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Mr. vegh, an economist in the European Department, was an economist in the Research Department when this paper was written. He holds a doctorate from the University of Chicago,
The author is grateful to Joshua Aizenman, Robert Murphy, and several colleagues in the Research Department for helpful comments and discussions.
Frenkel (1987) stresses the importance and usefulness of attacking the problem of inflationary finance in a public finance context.
The definition of the inflation tax used in this paper follows Auemheimer (1974). The consumer’s expenditure on holding money accrues to the govern-ment because, by issuing non-interest-bearing debt (money), the government avoids interest costs on the public debt. Phelps (1973) discusses alternative definitions of the concept “inflation tax”.
On the generality of Kimbrough’s (1986) result, see Guidotti and vegh (1988). They consider alternative assumptions about the transaction technology and the cases of both consumption and income taxation. For a related discussion, see also Woodford (1989).
Aizenman (1983) derives a relationship between collection costs and govern-ment spending, but not in a public finance context. Instead of incorporating collection costs, Aizenman (1986) assumes that consumption taxes are not feasible and studies the optimal combination of capital controls, tariffs, and in-flation in financing government spending. vegh (1989) shows that the presence of currency substitution also renders the use of inflationary finance optimal.
To simplify the analysis and sharpen the economic intuition, specific functional forms are used in deriving most results. These assumptions are spelled out in the text as they are incorporated into the analysis.
The analysis can, however, be readily reinterpretated to apply to a closed economy.
Given the nonnegativity constraint on the nominal interest rate, the restriction on the domain of v(X) implies no loss of generality because the consumer chooses Xwhen the nominal interest rate is zero.
This assumption—as opposed to assuming that v(Xs) equals a positive contant—ensures that, if there are no collection costs associated with the consumption tax, the optimal inflation tax is zero (as pointed out by Guidotti and vegh (1988)). For the purposes of this paper, this assumption is made in order to isolate the effects of the presence of collection costs on the optimal inflation tax.
The condition β; = 1/(1 + r), needed to ensure the existence of a steady state, has been assumed. It follows that there are no intrinsic dynamics in the model in the sense of Obstfeld and Stockman (1985).
The specification of the government revenues presupposes that the government acts honestly in the sense of Auernheimer (1974). This implies, as pointed out by Calvo (1978), that problems of time-inconsistency are assumed away.
In what follows, time subscripts wil be dropped. Because government spending is constant over time and undergoes only unexpected and permanent changes, the adjustment of the economy will be instantaneous because, as indicated earlier, there are no intrinsic dynamics in the model. For simplicity, it has been assumed that b0 = 0.
Because I = [i/(l + i] is an increasing function of (i it makes no qualitative difference whether one refers to I or i.
In the presence of currency substitution and consumption taxation (but no collection costs), the optimal inflation tax is also independent of the level of government spending. The optimal inflation tax is solely determined by the foreign nominal interest rate (vegh (1989)).
Note that, in view of equation (18) below, Xs - 1/2, so that it is required that d = ¼ for v (Xs) = 0 to be satisfied. Clearly, this particular function satisfies the assumption laid out in equation (1) for 0 a X Si X’.
The result that the inflation tax remains the same is a general one, as indicated earlier. The specification of the model adopted in this section, however, also implies that when marginal collection costs are constant, revenues from the inflation tax remain unchanged (that is, real money balances are independent of g). This feature may not be robust under alternative specifications.
If the (steady-state) budget deficit is defined as government spending minus net revenues from the consumption tax, it follows from the analysis that higher government spending leads to larger budget deficits and higher nominal interest rates.
This specification of J(z) enables one to isolate the distortion introduced by the need to finance a positive level of government spending. In other words, if (z) = 4>0+fez, the optimal inflation tax is positive even when g = k = 0, as follows from the previous discussion.
In the case in which k =0.5, the convexity becomes more evident for higher levels of government spending.
One would conjecture that this result, in particular, may not be robust under alternative specifications of the model because of the crucial role played by the particular form of the demand for money.