Finite-time singularity in the evolution of hyperinflation episodes

arXiv:0802.3553v1 [q-fin.CP] 25 Feb 2008 hyperinfl-own.tex Finite-time singularity in the evolution of hyperinflation episodes Martin A. Szybisz Departamento de Econom´ıa, Facultad de Ciencias Econ´omicas, Universidad de Buenos Aires, Av. C´ordoba 2122, RA–1120 Buenos Aires, Argentina and Departamento de Filosof´ıa del Derecho, Facultad de Derecho, Universidad de Buenos Aires, Av. Figeroa Alcorta 2263, RA–1425 Buenos Aires, Argentina Leszek Szybisz∗ Laboratorio TANDAR, Departamento de F´ısica, Comisi´on Nacional de Energ´ıa At´omica, Av. del Libertador 8250, RA–1429 Buenos Aires, Argentina Departamento de F´ısica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, RA–1428 Buenos Aires, Argentina and Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas, Av. Rivadavia 1917, RA–1033 Buenos Aires, Argentina (Dated: October 25, 2018) A model proposed by Sornette, Takayasu, and Zhou for describing hyperinflation regimes based on adaptive expectations expressed in terms of a power law which leads to a finite-time singularity is revisited. It is suggested to express the price index evolution explicitly in terms of the parameters introduced along the theoretical formulation avoiding any combination of them used in the original work. This procedure allows to study unambiguously the uncertainties of such parameters when an error is assigned to the measurement of the price index. In this way, it is possible to determine an uncertainty in the critical time at which the singularity occurs. For this purpose, Monte Carlo sim- ulation techniques are applied. The hyperinflation episodes of Peru (1969-90) and Weimar Germany (1920-3) are reexamined. The first analyses performed within this framework of the very extreme hyper-inflations occurred in Greece (1941-4) and Yugoslavia (1991-4) are reported. The study of the hyperinflation spiral experienced just nowadays in Zimbabwe predicts a singularity, i.e., a complete economic crash within two years. PACS numbers: 02.40.Xx Singularity theory; 02.50.Ng Monte Carlo methods in probability theory and statis- tics; 05.10.Ln Monte Carlo methods statistical physics and nonlinear dynamics; 64.60.F- Critical exponents; 89.20.-a Interdisciplinary applications of physics; 89.65.Gh Econophysics; 89.65.-s Social systems I. INTRODUCTION Since about one decade there is significant interest in applications of physical methods in social and economical sciences [1, 2, 3]. For example, it has been found that the logarithmic change of the market price in the case of a hyperinflation episode shows some universal characteris- tics similar to those observed in physical systems. In such a regime the price index increases more rapidly than a simple exponential law [4]. Moreover, it has been shown that such a super-exponential law indeed finishes with a finite-time singularity [5] like several physical systems. Let us recall that the rate of inflation i(t) is defined as i(t) = P(t) −P(t −∆t) P(t −∆t) = P(t) P(t −∆t) −1 , (1) where P(t) is the price at time t and ∆t is the period of the measurements. In economics the terminology “hy- perinflation” is used in rather rough sense to specify very hight inflation that is “out of control”, a condition in ∗Corresponding author; Electronic address: szybisz@tandar.cnea.gov.ar which prices increase rapidly as a currency loses its prop- erty as medium of exchange, store of value, and unit of account. No precise definition of hyperinflation is univer- sally accepted. One simple definition requires a monthly inflation rate of 20 or 30% or more. In informal usage the term is often applied to much lower rates. In 1956, Cagan published The Monetary Dynamics of Hyperinfla- tion [6], generally regarded as the first serious study of hyperinflation and its effects. There it is defined that “inflation rates per month exceeding 50%” determine a scenario of hyperinflation. During periods of very hight inflation the frequent change of prices destroys rapidly the real wages and the unknown future of the economic structure diminishes the flow of inversions. Such situations are very costly to so- ciety, the workers have to be paid more frequently (even daily) and there are rushes to spend the currency be- fore prices rise further causing enormous “shoe-leather costs” (in economics it means: resources wasted when inflation encourages people to do more trips to banks and stores wearing out their shoes). These effects are accompanied with a strong devaluation of the currency which causes a decline in real public revenues increas- ing the fiscal deficit. Hyperinflation reduces real value of taxes collected, which are often set in nominal terms and by the time they are paid, real value has fallen. This 2 feature is known as the Olivera-Tanzi effect, after Oliv- era [7] and Tanzi [8] who were the first to interpret it by means of standard analytical tools [9]. The occurrence of the Olivera-Tanzi effect may impulse a rapid expansion of nominal money and credit. If people exp

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