Abstract
Hyperinflation is a phenomenon characterized by destruction of money value at a finite time interval. Economic theory attempts to explain this phenomenon by using two alternative hypotheses: fundamentals and bubbles. In the first hypothesis, the model produces a steady state in which the real quantity of money is zero (m=0) and the price level is infinite, or hyperinflation occurs due to the nonexistence of an equilibrium solution of the model.
Originally published in Brazilian Review of Econometrics vol 22 (November 2002), pp. 215–238.
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Notes
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Other authors, such as Burmeister et al. (1994, p. 159) agree with OR and state that: “It is hard to imagine any circumstance when an investigator would feel comfortable assuming a money to be essential to the degree implied by \(\left [v(o) = -\infty \right ]\)”. Further ahead, they say “Since the implication of the assumption which underlies Brock’s work is unpalatable \(\left [\lim _{m\rightarrow 0}mv'(m) > 0\right ]\) the exclusion of bubbles must rest on posterior beliefs formed entirely from experience with data”.
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Bailey (1956, p. 109) had already noticed that the specification of Cagan equation for money demand could not be appropriate: “All but one (Hungary II) of Cagan’s regressions showed a high degree of serial correlation in the residuals (with respect to time); this suggests the possibility of inappropriate specification of the estimating system”.
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The finite difference equations for the models in both regimes can be written in function of the inflation tax. In the monetary regime, the equation is given by: \(m_{t+1} = \left (1+\mu \right )\left (m_{t} - i(m_{t})\right )\). In the fiscal regime, the corresponding equation is: m t+1 = m t + g − i(m t ), where, in both cases, i(m t ) is the function that associates the real amount of money with the inflation tax. In the monetary regime, stationary equilibrium m = 0 exists when i(0) = 0. In the fiscal regime, stationary equilibrium m=0 exists when g= i(0). By introducing function D(m) = m − i(m), both equations become: \(M_{t+1} = \left (1+\mu \right )D(m_{t})\) and m t+1 = D(m t ) + g, and the graphical and comparative analysis between both models can be easily performed in the phase diagram.
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The existence of hyperinflation is not reliant on the essentiality of money, contrary to what several authors, such as Blanchard and Fischer (1989, pp. 239–245), have affirmed.
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This model of hyperinflation offers a theoretical justification for the empirical evidence found by Sargent (1982) that the end of European hyperinflations, in the first half of the twentieth century, occurred by a credible change in the fiscal monetary policy regime.
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Cagan (1956, p. 79): “This fact [lag in expectations] helps to explain why a similar time pattern of [tax] revenue emerged in all the seven hyperinflations. The [tax] revenue was high at the start, when the expected rate of price increase was still low; tended to decline in the middle, as the expected rate started to rise considerably; and rose near the end, when the rate of new issues skyrocketed”. In footnote 36 (p. 79), he adds: “Part of this rise in revenue resulted from the failure of real cash balances to make further declines in the final months, apparently because the end of hyperinflation appeared imminent”.
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Obstfeld and Rogoff (1996, p. 545) stated that: “If there is no intrinsic value to paper money and if society can survive without it, there is nothing to rule out hiperinflation price bubbles that completely wipe out money’s value. This central result of modern monetary theory is fascinating. Because the use of money is grounded in social convention, free market forces alone cannot guarantee a finite price level, despite the fact that society as a whole is better off when money has value”. This proposition has to be qualified. It is valid for the monetary regime, when money is not essential or in the fiscal regime, if money is essential. Under any circumstance, the selection of the regime of economic policy solves the problem and market forces will determine the price level.
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Barbosa, F.d. (2017). Hyperinflation: Inflation Tax and Economic Policy Regime. In: Exploring the Mechanics of Chronic Inflation and Hyperinflation. SpringerBriefs in Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-44512-0_6
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