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Finite-Time Singularity Signature of Hyperinflation

Author

Listed:
  • D. Sornette

    (UCLA and CNRS-Univ. Nice)

  • H. Takayasu

    (Sony, Japan)

  • W. -X. Zhou

    (UCLA)

Abstract
We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of ``inflationary expectation'' or positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time $t_c$. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general nonlinear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time $t_c$, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.

Suggested Citation

  • D. Sornette & H. Takayasu & W. -X. Zhou, 2003. "Finite-Time Singularity Signature of Hyperinflation," Papers physics/0301007, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0301007
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    References listed on IDEAS

    as
    1. Ide, Kayo & Sornette, Didier, 2002. "Oscillatory finite-time singularities in finance, population and rupture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 63-106.
    2. Mizuno, T. & Takayasu, M. & Takayasu, H., 2002. "The mechanism of double-exponential growth in hyper-inflation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 411-419.
    3. Froyen, Richard T. & Waud, Roger N., 2002. "The determinants of Federal Reserve policy actions: A re-examination," Journal of Macroeconomics, Elsevier, vol. 24(3), pages 413-428, September.
    4. D. Sornette & K. Ide, 2003. "Theory Of Self-Similar Oscillatory Finite-Time Singularities," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 267-275.
    5. Johansen, Anders & Sornette, Didier, 2001. "Finite-time singularity in the dynamics of the world population, economic and financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 465-502.
    6. Jonathan Temple, 2000. "Inflation and Growth: Stories Short and Tall," Journal of Economic Surveys, Wiley Blackwell, vol. 14(4), pages 395-426, September.
    7. Paul De Grauwe & Magdalena Polan, 2014. "Is Inflation always and Everywhere a Monetary Phenomenon?," World Scientific Book Chapters, in: Exchange Rates and Global Financial Policies, chapter 14, pages 357-382, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hartwell, Christopher A & Szybisz, Martin Andres, 2021. "Corralling Expectations: The Role of Institutions in (Hyper)Inflation," MPRA Paper 105612, University Library of Munich, Germany.
    2. Hartwell, Christopher A., 2019. "Short waves in Hungary, 1923 and 1946: Persistence, chaos, and (lack of) control," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 532-550.
    3. Szybisz, Martín A. & Szybisz, Leszek, 2017. "Hyperinflation in Brazil, Israel, and Nicaragua revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 1-12.
    4. Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
    5. Zhou, Wei-Xing & Sornette, Didier, 2004. "Antibubble and prediction of China's stock market and real-estate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 243-268.
    6. D. Sornette & R. Woodard, "undated". "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    7. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
    8. Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2004. "Finite-time singularities in the dynamics of Mexican financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 253-268.
    9. Szybisz, Martín A. & Szybisz, Leszek, 2017. "Extended nonlinear feedback model for describing episodes of high inflation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 91-108.
    10. Diego Ardila & Dorsa Sanadgol & Peter Cauwels & Didier Sornette, 2017. "Identification and critical time forecasting of real estate bubbles in the USA," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 613-631, April.
    11. L. Lin & M. Schatz & D. Sornette, 2019. "A simple mechanism for financial bubbles: time-varying momentum horizon," Quantitative Finance, Taylor & Francis Journals, vol. 19(6), pages 937-959, June.
    12. Yan, Wanfeng & Woodard, Ryan & Sornette, Didier, 2012. "Diagnosis and prediction of rebounds in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1361-1380.
    13. Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
    14. Li Lin & Didier Sornette, 2016. "A Simple Mechanism for Financial Bubbles: Time-Varying Momentum Horizon," Swiss Finance Institute Research Paper Series 16-61, Swiss Finance Institute.

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