Adaptive learning in an expectational difference equation with several lags: selecting among learnable REE

It is demonstrated in this paper that adaptive learning in least squares sense may be incapable to reduce, in a satisfactory way, the number of attainable equilibria in a rational expectations model. The model inves-tigated, as an illustration, is the monetary approach to exchange rate determination that is augmented with technical trading in the currency market in the form of moving averages since it is the most commonly used technique according to questionnaire surveys. Because of technical trading in foreign exchange, the current exchange rate is dependent on jmax lags of the exchange rate, and the model has, therefore jmax + 1 nonbubble rational expectations equilibria (REE), where most of them are adaptively learnable. Howe-ver, by assuming that a solution to the model should have a solution to a nested model as its limit, it is possible to single out a unique equilibrium among the adaptively learnable equilibria that is economically meaningful.asset pricing; heterogenous agents; least squares learnability; rational expectations equilibria and technical trading

Is The Fiscal Theory of the Price Level Learnable?

This paper presents a prototype model for development of the “fiscal theory of the price level.” In this simple setting, the fiscal theory’s distinctiveness relies upon adoption of a bubble solution, rather than the rational-expectations fundamentals solution. The paper then shows that the fiscal solution is not adaptively learnable, by agents who estimate coefficients relevant for forecasting on the basis of available data, whereas the orthodox “monetarist” solution exists and is learnable. Finally, it is argued that similar results should be expected to apply in more complex models. JEL Nos. E5, E6, D8. Keywords: Monetary theory, fiscal theory, price level determination, learning, rational expectations.

Bifurcation Routes to Volatility Clustering under Evolutionary Learning

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically. Simple economic intuition why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.

When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the $n$-stage repeated version of the game exist if and only if both players have $\Omega(n)$ random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the $n$-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on "random-like" sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then $\Omega(n)$ random bits remain necessary for equilibria to exist

Robust Taylor rules in an open economy with heterogeneous expectations and least squares learning

The aim of this paper is threefold: (i) to investigate if there is a unique rational expectations equilibrium (REE) in the small open economy in Galí and Monacelli (2005) that is augmented with technical trading in the foreign exchange market; (ii) to investigate if the unique REE is adaptively learnable in a recursive least squares sense; and (iii) to investigate if the unique and adaptively learnable REE is desirable in an inflation rate targeting regime in the sense that a low and not too variable CPI inflation rate in equilibrium is achieved. The monetary authority is using a Taylor rule when setting the nominal interest rate, and we investigate numerically the properties of the model developed. A main conclusion is that the monetary authority should increase (decrease) the interest rate when the CPI inflation rate increases (decreases) and when the currency gets stronger (weaker) to have a desirable rule that is robust with respect to the degree of technical trading in the foreign exchange market. Thus, the value of the currency is a better response variable than the output gap in the most desirable parametrizations of the interest rate rule.determinacy; foreign exchange; inflation rate targeting regime; interest rate rule; robust monetary policy; technical trading

The Roadblock of Culturalist Economics: Economic Change á la Douglass North

In his 2005 book, Understanding the Process of Economic Change, North offers a rough account of economic change that can be called “culturalist economics.” In his account, he attributes the change of well being of individuals to, besides technology and demographics, cultural heritage or cultural beliefs. Using this basis, he then attributes "the mystery of the unique evolution of western Europe" to a causative view that combines "Christian dogma" and English "individualism." This combinatory belief assures property rights, and hence explains the success of Western Europe and the US and the failure of Islam and Latin America in terms of their respective economic development. But North’s culturalist economics faces a roadblock: it does not explain the origin of beliefs, and it neglects the role of rational choice in manufacturing beliefs. Specifically, it ignores the roles of agency, revolutionary change, and the dynamics of empire.cultural economics vs. culturalist economics; reification of culture; Christian dogma; individualism; mystery of rise of Europe; Islam

Market Mood, Adaptive Beliefs and Asset Price Dynamics

Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple "dynamic market fraction" model of two groups of traders, fundamentalists and trend followers, under a market maker scenario. Market mood and evolutionary adaption are characterized by fixed and adaptive switching fraction among two groups, respectively. Using local stability and bifurcation analysis, as well as numerical simulation, the role played by the key parameters in the market behaviour is examined. Particular attention is payed to the impact of the market fraction, determined by the fixed proportions of confident fundamentalists and trend followers, and by the proportion of adaptively rational agents, who adopt different strategies over time depending on realized profits.

Division of Labour and Social Coordination Modes : A simple simulation model

This paper presents a preliminary investigation of the relationship between the process of functional division of labour and the modes in which activities and plans are coordinated. We consider a very simple production process: a given heap of bank-notes has to be counted by a group of accountants. Because of limited individual capabilities and/or the possibilities of mistakes and external disturbances, the task has to be divided among several accountants and a hierarchical coordination problem arises. We can imagine several different ways of socially implementing coordination of devided tasks. 1) a central planner can compute the optimal architecture of the system; 2) a central planner can promote quantity adjustments by moving accountants from hierarchical levels where there exist idle resources to levels where resources are insufficient; 3) quasi-market mechanisms can use quantity or price signals for promoting decentralized adjustments. By means of a simple simulation model, based on Genetic Algorithms and Classifiers Systems, we can study the dynamic efficiency properties of each coordination mode and in particular their capability, speed and cost of adaptation to changing environmental situations (i.e. variations of the size of the task and/or variations of agents' capabilities). Such interesting issues as returns to scale, specialization and workers exploitation can be easily studied in the same model