dorsal/arxiv
View SchemaFinite-Time Singularity Signature of Hyperinflation
| Authors | D. Sornette, H. Takayasu, W. -X. Zhou |
|---|---|
| Categories | |
| ArXiv ID | physics/0301007 |
| URL | https://arxiv.org/abs/physics/0301007 |
| DOI | 10.1016/S0378-4371(03)00247-4 |
| Journal | Physica A 325, 492-506 (2003) |
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.
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"abstract": "We present a novel analysis extending the recent work of Mizuno et al. [2002]\non the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary\n(1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua\n(1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a\ngeneralization of Cagan\u0027s model of inflation based on the mechanism of\n``inflationary expectation\u0027\u0027 or positive feedbacks between realized growth rate\nand people\u0027s expected growth rate, we find that hyperinflations can be\ncharacterized by a power law singularity culminating at a critical time $t_c$.\nMizuno et al.\u0027s double-exponential function can be seen as a discrete time-step\napproximation of our more general nonlinear ODE formulation of the price\ndynamics which exhibits a finite-time singular behavior. This extension of\nCagan\u0027s model, which makes natural the appearance of a critical time $t_c$, has\nthe advantage of providing a well-defined end of the clearly unsustainable\nhyperinflation regime. We find an excellent and reliable agreement between\ntheory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and\nNicaragua, the super-exponential growth seems to be already contaminated\nsignificantly by the existence of a cross-over to a stationary regime.",
"arxiv_id": "physics/0301007",
"authors": [
"D. Sornette",
"H. Takayasu",
"W. -X. Zhou"
],
"categories": [
"physics.soc-ph",
"cond-mat.soft",
"physics.gen-ph",
"q-fin.ST"
],
"doi": "10.1016/S0378-4371(03)00247-4",
"journal_ref": "Physica A 325, 492-506 (2003)",
"title": "Finite-Time Singularity Signature of Hyperinflation",
"url": "https://arxiv.org/abs/physics/0301007"
},
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