Nonlinear dynamics in economic modelling

Decisions in Economics and Finance -     

A piecewise linear model of credit traps and credit cycles: a complete characterization

We reconsider a regime-switching model of credit frictions which has been proposed in a general framework by Matsuyama for the case of Cobb–Douglas production functions. This results in a piecewise linear map with two discontinuity points and all three branches having the same slope. We offer a complete characterization of the bifurcation structure in the parameter space, as well as of the attracting sets and related basins of attraction in the phase space. We also discuss parameter regions associated with overshooting, leapfrogging, poverty traps, reversal of fortune and growth miracle, as well as cycles with any kind of switching between the expansionary and contractionary phases.     

Insiemi invarianti globalmente attrattivi nell'interazione fra il “mercato dei beni” ed il “mercato della moneta”

Si studia il comportamento dinamico locale e globale di un modello macroeconomico che si rappresenta con un sistema nonlineare di due equazioni alle differenze (sistema dinamico discreto, o mappa). Si mostra come l'uso di un nuovo strumento di analisi, le linee critiche, consenta di studiare molte delle proprietà globali (quali i bacini di attrazione di insiemi invarianti) e delle biforcazioni globali, che si verificano in mappe del piano con inversa non unica. Si prova che il punto fisso localmente attrattivo è anche globalmente attrattivo, mentre in regimi di instabilità del punto fisso esistono curve chiuse, o altri insiemi invarianti (regolari o caotici) di attrazione, in aree assorbenti globalmente attrattive.

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Summary The local and global dynamical behaviour of a macroeconomic model, represented by a nonlinear system of two difference equations (discrete dynamical system or map), is studied. It is shown how several properties (as basins of attraction of invariant sets) and global bifurcations occurring in two-dimensional maps with a non-unique inverse can be studied by use of a new analytical tool, the critical curves. It is proven that the locally attractive fixed point is globally attractive, while closed invariant curves or other attractive invariant sets (regular or chaotic) exist in globally attractive absorbing areas, when the fixed point is repulsive.

     

One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets

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 systems. In particular, not much is known about discontinuous maps involving three branches. On the other hand, we seek to improve our understanding of the functioning of financial markets. We find, for instance, that such maps can generate complex bull and bear market dynamics.     

Quantile estimation of frontier production function

The purpose of the paper is to provide new information on the performance of frontier estimation methods, using data from Italian hotel industry. Quantile regression is also suggested as solution to frontier production function estimation. It is shown that, while the choice of estimation methods among conventional techniques significantly affects the economic analysis, quantile regression provides valuable new information by estimating the whole spectrum of production functions corresponding to different efficiency levels. In addition, the method makes available a coherent framework to analyze the performance of the conventional techiniques. Jel classification: C14, C16, D24We would like to thank the Co-Editor, the Associate Editor and an anonymous referee for comments and suggestions. The research was supported by the University Research Council and the National Research Council. The usual disclaimer applies.The estimates were computed using the Roger Koenker and StatLibS-Plus routine of quantile regression and the Tim Coelli and CEPA Web site FRONTIER 4.1 Program. The data set is provided by the Ho.Re.Ca. survey conducted by ISTAT in 1992.First version received: June 2001/Final version received: December 2002     

Correlating Lévy processes with self-decomposability: applications to energy markets

Decisions in Economics and Finance - Based on the concept of self-decomposability, we extend some recent multidimensional Lévy models built using multivariate subordination. Our aim is to...     

Growing through chaotic intervals

We consider a growth model proposed by Matsuyama [K. Matsuyama, Growing through cycles, Econometrica 67 (2) (1999) 335-347] in which two sources of economic growth are present: the mechanism of capital accumulation (Solow regime) and the process of technical change and innovations (Romer regime). We will shown that no stable cycle can exist, except for a fixed point and a cycle of period two. The Necessary and Sufficient conditions for regular or chaotic regimes are formulated. The bifurcation structure of the two-dimensional parameter plane is completely explained. It is shown how the border-collision bifurcation leads from the stable fixed point to pure chaotic regime (which consists either in 4-cyclical chaotic intervals, 2-cyclical chaotic intervals or in one chaotic interval).     

Border collision bifurcations in boom and bust cycles

Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smooth dynamic systems—in particular, results from the theory of border collision bifurcations—and show that the very existence of borders such as capacity constraints or nonnegativity constraints may lie behind abrupt changes in the dynamic behavior of economic variables.     

Regional consumption dynamics and risk sharing in Italy

In this paper, we propose a new method for investigating consumption insurance. Differently from the existing literature, we use error correcting VAR models in order to capture simultaneously the occurrence of risk sharing against permanent and transitory shocks. The proposed method is applied to the case of Italian regions. Empirical results obtained over the 1960–2001 period reveal that contrary to previous findings, Italian regions seem to shield against permanent shocks other than transitory ones. Although some biases are detected in the allocation process of resources, deviations from full consumption insurance are not as relevant as claimed in the previous literature on the Italian regions.