The literature dealing with the impact of inflation on taxation is so extensive that it may suggest that it would be difficult to write anything novel on this subject. Yet a close perusal of this literature shows that it has been biased by the recent experiences of the industrialized countries. For these countries, inflation has generally been associated with increases in the real value of tax revenues, so that many authors have been led to believe that the main inflation-induced problems are the prevention of this supposedly unwanted, or at least unlegislated, increase in revenue and the neutralization of the inevitable effects on the redistribution of the tax burden among income groups. The increase in real revenue is likely to occur mainly when (a) the lags in the collection of taxes are short, and (b) the tax systems are elastic. However, while these conditions seem to characterize many industrialized countries, they are not common to all countries.
When one deals with countries having somewhat longer lags in the collection of taxes, and tax systems with money-income elasticities not much greater, or even less, than unity, the consequences of inflation can be very different, especially when the rate of inflation becomes high. Unfortunately, these alternative situations are not products of an economist’s imagination but, on the contrary, have either existed or continue to exist in many developing countries, and perhaps even in some industrialized countries. For these countries, the problem has not been an increase, but rather an inflation-induced fall in real revenue. In many cases, this fall has, in itself, become a contributing factor in the inflationary process when the affected governments have financed the fiscal deficits through the printing of new money.
There has been hardly any analysis of what happens to real tax revenue when the tax systems are not elastic, the lags in tax collection are not short, and the rate of inflation becomes high. The main objective of this paper is to show that when the rate of inflation becomes high, the inevitable lags in the collection of taxes become very important and, unless compensated for by high elasticities, may often lead to a decrease in real revenue. The impact of lags has generally been ignored.1 After a theoretical discussion of the issues, the paper will use Argentina as a concrete example of a country in which the combination of high inflation, a relatively long average lag in tax collection, and a low elasticity of the tax system has recently brought about a drastic fall in real revenue. The paper will focus on the effects of the lags, and will thus ignore the inflation-induced distortions in taxable bases that may also affect real revenues.
R = real value of tax revenue accruing in period 0 but paid n periods later, in terms of resources in period 0 (i.e., the period the taxable event took place)
T = nominal value of accruals in period 0
P0 = price level at time 0
To give an economic interpretation to equation (3), one needs to take small discrete values of n and p.
E = elasticity of tax accrual with respect to changes in the price level (de jure elasticity)
Equation (4) can be rewritten as dT ET,
Dividing by POT, we get
where C is the constant of integration. From (8) we get
Substituting in equation (3), we get
Equation (11) can be differentiated partially with respect to the rate of inflation ṗ, the absolute price level P, the elasticity E, and the lag n. The equations so derived are as follows:
Equation (12) indicates that the real value of tax revenue R will fall with an increase in the rate of inflation as long as the lag n is greater than zero. If n = 0, R will not change with ṗ regardless of the size of elasticity E.
Equation (13) indicates that
Equation (14) indicates that, given the initial price level P0 and the rate of inflation ṗ then the higher elasticity E is, the higher real revenue R will be.
From equation (15) it can be seen that, given a positive rate of inflation, the longer the lag, the smaller real revenue will be.
Mr. Tanzi, Chief of the Tax Policy Division of the Fiscal Affairs Department, is a graduate of Harvard University. He was formerly a professor and Chairman of the Economics Department at American University. He is the author of The Individual Income Tax and Economic Growth and of numerous chapters in books and articles in professional journals.
One important exception is the paper by Teruo Hirao and Carlos A. Aguirre, “Maintaining the Level of Income Tax Collections Under Inflationary Conditions,” Staff Papers, Vol. 17 (July 1970), pp. 277–325. Hirao and Aguirre limit the discussion to the income tax, while the discussion in this paper refers to all taxes. Of interest also is the paper by Pedro Rado, “Income Payment Systems and Inflation” (mimeographed, July 2, 1975).
Legally the tax may be levied either on the seller or on the buyer, although, except for an expenditure tax, it is the seller who generally transfers the tax payment to the authorities.
By the same token, the real value of revenues would not be affected by inflation if the elasticity were one. Thus, if indexation of the tax system succeeded in making the elasticity equal to one, there would not be, m this lagless world, any inflation-induced increases in the ratio of taxes to national income. But, of course, this theoretical situation is not practically possible.
During this whole discussion the underlying legal structure is assumed to remain unchanged. This paper is, therefore, talking about automatic, or built-in, elasticity that excludes the effects of discretionary changes.
In order to use the table in connection with the Argentine situation, the results associated with monthly inflation rates of 1.5 per cent and 9.4 per cent are also shown.
To simplify the analysis and emphasize the impact of price changes, real growth during the inflationary period is assumed to be either zero or insignificant.
Even with zero inflation, the taxpayer gets some advantage owing to the postponement of taxes. The higher the rate of discount, the greater the advantage related to a given lag.
Even in this case, real revenue would be affected to the extent that inflation distorted the taxable bases (capital gains, interest, profits, property values, etc.). However, the change in real revenue would not be induced by the lag. It should be recalled that this paper has assumed a unitary price elasticity of the tax system. For an analysis of the inflation-induced distortions of interest income, see Vito Tanzi, “Inflation, Indexation and Interest Income Taxation,” Banca Nazionale del Lavoro, Quarterly Review, Vol. 29 (March 1976), pp. 64–76.
In most countries, income taxes, except for those withheld at the source, are collected with considerable lags.
But they still indicate how lags reduce the real value of each revenue dollar collected compared with the real value of a tax liability of a dollar at the time when it accrues—in other words, in relation to what real revenue would be in a lagless world.
It will be necessary to assume that the variance for these specific lags is so small that it can be ignored. If the variance is not small, the whole issue becomes much more complex and the method suggested in this section may give results that are no longer reliable.
The Government is, at the present time, contemplating the possibility of reducing some of these lags.
The revenue figures relate to 1974, which, by Argentine standards, can be considered a good year.
Since the change in real GDP was overwhelmed by the price change, the ratio of taxes to GDP is a close indicator of the behavior of real revenue.
The author wishes to thank William J. Byrne, economist in the Tax Policy Division, for his help with this mathematical appendix.