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Frenkel, J. A., “Inflation and the Formation of Expectations,” Journal of Monetary Economics, Vol. 1, (October 1975), pp. 403–421.
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Vegh, C., “Government Spending and Inflationary Finance: A Public Finance Approach,” Staff Papers, Vol. 36, (September 1989), pp. 657–677.
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The author wishes to particularly thank Mohsin Khan for suggesting this topic. Thanks are also due to Anupam Basu, Abbas Mirakhor, Vito Tanzi, and Peter Wickham for helpful suggestions. All remaining errors are the responsibility of the author. Brooks Calvo provided valuable research assistance.
As inflation rises, the real balance holdings decline as the public desires to hold less of a depreciating asset. This leads to increases in the velocity of money. Thus, the higher the inflation sensitivity of velocity, the lower the inflation rate at which the inflation elasticity for the demand for real balance becomes unity.
Aghevli (1977) is among the few who make a case for a certain amount of deficit financing leading to moderate rates of inflation in the context of a growing economy where inflation revenue is the only source of financing government capital expenditure.
This implies that the elasticity of real tax revenue with respect to changes in real income may be greater than, equal to, or less than unity.
For a derivation of this form, see footnote 2, p.10.
Relaxing this assumption does not alter the result of the ensuing analysis; it only affects the size of the equilibrium inflation rate.
A solution yielding a negative inflation is not considered here, although Friedman (1971) has raised the possibility of negative inflation in the steady state.
The second order derivatives of both f(π) and ø(π) are negative in the neighborhood of the low equilibrium inflation rate, thereby ensuring stability.
The fiscal schedule ø1(π) in Figure 1 indicates that there is no equilibrium even though in the conventional analysis an equilibrium could exist as long as the intended fiscal deficit is less than or equal to maximum revenue from inflation. In such situations, equilibrium can only be restored by a fiscal shock. Without such a shock, continual deficit financing leads to ever-widening fiscal gap.
π* is obtained from the solution of TR’(π) = F’ (π) + R’(π) = 0. The second order derivative is
Thus at π*, TR” < 0 so that TR(π*) is the maximum revenue from inflation and taxation.
These observations are based on the signs of the derivatives of π* with respect to α, β, Ro and mo.
A relatively high level of taxation would lead to a greater loss of real tax revenue and hence the revenue maximizing rate would be lower than if the level of taxation was relatively small.
A high value of α implies that the inflation elasticity of real balance is greater for a given expected rate of inflation. Thus, an increase in the expected rate of inflation would lower the desired real balance holdings more than it would if α were small. Hence, gains in revenue from inflation would be higher at a relatively low expected rate of inflation.
Introduction of the explicit cost of collection of fiscal revenue, as in Vegh (1989), would lower the maximum amount of total revenue since the revenue maximizing inflation rate would be raised because f’ = - R’ (1 - Ψ’) where Ψ(R) is the collection cost function and 0 ≤ Ψ’ < 1.
This argument is consistent with the experience of several high inflation debt-ridden countries. In these countries, the debt shock resulting from a rise in the foreign interest rate (as well as depreciation of domestic currency) increased the burden of interest payments on external debt on the budget, causing a rise in the real deficit. Financing such deficits in order to maintain real expenditure was accompanied by high rates of monetary expansion and inflation.
The welfare cost ratio is analogous to the cost-benefit ratio as in project selection. The inflation revenue acquired by the government is beneficial to the economy in the sense of the balanced-budget theorem, whereby an increase in real government spending, financed by forced savings, leads to an equivalent increase in real income. However, in equilibrium analysis, an increase in forced savings reduces disposable income and consumption.
A variant of this treatment of welfare cost has been employed by Aghevli (1977) in defining total utility of consumption goods in the context of inflationary finance. Total utility was defined as the consumption of goods, c, minus the welfare cost of inflationary finance, W(π); i.e. total utility, u(c, π) = c - w(π).
This can be seen from the net welfare cost function since wn(0) = 0 and wn(∞) = mo/α - Ro. For certain parameter values, the net welfare cost would become negative.
Tanzi (1977) estimated the average lag between a taxable event and payment of taxes for various categories of taxes for Argentina. However, the estimates were the weighted average of all the lags (the legal lag, which pertains to tax administration, and the delinquency lag, which exists when payment is made after the expiry of the legal lag).
Annual data covering the period 1970–87 were obtained for the following countries; Argentina, Costa Rica, Guatemala, Honduras, Peru, Bangladesh, Myanmar, India, Malaysia, Pakistan, Philippines, Singapore, Sri Lanka, Thailand, Botswana, Ethiopia, Ghana, Somalia, Sudan, Zaire, Zambia, Egypt, Islamic Republic of Iran, Jordan, Syrian Arab Republic, United Arab Emirates, Yemen Arab Republic, People’s Democratic Republic of Yemen. All data used in this study are taken from International Monetary Fund, International Financial Statistics and Government Finance Statistics.
Given the structure of taxation, real government current revenue, CR, can be written as a function of real income y as
where β1 = buoyancy of real government revenue to changes in real income. On the assumption that the average collection lag between accruals and payments of taxes is n-months and the annual rate of inflation is p, the amount of real government revenue collections is
Taking the limit as π tends toward zero and expressing real government revenue in terms of real income, it can be shown that R(π) = Royβ1-1e-βπ.
From a sample of 11 countries, five of which are common with the group chosen for the fiscal revenue equation in this study, Khan estimated the equation for actual real money balances in the spirit of rational expectations literature (e.g., see Frenkel, 1975).
The revenue maximizing rate would be raised or lowered as
Erosion of real fiscal revenue is estimated from
Maximum real total revenue is obtained from
Using pooled cross-section annual data covering the period 1970–87 for 24 of the group of 28 countries (excluding Ethiopia, Zaire, United Arab Emirates and P.D.R. of Yemen for lack of an adequate time series for the monetary base), the following relationship between price increase and the rate of monetary expansion was estimated:
From the above estimated equation, the persistence of price lag over such an extended period indicates that the public did not seem to have correctly anticipated monetary changes. This finding is consistent with the results reported by Khan and Knight (1982) for a shorter period (1968–75).
In Figure 2, the cluster of the countries indicates that the governments acquired real resources with average rates of monetary expansion as high as 30 percent. Beyond this point, price lag was virtually absent. Thus, there seem to be some threshold inflation rate beyond which the public seem to correctly anticipate further acceleration in monetary expansion.