Chapter

9 Lags in Tax Collection and the Case for Inflationary Finance: Theory with Simulations

Editor(s):
Mario Bléjer, and Ke-young Chu
Published Date:
June 1989
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Vito Tanzi*

I. Introduction

It has often been argued that many developing countries, in their pursuit of growth through capital accumulation, may have no choice but to run fiscal deficits in order to finance their development expenditures. The reasons given are the following: (a) that their tax bases are inadequate to allow a high tax burden; (b) that even when adequate tax bases are available, the countries’ tax administrations are too inefficient to take advantage of them; or (c) that, in any case, the political realities are such that high tax burdens are not possible.1 In the absence of developed capital markets or external borrowing, these fiscal deficits are often financed wholly or partly by central banks (i.e., through money creation). This printing of money brings about increases in the general price level and thus reduces the real value of the monetary unit. This reduction can be seen, as Friedman and Bailey showed many years ago, as a kind of tax on those who are holding money.2

If the real growth of the economy is zero (or is ignored) and if a steady rate of inflation π has established itself so that desired real balances are equal to actual real balances, the rate of inflation is equivalent to the rate of change of the money supply and is also equivalent to the tax rate. The tax base, on the other hand, is equivalent to the real cash balances held, (M/P). Therefore, the inflation tax revenue Rπ is

If the economy is growing at a rate of growth g, some additional real balances will be demanded to meet that growth.3 If the income elasticity of the demand for money is assumed to be unity, then equation (1) becomes

In this paper, the real growth of the economy will be ignored, as I shall be dealing with essentially short-run situations, so that equation (1) will continue to indicate the revenue from the inflation tax.

The case for or against inflationary finance has traditionally been argued on the basis of the welfare costs of this means of financing public expenditure as compared with alternative means. Those who have opposed deficit financing have followed Bailey’s contention that the ratio of welfare cost to government revenue becomes quite high at relatively low rates of inflation.4 Thus, the revenue from the tax system soon becomes preferable to inflationary finance on the basis of a welfare criterion.5 Aghevli, on the other hand, has argued that since additional normal tax revenue may not be available to developing countries, it may be academic to compare alternative revenue sources. In such a case, the relevant comparison should be between the total cost of inflationary finance and the benefits (in terms of additional future consumption) derived from the additional government expenditure.

There is, however, another important element that ought to be considered when the case for or against inflationary finance is argued—namely, the effect of inflation on the existing tax system. Depending on the character of the tax system of a country, inflation may (a) lead to an increase in real tax revenue; (b) lead to a decrease in real tax revenue; or (c) leave the real value of this revenue unaffected. Most writers dealing with inflationary finance have implicitly assumed the third of these alternatives, although the second alternative has been contemplated in a few studies.6 In this paper, the relationship between inflationary finance and the collection lag in tax revenue is explored in detail.7 The paper will consist of four sections. Section II is purely theoretical; it will discuss the factors that are important in determining the total amount of revenue that a government is likely to get when it pursues inflationary finance. Section III applies the theory developed in Section II to a simulation exercise that uses alternative sets of realistic values for the parameters. Section IV is a concluding section.

II. Theory

1. Revenue from Inflationary Finance

As indicated above, the revenue from inflationary finance is equivalent to the product of the inflation rate πt and the real cash balances (M/P). Given the real balances, an increase in πt generated by the money created to finance a deficit would be accompanied by higher inflationary finance revenue. And, alternatively, given the inflationary expectations, the higher are the real balances, the higher will be the revenue from inflationary finance. However, the real cash balances are affected by inflationary expectations. The higher are the latter, the lower will be the former.

As the cost of holding money increases, individuals try to economize on real balances. They reduce their balances to the point where the last monetary unit held gives them services (utility, productivity, etc.) worth at least the anticipated opportunity cost of holding that unit, which is assumed to be equal to the expected rate of inflation.8 This relationship is shown in Figure 1, where LL represents a demand schedule for real balances. When π = 0, M/P is equal to OA. At this point no money is being created to finance a deficit, the inflation tax is zero, and the real balances are higher than at any point where π > 0. As π assumes positive values, the revenue from inflation tax becomes positive.9 For a while, the positive effect on R* coming from higher values of π more than compensates for the negative effect coming from the fall in M/P.

Figure 1.Demand for Real Balances

At some combination of M/P and π, the product of these two variables would be maximized and the inflation tax would generate the highest revenue. This is assumed to occur at point C in Figure 1; the revenue is given by the area OBCD. At this point, the percentage increase in the rate of monetary expansion just equals the percentage decrease in M/P. An attempt by the government to raise more revenue by increasing the money supply at a faster rate than OD would be met with failure, since the LL curve would become elastic beyond point C— at that point the elasticity of the LL curve would equal -1.

Following Cagan10 and most empirical studies of the demand for real balances under inflationary conditions, the equation for the LL curve can be described as follows:

If one deals with short-run situations, this equation can be written as

where (M/Y)d denotes the ratio of money demanded to income; a denotes the reciprocal of the velocity of money when inflationary expectations are zero—that is, it denotes the M/F ratio when π = 0; π denotes inflationary expectations; e denotes the base for natural logarithms, and b measures the sensitivity of the demand for real balances to the anticipated rate of inflation. The absolute value of the exponent of e—that is, |bπ|—is the elasticity of the demand for money Em.

Combining equations (1) and (4); expressing the macrovariables (R and M) as ratios of income; and continuing to assume that actual price changes are equal to inflationary expectations, the equation for revenue from inflationary finance Rπ can be specified as follows:

If the value of b is known, this equation can be used to estimate Rπ for different rates of inflation reflecting different expansions of nominal money. Equation (5) is equal to zero when the rate of inflation is zero and reaches the maximum when dRπ/dπ = 0. This occurs when the elasticity of the demand for real balances is unity—at point C in Figure 1. At that point, || = 1, so that the revenue-maximizing rate of inflation is π = 1/b.11 Since b can be estimated econometrically, the revenue-maximizing rate can be determined for particular countries.12

Given b, the values of obtained in connection with alternative rates of inflation can easily be derived. Figure 2 shows the inflation revenue curve, OM, thus obtained. OM’ is the maximum amount obtained when the rate of inflation π is equal to 1/b.

Figure 2.Real Revenue from Inflation

The inflation tax could be evaluated according to standard tax analysis.13 In other words, one could ask the following questions: Is the tax equitable, vertically and/or horizontally? Is it shifted? Is it elastic if the economy is growing? Is it neutral? What are the welfare losses associated with it? What are its effects on growth? What are its effects in (a) a closed economy, and (b) an open economy? An analysis along these lines would be interesting but it is beyond the scope of this paper. In any case, many of these questions have been dealt with in extenso in the relevant literature. Here I shall be interested principally in the relationship between the revenues from the inflation tax and those from normal tax sources, a relationship that has received only scant attention.

One aspect of the relationship illustrated in Figure 2 that needs to be emphasized at this point is the importance of the monetary base. Even in the absence of expected price changes, the ratio of the money stock to national income would vary among countries, being quite small in some countries and much higher in others. Because of this, the inflationary consequences of a given deficit financed by money creation will differ among countries. Ceteris paribus, the higher is the ratio of money to national income, the lower will be the rate of inflation associated with a given deficit.

2. Inflation and Tax Revenue

Before proceeding, I need to elaborate a little on the meaning of the elasticity of the tax system in the context of this paper, as this concept is used in a somewhat unconventional way. This concept will refer, first, to built-in elasticity; thus, it will exclude any revenue owing to discretionary tax changes. Second, and perhaps more important, it is a concept that relates taxes collected in a given period to the income in the period when the event that created the legal ability occurred rather than to the income at the time of collection.14

In all countries, taxes are collected with lags, as it is always difficult, and for some taxes impossible, for exact payments to the tax authorities to be made at the same time that taxable events occur. For total tax revenue, these lags may be as short as one month for many advanced countries—where withholding at the source and advance payments are common for income taxes and where, owing to better accounting procedures, the tax liabilities related to indirect taxes can be determined more quickly—and as long as perhaps six months for developing countries. By the same token, the elasticity of total tax revenue as defined above may be less than unity, equal to unity, or more than unity. Industrialized countries are likely to have systems that have short collection lags and high elasticities (i.e., greater than one) unless inflation adjustments (i.e., indexation) introduced into the tax system have reduced the elasticity to unity. Developing countries, on the other hand, are more likely to have tax systems with lower elasticities and longer collection lags. If collection lags are characterized as short and long, we could have the following six combinations:

Collection Lags
ElasticityLongShort
< 1AB
= 1CD
> 1EF

Of these combinations, D and F would be more typical of industrialized countries—D for those with indexation of income taxes, and F for those without indexation—while A and C would be more typical of developing countries. A short lag combined with a unitary elasticity of the tax system (combination D) implies that inflation will have little effect on real tax revenue. A short lag combined with an elasticity greater than unity (combination F) implies that inflation will bring about increases in real tax revenue. A long lag and a unitary elasticity of the tax system (combination C) will inevitably lead to a fall in real tax revenue when prices rise.15 And this fall will be even more significant if the long lag is combined with an inelastic tax system (combination A).

In the analysis that follows, I shall ignore combinations B and E; furthermore, since A is just an extreme version of C, I shall discuss only C. Consequently, the discussion will be limited to cases D, F, and C. These three cases are illustrated graphically in Figure 3.

Figure 3.Inflation and Real Tax Revenue

The vertical axis of Figure 3 continues to measure the inflation rate. On the horizontal axis, we measure real tax revenue or, alternatively, the ratio of tax revenue to national income. Assume that, in the absence of inflation, real revenue would be OV. Assume also that the country enters an inflationary period.

If the country is characterized by combination D, its real tax revenue will hardly be affected. This situation can then be represented by line VD. If situation F prevails, real revenue would increase and would continue to increase as long as the average price level (not just the rate of inflation) continues to increase. If one assumes that the rates of inflation on the vertical axis are maintained, a higher inflation rate will always be associated with a higher price level. This situation can then be represented by line VF.16 If situation C (or A) prevails, inflation will bring about a fall in real tax revenue. This last situation is one that I wish to analyze in more detail.

At π = 0, revenue from taxes is equal to OV. As π increases, real revenue falls as shown by VC. The percentage fall in tax revenue depends not only on the rate of inflation but also on the collection lag, as long as we assume that the elasticity is equal to one.17 However, and this is the important point here, the absolute size of the fall depends also on the initial ratio of taxes to national income (i.e., on the initial tax burden). The higher is the initial tax burden, the greater will be the absolute loss in tax revenue associated with a given increase in the rate of inflation.

Let us take a numerical example. If the average lag in tax collection is seven months (and we continue to assume that Em = 1), an increase in the rate of inflation from 0 to 3 percent per month will reduce the real value of tax revenue by about 20 percent.18 If the initial tax burden had been 10 percent of national income, the reduction in the tax revenue would correspond to 2 percent of national income; however, if the initial tax burden had been 30 percent, the reduction would correspond to 6 percent of national income. If, in the absence of inflation, the budget had been in balance, inflation would bring about a deficit. But this deficit would be only 2 percent of national income in the first case and 6 percent in the second case.

The impact of different lags and rates of inflation on the real value of one dollar of tax revenue can be estimated by multiplying that dollar by 1/(1 + p)n where p is the monthly rate of inflation and n is the collection lag, expressed in months. If the elasticity of the tax system is unitary, the effect of inflation on the tax burden can be calculated by solving the following equation:

In equation (6), T0 denotes the ratio of tax revenue to national income when the rate of inflation is zero; Tπ denotes that ratio when inflation is π; and n denotes the collection lag, while p and π denote the rate of inflation on a monthly and on an annual basis, respectively.

3. Total Revenue During Inflation

In Subsection II.1., it was shown that the revenue gain from a given inflation tax is directly related to the base of this tax, which is the real stock of money. The higher is the ratio of this stock to national income M/Y, the larger, ceteris paribus, will be the revenue that can be obtained from inflationary finance. On the other hand, in Subsection II.2, it was found that the revenue losses (as percentages of national income) associated with given rates of inflation will be greater, the greater is the ratio of normal taxes to national income in the absence of inflation.

Given the collection lag, and assuming that we are dealing with situations where the elasticity of the tax system is either unitary or less than unity, if the initial M/Y is high while the initial T/Y is low, the inflation tax is more likely to make some significant contribution to total public sector revenue. On the other hand, if the initial M/Y ratio is low while the tax burden is high, the contribution that inflationary finance can make to total resources available to the government is much smaller. In this case, it is conceivable that the government might even gain from deflation, as this would be associated with increases in real tax revenue.

In any case, it should have become obvious from the above analysis that unless one assumes a tax system without lags and with unitary elasticity, one cannot isolate the revenue from inflationary finance from the inflation-induced changes in normal taxes, as has been done in the literature. In the case emphasized in this paper—line VC in Figure 3—inflationary finance will always bring about some losses in normal tax revenue.19 One interesting question then is the following: At what rate of inflation is total revenue (i.e., inflation tax revenue plus normal tax revenue) maximized? This question can be answered either algebraically or graphically.

Since the revenue from deficit financing is given by

and the revenue from the tax system by

total revenue (TR)π will be given by

Taking the derivative of TRπ with respect to π and setting it equal to zero would give us the value of π that maximizes total revenue.20

In Figure 4 the vertical axis continues to measure the rate of inflation. It should be recalled that we have assumed that expected inflation is equal to actual inflation and is equal also to the rate of change of the money supply. On the horizontal axis, the macrovariables are expressed as percentages of national income Y. As we have assumed away any change in real output, the horizontal axis also measures changes in real values.

Figure 4.Inflation, Tax Revenue, and Inflationary Finance

Curve OM measures the revenue from the inflation tax. This curve is the same as curve OM in Figure 2. Point 0 in Figure 4 indicates that, at zero inflation, the revenue from the inflation tax is also zero. As the rate of inflation increases, the inflation tax will generate more and more revenue. At point Ḿ́, the revenue from the inflation tax is maximized and is equal to OḾ. The corresponding rate of inflation is π1 (= 1/b).

Line VC corresponds to line VC in Figure 3. This line shows the behavior of normal tax revenue in relation to various rates of inflation. The higher the inflation rate, the lower will be the ratio of tax revenue to national income. Ignoring the possibility of negative rates of inflation, normal tax revenue is maximized at zero inflation (at point V).

Curves OM and VC can be added horizontally to get total (i.e., normal tax plus inflation tax) revenue in relation to inflation. This total revenue curve is VR. Total government revenues would be maximized at a rate of inflation of π2, where the curve VR reaches its easternmost point.21 This revenue would then be equal to OZ; inflationary finance would contribute ON’ (= K’Z); and normal tax revenue would contribute N’Z(= OK’). Since revenue from normal taxes has fallen by K’ V as a result of inflation, the net contribution of inflationary finance to total revenue is only VZ, which is much lower than the gross contribution ON’. Obviously, concentrating on the gross contribution of inflationary finance and ignoring the effect of inflation on normal taxes can lead to wrong policies. Figure 4 shows also that the rate of inflation, π1, that would maximize the revenue from inflationary finance could very well bring about a large enough fall in normal tax revenue to make the government end up with lower resources than it would have had in the absence of inflation.

Figure 4 thus indicates that a partial-equilibrium approach to inflationary finance will often give results that are not correct. The role of inflationary finance in generating net additional resources to governments can be evaluated only within a general-equilibrium framework that takes into account the effect of inflation on the tax system of a country.22 The response of the tax system to inflation varies from country to country, since it depends on the elasticity and the collection lag of the particular tax system. It is only in particular circumstances, typified by line VD in Figure 2, that the traditional partial analysis will give the correct answer. In most cases, inflation will distort the tax system so that normal revenue may increase or decrease, thus magnifying or (partially or totally) neutralizing the increase owing to inflationary finance. Figure 4 has dealt with this latter possibility.

III. A Simulation Exercise

In the previous section, it was shown that the total revenue that the government of a country can obtain from its existing tax system and from inflationary finance is related to the rate of inflation. It was also shown that, given the rate of inflation and assuming that the elasticity of the tax system is unity, the structural and/or institutional factors that determine total revenue are the following: T0, the ratio of total tax revenue to national income at a zero inflation rate; n, the average collection lag for the tax system; a, the reciprocal of the velocity of money—or the ratio of money to income—at a zero inflation rate; and 6, the sensitivity of the demand for money with respect to the rate of inflation.

To get a quantitative idea of how these variables may interact in different countries, I will take alternative, but realistic, estimates for each of them and provide solutions to the basic equations developed in Section I; this is done in this section. In the simulation exercise, I shall consider four alternative values for T0—namely, 0.10, 0.20, 0.30, and 0.40. These values cover most countries, with the exception of a few very poor ones—such as Nepal, Afghanistan, Bangladesh—and some very wealthy ones—such as Denmark, the Netherlands, Norway, and Sweden. For the collection lag, expressed in months, I shall use four alternative values—2, 4, 6, and 8. These four values are likely to cover the situations of most countries.

For the ratios of narrow money (M1) to income a, I shall take three alternative values—0.10, 0.20, and 0.30—that are typical of many countries. For the sensitivity b of the demand for money with respect to inflation, one can rely on published studies in which this parameter has been estimated for many countries that have gone through periods of significant inflation.23 In most of these studies, b has ranged from around 0.5 to around 3.0. Following Aghevli,24 I shall alternatively consider values of 0.5, 1.0, 2.0, and 3.0.

The impact of inflation on the ratio of taxes to income (assuming unitary elasticity of the tax system) is obtained by solving equation (6) for assumed values of T0 and n. Table 1 in the Appendix gives the results obtained in connection with annual rates of inflation ranging from 5 percent to 500 percent. The table is largely self-explanatory: the absolute revenue loss associated with a given rate of inflation increases with the size of the lag and with the size of the initial tax burden. Given the size of the lag, the higher is the initial ratio of taxes to income, the greater will be the revenue loss; and, given the initial tax burden, the longer is the lag, the greater will be the absolute fall in revenue. And, of course, given the initial tax burden and the lag, the higher is the rate of inflation, the greater will be the revenue loss.

The revenue from inflationary finance is obtained by solving equation (5) in connection with the alternative values of a, the initial ratio of money to income, and b, the sensitivity of the demand for money to inflation. Table 2 in the Appendix gives the results. This table is also self-explanatory. For each value of b, the maximum revenue from inflationary finance is obtained when the rate of inflation is equal to 1/b. It will be recalled that at that point the absolute value of the elasticity of the demand for real balances with respect to the rate of inflation—which is equal to |πb|—is one. Given the value of 6, the greater is the initial value of a, the greater will be the potential revenue from inflationary finance.

Combining the results in Tables 1 and 2 in the Appendix, one could obtain the answer to the basic question of the net effect of inflationary finance on total governmental revenue. However, a more direct and complete picture can be derived by directly solving equation (7) in connection with alternative values for a, b, T0, and n for annual rates of inflation ranging from 5 percent to 500 percent. Some of these results are given in Table 3 in the Appendix. For the calculation of these results, the assumed values for a, 6, To, and n are as above—namely,

Figure 5 illustrates the results for a = 0.2, b = 0.5, T0 = 0.2, and n = 6.

Figure 5.Inflation, Tax Revenue, and Inflationary Finance

Sources: Tables 1, 2. and 3 in the Appendix.

Figure 6 illustrates the impact of alternative values of T0 and n.25

Figure 6.Impact of Inflation on Tax Revenue and Inflationary Finance

Sources: Table 3 in the Appendix.

In most countries, policymakers would have some idea of the values of a and T0; and they should be able to derive a value for n.26 Thus, if a realistic value could be assumed for b, they could use these tables to estimate the net revenue that, ceteris paribus, they would obtain from inflationary finance. These tables indicate that total revenue is maximized at rates of inflation that are lower than 1/b. In fact, in cases where the initial tax burden is relatively high and the lag is relatively long, the government is likely to obtain maximum revenue at a zero rate of inflation, especially when the value of b is on the higher side of the range. These tables indicate that the scope for raising revenue through inflationary finance is far more limited than has been assumed in the literature.

Before leaving this section, a word of caution is necessary in connection with the use of these tables. They have been developed following a theoretical framework based on various important assumptions. These assumptions do not detract from the theoretical validity of this framework, but they must not be ignored when the tables are used to analyze actual experiences. In any case, these tables should be taken to indicate orders of magnitude rather than precise results.

The most important assumptions are the following: (a) The changes in tax revenue brought about by inflation are passive, or automatic, ones and do not reflect (and, in fact, specifically ignore) discretionary changes. Obviously, if the government of a country introduces new taxes, eliminates existing ones, or modifies the collection mechanism, or, alternatively, if taxpayers increase the degree of evasion or noncompliance, the actual performance of the tax system can be substantially different from the simulated performance, (b) Private banks do not share in the creation of money—that is, the money multiplier is assumed to be one; therefore, the total increase in nominal money accrues to the government as revenue. If private banks share in the process of money creation—that is, if the money multiplier is greater than one—the actual revenue from inflationary finance associated with a given rate of inflation will be lower than the simulated one. The higher the money multiplier, the greater this difference will be.

(c) The money supply changes only as a consequence of the financing of the deficit rather than for other reasons (such as accumulation of foreign reserves, extension of credit to the private sector). In reality, if the money supply is changing because of other factors, actual revenue from inflationary finance will differ from simulated revenue, (d) Inflationary expectations are identical to actual price changes; consequently, there is a direct and immediate correspondence between actual price changes and changes in the nominal stock of money. If inflationary expectations adjust with lags to actual price changes, actual revenue from inflationary finance for particular years would also differ from simulated revenue, (e) Only direct central bank financing of the deficit is assumed to bring about inflation through money creation. There is, however, the possibility that while the government may be financing a deficit through borrowing from the private sector by selling bonds, the central bank may, in turn, be creating money through open market operations. In such a case, the central bank financing of the deficit would be indirect, but would still lead to money creation and inflation.

IV. Summary and Conclusions

The extent to which lags in the collection of taxes can limit the role of deficit financing or can play a direct role in the inflationary process has not been appreciated. With the exception of the few studies cited in footnote 6, there is no literature on this subject. The role of lags in this process depends on several factors that, at the cost of being somewhat repetitive, are worth emphasizing.

The first factor is, of course, the price elasticity of the tax system. The lower is that elasticity, the greater will be the impact of the collection lag. To simplify the issues, in the previous analysis an elasticity of approximately unity has been assumed. This is probably a realistic assumption for many developing countries.27 The second factor is the ratio of tax revenue to national income (i.e., the tax burden). The existence of lags will bring about a given percentage fall in total tax revenue during inflation. This percentage fall will translate into a larger or smaller absolute fall, depending on the original tax burden. The third factor is the ratio of the money supply to national income. Ceteris paribus, the larger is that ratio, the lower will be the inflationary impact of a fall in revenue (or an increase in public expenditure) financed by printing money. The fourth factor, which is closely connected with the previous one, is the elasticity of the demand for real balances with respect to expected inflation. A high elasticity will bring about a substantial fall in the stock of real money, so that, a posteriori, the inflationary impact of a given deficit is likely to be greater than anticipated.

The model that has been developed provides, of course, a stylized version of what would happen in a given country that is pursuing inflationary finance. The model is inevitably based on several important assumptions that may or may not hold for particular countries. For example, to the extent that a developed capital market allows the government to finance its fiscal deficit through borrowing from the private sector, and to the extent that this borrowing “crowds out” some private expenditure, the inflationary implications of this action will be less serious than central bank financing of the deficit. Equally significant is the fact that the fiscal deficit and the subsequent money creation may lead to losses in foreign reserves, which could neutralize some of the effects of the fiscal deficit on money creation.

The major conclusion that can be derived from the foregoing analysis is that, on the basis of realistic assumptions supported by empirical evidence, the existence of lags in tax collection implies that a government’s gains from the pursuit of inflationary finance are likely to be lower than has commonly been assumed. If the lags are long and the initial tax burden is high, the loss in revenue may be substantial and may neutralize any gain coming from central bank financing of the deficit. This is an argument against inflationary finance that is quite different from the traditional one based exclusively on welfare-cost considerations of alternative sources of revenue. Even the most favorable case toward inflationary finance—in which all revenues are invested in productive investments projects28—appears to be considerably weakened by this analysis, as the net addition to government’s total revenue may, under plausible conditions, be zero or even negative.

Finally, this paper has shown that the literature on inflationary finance has dealt with just one special case, namely, the one in which inflation leaves real tax revenue unchanged—line VD in Figure 3. In most cases, however, inflation brings about changes in real tax revenue. These changes are positive for some countries and negative for others. In any case, these changes have to be taken into account in a truly general theory of inflationary finance. The foregoing analysis could be generalized to incorporate situations where the price elasticity of the tax system is different from one and where there is real growth in the economy.

Appendix
Table 1.Inflation and Revenue from Tax System1(Ratios of total tax revenue to gross domestic product)
To = 0.1To = 0.2To = 0.3To = 0.4
πn = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8
0.0500.0990.0980.0980.0970.1980.1970.1950.1940.2980.2950.2930.2900.3970.3940.3900.387
0.1000.0360.0970.0950.0940.1970.1940.1910.1880.2950.2910.2860.2820.3940.3870.3810.375
0.1500.0980.0950.0930.0910.1960.1910.1870.1820.2930.2860.2800.2730.3910.3820.3730.364
0.2000.0970.0940.0910.0890.1940.1880.1830.1770.2910.2820.2740.2660.3880.3760.3650.354
0.2500.0960.0930.0890.?860.1930.1860.1790.1720.2890.2760.2680.2590.3850.3710.3580.345
0.3000.0960.0920.0880.?840.1910.1830.1750.1680.2870.2750.2630.2520.3630.3670.3510.336
0.3500.0950.0900.0860.0820.1900.1810.1720.1640.2850.2710.2580.2460.3800.3620.3440.327
0.4000.0950.0890.0850.0800.1890.1790.1690.1600.2640.2680.2540.2400.3760.3580.3380.320
0.4500.0940.0880.0830.0780.1880.1770.1660.1560.2820.2650.2490.2340.3760.3530.3320.312
0.5000.0930.0870.0820.0760.1870.1750.1630.1530.2800.2620.2450.2290.3740.3490.3270.305
0.6000.0920.0830.0790.0730.1350.1710.1580.1460.2770.2560.2370.2190.3700.3420.3160.292
0.7000.0920.0840.0770.0700.1830.1680.1530.1400.2750.2510.2300.2110.3660.3350.3070.281
0.8000.0910.0820.0750.0680.1810.1640.1490.1350.2720.2470.2240.2030.3630.3290.2980.270
0.9000.0900.0810.0730.0650.1800.1610.1450.1300.2700.2420.2180.1960.3590.3230.2900.261
1.0000.0890.0790.0710.0630.1780.1590.1410.1260.2670.2380.2120.1890.3560.3170.2830.252
1.2000.0880.0770.0670.0590.1750.1540.1350.1180.2630.2310.2020.1770.3510.3080.2700.236
1.4000.0860.0750.0650.0560.1730.1490.1290.1120.2590.2240.1940.1670.3460.2990.2580.223
1.6000.0850.0730.0620.0530.1710.1450.1240.1060.2560.2180.1860.1590.3410.2910.2480.212
1.8000.0840.0710.0600.0500.1680.1420.1200.1010.2530.2130.1790.1510.3370.2840.2390.201
2.0000.0830.0690.0580.0480.1670.1390.1150.0960.2500.2080.1730.1440.3330.2770.2310.192
2.5000.0810.0660.0530.0430.1620.1320.1070.0870.2430.1980.1600.1300.3250.2630.2140.174
3.0000.0790.0630.0500.0400.1590.1260.1000.0790.2380.1890.1500.1190.3170.2520.2000.159
3.5000.0780.0610.0470.0370.1560.1210.0940.0730.2330.1820.1410.1100.3110.2420.1890.147
4.0000.0760.0580.0450.0340.1530.1170.0890.0680.2290.1750.1340.1030.3060.2340.1790.137
4.5000.0750.0570.0430.0320.1510.1130.0850.0640.2260.1700.1280.0960.3010.2270.1710.128
5.0000.0740.0550.0410.0300.1480.1100.0820.0610.2230.1650.1220.0910.2970.2200.1630.121

The inflation rate is denoted by π, the ratio of total tax revenue to gross domestic product at a zero inflation rate by T0, and the average collection lag for the tax system by n.

The inflation rate is denoted by π, the ratio of total tax revenue to gross domestic product at a zero inflation rate by T0, and the average collection lag for the tax system by n.

Table 2.Revenue from Inflationary Finance1(Ratios to gross domestic product)
a = 0.10a = 0.20a = 0.30
πb = 0.5b = 1.0b = 2.0b = 3.0b = 0.5b = 1.0b = 2.0b = 3.0b = 0.5b = 1.0b = 2.0b = 3.0
0.50000.00490.00480.00450.00430.00980.00950.00900.00860.01460.01430.01360.0129
0.10000.00950.00900.00820.00740.01900.01810.01640.01480.02850.02710.02460.0222
0.15000.01390.01290.01110.00960.02780.02580.02220.01910.04170.03870.03330.0287
0.20000.01810.01640.01340.01100.03620.03270.02680.02200.05430.04910.04020.0329
0.25000.02210.01950.01520.01180.04410.03390.03030.02360.06620.05840.04550.0354
0.30000.02580.02220.01650.01220.05160.04440.03290.02440.07750.06670.04940.0366
0.35000.02940.02470.01740.01220.05880.04930.03480.02450.08810.07400.05210.0367
0.40000.03270.02680.01800.01200.06550.05360.03590.02410.09820.08040.05390.0361
0.45000.03590.02870.01830.01170.07190.05740.03660.02330.10780.08610.05490.0350
0.05000.03890.03030.01840.01120.07790.06070.03680.02230.11680.09100.05520.0335
0.60000.04440.03290.01810.00990.08890.06590.03610.01980.13330.09880.05420.0298
0.70000.04930.03480.01730.00860.09870.06950.03450.01710.14800.10430.05180.0257
0.80000.05360.03590.01620.00730.10730.07190.03230.01450.16090.10780.04850.0218
0.90000.05740.03660.01490.00600.11480.07320.02980.01210.17220.10980.04460.0181
1.00000.06070.03680.01350.00500.12130.07360.02710.01000.18200.11040.04060.0149
1.20000.06590.03610.01090.00330.13170.07230.02180.00660.19760.10840.03270.0093
1.40000.06950.03450.00860.00210.13900.06900.01700.00420.20860.10360.02550.0063
1.60000.07190.03230.00650.00130.14380.06460.01300.00260.21570.09690.01960.0040
1.80000.07320.02980.00490.00080.14640.05950.00980.00160.21950.08930.01480.0024
2.00000.07360.02710.00370.00050.14720.05410.00730.00100.22070.08120.01100.0015
2.50000.07160.02050.00170.00010.14330.04100.00340.00030.21490.06160.00510.0004
3.00000.00690.01490.00070.00000.13390.02990.00150.00010.20080.04480.00220.0001
3.50000.06080.01060.00030.00000.12160.02110.00060.00000.18250.03170.00100.0000
4.00000.05410.00730.00010.00000.10830.01470.00030.00000.16240.02200.00040.0000
4.50000.04740.00500.00010.00000.09490.01000.00010.00000.14230.01500.00020.0000
5.00000.04100.00340.00000.00000.08210.00670.00000.00000.12310.01010.00010.0000

The inflation rate is denoted by π, the sensitivity of the demand for money with respect to the rate of inflation by b, and the ratio of money to income at a zero inflation rate by a.

The inflation rate is denoted by π, the sensitivity of the demand for money with respect to the rate of inflation by b, and the ratio of money to income at a zero inflation rate by a.

Table 3.Revenues from Taxes and Inflationary Finance1(Ratios to gross domestic product)
To = 0.1To = 0.2To = 0.3To = 0.4
πn = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8n = 2n = 4n = 6n = 8
a = 0.20; b = 0.50
0.0600.1090.1080.1070.1070.2080.2070.2050.2030.3070.3050.3030.3000.4070.4030.4000.397
0.1000.1170.1160.1140.1130.2160.2130.2100.2070.3140.3100.3050.3010.4130.4070.4000.394
0.1500.1260.1230.1210.1190.2230.2190.2140.2100.3210.3140.3080.3010.1190.4100.4010.392
0.2000.1330.1300.1270.1250.2300.2240.2190.2130.3270.3190.3100.3020.4240.4130.4010.390
0.2500.1400.1370.1340.1300.2370.2300.2230.2160.3330.3230.3120.3030.4300.4150.4020.389
0.3000.1470.1430.1390.1360.2430.2350.2270.2200.3390.3270.3150.3040.4350.4180.4020.387
0.3500.1540.1490.1450.1410.2490.2400.2310.2220.3440.3300.3170.3040.4390.4210.4030.386
0.4000.1600.1550.1500.1450.2550.2440.2350.2250.3490.3340.3190.3050.4440.4230.4040.385
0.4500.1660.1600.1550.1500.2600.2490.2380.2280.3540.3370.3210.3060.4480.4250.4040.384
0.5000.1710.1650.1600.1540.2650.2530.2410.2310.3580.3400.3230.3070.4520.4270.4040.383
0.6000.1810.1740.1680.1620.2740.2600.2470.2350.3660.3450.3260.3080.4590.4310.4050.381
0.7000.1900.1820.1750.1690.2820.2660.2520.2390.3730.3500.3290.3090.4650.4340.4050.379
0.8000.1980.1890.1820.1750.2890.2720.2560.2420.3790.3540.3310.3100.4700.4360.4050.378
0.9000.2050.1960.1870.1800.2940.2760.2600.2450.3840.3570.3320.3100.4740.4380.4050.376
1.0000.2100.2010.1920.1840.2990.2800.2630.2470.3890.3590.3330.3100.4780.4390.1040.373
1.2000.2190.2090.1990.1910.3070.2850.2670.2500.3950.3620.3340.3090.4820.4390.4010.368
1.4000.2250.2140.2040.1950.3120.2880.2680.2510.3980.3630.3330.3060.4850.4380.3970.362
1.6000.2290.2170.2060.1970.3140.2890.2680.2500.4000.3620.3300.3020.4850.4350.3920.355
1.8000.2310.2170.2060.1970.3150.2880.2660.2470.3990.3590.3260.2970.4830.4300.3850.348
2.0000.2300.2160.2?50.1950.3140.2860.2630.2430.3970.3550.3200.2910.4800.4240.3780.339
2.5000.2240.2090.1970.1870.3060.2750.2500.2300.3870.3410.3040.2730.4680.4070.3570.317
3.0000.2130.1970.1840.1740.2930.2600.2340.2130.3720.3230.2840.2530.4510.3860.3340.293
3.5000.1990.1820.1690.1580.2770.2430.2160.1960.3550.3030.2630.2320.4330.3640.3100.268
4.0000.1850.1670.1530.1420.2610.2250.1980.1770.3380.2840.2420.2110.4140.3420.2870.245
4.5000.1700.1520.1370.1270.2450.2080.1800.1590.3210.2650.2230.1910.3960.3210.2650.223
5.0000.1560.1370.1230.1120.2300.1920.1640.1430.3050.2470.2050.1730.3790.3020.2450.203
a = 0.20; b = 1.00
0.0500.1090.1080.1070.1060.2080.2060.2050.2030.3070.3050.3020.3000.4060.4030.4000.397
0.1000.1170.1150.1130.1120.2150.2120.2090.2060.3130.3090.3040.3000.4120.4060.3990.393
0.1500.1240.1210.1190.1170.2210.2170.2120.2080.3190.3120.3060.2990.4170.4080.3990.390
0.2000.1300.1270.1240.1210.2270.2210.2150.2100.3240.3150.3070.2980.4210.4090.3980.387
0.2500.1350.1320.1280.1250.2320.2250.2180.2110.3280.3170.3070.2970.4240.4100.3970.384
0.3000.1400.1360.1320.1280.2360.2280.2200.2120.3320.3190.3080.2960.4270.4110.3950.380
0.3500.1440.1400.1350.1310.2400.2300.2210.2130.3350.3210.3080.2950.4300.4110.3940.377
0.4000.1480.1430.1380.1340.2430.2320.2230.2130.3370.3220.3070.2930.4320.4110.3920.373
0.4500.1510.1460.1400.1350.2450.2340.2230.2140.3390.3220.3070.2920.4330.4110.3900.370
0.5000.1540.1480.1420.1370.2480.2350.2240.2130.3410.3230.3060.2900.4350.4100.3870.366
0.6000.1580.1510.1450.1390.2510.2370.2240.2120.3430.3220.3030.2850.4360.4080.3820.353
0.7000.1610.1530.1460.1400.2530.2370.2230.2100.3440.3210.3000.2800.4360.4050.3760.350
0.8000.1630.1540.1460.1390.2530.2360.2210.2070.3440.3190.2950.2750.4350.4010.3700.342
0.9000.1630.1540.1460.1380.2530.2350.2180.2040.3430.3150.2910.2690.4330.3960.3630.334
1.0000.1630.1530.1440.1370.2520.2320.2150.2000.3410.3120.2860.2630.4300.3910.3560.326
1.2000.1600.1490.1400.1310.2480.2260.2070.1910.3350.3030.2750.2500.4230.3800.3420.309
1.4000.1550.1440.1340.1250.2420.2180.1980.1810.3280.2930.2630.2360.4150.3680.3270.292
1.6000.1500.1370.1270.1170.2350.2100.1890.1700.3200.2830.2510.2230.4060.3560.3130.276
1.8000.1440.1300.1190.1100.2280.2010.1790.1600.3120.2720.2390.2110.3960.3430.2990.261
2.0000.1370.1230.1120.1020.2210.1930.1700.1500.3O40.2620.2270.1980.3870.3310.2850.246
a = 0.20; b = 1.00
2.5000.1220.1070.0940.0840.2030.1730.1480.1280.2850.2390.2010.1710.3660.3040.2550.215
3.0000.1090.0930.0800.0700.1890.1560.1300.1090.2680.2190.1800.1490.3470.2820.2300.189
3.5000.0990.0820.0680.0580.1770.1420.1150.0950.2550.2030.1630.1310.3320.2630.2100.168
4.0000.0910.0730.0590.04901680.1320.1040.0830.2440.1900.1490.1170.3210.2490.1940.151
4.5000.0850.0670.0530.0420.1610.1230.0950.0740.2360.1800.1380.1060.3110.2370.1810.138
5.0000.0810.0620.0480.0370.1550.1170.0880.0670.2290.1720.1290.0980.3030.2270.1700.128
a = 0.20; b = 2.00
0.0500.1080.1070.1070.1060.2070.2060.2040.2030.3070.3040.3020.2990.4060.4030.3990.396
0.1000.1150.1130.1120.1100.2130.2100.2070.2040.3120.3070.3020.2980.4100.4040.3980.392
0.1500.1200.1180.1150.1130.2180.2130.2090.2040.3150.3090.3020.2960.4130.4040.3950.387
0.2000.1240.1210.1180.1150.2210.2150.2090.2040.3180.3090.3010.2920.4150.4030.3920.381
0.2500.1270.1230.1200.1170.2230.2160.2090.2030.3190.3090.2990.2890.4160.4020.3880.375
0.3000.1290.1250.1210.1170.2240.2160.2080.2010.3200.3080.2960.2850.4160.3990.3840.369
0.3500.1300.1250.1210.1170.2250.2160.2070.1980.3200.3060.2930.2800.4150.3970.3790.362
0.4000.1300.1250.1200.1160.2250.2150.2050.1960.3200.3040.2890.2760.4140.3940.3740.356
0.4500.1310.1250.1200.1150.2250.2130.2030.1930.3190.3020.2860.2710.4130.3900.3690.349
0.5000.1300.1240.1130.1130.2240.2120.2000.1890.3170.2990.2820.2660.4110.3860.3630.342
0.6000.1290.1220.1150.1090.2210.2070.1940.1820.3140.2930.2730.2550.4060.3780.3520.329
0.7000.1260.1180.1110.1050.2180.2020.1880.1750.3090.2860.2650.2450.4010.3700.3410.315
0.8000.1230.1150.1070.1000.2140.1970.1810.1670.3040.2790.2560.2350.3950.3610.3300.303
0.9000.1200.1100.1020.0950.2090.1910.1750.1600.2990.2720.2470.2250.3890.3530.3200.291
1.0000.1160.1060.0980.0900.2050.1860.1680.1530.2940.2650.2390.2160.3830.3450.3100.279
1.2000.1090.0990.0890.0810.1970.1760.1570.1400.2850.2520.2240.1990.3730.3290.2910.258
1.4000.1030.0920.0820.0730.1900.1660.1460.1290.2760.2410.2110.1840.3630.3160.2750.240
1.6000.0980.0860.0750.0660.1840.1580.1370.1190.2690.2310.1990.1720.3540.3040.2610.225
1.8000.0940.0810.0700.0600.1780.1520.1290.1110.2630.2230.1890.1610.3470.2940.2490.211
2.0000.0910.0770.0650.0550.1740.1460.1230.1030.2570.2150.1810.1520.3400.2850.2380.200
2.5000.0850.0690.0570.0470.1660.1350.1100.0900.2470.2010.1640.1340.3280.2670.2170.177
3.0000.0810.0640.0510.0410.1600.1270.1010.0810.2400.1900.1510.1210.3190.2530.2010.160
3.5000.0780.0610.0480.0370.1560.1220.0950.0740.3340.1820.1420.1110.3120.2430.1890.147
4.0000.0770.0590.0450.0340.1530.1170.0900.0690.2300.1760.1340.1030.3060.2340.1790.137
4.5000.0750.0570.0430.0320.1510.1130.0650.0640.2260.1700.1280.0960.3010.2270.1710.128
5.0000.0740.0550.0410.0300.1480.1100.0320.0610.2230.1650.1230.0910.2970.2200.1630.121
a = 0.20; b = 3.00
0.0500.1080.1070.1060.1050.2070.2050.2040.2020.3060.3040.3010.2990.4050.4020.3990.396
0.1000.1130.1120.1000.1090.2120.2090.2060.2030.3100.3050.3010.2960.4090.4020.3960.390
0.1500.1170.1150.1120.1100.2150.2100.2060.2010.3120.3050.2990.2920.4100.4010.3920.384
0.2000.1190.1160.1130.1110.2160.2100.2050.1990.3130.3040.2960.2880.4100.3980.3870.376
0.2500.1200.1160.1130.1100.2160.2090.2030.1960.3130.3020.2920.2820.4090.3950.3810.368
0.3000.1200.1160.1120.1080.2160.2080.2000.1920.3120.2990.2880.2760.4070.3910.3750.360
0.3500.1200.1150.1110.1060.2150.2050.1970.1880.3100.2960.2630.2700.4050.3860.3690.352
0.4000.1190.1130.1090.1040.2130.2030.1930.1840.3080.2920.2780.2640.4020.3820.3620.344
0.4500.1170.1120.1060.1010.2110.2000.1890.1790.3050.2880.2720.2580.3990.3770.3560.336
0.5000.1160.1100.1040.0990.2090.1970.1860.1750.3030.2840.2670.2510.3960.3720.3490.328
0.6000.1120.1050.0990.0930.2050.1910.1780.1660.2970.2760.2570.2390.3900.3620.3360.312
0.7000.1090.1010.0940.0870.2000.1850.1710.1580.2920.2690.2470.2280.3830.3520.3240.298
0.8000.1050.0970.0890.0820.1960.1790.1640.1500.2870.2610.2380.2170.3770.3430.3130.285
0.9000.1020.0930.0850.0770.1920.1740.1570.1420.2820.2540.2300.2080.3720.3350.3020.273
1.0000.0990.0890.0810.0730.1880.1690.1510.1360.2770.2480.2220.1990.3660.3270.2930.262
a = 0.20; b = 3.00
1.2000.0940.0830.0740.0660.1820.1600.1410.1250.2700.2370.2090.1840.3570.3140.2760.243
1.4000.0910.0790.0690.0600.1770.1540.1330.1160.2630.2280.1980.1720.3500.3030.2620.227
1.6000.0860.0750.0650.0660.1730.1480.1270.1080.2580.2210.1690.1610.3440.2940.2510.214
1.8000.0860.0730.0610.0520.1700.1440.1210.1020.2540.2140.1810.1530.3390.2850.2410.203
2.0000.0840.0700.0590.0490.1680.1400.1160.0970.2510.2090.1740.1450.3340.2780.2320.193
2.5000.0810.0660.0540.0440.1630.1320.1070.0870.2440.1980.1610.1300.3250.2640.2140.174
3.0000.0790.0630.0500.0400.1590.1260.1000.0790.2380.1890.1500.1190.3180.2520.2000.159
3.5000.0780.0610.0470.0370.1560.1210.0940.0730.2340.1820.1410.1100.3110.2420.1890.147
4.0000.0760.0580.0450.0340.1530.1170.0890.0680.2290.1750.1340.1030.3060.2340.1790.137
4.5000.0750.0570.0430.0320.1510.1130.0850.0640.2260.1700.1280.0960.3010.2270.1710.128
5.0000.0740.0550.0410.0300.1480.1100.0820.0610.2230.1650.1220.0910.2970.2200.1630.121

The inflation rate is denoted by π, the ratio of total tax revenue to gross domestic product at a zero inflation rate by T0 the ratio of money to income at zero inflation by a, the sensitivity of the demand for money with respect to the rate of inflation by b, and the average collection lag for the tax system by n.

The inflation rate is denoted by π, the ratio of total tax revenue to gross domestic product at a zero inflation rate by T0 the ratio of money to income at zero inflation by a, the sensitivity of the demand for money with respect to the rate of inflation by b, and the average collection lag for the tax system by n.

Bibliography

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This paper is a modified version of my article, “Inflation, Real Tax Revenue, and the Case for Inflationary Finance: Theory with an Application to Argentina,” which appeared in the September 1978 issue of International Monetary Fund Staff Papers. In the preparation of this paper, I have benefited from the assistance of various people. Particular thanks must go to Ke-young Chu, Andrew Feltenstein, and Mohsin S. Khan. Ke-young Chu provided very helpful suggestions concerning revisions I made to the paper in developing its current version. I would also like to thank Hernan Puentes and Dante Simone. Mrs. Chris Wu provided very competent research assistance.

These arguments have often been made in connection with Latin American countries. They form one of the key elements of the structuralist view of inflation. A good review of the theoretical case for inflationary finance to sustain development expenditure is contained in Aghevli (1977), pp. 1295-1307.

See Friedman (1942). See also Bailey (1956). More than six decades ago, Keynes was also interested in the issue of inflationary finance; see Keynes (1923), Chap. 2, pp. 37-60.

See Aghevli (1977) and, especially, Friedman (1971).

See Bailey (1956). The welfare cost is measured by the area under the demand curve for real balances.

Bailey estimated that the total collection costs of normal tax revenues (i.e., welfare costs, compliance costs, and direct administrative costs) amounted to about 7 percent of revenue collected. This figure seems low for developing countries.

The first of these studies seems to have been Olivera (1967). Another treatment can be found in Aghevli and Khan (1977) and (1978). Of interest also is Dutton (1971).

For an analysis of collection lags in an inflationary situation, see Tanzi (1977). The collection lag is the time that elapses between a taxable event (i.e., earning of income, sale of a commodity) and the time when the tax payment related to that taxable event is received by the government.

Positive real interest rates are ignored for the sake of convenience.

Throughout this theoretical discussion it is assumed that the change in the rate of inflation is owing exclusively to changes in nominal money and that changes in nominal money are brought about exclusively by the central bank’s direct financing of the fiscal deficit. Of course, in the real world, money creation can come through other channels—for example, through the balance of payments.

Ibid., pp. 80-81.

The value of b has been determined for many countries. Some representative values are used in the simulation exercise in Section III.

Some evaluation along this line is contained in Shoup (1969), pp. 452-61.

For more details, see Tanzi (1977), pp. 155-56. Since real growth is ignored in this paper, the concept of elasticity is related to price changes alone and is thus unaffected by real income changes.

This is the situation that was analyzed in detail in Tanzi (1977). It must be recalled that discretionary changes are being ruled out.

It should be remembered that the movement from V toward F is not reversible, since it is the level of prices, rather than the rate of inflation, that determines real tax revenue. The price index will continue to rise as long as π > 0.

See Tanzi (1977), Table 1, p. 158.

Ibid.

On the other hand, if the case typified by line VF were assumed, inflationary finance would bring about gains in normal tax revenue.

From equation (7), we get

The issue of whether this rate would be dynamically stable is ignored here.

By the same token, the welfare cost of inflationary finance cannot be limited to measurement of the area under the demand-for-money function, as suggested by Bailey, but must take into account the distortions introduced into the tax system itself by inflation. These distortions may be as significant as the traditional welfare cost.

See, inter alia, Cagan (1956), Campbell (1970), Diz (1970), Vogel (1974), and Aghevli and Khan (1977).

Ibid.

Note that in contrast to the practice followed in Figures 1-4, where the rate of inflation was shown along the vertical axis, the rate of inflation is hereinafter shown along the horizontal axis.

The method followed in the determination of n is described in Tanzi (1977).

The validity of this assumption is supported by the empirical results obtained for Brazil, Colombia, the Dominican Republic, and Thailand in Aghevli and Khan (1978).

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