the other hand, is more flexible and is represented by a one-dimensional discontinuous piece...

We develop a financial market model with heterogeneous interact- ing agents: market makers adjust prices with respect to excess demand, chartists believe in the persistence of bull and bear markets and funda- mentalists bet on mean reversion. Moreover, speculators trade asymmetrically in over and undervalued markets and while some of them determine...

We present a simple one-dimensional discontinuous piecewise-linear agent-based financial market model in which prices evolve with respect to the trading activity of heterogeneous speculators. In line with empirical evidence, speculators rely on technical or fundamental trading rules to determine their orders. The general setup that comes out of our...

We develop a simple behavioral macromodel to study interactions between the real economy and the stock market. The real economy is represented by a Keynesian-type goods market approach while the setup for the stock market includes heterogeneous speculators. Using a mixture of analytical and numerical tools we find, for instance, that speculators ma...

We revise Metzler’s well-known inventory model by developing a framework in which producers can either apply a simple but cheap extrapolative or a more sophisticated but expensive regressive forecasting rule to predict future sales. Producers are boundedly rational in the sense that they tend to select forecasting rules with a high evolutionary fit...

This paper investigates the impact of speculative behavior on house price dynamics. Speculative demand for housing is modeled using a heterogeneous agent approach, whereas ‘real’ demand and housing supply are represented in a standard way. Together, real and speculative forces determine excess demand in each period and house price adjustments. Thre...

In this paper we continue exploring a recently introduced financial market model in which boundedly rational agents follow technical and fundamental trading rules to determine their orders. Amongst other things, our model reveals that interactions between heterogeneous speculators can generate interesting boom-bust cycles. In addition, we provide a...

The paper estimates an elementary agent-based financial market model recently put forward by the same authors. Invoking the two trader types of fundamentalists and chartists, it comprises four features: price determination by excess demand; a herding mechanism that gives rise to a macroscopic adjustment equation for the population shares of the two...

In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous...

In this chapter we consider a simple financial market model following the pioneering works by R. Day, described by one-dimensional piecewise linear maps, either being continuous or discontinuous. We shall see how rich the related dynamics are, with sequences of stable cycles and chaotic intervals. Our results explain, among other things, the emerge...

We present a simple financial market model with interacting chartists and fundamentalists. Since some of these speculators only become active when a certain misalignment level has been crossed, the dynamics are driven by a discontinuous piecewise linear map. The model endogenously generates bubbles and crashes and excess volatility for a broad rang...

The paper proposes an elementary agent-based asset pricing model that, invoking the two trader types of fundamentalists and chartists, comprises four features: (i) price determination by excess demand; (ii) a herding mechanism that gives rise to a macroscopic adjustment equation for the market fractions of the two groups; (iii) a rush towards funda...

According to empirical studies, speculators place significant orders in commodity markets and may cause bubbles and crashes. This paper develops a cobweb-like commodity market model that takes into account the behavior of technical and fundamental speculators. We show that interactions between consumers, producers and heterogeneous speculators may...

We enrich the classical cobweb framework by allowing producers to enter different markets. The market entry decision is repeated every period and depends on the markets' historical profit differentials. As a result, the number of producers in a market and thus also a market's total supply vary over time. Analytical and numerical investigations of o...

We re‐explore the consequences of some popular countercyclical intervention rules in a simple Keynesian‐type macroeconomic model in which the dynamics of consumer sentiment and business cycles are intertwined. We find that fiscal policy does not only have a direct effect on national income via the well‐known Keynesian multiplier process but also an...

We propose a simple agent-based macroeconomic model in which firms hold heterogeneous sales expectations. A firm may either optimistically expect an increase in its sales or pessimistically expect the opposite. Whether a given firm is optimistic or pessimistic depends on macroeconomic conditions and the average mood prevailing within its social/loc...

We develop a financial market model with heterogeneous interacting agents: market makers adjust prices with respect to excess demand, chartists believe in the persistence of bull and bear markets and fundamentalists bet on mean reversion. Moreover, speculators trade asymmetrically in over- and undervalued markets and while some of them determine th...

We develop a discrete-time model in which the stock markets of two countries are linked via and with the foreign exchange market. The foreign exchange market is characterized by nonlinear interactions between technical and fundamental traders. Such interactions may generate complex dynamics and recurrent switching between “bull” and “bear” market p...

We explore how disclosure requirements that regulate the release of new information may affect the dynamics of financial markets. Our analysis is based on three agent-based financial market models that are able to produce realistic financial market dynamics. We discover that the average deviation between market prices and fundamental values increas...

The motivation of this paper is to understand the effects of coupling a macroeconomic model of inflation rate dynamics, relying on an aggregate expectation, to a heterogeneous expectations framework. A standard model composed of Okun's law, an expectations-augmented Phillips curve and an aggregate demand relation is extended to allow agents to sele...

In this chapter we consider a simple financial market model following the pio-neering works by R. Day, described by one-dimensional piecewise linear maps, either being continuous or discontinuous. We shall see how rich the related dynamics are, with sequences of stable cycles and chaotic intervals. Our results explain, among other things, the emerg...

This paper proposes a simple asset pricing model with three groups of traders: chartists who believe in the persistence of bull and bear markets, fundamentalists who bet on a reduction of the observed mispricing, and investors who follow a buy-and-hold strategy. The innovative feature of the model concerns the frequency of trading: rather than rema...

In a previous paper Tramontana et al. (2009), we developed a three-dimensional discrete-time dynamic model in which two stock markets of two countries, say H(ome) and A(broad), are linked via and with the foreign exchange market. The latter is modelled in the sense of Day and Huang (1990), i.e. it is characterized by a nonlinear interplay between t...

This paper explores the steady-state properties and the dynamic behavior of a gener-alization of the classical cobweb model. Under fairly general demand and cost functions, producers form naïve expectations about future prices and select their output so as to max-imize expected profits. Unlike the traditional setup, producers have the choice betwee...

In the recent past, a number of interesting agent-based financial market models have been proposed. These models successfully explain some important stylized facts of financial markets, such as bubbles and crashes, fat tails for the distribution of returns and volatility clustering. These models, reviewed, for instance, in Chen, Chang, and Du (in p...