Article

Inflation Adjustment Schemes Under the Personal Income Tax

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1975
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AMALIO HUMBERTO PETREI *

A progressive personal income tax combined with inflation can produce both increased revenue for government and significant changes in the distribution of the tax burden among individuals.1 As money income rises, even if real income is unchanged, taxpayers are moved upward in the tax schedule and are thus subject to higher tax rates. In addition, persons who were not taxed previously because their incomes were below the limits fixed by law may become liable to taxation as a result of a general rise in money incomes. Other exemptions and deductions defined in nominal fixed amounts may similarly lose their importance in relation to income, so that taxpayers with the same real incomes may end up paying very different amounts in income tax. If government took no action and inflation proceeded at high rates, a substantial number of people would eventually become subject to the highest marginal rate of income tax. This kind of interaction between inflation and progressivity affects not only the distribution of income and the level of tax revenue but also the built-in stabilizing power of the tax structure and various economic incentives.

The increased tax burdens faced by individuals as a result of inflation have led in many countries to corrective action by governments, either on their own initiative or in response to greater pressure from taxpayers. The most common method adopted has been to adjust, from time to time, the principal items legally defined in money terms—for example, lowering tax rates or raising exemption levels. A few countries have gone one step further and have introduced legal provisions to ensure more automatic adjustment of these items in response to price level changes. In addition, there have been academic discussions and proposals for the implementation of automatic adjustment schemes. This paper examines existing and proposed inflation adjustment schemes and discusses the effects of introducing them for the personal income tax.

Section I describes the various schemes and proposals incorporating automatic provisions to cope with the problem of unintended tax burden changes as a result of inflation. Section II then compares the technical aspects of the different schemes. Finally, Section III discusses advantages and disadvantages of adopting an adjustment scheme for the personal income tax, with major emphasis on the distributional effects of inflation on the progressive tax, since this concern has given rise to most adjustment schemes.

I. Inflation Adjustment Schemes

Two basic methods may be used to deal with the problem created by the combination of inflation and progressivity in the personal income tax. One method is to introduce discretionary changes from time to time to offset the rise in effective tax rates; another is to make these changes in accordance with prescribed rules. Some schemes, while basically governed by a set of rules, allow scope for discretionary adjustments. The principal aim of all inflation adjustment schemes is to avoid unintended changes in tax burdens, although their introduction into the tax system may have other important effects (discussed briefly later).

One type of automatic adjustment scheme involves calculation of the tax on real income for some base year and determination of the current liability by converting this amount to current prices. Another type is based on yearly adjustments of income brackets and of other items defined in money terms by means of some index. A variant of this type is the adjustment of exemptions and deductions only. A third type consists of altering tax rates according to some index while keeping income brackets unchanged.

real income adjustment schemes

The first type of adjustment scheme, developed by Amotz Morag, would operate as follows: Income is first expressed in terms of base year prices; tax liability is then calculated in terms of base year income; and finally the tax liability in terms of current prices is obtained through multiplication of the base year tax liability by the reciprocal of the price index.2 The Swiss Canton of Basel-Land has adopted this procedure. The taxable income is recomputed to express it approximately in 1953 prices. The cost of living index is used to estimate the increase in prices, but for tax purposes the change in the value of the index is made only in steps of 10 per cent, using the index for 1953 as a base. For example, while the index for 1969 was 145 (1953 = 100), the income adjustment factor was 1.4.3

index adjustment schemes

The second type of automatic adjustment scheme operates in Chile, Brazil, Iceland, the Netherlands, and Canada. A partial system of adjustment also operates in Argentina. France has a system which operates as a semi-indexation corrective mechanism and can be considered as this type of adjustment scheme. Denmark and the Swiss Canton of Aargau have a system of this type, although their legislation also enables tax rate changes to be made.

In 1954 Chile introduced provisions by which several important items of the income tax law were defined in terms of basic wages (sueldos vitales). The Chilean law regulates two income taxes: the schedular tax and the global tax. The first is levied at flat rates according to sources of income; the second is progressive and is levied on income from all sources. The exemptions from the schedular tax (that is, wages, salaries, and professional earnings) are defined in terms of basic wages; the same unit is used to define the brackets for the global complementary tax.4 The value of the basic wage for tax purposes is that fixed by law and in force at the end of the year for which the tax report is made.5 Since 1961 the basic wage has been adjusted annually in accordance with the rise in the consumer price index during the preceding 12 months.6 In Chile the basic wage varies by region and occupation. The income tax law does not specify which wage is applicable for tax purposes, but it is understood to be that of industry and commerce employees in the District of Santiago.7 Since 1954 the Chilean income tax law has undergone several changes, some of which have affected the exemptions and the brackets expressed in terms of wage units. However, the practice of defining the important items in units of basic wages has remained the same.

Brazil’s adjustment system, introduced in 1961,8 similarly fixed the income brackets and the personal exemptions in terms of units of a fiscal minimum wage, defined as the largest monthly minimum wage in effect in the country (normally that of the State of Guanabara) rounded off to the nearest thousand cruzeiros.9 Minimum wages were adjusted by the Brazilian Government every year, generally in line with the change in the price index. However, the scheme proved unsatisfactory after 1964, when minimum wages were increased at a rate less than the rate of inflation, resulting in increased tax burdens at all levels of real income. Shortly thereafter the system was changed, and the income brackets were defined in terms of conventional monetary units instead of minimum wage units.10 At the same time, however, a provision was added stating that these income brackets must be adjusted in proportion to the change in prices whenever the general price index registered an increase of 10 per cent or more in any one year, or a 15 per cent or more increase over three consecutive calendar years. Coefficients of monetary correction, established until 1967 by the National Economic Council and subsequently by the Ministry of Planning, are used for the legally stated “general price index.” However, the Government has used some discretion in adjusting exemptions and brackets. In 1973 and 1974, upper bracket limits were increased in line with the rate of inflation, while the exemption and lower bracket limits were increased at a significantly higher rate.

Since 1966 Iceland has had a regulation providing that exemptions and income tax brackets should be adjusted annually according to a tax index. The law does not specify how the tax index is to be calculated, although the original idea was apparently that it should reflect the average of the increases in prices and in real income. A similar system was proposed by Vito Tanzi, who suggested that once the brackets and exemptions of the personal income tax were defined they should be adjusted annually by an index reflecting the change in the country’s per capita income in the previous year.11 In practice, however, the Icelandic Government has made discretionary use of the tax index. For example, in 1968 no adjustment was made, and in 1972 the index reflected only the increase in the general price level (measured by the increase in the cost of living index between 1970 and 1971).

In April 1971 the Netherlands established a system (effective January 1972) for adjusting tax rates to inflation.12 The basic table containing tax brackets, dependency allowances, and age and disablement deductions is replaced every year by a new one. This is constructed by multiplying the figures of the previous year by a correction factor representing the ratio of the average of the consumer price index for the eighteenth to seventh months preceding the beginning of the year and an average of values of the same series for the thirtieth to the nineteenth preceding months. The law states that the price index used should be adjusted to remove the effects of tax changes and subsidies that are assumed to be directly related to the price of goods. The price correction factor is published by the Minister of Finance, who can make a downward adjustment of not more than 20 per cent in the factor computed as described above. In October 1971 when the adjustment scheme was implemented for the first time, the Minister used the maximum downward adjustment for the 1972 tax year. The correction factor as calculated would have been 1.057; instead, he declared it to be 1.0456. The main reason for this adjustment was to avoid major conflicts with other policy measures designed to curb a wages and prices spiral.13

In September 1972 the full downward adjustment was again made for the 1973 tax year. The reason given by the Minister of Finance was that, if the full adjustment had been applied, revenue losses would have been large. By setting the correction factor at 80 per cent, another 20 per cent of the expected revenue losses would be covered. Alternative ways of financing the difference were to be found.14 The application of this system was suspended for the 1974 fiscal year. The impact of inflation on people in lower income brackets was compensated by a 5 per cent increase in the income level at which tax liability begins.

In Canada indexing of the personal income tax exemptions, some deductions, and brackets went into effect in 1974. Every year these items will be changed according to an adjustment factor, which is to be computed as the ratio of the average of the consumer price index of the 12 months ending September 30 of the preceding tax year to a comparable average for the previous year.15 Unlike the system in the Netherlands, no adjustment for sales tax changes will be made in the price index before it is used for adjustment purposes. For 1974 the indexing factor was 6.6 per cent.

A problem in Canada is that a large part of provincial revenues is raised through personal income taxes, which are collected by the central government for nine of the ten provinces. The base of this tax is, for most provinces, the same as that for the federal tax. An adjustment mechanism would reduce provincial income tax collections, and some provinces are quite concerned about finding alternative sources to finance their expenditures.16 An estimate by the Ontario Tax authorities for Ontario and seven other provinces showed that for 1974 revenue losses from indexing as a percentage of income tax revenue will range from 3.8 per cent for British Columbia to 5.4 per cent for Newfoundland, and would be from 12.4 to 16.9 per cent in 1977.17

Although no country has yet adopted it, a system that defines brackets in a continuous way by means of a tax function including a correction parameter for inflation is closely related to the schemes described above. Such a system has been proposed by Seidl, Topritzhofer, and Grafendorfer.18 Most income tax legislation defines brackets for different marginal tax rates. Sometimes exemptions or reductions are defined as a proportion of income with varying ratios for income levels; sometimes they are defined in money terms for income levels. Such practices give rise to a distribution of tax burdens which changes from income level to income level in a discrete fashion. To avoid this problem Seidl, Topritzhofer, and Grafendorfer propose a continuous income tax function; the tax base and the abatements can be linked to income by means of a mathematical formula. They define a set of properties desirable for a progressive income tax function and then suggest several formulas. Their proposal includes a parameter in the tax function to reflect changes in prices, and this parameter would be changed every year. It would be computed as a ratio of the value of the cost of living index in a given tax period to the value for the same series in the year the tax function is enacted.

Argentina introduced a system of inflation adjustments for exemptions and deductions at the end of 1972. While the Argentine legislation is probably the most comprehensive in regard to exemptions and deductions, it does not cover income brackets. The system was first implemented in 1973. The correction factor was to be estimated according to changes in the cost of living index from July of the year preceding that for which tax liability was being computed to June of that year.19 The system was altered in October 1973; the consumer price index replaced the cost of living index, and the period January to December of the preceding fiscal year replaced the July to June period as the basis of computations of price level changes.20 An important reason seemed to have been the attempt to alleviate revenue losses under the adjustment system. It was also established that the correction factor for 1973 should be computed according to changes in the consumer price index from January 1973 to June 1973, and that for 1974 it should be computed from January to December 1974. Consequently, 1972 values of exemptions and deductions were increased by 28.2 per cent for 1973.21 If the adjustment had been made according to the original system, the increase would have been 56.9 per cent.

At the end of 1973 major changes occurred in the Argentine tax system, and the income tax law was completely redrafted. Although the adjustment for exemptions and deductions is the same, the new law redefines the absolute basic values of exemptions and deductions and will go into effect for the 1975 fiscal year.22

In 1969 Denmark made the income tax less responsive to inflation.23 The Danish system is a combination of the second and third types of adjustment schemes. On the one hand, the personal exemptions and brackets are to be adjusted every year according to changes in the cost of living index. (A number of other items, stated in the income tax law in money terms, are not subject to this adjustment). The adjustment is made to reflect changes in prices from January to January in steps of 3 per cent for each four points by which the cost of living index moves in relation to the index for January 1969, which was 131 (a figure explaining the seemingly less than proportional adjustment). On the other hand, the 1969 law also established the tax rates fixed in the income tax law as basic. Every year, however, a new law fixes the percentages at which the basic rates apply. A maximum limit of 105 per cent has been imposed, but there is no minimum. For 1970 the basic rates were applied at 95 per cent24 and for 1971, at 91 per cent.25

In Switzerland a system of adjustment for inflation similar to that in Denmark has been in effect in the Canton of Aargau since January 1971. On the one hand, tax rates are fixed every year as some multiple of given basic rates; on the other hand, if the consumer price index changes by no less than 10 per cent, the Cantonal Grand Council is authorized to raise income brackets and exemptions by a uniform percentage or to lower them to the original values. These changes are made six months before the actual assessment of the tax.26 In fact, the Canton of Aargau has had a system of adjustment for inflation since 1966, but from 1966 to 1971 it was only loosely defined.27

Since 1968 France has had a system which stipulates that the personal income tax schedule must be changed whenever the annual rate of inflation exceeds 5 per cent. The authorities may adjust brackets in different ways. For example, between 1968 and 1972 the consumer price index rose by 25.5 per cent and upward adjustments in the limits of each taxable income bracket were made, ranging from 31.6 per cent for the lowest bracket to 20.2 per cent for the highest bracket. At the same time rates were changed, and a downward adjustment of three percentage points was applied to all brackets.

rate adjustment schemes

The third type of adjustment scheme—namely, lowering tax rates according to a particular index—is not found explicitly in any country. However, several countries (including Sweden and 22 Swiss cantons) have legislative provisions that could facilitate implementation of such a scheme.

In Sweden the income tax law contains a provision to facilitate rate adjustments to offset inflation. Rates and brackets are defined by law, and each year the Government has to declare the proportions to which these basic rates apply.28 Tax rates may be higher than those of the basic table, although the highest tax rate on any part of the taxable income cannot exceed the maximum marginal rate of the basic tables. This adjustment provision was apparently designed as a countercyclical tool, but it could also be used, if desired, as one means of offsetting some of the distortions in tax distribution created by persistent inflation. However, although prices in Sweden rose by 77 per cent in the period from 1958 to 1972, the income tax rates were applied throughout the period at 100 per cent of those established by law, with three major changes being made in tax rates without any reference to the index. Recently, there has been discussion of this question, but a public committee appointed in 1972 by the Government to review personal income taxation was explicitly asked not to deal with indexation.29

Most of the Swiss cantons (22 out of 25) have a system similar to that in Sweden. The basic rates are defined in the cantonal tax laws, and the effective rates are fixed annually when the authorities establish a coefficient of adjustment known as the “multiple.” 30 Although the system can be used to adjust rates for inflation, it seems to be mainly a flexible instrument for adjusting revenues to changes in cantonal needs.

II. Comparison of Adjustment Techniques

The principal aim of each system of inflation adjustment described in Section I is to continue taxing each level of income at approximately the same rate as in the base year. In effect, the tax rates for the initial year are thus presumed to reflect a socially desired income tax burden distribution.

If the situation in the initial year is considered desirable, then the introduction of an adjustment mechanism in the income tax legislation appears broadly justifiable in equity terms. Even if the initial situation is unsatisfactory, it would seem preferable to make any desired changes explicitly rather than to rely on the less visible influence of inflation. Since the final effects of inflation on tax rates are not strictly controllable, discretionary changes in the tax schedule seem to be a superior method of achieving a desired distribution of tax burdens. Once this is achieved, however, an inflation adjustment scheme could take care of some of the deviations created by inflation.

Assuming that the equitable distribution of tax burdens is the underlying rationale for inflation adjustment schemes, systems of the first type described in Section I (real income) seem unnecessarily complicated. The second type (index adjustment) can accomplish the same result in a much simpler way, especially from the point of view of taxpayers.

Systems of the third type (rate adjustment), while equally simple, involve a continuous lowering of the marginal tax rates for persons whose income falls in the uppermost income bracket. If a system of lowering tax rates is implemented so as to make a downward adjustment in tax rates in proportion to price increases, the most likely result will be a decrease in the average tax rate for practically all taxpayers. Two counteracting effects are at work here. One is a reduction in taxes on the level of preinflation income, and the other is an increase in the tax liabilities at the margin (which is the product of the marginal tax rate times the increase in money income). In practice it seems unlikely that the second effect will outweigh the first. Unless the tax rate increases very rapidly from one bracket to the next, the result will be a lowering of the average tax rate (see Appendix I for a mathematical proof of this argument).

On balance, systems based on periodic adjustments of income tax brackets and of other items fixed in money terms by means of a given index appear superior. The choice of the index, the degree of discretion with respect to applying the correction factor, and the range of items covered by the automatic adjustment scheme give rise to several variants of this approach.

variants of adjustment schemes

The Brazilian variant, as first implemented, showed that when the adjustment scheme is tied to some other economic variable, the whole structure of the tax may become linked to other policy measures in ways that could result in conflict with the goal of the adjustment scheme. For example, the state may wish to change the level of minimum wages in pursuit of either long-run structural changes or short-run stabilization policies; but changes in the minimum wage would also affect the structure of the income tax, which may be undesirable. The same could happen in Chile. Although the basic wages are determined strictly in accordance with changes in the price level, the Chilean Government may in the future prefer a different approach which would affect the whole structure of the income tax.

The idea behind the scheme proposed by Tanzi (and perhaps that used in Iceland) is to permit the establishment of an incomes policy that will give taxpayers a share in the benefits of growth. Although the idea seems attractive, a full examination of it is beyond the scope of this paper. Again, mixing two policy objectives could create problems in policy design.

The variant adopted by the Netherlands is also potentially a mixed package. On the one hand, a full adjustment scheme is provided; on the other hand, the use of the adjustment to increase revenue or to keep the system more flexible is also contemplated. In addition, the flexibility is asymmetrical in the sense that the adjustment of the correction factor can be made downward but not upward—that is, a reduction in real tax rates cannot be accomplished by means of the adjustment procedure.

A system of adjusting only exemptions and deductions affects more taxpayers in the lower income brackets; presumably, further changes in the distribution of the income tax burden are being sought through inflation. However, if inflation proceeds at relatively high rates, those in the middle income level will soon be taxed at high rates. As mentioned earlier, several studies have shown that the combination of inflation and progressivity affects most people in the lower income level and people with a greater number of dependents. If that is so, a partial adjustment scheme, like that in Argentina, seems preferable to no adjustment at all.

A minor point should be added here. As was mentioned before, the aim of most adjustment schemes is to maintain taxes at a given proportion of income for each level of income in real terms. However, adjustments are usually made to the exemptions and brackets at the beginning of the current year on the basis of inflation experienced in a previous period. When inflation is moderate, or when the rates of price increase do not vary much from year to year, this procedure is adequate. But when inflation takes place at variable rates and is high, the fluctuations of the level of taxation for different income levels may become significant. Also, this procedure means that any inflation during the current year will result in some increase in real tax rates. To avoid this, it would be necessary to include in the adjustment factor the expected rate of inflation during the current period, or to issue a “corrected” table before the due date for final income tax reports. If the tax is collected at source under a withholding system, weekly or monthly adjustments might even be required. It seems unlikely, however, that any inflation adjustment scheme warrants such refinements.

To sum up, if the principal or sole consideration is equity and the objective is to maintain through time a given distribution of tax burden among different levels of real income, an adjustment system that alters rate brackets, exemptions, and other items fixed in monetary terms in accordance with an appropriate price index seems preferable to other approaches.

choice of index

The choice of index may also be important. Ideally, the best approach would probably be to use several indexes, each reflecting the increase in prices of the goods purchased by a category of taxpayers, say, those with a given average real income. Clearly, this approach is extremely difficult, if not impossible, in most countries.31 An alternative is to use an index that reflects the changes in prices of goods acquired by the largest number of taxpayers. No general index can be prescribed, since the situation may vary from country to country, but either the consumer price index or the cost of living index seems most appropriate. However, income groups whose expenditure problems are not well measured by changes in the consumer price index will be affected differently by inflation, even with an adjustment scheme, from those (for example, urban industrial workers) whose purchases correspond more closely to the “market basket” measured by the index.

Inflation adjustment schemes differ as to the treatment of the influence of indirect taxes on the price index adopted. In the Netherlands a correction is made for changes in the cost of living as a result of indirect tax changes, while no such correction is made in Canada. The case for this correction is that if the government wants to raise (or lower) taxes for stabilization purposes, there is no reason to offset the increase (or decrease) in tax collection by a countermeasure. On the other hand, a reason for ignoring indirect tax changes is that taxpayers will be affected in exactly the same way whether an increase in prices comes from a rise in taxes or from any other source. Therefore, given the distributional considerations on which inflation adjustments are based, it appears more appropriate not to make allowances for price changes due to indirect tax changes. A better way of handling the problem of conflicting goals—such as equity and stabilization—may be to allow the correction factor to deviate somewhat from what it would be if the chosen index is strictly applied. In this way, the desired tax burden distribution can be maintained, while the total income tax yield is adjusted to economic conditions.

III. Considerations in the Adoption of an Inflation Adjustment Scheme

This section explores arguments for and against the adoption of an adjustment mechanism, particularly those related to equity. Countries considering adopting such a scheme should also examine the built-in stabilization properties of the income tax and the effects on resource allocation, as well as arguments of an administrative and political nature. These matters are only briefly outlined here.32

equity considerations

Probably the main consideration favoring adoption of an inflation adjustment mechanism is equity. As noted earlier, the introduction of such a system seems justifiable if the initial tax burden distribution corresponds to the preferences of the society, but its desirability is less clear if the society considers that the distribution of the tax burden should be altered.

Progressivity in the income tax law, coupled with inflation, can modify the distribution of the tax burden, perhaps in the direction society desires. But it seems doubtful that the combination of inflation and progressivity will produce the precise change that will fit the preferences of society. If the distribution of that tax burden is to be changed, it seems preferable to alter the tax schedule explicitly to reflect the desired change in tax liabilities for different levels of income, rather than to allow inflation to produce somewhat unpredictable results. Once the desired change is achieved, the adoption of an automatic inflation adjustment scheme will allow that distribution to be maintained.

As regards horizontal equity, it is clear that inflation has different effects on taxes levied on income from different sources. Bossons and Wilson have observed, for example, that taxes on income from labor in Canada rose during the period 1961–70 at a faster rate than those on income from capital.33 A plausible cause for this is the way in which inflation has affected the personal income tax. Inflation tends to move people from one income bracket to a higher one. As one moves upward in the income schedule, on the average an increasing proportion of total income consists of income from capital. Furthermore, capital gains constitute a larger proportion of the higher incomes. The proportional taxation of business income and the favorable treatment of capital gains in most countries thus tend to mitigate the increase in tax rates that people in the higher brackets would otherwise face when inflation moves them upward in the tax schedule.

Similarly, the existence in most industrial countries of an income tax withholding system for wages and salaries involves discrimination against income from labor. In effect, withholding means that labor income is likely to be subjected to higher real tax rates in periods of inflation than property income. Withholding at source does not allow any lag between the time of receiving income and the time of tax payments. In an inflationary economy, however, taxpayers will pay less tax in real terms if they are able to delay payments. Since those in the lower and middle income brackets typically receive more labor income, an inflation adjustment mechanism will be relatively more beneficial to income from labor and thus to persons in the lower and middle income brackets. This line of argument may suggest that the adjustment perhaps ought to be applied to labor income only. While such a limitation would be in conflict with the general world-wide tendency to move away from the schedular type of income tax and toward the global type, in reality there are already so many differences in the tax treatment of income from different sources in the income taxes of most countries that the “global” nature of the income tax often seems more apparent than real. At the very least, the relative discrimination against labor income as a result of the interaction of withholding, progressivity, and inflation deserves careful attention in designing inflation adjustment systems.

A related issue concerns the tax treatment of capital gains. If the initial tax burden distribution is regarded as equitable, provision of an adjustment scheme for some taxpayers and not for others could itself be considered to be inequitable. Therefore, it may seem reasonable to contemplate means to free the taxation of capital gains from the influence of inflation. Since most countries already provide some sort of favorable tax treatment to capital gains, the argument for an adjustment scheme for capital gains becomes somewhat weaker. Most authorities on public finance claim that the appropriate definition of income should be consumption plus changes in net wealth. If this concept were adopted, it would seem reasonable to include capital gains in an adjustment system. The inclusion of capital gains in turn gives rise to several problems concerning the specific techniques to be used, the kind of assets to be covered, and the type of index to be adopted. In principle, however, it seems possible to implement an automatic revaluation system, which would permit the periodic revaluation of assets, say, every year by applying to the values of previous periods some index fixed by law. Clearly, this procedure would have to be coordinated with the tax treatment of capital gains that are not influenced by inflation. As these questions have been treated extensively in other works, especially by Helliwell,34 they will not be pursued further here.

On balance, inflation adjustment schemes for the personal income tax, no matter how well designed, can at best eliminate only some of the undesirable distributional effects of inflation. In addition to the problems of treating fairly recipients of incomes from different sources and those with different expenditure patterns, the income tax consequences of inflation represent only a minor part of its total distributional effect. As Helliwell has noted, “adjusting personal income tax rates for inflation could reduce the relative tax burden of those least protected against inflation. However, this effect is too small to be of much help to those who are unable to protect their relative incomes when inflation takes place. Not surprisingly, the basic solution to their plight must lie elsewhere.” 35 Thus, far from offering a completely satisfactory solution to the distributional problems arising from inflation, inflation adjustment schemes for personal income tax would appear to offer an improvement over the situation as it would be without adjustment. They therefore warrant serious consideration.

stabilization aspects

The stabilization aspects of taxation can be analyzed in either a static or a dynamic framework. Within a static framework, a relatively simple model of the economy is usually specified, and income multipliers are derived under varying assumptions with respect to taxation. The built-in flexibility of a particular tax is then derived from a differing response of prices and/or income to an exogenous change in the presence of the tax, as compared to the response in a no-tax situation.36 Clearly, if prices are assumed constant, the exercise refers to the flexibility of the tax in response to changes in real income, while if real income is assumed constant, it refers to the price flexibility of the tax. In practice this distinction is often not made, and flexibility is measured with respect to changes in money income levels.

The changes in the built-in stabilization properties of the system resulting from the introduction of an inflation scheme can also be studied in relation to two alternative situations: one in which no adjustments for inflation are made, and one in which tax rates are changed from time to time to offset some of the effects of inflation.

Assuming that both income and prices move in the same direction, it is likely that the adoption of an inflation adjustment scheme (as compared with the no-adjustment case) will tend to reduce but not eliminate the built-in flexibility of a progressive income tax structure. As real income grows, individuals will continue to enter higher income brackets and become subject to higher rates. Tax collections will thus increase at a rate greater than the rate of growth of income. If there is a recession, the converse will hold. The greater the progressivity of the tax and the greater the proportion of total tax collections contributed by income tax, the greater the stabilizing power of the tax system will tend to be, whether there is an inflation adjustment or not. However, if the increase in nominal income comes entirely from a rise in prices, the built-in stabilizing properties of the tax will be the same in this framework as that of the proportional income tax.

If an inflation adjustment scheme is compared with a system of discretionary changes, introduced from time to time, no definite conclusions as to their relative performance can be reached. With a system of ad hoc discretionary changes, the timing of the adjustments becomes crucial. If the reduction is made in the downswing of the cycle—for example, to adjust for previously accumulated distortions from inflation, then such a system will normally tend to be stabilizing. If it is made in the upswing of the cycle, it could be destabilizing. The outcome of a comparative evaluation of the two systems in this framework is uncertain, being dependent on the precise timing of the discretionary adjustments compared with that of the more automatic adjustment scheme.

This discussion assumes that price and activity levels move together, but price inflation has frequently been accompanied by declining real activity in recent years. The behavior of unadjusted income tax receipts in such a situation would seem to be the reverse of what is required for stabilization purposes, since they might be rising sharply in response to price increases at a time when the level of real activity in the economy is falling. Hence, given a combination of inflation and declining real activity, the adoption of an automatic adjustment scheme should normally tend to increase, rather than decrease, the stabilizing power of the tax system with respect to changes in real income.

On the other hand, introduction of an adjustment scheme such as those discussed in this paper will render the personal income tax neutral as a price stabilizer (apart from the lag in applying correction factors in most real world systems).37 An increase in prices will call for an adjustment in taxes which, under the assumption of automatic and instantaneous response and holding other things equal, will mean an unchanged proportion of tax collections with respect to money income. In contrast, a system involving no adjustment of the income tax structure in the face of rising money income is, in principle, both an income and a price stabilizer. An income tax introducing discretionary changes from time to time could be either stabilizing or destabilizing, depending on the timing of the corrective action.

If the aim is to maintain the built-in stabilizing power of the income tax at the highest possible level, the use of a variable correction factor thus appears desirable. A method similar to the Netherlands system described above could perhaps be used, modified so that the correction factor could be adjusted upward or downward in accordance with economic conditions. An alternative might be to rely on surtaxes or tax rebates computed in proportion to adjusted income tax payments and fixed according to the cyclical situation. Either of these approaches would achieve the desired macroeconomic effect from the tax system without distorting the intended distribution of the tax burdens. The combination of an adjustment scheme and one of the devices mentioned above would thus enable policymakers to use different instruments for different goals.

In the static approach taken up to this point, it is assumed that the adjustment of the economy to a given shock is made entirely within the current period. In the real world this is often not the case; there are lags in the reaction of economic variables to a given stimulus and the adjustment process often extends beyond a single period. The existence of lagged responses significantly limits the usefulness of static analysis in evaluating the stabilization implications of any policy measure.

An alternative approach that is useful to test the efficacy of an automatic stabilizer is the extent to which it stabilizes a system subject to an exogenous shock or a series of such shocks. To conduct such a test, a dynamic model is required for a comparison of the time paths of endogenous variables with and without automatic stabilizers.38 Bossons and Wilson used such an econometric model to simulate the response of the Canadian economy to an inflation adjustment scheme for personal income tax.39 Their conclusion was that adoption of such a scheme would tend to increase rather than to decrease the automatic stabilizing power of income tax.

However, this conclusion has been demonstrated only for one particular economy in the context of one econometric model. The assumption that the fitted lag structure will be maintained in the future may lead to serious error.40 Different lag structures can lead to identical reduced forms, and different reduced forms may not differ significantly as to goodness of fit, while generating quite different time paths. Further, the estimated lag structure is an average of the actual lags, and this average lag may conceal significant variations. Therefore, it is difficult to place a great deal of reliance on the results of simulation exercises such as those on the Canadian model. Since no other approach seems as promising, however, further investigation of the stabilization properties of alternative tax structures should probably employ it.

Finally, in any simulation exercise of this kind, the standard of comparison is of crucial importance. In the Bossons and Wilson paper, for instance, the automatic adjustment scheme is compared with a policy of no change at all in the tax structure. As suggested above, it might be more relevant in many countries to compare it with a policy of discretionary tax adjustments from time to time.

efficiency considerations

Any tax measure may affect either the degree of utilization of available quantities of factors of production, or their long-run supply, or both. It is thus of interest to speculate on the probable economic effects of the introduction of an adjustment scheme, such as its effects on risk-taking and savings. However, definitive conclusions on these and similar matters are lacking.

With no adjustments, or with irregular discretionary adjustments, tax liabilities tend to vary in a rather arbitrary way, and this variation causes uncertainty. For a typical asset holder with a given degree of total acceptable risk, this uncertainty creates a greater risk for the assets already held, and asset holders may try to compensate by moving toward less risky assets. Thus, the introduction of an automatic adjustment scheme may, by reducing uncertainty, be favorable with respect to risk-taking.

As regards savings, if the so-called ratchet effect operates with respect to consumption, the adjustment scheme may increase savings. According to the relative income hypothesis, an important factor determining consumption is the highest level of real income in any previous period. If real disposable income fluctuates as a result of variations in tax burden owing to inflation, a probable outcome would be lower savings. The introduction of an automatic adjustment scheme would reduce variations in tax liabilities in real terms, thus reducing some of the fall in real disposable income caused by inflation and by periodic changes in legislation and presumably increasing savings. The magnitude of this effect, if it exists, can never be known, given our present lack of knowledge on the relation between financial and real variables.

political and administrative arguments

The adoption of an adjustment system would mean the abandonment of an extremely convenient method of increasing tax revenue. When the limits of tax brackets, exemptions, and the like are fixed in money terms, an increase in nominal incomes will lead to a rise in real tax revenues without any great resistance from the taxpayers (at least during periods of mild inflation). The willingness of citizens to pay a tax is a proper consideration in the formulation of any tax policy. It is often argued that the opposition of taxpayers is greater as their awareness of the tax is greater.41 If a government adopts an inflation adjustment scheme, income tax collections are usually reduced and alternative means of financing must be found. These alternatives may entail greater taxpayer resistance than that caused by inflation and progressivity, with a resulting slower rate of expansion of the government sector. Also, there is no assurance that the net distributional outcome of the inflation adjusted income tax and the new revenue sources drawn on to replace the inflation “bonus” will be more progressive than the unadjusted tax; they may equally well be more regressive.

Not ignoring the fact that much of the tax they pay is perceived by taxpayers only very vaguely, a different view would hold that in a democratic society a high degree of tax consciousness is desirable. With an inflation adjusted income tax and the probable need for more frequent recourse to explicit tax increases, taxpayers may become more aware of their role in government finance and may have a feeling of increased participation in the economic decisions of the nation or of dissatisfaction with these decisions. The social and political ramifications of adjusting for inflation are thus potentially of considerable importance.

As inflation becomes a permanent fact in an economy, many items tend to become linked to changes in the price level. Wages, debts, rents, and so on, tend to become more or less automatically adjusted to inflation. It seems likely that public awareness of rising tax rates will similarly increase over time as inflation persists in many countries. Awareness of higher income tax rates is also said to be a growing issue in wage bargaining in most industrial countries. It thus seems probable that inflation adjustment schemes will become a political and economic issue in an increasing number of countries.

IV. Conclusions

The main arguments for the adoption of an inflation adjustment system rest on equity considerations. On these grounds, once a desirable distribution of the tax burden has been achieved, changes not deliberately sought can to some extent be avoided by introducing a system of automatic adjustment. Its introduction may sometimes impair the built-in stabilizing power of the tax system, but its use can be combined with other measures in order to preserve the income tax as a useful tool for stabilization purposes. On the other hand, the stabilizing effect of the income tax may even be improved by the introduction of an inflation adjustment scheme. On the side of efficiency, not much can be said with any confidence, but its seems that by removing an element of uncertainty caused by inflation and periodic changes in legislation the system may work in favor of increased risk-taking. Perhaps most importantly, the adoption of an adjustment scheme will deprive governments of a conveniently invisible method of increasing tax revenues; to replace the proceeds that otherwise would be collected will require an effort in tax planning and implementation by countries adopting such schemes.

The question of the adoption of an inflation adjustment scheme for the personal income tax seems relevant for both developed and developing countries. The high rates of inflation experienced in some developing countries have already led some of them to adopt a system of automatic adjustment. The inflation that has now become a pervasive phenomenon in the industrial world has recently caused several developed countries to consider the problem, and the introduction of adjustment systems like those analyzed here seems very likely soon to become an issue in other countries as well.

APPENDICES
I. A Technical Note on a System of Lowering Tax Rates in Proportion to a Rise in Prices

A system of lowering tax rates in proportion to the rate of inflation can have different results, depending on the tax schedules and the rate of inflation, but generally the average tax rates will decrease.

This procedure of inflation adjustment has two effects: (1) The tax liability on the preinflation income is reduced by the application of lower tax rates across the board. (This reduction is represented by the shaded area A in Chart 1.) (2) A tax on the increase in money income due to inflation is levied at a rate equal to the marginal rate faced by the taxpayer (represented by shaded area B in Chart 1). Normally the second effect will be greater than the first. However, unless the tax schedule is steeply progressive, the decrease in real terms in tax liabilities due to inflation will more than offset the increase in nominal revenues.

Chart 1.Effects of Inflation Adjustment on Tax Rates

For tax liability to increase in real terms, it is generally required that the marginal tax rate be at least twice the average tax rate. More precisely, the average tax rate can increase only if the marginal rate in the original tax schedule is greater than the average rate in the preinflation period multiplied by two and plus the rate of inflation.

Definition of terms

Ti=total tax liability in period i
Yi=taxable income in period i
ai=T1Y1 average tax rate in period i
d=rate of inflation from period 1 to period 2
tm=marginal tax rate coming into effect at income Y1 in the original tax schedule

The average tax rate in period 1 may thus be compared with that of period 2:

Tax liability in period 2 is equal to that of period 1, minus the tax liability corresponding to the shaded area A in Chart 1—represented by the second term in the right-hand side of this equation: d1+d is the rate of reduction of tax rates equivalent to the rate of inflation, plus the increase in the tax corresponding to shaded area B, represented in the equation by the third term (dY1 is the increase in income, and tm11+d is the marginal tax rate in the postinflation period).

Since Y2 = Y1(1 + d), therefore

That is, a2 is greater than a1 only if the average tax rate in period 1 times (2 + d) is smaller than the marginal tax rate in the original tax schedule.

II. Income Tax Rates and Inflation: A Simulation Study

This appendix describes a simulation study of the average tax rates for different categories of taxpayers in several countries.

The study analyzed how the combined forces of inflation and progressivity have altered tax liabilities for taxpayers at various income levels; considered how much legislative changes compensated for augmented tax burdens; and indicated how average tax rates would have moved if legislation had remained unchanged. The study was essentially one of formal incidence—that is, tax liabilities of the taxpayers were estimated according to the legal provisions on the assumption that there was no shifting or evasion.

Similar studies have been carried out for individual countries. One study by Goetz and Weber is based on U. S. data for the period 1954–70.42 The authors showed that a considerable change in effective income tax rates occurs automatically when prices increase. One of their principal conclusions was that, in spite of two major downward revisions in statutory tax rates, large categories of taxpayers in the United States were liable to higher income tax rates in 1970 than in 1954 on the same real incomes. Changes in the real value of exemptions as a result of inflation had an important influence on these changes in effective tax rates, so that the increase in tax burdens was felt relatively more by taxpayers in the lower income brackets and by those having a large number of exemptions.

Goetz and Weber attempted further to show the distribution of changes in tax burdens among the total number of taxpayers through an exploratory analysis of the distribution of exemptions among income levels, but they could not draw very definite conclusions because of the limited availability of information. The report of their study includes tables and graphs showing variations in average and marginal tax rates and absolute changes in real disposable income.

A similar study was carried out by Vukelich for Canada, also for the period 1954–70.43 His paper concluded that low income, multichild families were, as in the United States, the most adversely affected by the combined forces of inflation and progressivity. In comparison with the United States, however, Canada has had a greater increase in tax rates because, while inflation rates have not differed significantly between the two countries, Canada took less corrective action during the period.

Tables similar to those in the U. S. study are found in Vukelich’s paper. In addition, he calculated changes in tax liabilities in which the effects of inflation were isolated from the results of statutory changes. The study also forecast changes in tax liabilities for the period 1970–76, based on the new income tax provisions that came into effect in Canada in January 1972 and on an assumed annual rate of inflation of 3 per cent. It did not, of course, allow for the effects of the system of inflation adjustments that came into operation in January 1974.

Description of the simulation exercise

The present study was carried out for 17 countries, covering the years 1958–70. Ten of these countries (including Canada and the United States) may be classed as developed and seven as developing. The choice of countries was dictated partly by the availability of information and partly by the desire to encompass a wide range of experience. For each country, average tax rates at different income levels were computed for selected years and for five categories of taxpayers. Changes in tax legislation were taken into account in estimating the amount of tax that would have been paid annually by “typical” taxpayers at hypothetical levels of real income.

The income levels for which tax rates were computed were equal to multiples of the average industrial worker’s income in each country for the initial year.44 Real income in each of the following years was calculated by multiplying the initial year’s income by the ratio of the annual consumer price index to the value of this index in the initial year.

The five different categories of taxpayers considered were: a single taxpayer without dependents, a married couple without children, and a married couple with two, four, and six children. It was assumed throughout that all income was in the form of wages and salaries, that the spouse earned no income, and that the children were not attending school.

All major changes in legislation over the period were taken into account.45 The most important deductions were considered, and in all cases the study took into account such general measures as earned income allowances, dependency allowances, and minimum personal exemptions. Transitory measures, such as a surtax or a global tax rebate, were also allowed for explicitly.

As mentioned above, the idea of this exercise is to obtain estimates of constant real income during the period for each level of income. People in different income brackets often have quite different consumption patterns. In theory, then, one needs separate price indexes for each income level, but because this information is not easily available the general consumer price index was used in this study.46 A consumer price index usually reflects changes in the purchasing power of income at some given level, usually of a relatively low income bracket. Prices corresponding to the goods purchased by other income recipients could move in different directions, affecting real income in several ways. It is beyond the scope of this paper to investigate this question thoroughly. The wholesale price index may be a reasonable alternative choice. Although this index frequently includes more items than the consumer price index and may better represent the basket of goods for a higher income group, the adjustment lag in consumer response is not well represented by it. On the whole, the consumer price index seems to be a more suitable choice. The implicit price deflator, widely used in studies where financial assets rather than real assets are involved, is not conceptually the most suitable for this case, since this study deals with inflation not as it affects the purchasing power of money in general but as it affects the purchasing power of income for given groups of people.

The assumptions regarding exemptions and deductions, and the categories of taxpayers covered in this study, were intended to facilitate comparison. Another important consideration was to facilitate the collection of data and computational work. However, it seems likely that, despite the many simplifications in this analysis, at least four of the five cases represent broad categories of taxpayers. The fifth case (the six-child family) was included to test how many general conclusions could be drawn from earlier studies regarding the adverse effects on multichild families.

In addition to computing average tax rates for given income levels, the mean, the standard deviation, and the coefficient of variation of the rates through time were computed to indicate the variability of average tax rates over time. The standard deviation measured the absolute dispersion of values around the mean, while the coefficient of variation, equal to the standard deviation divided by the mean, measured the relative dispersion of average tax rates for each particular income level. Parameters of trend lines of the average tax rates were estimated by least squares, and the average rate of growth of these tax rates over the period was also calculated.

Results of the simulation exercise

The results of this study suggest certain general conclusions. Faced with the effects of inflation on income taxes, some countries have taken corrective action continuously, while others have taken advantage of the increase in real tax rates brought about by inflation before introducing changes in legal provisions. A greater degree of relative variability in average tax rates is experienced at the lower income levels and by taxpayers with a relatively large number of exemptions. In most cases, over the period examined, the increase in average tax rates was greater at lower income brackets. When average tax rates declined, the fall in tax burdens was smaller in relative terms for the lower income brackets.

When statutory changes in legislation are taken into account, the average tax rates increase, decrease, or fluctuate through time. But when legislation is assumed constant, average tax rates increase in almost all cases, and naturally, the higher the rate of inflation, the greater is the increase in average real tax rates. Furthermore, the general conclusion that the increase in tax rates is greater for taxpayers with lower incomes and larger families is strengthened when legislation is assumed constant, because these are the taxpayers whose marginal rates increase most rapidly as taxable income increases.

In practically all cases, the absolute as well as the relative increase in tax rates would have been substantially lower in the uppermost income bracket because, in effect, the top bracket of any rate schedule is liable to a proportional rate. The relative variability of tax rates would have been most marked in the middle income levels.

In the situation of unchanged legislation, the calculated increase in average tax rates for taxpayers with an income equal to that of the average industrial wage earner (in the countries in which these low income groups are liable to income tax) ranged from 30 per cent for Kenya to more than 120 per cent for Israel. For incomes twice as large, the increase in tax rates ranged from 20 per cent for the United States to more than 170 per cent for Jamaica, with most values concentrated in the 20 to 50 per cent range.

The study covered ten developed countries and seven developing countries. The level of income at which people start paying income tax differs sharply from country to country. In lower income countries people with income many times higher than the average industrial worker’s earnings may pay no taxes, while in developed countries the starting limit for paying income tax, measured as a proportion of the average industrial worker’s income, is generally much lower. In recent years inflation has lowered, in real terms, the minimum income on which taxes have to be paid; hence, people who previously were paying no taxes are now brought under the income tax (at least in these calculations). This is the case, for example, in Ghana, India, and Singapore. A sustained inflation may thus over time turn the income tax in developing countries into a mass tax, if its effects are not offset by legislative change or administrative ineffectiveness.

Mr. Petrei was an economist in the Tax Policy Division of the Fiscal Affairs Department at the time this article was written. He is now Director of Training in Project Formulation and Evaluation at the Organization of American States (OAS). Mr. Petrei has doctoral degrees in economics from the National University of Córdoba (Argentina) and from the University of Chicago. He was a member of the faculty at the National University of Córdoba, and served as OAS Advisor on Investment Planning to the Mexican Government before joining the Fund. Mr. Petrei is the author of numerous professional articles.

Studies by Goetz and Weber for the United States and Vukelich for Canada have shown that low income, multichild families are those which are most affected by this aspect of inflation. See Charles J. Goetz and Warren E. Weber, “Intertemporal Changes in Real Federal Income Tax Rates, 1954–70,” National Tax Journal, Vol. 24 (March 1971), pp. 51–63; and George Vukelich, “The Effects of Inflation on Real Tax Rates,” Canadian Tax Journal, Vol. 20 (July-August 1972), pp. 327–42. A more extensive study of a number of other countries, made at the Fund, suggests similar patterns on the whole (see Appendix II).

Amotz Morag, On Taxes and Inflation (New York, 1965), especially Chapter 7.

European Taxation, Switzerland—9, Section B. Tax Tables for Individuals, Canton of Basel-Land, No. 5 (May 1973).

Joint Tax Program of the Organization of American States and the Inter-American Development Bank, Sistemas Tributarios de América Latina—Chile (Washington, 1964), pp. 16–17.

Chile, Public Law No. 15564, Article 43, Diario Oficial (February 14, 1964).

Chile, Public Law No. 14688, Diario Oficial (October 21, 1961).

Roberto Poblete M., editor, Impuestos a la Renta Vigentes en 1970, Divulgación Tributaria, No. 20 (Santiago, February 1970), p. 7.

Brazil, Law No. 3898 (May 19, 1961); see also Carl S. Shoup, The Tax System of Brazil, report to the Getúlio Vargas Foundation (Rio de Janeiro, 1965).

Brazil, Law No. 4140 (September 17, 1962).

Brazil, Law No. 4506 (November 30, 1964).

Vito Tanzi, “A Proposal for a Dynamically Self-Adjusting Personal Income Tax,” Public Finance, Vol. 21, No. 4 (1966), pp. 507–20.

The Netherlands, Public Law No. 259 (April 23, 1971), Staatsblad (1971). pp. 640–41.

The Netherlands, Minister of Finance, Order B71/19821 (October 20. 1971).

The Netherlands, Department von Financiën, Miljoenennota 1972 (September 19, 1972), p. 43.

Canada, House of Commons Debates, Vol. 117, No. 33; 1st Session, 29th Parliament (February 19, 1973), especially pp. 1434–45.

Canada, Ministry of Treasury, The Ontario 1973 Budget, (Toronto, April 1973), Budget Paper B, pp. 13–21.

Canada, Ministry of Treasury, Economics and Intergovernmental Affairs, Taxation and Fiscal Policy Branch, “The Dynamic Impact of Indexing the Personal Income Tax,” Ontario Tax Studies, No. 9 (Toronto, 1973).

Christian Seidl, Edgar Topritzhofer, and Walter Grafendorfer, “An Outline of a Theory of Progressive Individual Income Tax Functions,” Zeitschrift für Nationalökonomie, Vol. 30, Nos. 3 and 4 (1970), pp. 407–29.

Argentina, Law 20046, December 28, 1972.

Argentina, Law 20544, October 27, 1973.

Argentina, Dirección General Impositiva, Resolución-General No. 1572, October 31, 1973.

Argentina, Law 20568, December 29, 1973.

Denmark, Law No. 330, June 18, 1969.

United Kingdom, Board of Inland Revenue, Income Taxes Outside the United Kingdom, 1971 (Her Majesty’s Stationery Office, London, 1973), Vol. 2, p. 238.

Ibid.

Aargau (Switzerland), Cantonal Law of November 10, 1970.

Aargau (Switzerland), Cantonal Law of May 17, 1966, Article 34.

United Kingdom, Board of Inland Revenue, op. cit., several issues; and Sweden, Decree No. 576, January 21, 1947 (amended up to date).

See Lars Matthiessen, “Index-Tied Income Taxes and Economic Policy,” Swedish Journal of Economics, Vol. 75 (March 1973), pp. 49–66, where useful references for the Swedish case can be found, although Matthiessen did not mention the provisions referred to in this paragraph.

European Taxation, Switzerland, No. 9, Section B, Master page (May 1973).

However, indexes for different income groups have been calculated in the United States and Japan at least. See Eleanor M. Snyder, “Cost of Living Indexes for Special Classes of Consumers,” in The Price Statistics of the Federal Government, National Bureau of Economic Research, No. 73, General Series 1961 (Washington, 1961), pp. 337–72; and Ryōtarō Iochi, Measurement of Consumer Price Changes by Income Classes (Tokyo, 1964).

Further consideration of some of these issues may be found in, for example, Robert M. Clark, “Inflation, Taxation and the White Paper,” Report of Proceedings of the Twenty-Second Tax Conference (Canadian Tax Foundation, Toronto, 1970), pp. 213–29; Richard A. Musgrave, “Tax Structure, Inflation and Growth,” paper presented at a meeting of the International Institute of Public Finance, Barcelona, Spain, Sept. 1973; and A. R. Prest, “Inflation and the Public Finances,” Three Banks Review, No. 97 (March 1973), pp. 3–29.

John Bossons and Thomas A. Wilson, “Adjusting Tax Rates for Inflation,” Canadian Tax Journal, Vol. 21 (May-June 1973), pp. 185–99.

John F. Helliwell, “The Taxation of Capital Gains,” Canadian Journal of Economics, Vol. 2 (May 1969) pp. 314–18; Hirofumi Shibata, “The Taxation of Capital Gains: A Comment,” Canadian Journal of Economics, Vol. 3 (February 1970), pp. 151–53; and John F. Helliwell, “The Taxation of Capital Gains: Reply,” Canadian Journal of Economics, Vol. 3 (February 1970), pp. 154–58.

John F. Helliwell, “Towards an Inflation-Proof Income Tax,” in Report of Proceedings of the Twenty-Fourth Tax Conference (Canadian Tax Foundation, Toronto, 1973), p. 166.

An appropriate measure of flexibility has been suggested by E. Cary Brown, “The Static Theory of Automatic Fiscal Stabilization,” Journal of Political Economy, Vol. 63 (October 1955), pp. 427–40. He measures flexibility as dA2dydA1dy, where dA2 and dA1 are the amounts of shifts in aggregate demand necessary to secure a unit shift in income in two cases—dA2, the case in which there is a given tax, and dA1 the case without tax.

If prices are rising, a good stabilizing performance presumably requires real taxes to rise. For a tax to be a price stabilizer, the elasticity of money taxes with respect to prices must exceed unity; unitary elasticity (that of proportional taxation) would be neutral. See E. Cary Brown, ibid., pp. 435–36.

A useful reference for the dynamic approach is John F. Helliwell and F. Gorbet, “Assessing the Dynamic Efficiency of Automatic Stabilizers,” Journal of Political Economy, Vol. 79 (July-August 1971), pp. 826–45. Another useful reference covering both the static and the dynamic approaches is D. A. Auld. “Automatic Fiscal Stabilizers: Problems of Identification and Measurement,” Public Finance, Vol. 26, No. 4 (1971) pp. 513–30.

Bossons and Wilson, op. cit.

On the problems of determining lag structures, see Evi Griliches, “Distributed Lags: A Survey,” Econometrica, Vol. 35 (January 1967), pp. 16–49.

Richard M. Bird, “The Tax Kaleidoscope: Perspectives on Tax Reform in Canada,” Canadian Tax Journal, Vol. 18 (September-October 1970), pp. 444–73.

C. J. Goetz and W. E. Weber, “Intertemporal Changes in Real Federal Income Tax Rates, 1954–70,” National Tax Journal, Vol. 24 (March 1971), pp. 51–63.

George Vukelich, “The Effect of Inflation on Real Tax Rates,” Canadian Tax Journal, Vol. 20 (July-August 1972), pp. 327–42.

Average tax rates were computed for ten levels of income. The multiples used were: 0.5, 1, 1.5, 2, 3, 4, 6, 10, 20, and 30. The source for an average industrial worker’s income was: International Labor Organization, Yearbook of Labour Statistics (Geneva), various issues.

The basic source of information for legal provisions was the United Kingdom, Board of Inland Revenue, Income Taxes Outside the United Kingdom (cited in footnote 25), various issues, 1965–70.

The source for the consumer price index was the International Monetary Fund, International Financial Statistics (Washington), various issues.

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