Crisis curves in nonlinear business cycles

Intermittent behavior of economic dynamics is studied by a nonlinear model of business cycles when two of its control parameters, amplitude and frequency of a periodic exogenous driving force, are changed. This study points out how similar wanted situations may be reached by changing any of both parameters, and it gives a deeper understanding of what happens in actual economic data when some control parameters are changed at the same time.     

Order and disorder in business cycles

It is shown that a very simple business cycle model of the multiplier-accelerator type can produce chaotic motion. The model uses a cubic approximation of the nonlinear floor-roof type of investment function, and a two-period distributed lag for consumption. It can be cast as a cubic iterative map for income differences, so that chaotic motion for the differences results in Brownian random walk for income itself. The case can be analyzed by means similar to those used in the study of the iterated quadratic mapping. The cubic, except being based on economic principles, has the advantage over the quadratic that it produces cyclical change. In the fast process for income differences the slowly moving income itself becomes a parameter responsible for feedback causing bifurcations between chaotic and ordered behaviour.     

An incomplete markets model of business cycles

This paper explores the effects of incomplete markets and positive spillovers on aggregate and industry output behavior. We consider an economy composed of a fixed set of infinitely-lived industries. When industries coordinate production decisions they jointly improve their productivity. Markets are missing, however, in the sense that industries cannot automatically form the most productive coalitions due to the presence of communication frictions. The degree of coordination between industries is determined by a random matching process from which complex coalitions of industries emerge through bilateral industry interactions. High production by an industry improves the probability with which it communicates with other industries, creating a positive spillover effect on the productivity of the rest of the economy. Aggregate output behavior exhibits both persistent fluctuations as well as procyclical productivity.     

On nonlinear theories of economic cycles and the persistence of business cycles

This paper explores the dynamical structure of various linear and nonlinear theories of economic cycles. It focuses, Fin particular, on the importance of limit cycle theories for macroeconomic dynamics. It develops and simulates a model of self-sustained cycles and demonstrates the existence of a limit cycle by utilizing the Poincare´-Bendixson theorem.     

Economic intermittency in a two-country model of business cycles coupled by investment

Intermittent behavior of economic dynamics is investigated by a two-country model of Keynes-Goodwin type business cycles. Numerical simulations show that after an economic system evolves from weak chaos to strong chaos the system keeps its memory before the transition and its time series alternates episodically between periods of weakly and strongly chaotic fluctuations. In addition, we examine the intermittent phenomena from the view point of business cycle patterns near the crisis point.     

Planning for repetitive cycles using an infinite horizon linear program

Summary Termination conditions are often difficult to model in a linear program. This paper discusses the use of an infinite horizon linear program which may enable the termination conditions to be modeled more accurately. It can be applied situations where a repetitive cycle (i. e. season) exists and generates steady state values of the decision variables. Examples are then given illustrating the use of the infinite horizon linear program.

---

Zusammenfassung Vielfach ist es schwierig, Abschlußbedingungen in ein LP-Modell einzubauen. In diesem Aufsatz wird die Verwendung eines linearen Modellansatzes mit unendlichem Horizont diskutiert, der es ermöglicht, Abschlußbedingungen auf sehr sorgfältige Weise zu formulieren. Er kann in solchen Fällen verwendet werden, in denen ein sich wiederholender Zyklus (z.B. Saisonzyklus) gegeben ist, und liefert stabile Werte für die Entscheidungsvariablen. Es werden Beispiele zur Anwendung des linearen Modellansatzes mit unendlichem Horizont gegeben.

---

---

The author thanksJohn McClain of Cornell University for suggesting this topic and making numerous helpful suggestions.     

A microeconomic model of business growth,decay and cycles

Summary This paper presents a dynamic theory of price, output, working capital and interest for the firm and industry. It yields many of the standard properties of the firm and industry at equilibrium, and in addition, a new microeconomic theory of growth, decay and business cycles. This is achieved by adding a working capital or budget constraint to the conventional atomistic single product firm and assuming a one period input-output lag. The theory leads to a simple but instructive example of a new mathematical system called recursive programming that represents ex ante optimizing while at the same time exhibiting ex post nonoptimality under certain conditions.

---

Zusammenfassung Die Arbeit bringt eine dynamische Theorie von Preis, Ausstoß, Betriebskapital und Zins für die Unternehmung und Branche. Es werden allgemeine Eigenschaften einer Unternehmung und der Branche im Gleichgewicht und darüber hinaus Grundzüge einer mikroökonomischen Theorie von Wachstum, Schrumpfung und Konjunkturzyklen dargelegt. Dies wird erreicht, indem bei der konventionellen, sich in atomistischer Konkurrenz befindlichen Einproduktunternehmung eine Betriebskapital- oder Budgetbeschränkung eingeführt wird und ein einperiodischer input-output lag angenommen wird. Die Theorie führt zu einem einfachen aber instruktiven Beispiel einer neuen, Rekursive Programmierung genannten Methode der ex ante Optimierung, wobei aber unter bestimmten Bedingungen ex post Nicht-Optimilität auftreten kann.

---

---

Vorgel. v.:W. Wittmann.     

Prevalence of hyperbolicity for complex singular cycles

In this article we consider two kinds of complex singular cycles arising for vector fields defined on three-dimensional manifolds. We prove that, under some generic conditions, any one parameter family of vector fields passing through these cycles has the following property: Hyperbolicity is a prevalent phenomena.Dedicated to the memory of Professor R. Mañé.Partially Supported by Fondecyt 1941080 and Dirección de Investigación Universidad de Santiago de Chile     

Algebraic cycles and realification of complex projective varieties

We investigate some properties of underlying real algebraic structure on complex projective varieties.     

Measuring length of business cycles across countries using a new non‐stationary unit‐root cyclical approach

This article examines the length of the cycles in the gross domestic product (GDP) real per capita series of 15 countries by means of new statistical techniques based on unit root cycles. We propose tests for unit root cycles at each of the frequencies of the process. Using this approach, we are able to approximate the number of periods per cycle. The results show that the cycles have a periodicity of approximately six years when the disturbances are white noise. However, if we permit autocorrelation, they may also occur at smaller intervals of time. Copyright © 2006 John Wiley & Sons, Ltd.     

An analogue of the Novikov Conjecture in complex algebraic geometry

We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain ``higher Todd genera' are birational invariants. This implies birational invariance of certain extra combinations of Chern classes (beyond just the classical Todd genus) in the case of varieties with large fundamental group (in the topological sense). We prove the conjecture under the assumption of the ``strong Novikov Conjecture' for the fundamental group, which is known to be correct for many groups of geometric interest. We also show that, in a certain sense, our conjecture is best possible.