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143 "Inflation can also arise if policymakers do not know the correct model of the economv Suppose that pohcymakers believe that the costs of moderate inflation are small and that there is (or that there may be) a permanent outputinflation tradeoff. Then they are likely to pursue expansionary policies, and to be slow to dismflate when inflation sets m This ma\ be a good description of what happened in the United States in the 1960s and 1970s (see. for example, Freedman, 1993). "An important question is how the political process leads to situations that require such large amounts of seignorage. The puzzle is that given the apparent high costs of the resulting inflation, there appear to be alternatives that all parties prefer. See Alesina and Drazen (1991) for one attempt to answer this question. level of unemployment that is sustainable. None of these theories, however, have yet been formulated rigorously or tested empirically. 9.7 Seignorage and Inflation The existence of an outputinflation tradeoff cannot plausibly lead to hyperinflations, or even to very high rates of inflation that fall short of hyperinflation. By the time inflation reaches triple digits, the costs of inflation are almost surely large, and the real effects of monetary changes are almost surely smah. No reasonable policymaker would choose to subject an economy to such large costs out of a desire to obtain such modest output gains. The underlying cause of most, if not all, episodes of high inflation and hyperinflation is governments need to obtain seignoragethat is, revenue from printing money (BrescianiTurroni, 1937; Cagan, 1956). Wars, falls in export prices, tax evasion, and political stalemate frequently leave governments with large budget deficits. And often investors do not have enough confidence that the government will honor its debts to be willing to buy its bonds. Thus the governments only choice is to resort to seignorage. This section therefore investigates the interactions among seignorage needs, money growth, and inflation. We begin by considering a situation where seignorage needs are sustainable, and see how this can lead to high inflation. We then consider what happens when the seignorage needs are unsustainable, and see how that can lead to hyperinflation. The Inflation Rate and Seignorage As in Section 9.2, assume that real money demand depends negatively on the nominal interest rate and positively on real income (see equation [9.1]): P (9.31) = I(r + 7 Y), I, < 0, Ly> 0. Since we are mterested in the governments revenue from money creation.
MM (9.33) Equation (9.33) shows that in steady state, real seignorage equals the growth rate of the money stock times the quantity of real balances. The growth rate of money is equal to the rate at which nominal money holdmgs lose real value, 7 . Thus, loosely speaking, seignorage equals the "tax rate" on real balances, , times the amount being taxed, M/P. For this reason, seignorage revenues are often referred to as mflationtax revenues."* Substituting (9.32) into (9.33) yields S = 7 + , ). (9.34) Equation (9.34) shows that an increase in increases seignorage by raising the rate at which real money holdings are taxed, bul decreases it by reducing the tax base. Formally, "Phelps (1973) shows that it is more natural to think of the tax rate on money balances as the nominal interest rate, since the nominal rate is the difference between the cost to agents of holding money (which is the nominal rate itself) and the cost to the government of producing it (which is essentially zero). In our framework, where the real rate is ftxed and the nominal rate therefore moves oneforone with inflation, this distinction is not important. M should be interpreted as highpowered money (that is, currency and reserves issued by the government). Thus !(•) is the demand for highpowered money. For the moment we focus on steady states. It is therefore reasonable to assume that output and the real interest rate are unaffected by the rate of money growth, and that actual inflation and expected inflation are equal. If we neglect output growth for simplicity, then in steady state the quantity of real balances is constant. This implies that inflation equals the rate of money growth. Thus we can rewrite (9.31) as  = + ,¥), (9.32) where 7 and Y are the real interest rate and output and where is the rate of money growth, M/M. The quantity of real purchases per unit time that the government hnances from money creation equals the increase in the nominal money stock per unit time divided by the price level:
= L(r + , Y) + + , Y), (9.35) where Li(*) denotes the derivative of !(•) with respect to its first argument. The first term of (9.35) is positive and the second is negative. The second term approaches zero as approaches zero (unless L\{r + Qm, Y) approaches minus infinity as approaches zero). Since 1(7, ) is strictly positive, it follows that dSldgu is positive for sufficiently low values of That is, at low tax rates, seignorage is increasing in the tax rate. It is plausible, however, that as becomes large, the second term eventually dominates; that is, it is reasonable to suppose that when the tax rate becomes extreme, further increases in the rate reduce revenue. The resulting "inflationtax Laffer curve" is shown in Figure 9.7. As a concrete example of the relation between inflation and steadystate seignorage, consider the moneydemand function proposed by Cagan (1956). Cagan suggests that a good description of money demand, particularly under high inflation, is given by In = a  foz b In y, fo>0. (9.36) Converting (9.36) from logs to levels and substituting the resulting expression into (9.34) yields ♦ = Cg e", (9.37) FIGURE 9.7 The inflationtax Laffer curve
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