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Finite-time singularities in the dynamics of hyperinflation in an economy

Martín A. Szybisz

Leszek Szybisz^*

Departamento de Economía, Facultad de Ciencias Económicas, Universidad de Buenos Aires, Av. Córdoba 2122, RA-1120 Buenos Aires, Argentina

Laboratorio TANDAR, Departamento de Física, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, RA-1429 Buenos Aires, Argentina; Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, RA-1428 Buenos Aires, Argentina; and Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917, RA-1033 Buenos Aires, Argentina

^*Corresponding author; szybisz@tandar.cnea.gov.ar

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Phys. Rev. E 80, 026116 – Published 17 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026116

Abstract

The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective “adaptive inflation expectations” with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, $r (t)$ , changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time $t_{c}$ . By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, $p (t)$ . One is given by the already reported form $p (t) \approx {(t_{c} - t)}^{- α}$ (with $α > 0$ ) and the other exhibits a logarithmic divergence, $p (t) \approx ln [1 / (t_{c} - t)]$ . The singularity is a signature for an economic crash. In the present work we express $p (t)$ explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of $r (t)$ and $p (t)$ performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941–1944) and Yugoslavia (1991–1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.

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References (29)

S. Moss de Oliveira, P. M. C. de Oliveira, and D. Stauffer, Evolution, Money, War, and Computers (Teubner, Stuttgart, Leipzig, 1999).
R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, England, 1999).
D. Sornette, Why Stock Markets Crash (Critical Events in Complex Financial Systems) (Princeton University Press, Princeton, 2003).
T. Mizuno, M. Takayasu, and H. Takayasu, Physica A 308, 411 (2002).
D. Sornette, H. Takayasu, and W.-X. Zhou, Physica A 325, 492 (2003).
P. Cagan, in Studies in the Quantity Theory of Money, edited by M. Friedman (University of Chicago Press, Chicago, 1956).
J. H. G. Olivera, Banca Nazionale del Lavoro Quarterly Review 20, 258 (1967).
V. Tanzi, IMF Staff Papers 24, 154 (1977); 25, 417 (1978).
A. J. Canavese and D. Heymann, Q. Rev. Econ. Finance 32, 100 (1992).
Z. Anušić and S. Švaljek, http://www.eizg.hr/AdminLite/FCKeditor/UserFiles/File/ces3-anusic-svaljek.pdf
V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett. 85, 5659 (2000).
M. A. Szybisz and L. Szybisz, e-print arXiv:0802:3553.
Table of the International Monetary Fund, http://www.imf.org/external/pubs/ft/weo/2002/01/data/index.htm
H. K. Moffatt, Nature (London) 404, 833 (2000).
A. Bhattacharjee and X. Wang, Phys. Rev. Lett. 69, 2196 (1992); A. Bhattacharjee, C. S. Ng, and X. Wang, Phys. Rev. E 52, 5110 (1995).
J. Vrabec, G. K. Kedia, G. Fuchs, and H. Hasse, Mol. Phys. 104, 1509 (2006).
A. Widom, Phys. Rev. A 3, 2042 (1971).
P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw Hill, New York, 1969).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge University Press, Cambridge, 1996).
P. Petrović and Z. Mladenović, J. Money, Credit, Banking 32, 785 (2000).
B. Nielsen, http://www.nuffield.ox.ac.uk/economics/papers/2004/w31/NielsenYugo.pdf
Tables of the Central Statistical Office and Reserve Bank of Zimbabwe.
N. C. Garganas, Why is the role of the central bank important? Dissertation at the celebrations marking the 75th anniversary of the Bank of Greece (Athens, 3 November 2003) at the website, http://www.bis.org/review/r031113d.pdf
M. Palairet, The Four Ends of the Greek Hyperinflation of 1941–1946 (Museum Tusculanum Press, University of Copenhagen, Copenhagen, 2002).
A. Lykogiannis, Britain and the Greek Economic Crisis, 1944–1947: From Liberation to the Truman Doctrine (University of Missouri Press, Columbia, 2002).
K. Juselius and Z. Mladenović, Discussion papers 02–03, University of Copenhagen, October 2, 2002.
T. Chao, Paper Money Gallery, http://tomchao.com/hb.html
A. Makochekanwa, http://web.up.ac.za/UserFiles/WP_2007_10.pdf
J. M. Keynes, The Economic Consequences of Peace (Macmillan Press, London, 1920); A Treatise on Money (Harcourt, Brace and Co., New York, 1930) Vols. I and II; The General Theory of Employment, Interest, and Money (Macmillan and Co., London, 1936); the latter two reprinted in The Collected Writings of John Maynard Keynes, edited by D. E. Moggridge (Macmillan, London, 1973).

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Finite-time singularities in the dynamics of hyperinflation in an economy

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