nach oben

Decisions in Economics and Finance

Erschienen in:

07.11.2018

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

verfasst von: Kiminori Matsuyama, Iryna Sushko, Laura Gardini

Erschienen in: Decisions in Economics and Finance | Ausgabe 2/2018

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

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.

Vorheriger Artikel Some reflections on past and future of nonlinear dynamics in economics and finance

Nächster Artikel Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries

After the financial crisis, this literature has exploded and it continues growing, so that any attempt to survey would become quickly outdated. For a brief survey of the prefinancial crisis literature, see Matsuyama (2007b).

Notice that also in Asano et al. 2011, the Matsuyama credit cycle model has been investigated for the case of Cobb–Douglas production functions, and for the parameters belonging to Region B.

Notice that the absorbing interval is a closed interval independently on the definition of the map in the discontinuity point \(d_{1}\).

Let us call two symbolic sequences symmetric if these sequences are obtained from each other exchanging R and L with L and R, respectively.

Asano, T., Kunieda, T., Shibata, A.: Complex behaviour in a piecewise linear dynamic macroeconomic model with endogenous discontinuity. J. Differ. Equ. Appl. 18, 1889–1898 (2011). https://doi.org/10.1080/10236198.2011.601301 CrossRef

Avrutin, V., Schanz, M., Gardini, L.: Calculation of bifurcation curves by map replacement. Int. J. Bifurc. Chaos 20(10), 3105–3135 (2010)CrossRef

Diamond, P.: Government debt in a neoclassical growth model. Am. Econ. Rev. 55, 1126–1150 (1965)

Gardini, L., Tramontana, F., Avrutin, V., Schanz, M.: Border collision bifurcations in 1D PWL map and Leonov’s approach. Int. J. Bifurc. Chaos 20(10), 3085–3104 (2010)CrossRef

Gardini, L., Merlone, U., Tramontana, F.: Inertia in binary choices: continuity breaking and big-bang bifurcation points. J. Econ. Behav. Org. 80, 153–167 (2011)CrossRef

Hao, B.-L.: Elementary Symbolic Dynamics and Chaos in Dissipative Systems. World Scientific, Singapore (1989)

Keener, J.P.: Chaotic behavior in piecewise continuous difference equations. Trans. Am. Math. Soc. 261(2), 589–604 (1980)CrossRef

Leonov, N.N.: On a pointwise mapping of a line into itself. Radiofisica 2(6), 942–956 (1959)

Leonov, N.N.: On a discontinuous pointwise mapping of a line into itself. Dolk. Acad. Nauk SSSR 143(5), 1038–1041 (1962)

Matsuyama, K.: Credit traps and credit cycles. Am. Econ. Rev. 97, 503–516 (2007a)CrossRef

Matsuyama, K.: Aggregate Implications of Credit Market Imperfections, NBER Macronecomics Annual, vol. 22. University of Chicago Press, Chicago (2007b)CrossRef

Tramontana, F., Gardini, L., Ferri, P.: The dynamics of the NAIRU model with two switching regimes. J. Econ. Dyn. Control 34, 681–695 (2010)CrossRef

Tramontana, F., Gardini, L., Agliari, A.: Endogenous cycles in discontinuous growth models. Math. Comput. Simul. 81, 1625–1639 (2011)CrossRef

Tramontana, F., Gardini, L., Avrutin, V., Schanz, M.: Period adding in piecewise linear maps with two discontinuities. Int. J. Bifurc. Chaos. 22(3), 1250068 (2012). https://doi.org/10.1142/S021812741250068X CrossRef

Titel: A piecewise linear model of credit traps and credit cycles: a complete characterization
verfasst von: Kiminori Matsuyama
Iryna Sushko
Laura Gardini
Publikationsdatum: 07.11.2018
Verlag: Springer International Publishing
Erschienen in: Decisions in Economics and Finance / Ausgabe 2/2018
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-018-0220-5

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 2/2018

Advertising a product to face a competitor entry: a differential game approach

Proper strong-Fibonacci games

Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity

Steady states, stability and bifurcations in multi-asset market models

Sense, nonsense and the S&P500

An evolutionary model with best response and imitative rules