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    • We have two cases i

    2018-10-25

    We have two cases: (i) strong hyperinflation: and (ii) weak hyperinflation; .Fig. 1 shows the strong hyperinflation case. The fiscal deficit starts at f(0) and the real quantity of money is equal to m(0). The fiscal deficit increases and in the last moment it no reaches f(t) when the real quantity of money is equal to zero. The hyperinflation path is HH, as indicated by the arrows that point out the fiscal deficit sliding up the inflation tax curve. Fig. 2 shows the phase diagram of a weak hyperinflation since the rate of inflation has an upper limit. The fiscal deficit starts at f(0) and the real quantity of money is equal to m(0). The hyperinflation path is HH, showing the fiscal deficit sliding up and then down the Laffer curve. If the hyperinflation lasts until the last moment, when the real quantity of money is equal to m(t) the fiscal deficit is equal to f(t). In the hyperinflation experiences Cagan analysed inflation tax revenue decreased after inflation rate had exceeded the inflation tax maximizing inflation rate. The weak hyperinflation path is consistent with this fact, as can be seen in Fig. 2. Furthermore, the fiscal crisis model provides a rationale for this outcome, since inflation and the real quantity of money will reach the “wrong” side of the Laffer curve. Financing an increasing level of government expenditures through money issue, which characterizes a fiscal crisis and introducing rational expectations, can yield several outcomes depending upon the shape of the demand for money function. When the demand for money is non-inelastic the model generates a weak hyperinflation. Before the unfolding of the fiscal crisis the economy is in the low inflation equilibrium. Once the fiscal crisis is in motion, this policy yields a dynamic path that takes the economy from the low inflation equilibrium towards the slippery side of the Laffer curve. When the demand for money is inelastic, the model yields a strong hyperinflation as the rate of inflation goes to infinite. The driving force behind both the weak and the strong hyperinflation is the fiscal crisis. When the demand for money is inelastic there is also the possibility of a hyperinflation bubble, as indicated by the horizontal arrows in Fig. 1. Most specifications to test hyperinflation bubbles, including the seminal paper by Flood and Garber (1980), have used an inappropriate theoretical framework. The price solutions are obtained by solving the money demand equation forward recursively, and the fundamental price solution depends on the expected sequence of current and future money supply. In such a setup there is a bubble solution, since they do not take into account the government budget constraint. However, when the budget constraint is taking into consideration, due to the fact that money is being issued to finance the fiscal deficit, there is no bubble solution for Cagan\'s money demand rational expectation specification. The horizontal arrow away from the origin indicates that a bubble is not feasible when money is non-inelastic, as shown in Fig. 2.
    Inflation tax curve: specification and first look at the Brazilian data The inflation tax revenue (τ) equals the tax rate (π) times the tax base (m). That is: τ=πm. Both the inflation tax revenue and the real quantity of money are defined in relation to real GDP, assuming an income elasticity of money equal to one. It is more convenient to write the inflation tax revenue in logarithmic form: Note that the specification of Eq. (8) depends on the demand for money functional form. The two specifications below correspond, respectively, to the semi-logarithmic and logarithmic cases. In the first case the semi-elasticity is constant and the absolute value of the real demand for money inflation elasticity η is proportional to the inflation rate. In the second case the elasticity is constant. Hence the inflation tax revenue functional forms for each case are as follows: Fig. 3a shows the inflation tax curve produced by Eq. (11), in which the semi-elasticity is constant. That curve has a maximum for a given inflation rate, that is, the inflation tax revenue initially increases with inflation and after a certain rate it begins to decrease. Fig. 3b shows the inflation tax curve yielded by Eq. (12), in which the demand for money curve has a logarithmic specification. The curve is a straight line, that is, the inflation tax revenue increases as the inflation rate increases. In this case money is essential since the elasticity of the demand for money with respect to the inflation rate is always less than one (Barbosa and Cunha, 2003; Barbosa et al., 2006).