Learning of cycles and sunspot equilibria by Genetic Algorithms

We analyze the learning behaviour of a Simple Genetic Algorithm in an overlapping generations model with one consumption good and fiat money. It is shown by simulations, that in cases where periodic equilibria exist the equilibrium of period two is learned by a Genetic Algorithm and not the monetary steady state. We further show that proper coding leads to convergence of the GA towards the sunspot equilibrium. If individuals who believe in the impact of sunspots are brought together with individuals who ignore the sunspots, the sunspot believes will in most cases drive the other individuals out of the population.     

Sunspots, GDP and the stock market

A correlation has been observed between the US GDP and the number of sunspots as well as between the Dow Jones Industrial Average and the number of sunspots. The data cover 80 years of history. The observed correlations permit forecasts for the GDP and for the stock market in America with a future horizon of 10 years. Both being above their long-term trend they are forecasted to go over a peak around Jun-2008.     

Market imperfections and the instability of open economies

In the presence of small market imperfections, the transitional dynamics of an open economy can become indeterminate, in that there exist an infinite number of equilibrium paths converging to a unique steady state. In contrast to closed economy models, in the open economy, such indeterminacy can arise independently of the curvature of the utility function in consumption. The results suggest that with market imperfections, open economies can be subject to fluctuations caused by randomness unrelated to the economy's fundamentals.     

Local Sunspot Equilibria Reconsidered

We generalize the usual notion of local sunspot equilibria. We say such equilibria exist around a steady state of an OLG economy whenever stationary sunspot equilibria of arbitrarily close economies exist within any neighborhood of the steady state. Unlike the usual notion, this generalization allows to address the following identification problem: Can an analyst distinguish empirically small fluctuations due to small shocks to the fundamentals from pure expectations-driven fluctuations? We study conditions under which these generalized local sunspot equilibria exist in OLG economies, and show that they may exist around not only indeterminate but also determinate steady states.     

Sunspot cycles

Summary. This paper shows new properties about the equilibria of a stationary OG economy by establishing a connection between its stationary equilibria and those of a finite economy, with and without extrinsic uncertainty. Specifically, it shows the countability and local uniqueness with respect to the sup metric of the so-called sunspot cycles introduced here, that encompass both the deterministic cycles and the usual finite Markovian stationary sunspot equilibria. These sunspot cycles are, moreover, able to generate, at a lower cost in terms of assumptions than other sunspot equilibria, time series with the recurrent but irregular fluctuations typical of economic time series. Received: July 26, 2001; revised version: March 5, 2002 RID="*" ID="*" I want to thank an anonymous referee for comments that have helped greatly to improve this paper, as well as the comments about its contents received from several audiences in different seminars and conferences (the Economic Theory seminar of the University of Pennsylvania, the 2001 Meeting of the Econometric Society held at New Orleans, the 2000 Econometric Society World Congress, the 2000 Society for Economic Design Conference) and from comments to a previous paper, Dávila [10], specially from Jim Peck at the 1997 Workshop on General Equilibrium held at the University of Venice, that eventually lead to this one.     

Evaluating currency crises: A Bayesian Markov switching approach

In this paper we examine the nature of a currency crisis. We do so by employing an out-of-sample forecasting exercise to analyse the Mexican crisis in 1994. Forecast evaluation was based on modern econometric techniques concerning the shape of forecaster’s loss function. We also extend the empirical framework suggested by Jeanne and Masson [Jeanne, O., Masson, P., 2000. Currency crises and Markov-switching regimes. Journal of International Economics 50, 327–350] to test for the hypothesis that the currency crisis was driven by sunspots. To this end we contribute to the existing literature by comparing Markov regime switching model with a time-varying transition probabilities with two alternative models. The first is a Markov regime switching model with constant transition probabilities. The second is a linear benchmark model. Empirical results show that the proxy for the probability of devaluation is an important factor explaining the nature of currency crisis. More concretely, when the expectation market pressure was used as a proxy of probability of devaluation, forecast evaluation supports the view that currency crisis was driven by market expectation unrelated to fundamentals. Alternatively, when interest rate differential is used as a proxy for probability of devaluation, currency crisis was due to predictable deterioration of fundamentals.     

A note on conspicuous leisure,animal spirits and endogenous cycles

This paper investigates general equilibrium effects of conspicuous leisure. It finds that leisure externalities reduce the degree of other market imperfections needed to generate indeterminacy or sunspot equilibria - endogneous cycles become empirically more plausible. Sunspot equilibria are possible with a downward-sloping labor demand schedule. The economic reasoning behind the result is that with conspicuous-externalities, labor is drawn more easily in and out of leisure to help fulfill agents expectations.Received: June 2003, Accepted: January 2004, JEL Classification: E32Mark Weder: I thank Paulo Brito (the Editor), Michael Burda and an anonymous referee for very helpful comments and suggestions. All remaining errors are my own. Support by the Deutsche Forschungsgemeinschaft in the form of a Heisenberg Fellowshipis gratefully acknowledged.     

The relation between sunspot effects and multiplicity in incomplete markets models with numeraire assets

This paper considers the necessity and sufficiency of multiple certainty equilibria for sunspot effects, and shows that neither implication is valid. This claim is made for models with incomplete markets and numeraire assets. First, I prove that a multiplicity of certainty equilibria is neither necessary nor sufficient for sunspot effects by way of two counter-examples. Second, I verify over an entire subset of economies that equilibrium with sunspot effects can never be characterized as a randomization over multiple certainty equilibria.     

Can indeterminacy resolve the cross-country correlation puzzle?

Are productivity shocks the only driving force of international business fluctuations? In this paper I argue that another source of uncertainty—changes in market expectations or ‘sunspots’ – is also important. One major shortcoming of existing IRBC models is the ‘cross-country correlation puzzle’: models tend to generate cross-country consumption correlations that are too high and output, investment and employment correlations that are too low when compared to the data. I show that with empirically supported level of increasing returns, an otherwise standard model possesses multiple, indeterminate convergent paths to the steady state, which allow for sunspots to influence the economy. The model displays time series properties that in many ways match the data better than the conventional model. It is especially successful in generating realistic consumption and output correlations.