Howell H. Zee

Taxation and Efficiency

Howell H. Zee

  • How does taxation lead to a loss of efficiency?

  • What are the alternative measures of tax-induced efficiency loss?

The imposition of a tax, under most circumstances, has both efficiency and equity consequences. This section focuses on the concept and measurement of the former,1 while those of the latter are discussed in the following section on taxation and equity. Examining these two consequences separately eases the analytical exposition of certain key concepts in the theory of optimal taxation. In reality, they are, of course, necessarily intertwined, and the choice of a particular tax policy frequently involves an implicit or explicit calculation of the trade-off between efficiency and equity concerns. This is most clearly brought out in the context of the theory of optimal income taxation, discussed in Chapter IV.

To abstract from equity considerations, the discussion in this section assumes the existence of a representative consumer, so that his individual welfare can be taken to represent social welfare as well.

Defining Efficiency Loss

A tax, except in the form of a lump-sum levy (see below), reduces the consumer’s welfare in two ways: directly through a transfer of resources from him to the government, and indirectly through a rise in the consumer (i.e., tax-inclusive) prices of taxed commodities relative to those of nontaxed ones.2 The former produces a (direct) income effect, while the latter gives rise to both an (indirect) income effect and a substitution effect in the standard manner following a relative price change. The efficiency loss of a tax refers to the excess of the reduction in the consumer’s welfare above and beyond that which can be accounted for by income loss due to payment of the tax. For this reason, the efficiency loss is usually referred to as the excess burden of the tax.3 Note that this excess burden arises purely from the tax-induced change, or distortion, in the relative prices of taxed and nontaxed commodities. Hence, a lump-sum tax, which by definition does not distort relative prices, cannot have any excess burden. It then follows that the excess burden of a tax can be alternatively stated as the additional welfare loss from the tax relative to a lump-sum tax of the same revenue yield.

Two important implications follow immediately from the above discussion. First, even if the consumer’s demand for the taxed commodities is such that it is not affected by the tax-induced change in their consumer prices (i.e., the demand curves for the taxed commodities are vertical), the tax would still entail an efficiency loss because of the induced relative price change (see below). Second, if all commodities are taxable and are being taxed at the same rate, then no relative price change, and, therefore, no excess burden, can occur. The significance of this second implication for tax policy is elaborated in the section on optimal commodity taxation in Chapter III.

Measuring Efficiency Loss

How can the excess burden of a tax, defined above, be measured, that is, be expressed in some equivalent monetary units? For simplicity, the discussion in this section focuses on the case of a single taxed commodity. Complications arising from the taxation of multiple commodities are considered in the following section.

Dupuit-Marshall-Harberger measure

The Dupuit-Marshall-Harberger (henceforth DMH) measure of a tax’s excess burden relies on the use of the concept of consumer surplus as a measure of the consumer’s net welfare in consuming a commodity. In Figure II.1, DD’ is the consumer’s ordinary demand curve for commodity X, with X0 being the quantity demanded at the initial price P0 with no tax. The consumer surplus is then the familiar area below the demand curve but above the price line, that is, the area of the triangle DP0 B. Consider now a tax at the ad valorem rate t imposed on X, so that its consumer price rises to P1 = (1 + t)P0, resulting in a decrease in the quantity of X demanded from X0 to X1. Compared with the pretax situation, consumer surplus has now declined by the area of the trapezoid P1 ABP0. The area of the rectangle P1 ACP0 represents, however, the total tax payment. Hence, the excess burden of the tax is the area of the triangle ABC, which measures the excess of the reduction in consumer surplus above and beyond that due to the tax payment.

Figure II.1.
Figure II.1.

Dupuit-Marshau-naroerger Measure of Excess Burden

The area of the triangle ABC can be calculated in a straightforward manner, since it is given by one half of its base multiplied by its height. Let the symbol Δ denote a change in a variable. Then the base of the triangle ABC is -ΔX (note that the term ΔX itself is negative, since the quantity of X demanded has fallen because of the tax), its height ΔP, and the excess burden of the tax can be expressed as


By definition, the absolute value of the price elasticity of demand (e) in the pretax situation, that is, at the point B on the demand curve, is


which can be rearranged to give


Substituting equation (3) into equation (1) yields


Noting, however, that ΔP=P1P0=(1+t)P0P0=tP0, equation (4) can be rewritten as


Hence, the excess burden of the tax varies positively with both the price elasticity of demand in the pretax situation and the magnitude of the (squared) tax rate itself.4 Since equation (5) only involves parameters that are in principle readily observable, the calculation of the area ABC is relatively straightforward.

There is much controversy in the literature about the DMH measure of excess burden. At the root of the controversy is the question concerning the validity of using the concept of consumer surplus as a measure of consumer net welfare. While much of the debate involves highly technical issues beyond the scope of this Handbook, it is instructive to illustrate the following problematic aspect of the DMH measure. As noted earlier, any change in the price of a commodity entails both an indirect income effect and a substitution effect. Hence, a movement along an ordinary demand curve, such as the one from point B to point A in Figure II.1, represents the consumer’s response not only to the change in the price of the commodity, but also to how the price change has indirectly affected his valuation of his income position, and therefore his welfare. This implies that the area ABC does not represent the true amount of monetary compensation the consumer would require, relative to the pretax situation, to leave him as well off in the posttax situation as in the pretax situation.

The above reasoning is most easily appreciated in an example where the ordinary demand curve is vertical, so that the quantity demanded is not affected by any price change. In this case, the DMH measure of excess burden will vanish, as can be visualized from Figure Figure II.1 with a vertical DD’ curve, or confirmed from equation (5) with ε = 0. Yet, the consumer’s welfare must have changed (beyond that which can be accounted for by the tax payment), since the tax has distorted relative prices compared with the pretax situation. Hence, the DMH measure would provide an inaccurate picture of the true excess burden of the tax.

Hicksian measures

To circumvent the problem of the DMH measure, Hicks proposed replacing the use of ordinary demand curves with compensated demand curves. A compensated demand curve abstracts from the indirect income effect of any price change. It thus depicts the relation-ship between the price and the quantity demanded of a commodity purely on the basis of the substitution effect. The relationship between the ordinary and compensated demand curves, given particular initial situations, is provided in the two panels of Figure II.2, which also reproduces all the important aspects of Figure II.1.

Figure II.2.
Figure II.2.

Hicksian Measures of Excess Burden

Consider panel (a) of Figure II.2. The rise in the price from P0 to P1 as a result of the tax reduces the quantity of X demanded from X0 to X1 as before. Suppose now that the consumer receives, simultaneously with the price increase, a monetary compensation just sufficient to offset its associated adverse welfare impact. It is then easy to infer that the reduction in his quantity of X demanded with compensation (such as from X0 to XM) would normally be less severe than that without compensation (such as from X0 to X1). Hence, starting with a given initial situation such as point B, for every price change, a point such as M can be ascertained after the consumer has been fully compensated. The curve that traces out all such points is the compensated demand curve associated with the given initial situation. In panel (a) of Figure II.2, this curve is denoted by HB HB’. The compensated demand curve is always negatively sloped on account of the substitution effect, and would be more steeply sloped than the ordinary demand curve whenever the commodity in question is a normal good, that is, a good with a positive income elasticity of demand.

Since the derivation of the compensated demand curve requires that the consumer be fully compensated for the indirect income effect of a price change, movements along it will, by definition, maintain a constant level of consumer welfare. The amount of compensation that is required to ensure this welfare constancy following any price change, which is known as the compensating variation, is measurable by the area of the trapezoid between the new and old price lines under the compensated demand curve, that is, the area P1MBP0 in panel (a) of Figure II.2, following the price increase from P0 to P1. With compensation, however, the consumer would be demanding XM of commodity X, and his tax payment would be the area of the rectangle P1 MC’P0. Hence, the excess burden of the tax, based on the Hicksian compensating variation, is the area of the triangle MBC. Clearly, this area is smaller than the corresponding DMH measure of excess burden, given by the area ABC.

Given the methodology of deriving compensated demand curves described above, a separate compensated demand curve can be obtained for every point on the ordinary demand curve, each representing a particular underlying level of consumer welfare associated with that point. In panel (b) of Figure II.2, the compensated demand curve associated with the posttax situation (i.e., point A on the ordinary demand curve) is shown as HAHÁ. Since the price at point A is higher than that at point B, the welfare level associated with HAHÁ, must be lower than that associated with HBHB’. Hence, once the consumer is in the posttax situation, the amount of money he is willing to pay to have the tax abolished to maintain his posttax welfare level, which is known as the equivalent variation, is generally not the same as the amount of monetary compensation (the compensating variation discussed above) that is required to keep him at the same pretax welfare level for accepting the tax. The equivalent variation is measurable by the area of the trapezoid P1ANP0 in panel (b) of Figure II.2. The excess burden of the tax, based on the Hicksian equivalent variation, is the area of the triangle ANC. This area is also smaller than the corresponding DMH measure of excess burden.

The Hicksian measures underscore the importance of the choice of the reference point in measuring the efficiency loss of a tax, since the value the consumer places on his income position changes in general with his income level (e.g., he may value a marginal dollar higher when he is relatively poor than when he is relatively wealthy). In other words, the efficiency loss of a tax of a particular magnitude is generally not unique and depends on a number of factors that define the reference point against which the loss is to be evaluated. The particular policy question to which this evaluation is designed to respond usually provides an indication for the correct choice of the reference point, which in turn would dictate which of the two Hicksian variations would be the appropriate measure to use.5 For example, the compensating variation would provide the appropriate measure of the efficiency loss in introducing a given tax, while the equivalent variation would provide the efficiency gain in abolishing an existing tax.

A shortcoming of the Hicksian measures is that, un-like the DMH measure, neither of them can be calculated in a straightforward manner. The quantities XM (panel (a) of Figure II.2) and XN (panel (b) of Figure II.2), for example, cannot be obtained directly from consumption data. Yet, they must be ascertained before the respective areas MBC and ANC can be computed. While fairly sophisticated methods are available in economics to estimate a compensated demand curve, their information requirements are usually too severe for them to be applicable in most developing countries. Hence, the question arises as to what extent the DMH measure could be used as an approximation of the true excess burden of a tax.

Approximating excess burden

It is clear from the above discussion that, in the absence of income effects (the so-called vertical Engel curve case),6 the ordinary demand curve is identical to the compensated demand curve, and the DMH and Hicksian measures will all be the same. Save for this special case, the use of the DMH measure will always involve an error, and the magnitude of the error will depend on the magnitude of the underlying income elasticity of the commodity in question. The bounds of this error have been numerically simulated by Willig (1976) based on alternative upper and lower bounds of income elasticity values within a given price range. Not surprisingly, a general conclusion that can be drawn from the simulation results is that the closer these upper and lower bounds are to each other, the smaller the proportionate error involved in using the DMH measure to approximate either of the Hicksian measures. Whether any such error is considered acceptable must lie entirely with the judgment of the policymaker.

Complications with Multiple Taxed Commodities

There are primarily two separate, but related, complications arising from the taxation of multiple commodities. The first involves the problem of the interdependence of demand; the second is concerned with the path dependence of multiple price changes.

Consider first the DMH measure of excess burden. If the demand for commodity X depends, in addition to its own price, on the price of commodity X then the combined excess burden in taxing both commodities would not simply be the sum of the excess burdens of the two taxes computed independently of each other, as the ordinary demand curve for X is shifted by the tax on X and vice versa. On the surface, it seems that this demand interdependence can be easily overcome by adding the two relevant excess burdens after incorporating the effect of such shifts. In actuality, however, a rather serious conceptual difficulty is involved, which is that the manner in which the shirts will occur depends on the sequence (i.e., path) of the two price changes. Intuitively, the path dependence problem can be understood in the context of the reference-point issue discussed earlier in connection with the Hicksian measures. Hence, the extent of the shift in the ordinary demand curve for Y as a result of a tax on X, when a tax on Y has already been introduced, is generally different from that when the tax on Khas not been introduced, because the presence or absence of the tax on Y can give rise to the consumer placing a different value on his income position. It is a similar situation for the shift in the ordinary demand curve for X. Only in the special case where a given income change would induce the same proportionate change in the demand for both goods would such shirts in the ordinary demand curves be path independent.7

In contrast to the DMH measure, the two Hicksian measures are always path independent, by virtue of the unique (albeit different) reference point that underlies each of them. The calculation of the consumer’s required monetary compensation (his compensating variation), for example, to leave him as well-off in the posttax situation as in the pretax situation, involves only his welfare level in the pretax situation as a yardstick; the path of subsequent price changes is, therefore, immaterial in the assessment process. The very derivation of the DMH measure, on the contrary, which requires calculations involving situations with different welfare levels, makes its dependence on the path of price changes inevitable.

As with the case of the single taxed commodity, the extent of the error involved in using the DMH measure in the multiple taxed commodity case, notwithstanding its path dependence problem, is related to the income tax elasticities of the various commodities concerned. The smaller the variations among these income elasticities, the closer the DMH measure approximates the Hicksian measures.

Taxation and Equity

Howell H. Zee

  • What are the different concepts of equity, and how do they translate into different principles of taxation?

  • What are the alternative measures of income inequality and their implications for tax equity?

  • What are the alternative theories of distributivejustice and their implications for tax equity?

In formulating tax policy, the policymaker usually cannot avoid undertaking an evaluation, either explicitly or implicitly, of both the efficiency and equity implications of alternative tax measures, even though he may choose to assign unequal weights to them in the evaluation process. The concept and measurement of efficiency have been addressed in the previous section. The present section considers the equity aspects of taxation. The theory of optimal income taxation, which conveniently brings together the policymaker’s efficiency and equity objectives, is discussed in Chapter IV.

Broadly speaking, equity means fairness. But any notion of fairness necessarily involves value judgment. A full treatment of the ethical foundations of alternative notions of fairness is beyond the scope of this Handbook. Instead, the emphasis here is placed on the operational significance, rather than on philosophical underpinnings, of a few important aspects of equity considerations in formulating tax policy.

Basic Concepts and Principles8

Equity issues in taxation are generally examined under the two complementary rubrics of horizontal equity and vertical equity, the former calls for the equal tax treatment of equal individuals, while the latter calls for the unequal tax treatment of unequal individuals. While certainly appealing as general conceptual premises, these two equity concepts are of limited practical value unless and until (a) the basis for measuring equality (and inequality) among individuals is defined; (b) the meaning of equal (and unequal) tax treatment is specified; and (c) implementable tax principles to guide policy are derived. Unfortunately, none of these problems has an easy solution.

Defining equality among individuals

Consider first the problem of defining equality among individuals. This could be done either subjectively, such as in terms of individual welfare (commonly referred to as utility), which in turn is presumably dependent on a set of attributes deemed important to the individual concerned; or objectively, such as in terms of the individual’s measurable income. Two individuals are then regarded as equal if they have the same level of utility using the former basis, or the same level of income using the latter basis.9 The use of the subjective basis would clearly pose difficult measurement problems; while that of the objective basis is also not without ambiguity, since income is not the only available yardstick by which equality can be measured. Why not total wealth, for example, or consumption, or some combination of all three?

Even if income is the selected yardstick, some fundamental issues remain to be resolved. Should income be measured with reference to the initial state or the end state? The initial-state criterion is associated with the endowment (or entitlement) theory of social justice, of which a well-known modern version is that of Nozick’s (1974). According to this theory, an unequal distribution of income at any given time between two individuals may well arise from a difference in their initial endowments (e.g., innate productivity), to which both are equally entitled, and a subsequent just process (e.g., the market mechanism), to which both have equal access. In this case, the two individuals should effectively be treated as equals (i.e., no redistribution is called for). In contrast, the end-state criterion, to which both the traditional welfare economics and the celebrated contractual theory of social justice of Rawls (1971) (see below) adhere, is, as argued by Nozick, a historical and overlooks the process by which the end state is arrived at. While Nozick’s interpretation of the traditional welfare economics is open to question, his fundamental point nevertheless has important implications for tax policy: if one views the initial endowments of individuals as just, and the free market is a just process through which production and exchange are carried out, then the redistributive role of taxation would simply disappear.

Assuming that the more traditional end-state criterion is to be used, one is still left with the problem of determining its appropriate time dimension. Should income be measured at a given slice of time, say, annually, or intertemporally, say, over the individual’s lifetime, or even intergenerationally, when different generations are linked by bequests? Equity implications of many tax policies are quite different depending on one’s chosen perspective regarding the above issues.

Specifying equality in tax treatment

As with defining equality among individuals, equality in tax treatment can also be specified in a number of ways. The most general specification would be in terms of equality of net sacrifice in individual utilities as a result of the tax, that is, gross sacrifice less benefits received from public expenditures financed by tax revenue. This specification requires not only an interpersonal comparison of utilities, but also a method for measuring the benefits of public expenditures, which, in the presence of externalities or the free-rider problem or both, is known to be difficult if not impossible.

Even if a much narrower specification is used, such as one based entirely on readily measurable nominal tax payments, there are still various possible choices of the measurement basis. For example, should equality in tax treatment be measured in absolute amounts or in relative (e.g., to income) terms? And if the relative basis is chosen, should an average or marginal rate be used? Equity evaluation cannot proceed until a decision on these matters has been made.

Tax principles

There are two common, but fundamentally different, tax principles by which the equity of a tax system can be examined. The first is the benefit principle, which states that individuals should be taxed according to the benefits each would receive from expenditure programs to be financed by tax revenue. This principle is consistent with both horizontal and vertical equities, since individuals receiving the same (different) benefits will be identically (differentially) taxed. It also implies, at the margin, that no individual would bear any net sacrifice in utilities from taxation.

Apart from the obvious difficulty, as noted earlier, in measuring the benefits of public expenditures, the application of the benefit principle ties tax policy exclusively to expenditure policy. While under certain circumstances it may serve as a guide for identifying equitable sources of financing for some specifically targeted expenditure programs (such as in designing user fees), the benefit principle is of limited relevance in practice when equity aspects of tax policy must frequently be addressed on their own.

The second tax principle is the ability-to-pay principle, which is an alternative to the benefit principle and states that individuals should be taxed according to their abilities to bear the tax burden. Clearly, this principle is also consistent with both horizontal and vertical equities, and, at the same time, it severs the tie between tax and expenditure policies. Its practicality, however, depends on making the concept of ability to pay operative.

A reasonable indicator of ability to pay is certainly income, although other indicators, in particular wealth, could be as compelling. If income is chosen, this principle is usually invoked to support a progressive income tax on grounds of vertical equity, although the idea of progressivity is again subject to the kind of alternative interpretations noted above (absolute versus relative and average versus marginal).

Equity as Redistribution

A possible way to give concreteness to the meaning of equity is to interpret it only in the context of redistribution (of income, wealth, and/or other variables of interest). Hence, a tax is equitable (inequitable) if the degree of inequality in the distribution of a relevant variable in the posttax situation is less (more) than that in the pretax situation. Furthermore, such an approach lends itself directly to an evaluation of relative degrees of equity in alternative taxes.

To give practical content to the above interpretation of equity, an index that measures the degree of inequality is required.10 Two such indices are discussed below: the widely used Gini coefficient, which is ostensibly positive (or descriptive), but which can be shown to make use of an implicit set of weights on different income levels in its construction, and the more recent Atkinson index (1983), which is explicitly normative (ox prescriptive). The normative nature of the Atkinson index is particularly important because it can easily be interpreted in ways that would encompass a broad spectrum of theories of distributive justice.

Gini coefficient

Formally, the Gini coefficient, G, of a given distribution of income is computed as half of the arithmetic average of the absolute differences between all pairs of income levels in the distribution. It is best understood in terms of the distribution’s Lorenz curve (Figure II.3), which shows the relationship between the percentage of income (vertical axis) and the percentage of individuals (horizontal axis). If the distribution of income is completely equal among individuals, the Lorenz curve would coincide with the diagonal line 00’. The Gini coefficient is simply the ratio of the area above the Lorenz curve (area A) to that below the diagonal line 00’( sum of areas A and B). Its value is therefore bounded between zero (complete equality) and unity (complete inequality, i.e., the entire income accrues to one individual).

Figure II.3.

Algebraically, the Gini coefficient can be stated as


where n is the number of individuals, y1 is the income level of individual i, with y1y2 ≥.... ≥yn, and μ is the average income. equation (6) makes it clear that the Gini coefficient involves assigning weights to the different income levels based on their rank order, that is, the highest income level (y1) has a weight of unity, while the lowest income level yn has a weight of n.

To be consistent and meaningful, any inequality index must possess the fundamental property (the so called Dalton transfer principle) that, for a given total income, a redistribution of income from a richer to a poorer individual must reduce its measure of inequality (and vice versa). The Gini coefficient has this property, as can be easily verified from equation (6), or deduced from Figure II.3. A redistribution from the rich to the poor would raise the Lorenz curve toward the diagonal line 00’ and the Gini coefficient would accordingly be reduced.

There is, however, a conceptual difficulty in using the Gini coefficient. If two different income distributions have Lorenz curves that cross each other, so that their relative degrees of inequality vary across income ranges, their computed Gini coefficients would be problematic for comparing the relative inequalities between the two distributions over their entire income ranges as a whole, since the rank order of the numerical values of the coefficient for the different distributions is an artifact of the particular (and arbitrary) pattern of weights, noted above, in the coefficient’s computation formula. This difficulty is overcome by the Atkinson index through the use of an explicit normative parameter.

Atkinson index

The Atkinson index, A, is given by


where ye is the “equally distributed equivalent income,” or the amount of income, if distributed equally, that would produce the same level of “social welfare” as the actual distribution. It is given by


where ε ≤ 1 and whose value represents the policy-makers’ explicit value judgment about how inequality impacts on social welfare.11 The significance of the parameter e can be appreciated intuitively by noting the following. If yt = μ for all/in equation (8), that is, if there is complete equality in income distribution, then ye = μ regardless of the value for e. In this case, by equation (7), A = 0, that is, the index indicates that there is no inequality as expected. However, even if a single individual receives all the income, A would still be zero if ε = 1; that is, irrespective of the underlying actual distribution, the index would show “no inequality” because the policymaker does not care about how income is distributed. Putting it differently, redistribution in this case would have no impact on social welfare. As the value of e (which could be negative) is lowered, the social welfare impact of any redistribution from the rich to the poor will be increasingly significant for any existing unequal income distribution. A direct implication of the above is that the Atkinson index satisfies the Dalton transfer principle for all allowable values of ΅ except when it equals unity—a limiting case that corresponds precisely to a particular theory of distributive justice (see below).

Strictly speaking, then, the Atkinson index measures not the degree of inequality per se, but rather the social welfare loss from inequality. The main advantage it enjoys over an alternative inequality measure such as the Gini coefficient is that, if the Atkinson index of one distribution is found to be higher than that of another for all values of ε, then the Lorenz curve of the former would lie entirely below that of the latter (and vice versa), in which case the Gini coefficient would yield an identical rank order.12 The case of the intersecting Lorenz curves would be detected by one or more reversals in the rank order of the Atkinson index for some value(s) of e. In this case, the relative inequalities between the two distributions will depend on the chosen value of ΅ which, as stated earlier, represents an explicit value judgment on the part of the policy-maker.13

Distributive Justice

In the traditional welfare economics approach, distributive justice is examined through the conceptual construct of a social welfare function— a function showing the relationship between individual welfare (or utilities) and welfare for the society as a whole. If individual i’s utility, Ut, depends on his income yt, that is, Ut = Ut(yt), then the social welfare function is simply a formula which combines all the Ut’S into an index for social welfare, W:


Differences among alternative theories of distributive justice can then be sought in the different formulae used in constructing the social welfare index W. Three important benchmark theories of distributive justice are discussed below and illustrated in the three panels of Figure II.4 for the simple case of a two-individual world.

Figure II.4.
Figure II.4.

Three Benchmark Theories of Distributive Justice


The utilitarian theory states that society’s welfare is simply the sum of individual utilities:


Equation (10) implies that there is a strict one-to-one tradeoff between the utilities of two individuals for a given level of social welfare, that is, the distribution of utilities between them is totally inconsequential. This case is depicted graphically in panel (a) of Figure II.4 by an iso-welfare contour— a contour that traces out all the combinations of U1 and U2 that would give rise to a given level of social welfare W* As illustrated, under utilitarianism, the iso-welfare contour is a straight line with a negative slope of unity. Hence, social welfare is the same regardless of whether W* is allocated entirely to individual 1 (point A), entirely to individual 2 (point B), or equally between them (point c).


In contrast to the utilitarian theory, the Nash theory of distributive justice gives weight to the underlying distribution of individual utilities in the form of


Equation (11) implies that, in attaining a given level of social welfare, the trade-off between the utilities of two individuals is not a one-to-one relationship, that is, their relative utilities matter. The iso-welfare contour under Nash is depicted graphically in panel (b) of Figure II.4. It has a slope of negative unity only at the 45-degree line, along which individual utilities are equal. As one moves away from the 45-degree line in either direction, the slope of the contour steepens with respect to the axis of the poorer individual, that is, in computing social welfare, the equivalent worth of the utility of the poorer individual, in terms of that of the richer individual, increases as one deviates further from equality.


The Rawlsian theory of social justice goes beyond Nash’s in attaching importance to the underlying distribution of utilities. In fact, it states that society’s welfare is simply represented by the individual who has the least utility:

W=minimum of[U1, U2].(12)

Because Rawls equates social welfare with the welfare of the least well-off, this theory is strongly egalitarian; that is, no amount of increase in the utility of the richer individu can offset a decrease in that of the poorer individual in a taining any given level of social welfare. This is depicted panel (c) of Figure II.4, where the slope of the iso-welfare contour is vertical with respect to the axis of the poorer i dividual in either direction away from the 45-degree line. As social welfare cannot be increased unless the welfare the least well-off is increased, the Rawlsian theory is commonly referred to as the max-min theory of distributive justice.14

A synthesis

Clearly, the utilitarian and Rawlsian theories represent two limiting cases of distributive justice: the former assign no weight to inequality in distribution, the latter views equal distribution as the all-important goal. The Nash the ory lies somewhere in between. The following is a social welfare function that could encompass the entire spectrui of distributive justice—from utilitarian to Rawlsian—by varying a single normative parameter:


with ε ≤ 1. equation (13) reduces to equation (10)—the utilitarian case—with ε = 1, and to Equation (12)—the Rawlsian case—with e approaching -oo. Letting e approac zero yields the Nash case.15

A comparison between equations (8) and (13) reveals that the latter is essentially the same formula used to calculate ye in the Atkinson index of inequality, except that utilities, rather than incomes, of individuals appear in the social welfare formula. If the utility functions of all indivi uals are the same, equal utility distribution would imply equal income distribution; otherwise, this obviously will not hold.

The social welfare formula of equation (13) provides the policymaker with a concrete way of integrating equity co cerns into tax analyses, and, by having to choose a value for ε, forces him to make his notion of distributive justice explicit.

Concepts of Tax Incidence

Russell Krelove

  • What are convenient ways to describe the effects of a tax?

  • What is the process by which the economic incidence of a tax can differ from the statutory incidence?

  • What factors determine the incidence of a tax?

  • How can future taxes be borne in the present?

Tax incidence is the positive analysis of the allocation of the burden of a tax, or of a system of taxes, among economic agents. The goal is to identify who in the economy ultimately bears the burden of a tax or taxes that might initially be levied on a particular economic activity or agent. Underlying this analysis is the assumption that the burden of taxation is described by its effects on the well-being of persons (and not on institutions), in their roles as consumers, producers, and factor suppliers.

The incidence analysis of tax burdens must be built upon a structure of assumptions about how the economy works. In particular, it relies on a theory of behavior and of economic equilibrium. In principle, the analysis is a straightforward two-step procedure. First, the equilibrium both before and after the change in tax policy is calculated. Second, the induced changes in equilibrium magnitudes, in particular the changes in prices and incomes, are used to calculate the changes in well-being of individuals as a consequence of the policy change. As such, the ideal incidence analysis demands data on the universe of tastes and technologies in the economy, an impossible goal. The challenge is to find fruitful simplifications, allowing the analyst to usefully describe the effect of policy while working within the usually strong informational constraints encountered both in developing and in developed economies. This section presents some examples of simple tax incidence analyses, drawing out four simple principles, presented below, that have great power and general applicability.

• In the standard competitive setting, who actually pays the tax (the economic incidence), that is, who ultimately bears the burden, is independent of who is statutorily required to pay the tax (the legal, or nominal incidence). This is one of the major insights of economic analysis applied to taxation: that the actual burden of a tax does not necessarily rest on the agents upon whom the tax is levied. It has the important implication that a tax policy can have unintended consequences, as the burden is “shifted” elsewhere in the economy.

• The agents upon whom the tax is levied can shed some part of the burden of the tax only by altering their behavior in markets. The degree to which the tax can be “shifted” to others depends on the flexibility to alter behavior. In economics, such flexibility is usually measured by means of elasticities. The second principle is that economic incidence depends on elasticities, of demand, supply, and substitution. Generally, those individuals least able to alter their behavior in response to a tax change will bear a greater portion of the burden of the tax.

• It may take time for individuals to adjust behavior, as previously entered into commitments diminish or expire with time. Hence, long-run elasticities can differ from short-run elasticities, so that the long-run incidence of a tax can be different from the short-run incidence.

• Future tax liabilities on the return to a long-lived asset can have consequences in the present, as the future tax liability becomes incorporated into the price of the asset.

While incidence analysis is positive, it has a distinctly normative motivation. The purpose of incidence analysis is to help design good policy. Rational choice among available tax options to meet, inter alia, equity precepts requires the best available knowledge concerning which persons or classes of persons will ultimately bear the burden of the tax. The theory of incidence is thus an important and necessary step in tax policy recommendations.

Describing the Incidence of a Tax

In principle, one would like to calculate what happens to every individual in the economy as a result of the imposition of a tax. Since this is impossible, incidence analysis simplifies by focusing on the effect on certain clearly identifiable groups in the economy. A variety of distinctions have been employed. One useful categorization—the budget incidence approach—describes the distribution of the effect according to the personal distribution of income, where the incidence is measured with respect to the position of individuals at different points in the income distribution. In this classification, taxes are described as being regressive or progressive as the burden tends to fall more heavily on lower income or higher income groups, respectively, and proportional when the pattern of incidence is uniform across income groups. Second classification—the partial equilibrium approach—involves a similarity of roles in the product market: the tax can be borne by producers, through a reduction in profit income; it can be borne by suppliers of factors to producers in this industry, through a reduction in their incomes; and it can be borne by consumers, through a reduction in consumers’ surplus. In a third classification—general equilibrium approach—the effect of a tax is distributed among the main factors of production, the historically most important categories of factors being labor and capital. Other classifications include the regional distribution of the burden and the intertemporal distribution of the burden across generations. The partial equilibrium approach is adopted in this section, while the budget incidence and the general equilibrium approaches are developed in a subsequent section.

Incidence of an Excise Tax in One Market

In this section, we analyze the effect of an excise tax imposed on transactions in a commodity to allocate the burden of the tax among consumers, producers, and factor suppliers. As mentioned previously, conclusions about the distribution of tax burdens are based on a foundation of assumptions about how the economy works. Assume that participants in the market for the taxed commodity act competitively, so that equilibrium prices and quantities are determined at the intersection of market demand and supply curves which, as usual, are graphical descriptions of competitive, maximizing, demand and supply behavior. Also, assume that repercussions on other markets from the imposition of the tax on the market under consideration are of second order magnitude and as such, can be ignored in the incidence calculations; that is, the analysis is partial equilibrium in nature.

The effect of the imposition of an excise tax on a competitive market16

Consider the market for some good, called good X. This market is perfectly competitive, with behavior on the two sides of the market summarized by market demand and market supply curves. The initial equilibrium is at a price po, and industry quantity Qo. At this equilibrium, if the demand curve is negatively sloped, there is some consumers’ surplus generated, which is represented geometrically by the area under the demand curve and above the price line. Similarly, if the market supply curve is positively sloped, the initial equilibrium generates some producers’ surplus, represented geometrically by the area above the supply curve and below the price line. The market supply curve may have a positive slope for a number of reasons, and the recipient of the producers’ surplus depends on the factor generating the finite elasticity. If supply price rises with quantity because of the presence of a fixed factor, the producers’ surplus represents the return to this fixed factor. Alternatively, if supply price rises with quantity because other factors must be paid a higher return to be attracted away from employment in other industries, then producers’ surplus is a measure of the inframarginal rents to this factor generated in this market.

Now, if a tax is imposed on the consumption of commodity X, a wedge is placed between the prices faced by consumers and producers. Consumers care only what must come out of their pocket to purchase the good; this is the consumer price, denoted q, that determines consumer behavior. Producer supply behavior, however, is determined by the portion of the amount paid by consumers that suppliers can keep; this is denoted p, the producer price of X. The difference, of course, is the amount of the tax, the share of the price taken by the government. The tax induces a new equilibrium in this market, with lower equilibrium quantity transacted, written Q1. Consumers now pay price q1, higher than the initial price po, and suppliers receive pi, less than the original price po. Both producers’ surplus and consumers’ surplus have decreased as a result of the tax: the fall in consumers’ surplus is approximately equal to dq.Q1, where dq = q1 - p0 is the change in consumer price, and the fall in producers’ surplus is approximately equal to dp.Q1, where dp = p0 - p1 is the absolute value of the change in producer price. Note that the sum of the lost consumers’ surplus and producers’ surplus is dqQ1 + dpQ1 = (q1 - p1)Q1, which is just equal to the tax revenue collected, since q1 - p1, which measures the wedge between consumer and producer prices, is just equal to the tax per unit.

If consumers are paying a higher price after the imposition of the tax and if producers are receiving a lower price, then both consumers’ surplus and producers’ surplus fall; that is, both producers and consumers pay some portion of the tax. On the supply side, the incidence of the tax is on the claimant of the producers’ surplus, either the owners of the fixed factor, or the suppliers of the factor whose factor payment falls as demand for that factor falls as output falls in this industry.

Incidence is independent of the taxed side of the market

The tax places a wedge between the consumer and producer prices of the product. It is these prices that determine demand and supply behavior, respectively, and thus the equilibrium quantity in the market. What is determining is the magnitude of the wedge itself and not how the wedge is generated, whether by placing the legal requirement to remit the tax on consumers or on producers. Since the equilibrium outcome in the market is independent of the legal incidence of the tax, the economic incidence is likewise independent. It follows that levying the tax assessment on consumers or producers, or dividing the tax assessment between them in any proportion, has no effect on the incidence of the tax.

Incidence depends on elasticities of supply and demand

It can be shown that, to a first order approximation, the share of the excise tax borne by demanders, measured by the fall in consumers’ surplus, is given by the expression eS/(eD + eS), where eS is the elasticity of the supply curve, and eD is the (positive) elasticity of demand. That is, economic incidence depends on elasticities of supply and demand. This expression indicates that when consumers cannot easily adjust their behavior in response to the tax, that is, when eD is close to zero, demanders tend to bear the greater proportion of the tax. When demand is perfectly inelastic (eD is equal to zero), consumers bear all of the tax. Similarly, when suppliers cannot easily adjust their behavior, that is, eS is close to zero, consumers pay only a small portion of the tax. When supply is perfectly inelastic (eS is equal to zero), producers bear all of the tax. Thus, the burden of the tax tends to fall on lowelasticity agents in the market, those who cannot easily adjust their behavior in response to the tax. The greater buyers’ abilities to substitute other commodities for the taxed commodity, the greater their ability to shift taxes. Likewise, if producers can easily leave an industry where taxes are being levied, the supply curve is elastic and the tax tends to be borne by consumers. For if sellers were forced to bear the tax, they would earn a sub-normal rate of return leading them to cease production.

To measure the incidence effects of the tax on consumers and producers, data are required on the elasticities of supply and demand.

Applications and Extensions

Incidence of a subsidy

It is useful to consider a subsidy on purchases of a commodity as equivalent to a tax, levied at a negative rate. As such, the previous analysis applies. Thus, it is irrelevant whether the subsidy is paid to producers or to consumers. Further, those who actually receive the subsidy (pay the negative tax) are not necessarily the ultimate beneficiaries of the subsidy program. The benefit of the subsidy is distributed among consumers and producers according to the elasticities of supply and demand, with the consumers’ share given by eS/(eD + eS).

Incidence of a tax on labor

The principles of incidence derived above apply to all taxes levied on competitive markets, including factor markets. Consider for example the imposition of a payroll tax in a labor market. Then, as before, the incidence of this tax is independent of the distribution among employers and workers of the legal obligation to pay the tax. The incidence depends on the elasticities of supply and demand. If, as is frequently claimed, the supply of labor is relatively inelastic, most of the burden of the tax falls on workers, regardless of the legal imposition of the tax.

If leisure is a normal good for workers, then income and substitution effects on labor supply of a change in price are offsetting, and it is possible under these circumstances that the labor supply curve bends backwards. Then if the initial equilibrium lies in the range where labor supply is negatively sloped, the imposition of a tax on this market can be more than 100 percent borne by labor—that is, the wage falls by more than the amount of the tax. This occurs because the decrease in wages induces a positive labor supply response, which further drives down the wage. Since workers in this case bear more than all the tax, the demanders of labor, that is employers, must actually benefit from the imposition of the tax on labor.

Tax capitalization—future taxes can be borne in the present

Future taxes levied on durable assets or on their return, or future taxes that are shifted onto durable assets, can be borne in the present, through their effect on current asset prices. This outcome is referred to as tax capitalization. The most obvious example arises with respect to a tax levied on the rent of land, which, applying a previously derived principle, is borne by land, since the supply is fixed. Asset-market equilibrium then requires that the price of land fall to equate the return to holding land with the returns from other assets.

Because of tax capitalization, the owner of a durable asset at the time of the unexpected change in the tax rate would bear the full burden of the whole stream of future payments. A purchaser who came along later would bear none of that burden because he would have obtained the property for an amount less than he would have had to pay before the tax increase. Similarly, the removal of a tax on a durable asset benefits the current owner, who may differ from the owner at the time the tax was imposed, the person who bore the burden of the tax in the first place.

More generally, to the extent that a tax on a durable asset cannot be shifted, or to the extent that a tax is shifted to a durable asset, the burden of present and future taxes is borne by the owner at the time the tax is levied.

As a corollary of tax capitalization, some of the effects of a tax may be felt even before the tax is imposed. Such effects are commonly labeled “announcement effects.” When an announcement is made concerning the future tax treatment of an asset, it has an immediate impact on the value of the asset, through its impact on the present value of the return to holding that asset. In this case, holders of the asset at the time the announcement is made will bear part of the tax burden.

Transition incidence

In most industries, a distinction can usefully be made between the short run and the long run. In the short run, many things are fixed that in the long run can vary. While capital presently being used in some industry cannot easily be converted for use to produce other goods, in the longer run, new investment can be diverted elsewhere, while the capital presently employed depreciates and is not replaced. Thus, in the long run, the supply elasticity is much higher than in the short run. A tax on the return to capital in this industry will then be borne by owners of capital until that capital wears out. But in the longer run, new investment does not occur, output falls, and output price rises, so as to generate a rate of return to capital in this industry equivalent to the return in other industries. During the transition, the tax is borne by capital. This is the transition incidence of the tax. In the long run, however, when the supply of capital is elastic, the tax is borne by other factors and by consumers.

If there is free entry of capital into an industry in the long run, supranormal profits in that industry cannot persist. Then, since a subsidy can be considered a negative tax, preferential tax treatment of an industry can benefit capital owners in that industry during the transition, since they will earn above normal profit. This advantage will be competed away in the long run, as the above normal profit attracts new investment to the industry. The advantage during the transition, however, can be substantial enough to make it worthwhile for producers in the industry to lobby for the preferential treatment.

Similar transition incidence effects arise in a variety of economic circumstances involving the longer-term nature of some commitments, including human capital investments.17

General Equilibrium Incidence of Taxes

Russell Krelove

  • Why is it important in incidence analysis to consider the general equilibrium interactions?

  • What are the types of incidence results possible in tractable models that allow for interactions between markets? What are the strengths and limitations of the approach?

  • What are the types of results possible from judgmental empirical studies and computable general equilibrium analyses of tax incidence, and what are the strengths and weaknesses of these approaches?

For a tax on a commodity that will induce significant flows of resources between markets, analyzing incidence by focusing on just one market (i.e., engaging in partial equilibrium analysis, as in the previous section) can be misleading, both qualitatively and quantitatively. Conversely, the industry that is being analyzed can be affected by a change in the tax treatment in other industries. Furthermore, it is often not appropriate to focus on one market when considering taxes that apply across many markets, for example, broad-based sales taxes or factor taxes, since many prices will change in response to a change in the tax. What is necessary in these cases is to consider the interactions, that is, the equilibrating price changes in all markets, and the consequent change in the distribution of wellbeing. Price changes for both inputs and outputs for every market should be considered to arrive at an accurate assessment of incidence. For example, a tax on wheat which increases the demand for maize will increase the price of maize, which will feed back into the demand for wheat. On the supply side, if production of wheat falls, resources are released and if they are to be re-employed, must be absorbed into the production of other commodities, including maize. If the quantities of resources released are large, then the factor prices will change to induce other industries to absorb the surplus. These price changes will affect the well-being of owners of these factors. In addition, factor price changes imply cost changes for industries using those factors, so that competition will lead to changes in output prices. These price changes will affect the well-being of purchasers of commodities. Ripple effects involving adjustments of quantities of inputs and outputs across many markets will result in associated equilibrating price changes. Thus the change in the tax on wheat can induce widespread price changes, and an accurate incidence assessment must account for the effect of the totality of these changes on well-being.

Focusing on the effects of a tax in just the market where it is imposed may be reasonable when considering a tax on an activity that is “small” in relation to the economy as a whole. Under these circumstances, partial equilibrium analysis, a straightforward application of supply and demand, focusing on incidence on producers and consumers of that commodity, can provide considerable insight. Whenever the interactions are significant, however, a general equilibrium approach is necessary. This is especially the case with regard to taxes on the use of factors in some industries, for example, a tax on the income from capital used in the corporate sector, or a tax that applies to capital used in the agricultural sector only, or applies only to housing capital, or a tax levied on labor employed in the formal sector, with informal sector labor untaxed. In these and in other cases, a partial equilibrium analysis can be misleading, both quantitatively and qualitatively.

The purpose of this section is to provide an outline of the static general equilibrium analysis of taxation, roughly following the historical development of the topic. The focus lies on the analysis of taxes on factors; since factors, at the level of aggregation usually employed, are used across many markets, the estimation of changes in factor prices requires an essentially general equilibrium analysis. The next section outlines incidence results in the simplest possible model that can be used to analyze many important taxes, including a partial factor tax, that is, one that taxes the income of a factor only in selected sectors. Although the partial equilibrium results need to be modified when interactions are important, two important results from that analysis persist: that economic incidence is independent of the statutory incidence of the tax and that economic incidence depends on elasticities of demand of supply, and also of commodity and factor substitution. Extensions and Limitations of the model are then considered. Subsequent sections examine two other empirical approaches to incidence analysis, judgmental studies of the burden distribution of taxes, which have tended to show that in developed countries the overall tax system is roughly proportional; and large scale computer models that solve for the general equilibrium of a stylized representation of the economy. These studies attempt to explicitly model the interconnections among markets, overcoming the limitations of the implicit modeling of the judgmental studies.

An Important Example: Incidence Analysis in a Simple Competitive General Equilibrium Model

Model structure

In principle, the method of general equilibrium incidence analysis is straightforward: the general equilibrium of the economy is calculated first at the status quo, and again after the change in tax regime. The positions of all individuals in the two equilibria are then compared to determine the incidence of the tax. Practical incidence analysis involves making fruitful simplifications. One simplification is to aggregate so as to restrict the number of markets and the number of types of individuals to be considered. The simplest model has two consumption goods, produced with just two factors, capital and labor, that share the total income generated in the economy. Thus, there are four markets. The economy’s fixed capital and labor endowments can be allocated to production of either good. The demand side of the economy—for goods—is treated as operating as if there were a single consumer. Because of this assumption, incidence effects resulting from differences in tastes among consumers cannot arise, so the focus is on the functional distribution of income, that is, the distribution of income between the owners of the two factors. Since this is general equilibrium, the use to which the tax revenue is put must be specified; the usual treatment is that the revenue is returned in a nondistortionary manner to the household sector.18

Possible taxes

A variety of taxes can be analyzed in this context. A general sales tax involves taxation of purchases of both goods. A general income tax would tax the income of both factors employed in both sectors. An excise tax would tax just purchases of one of the goods. A factor tax would tax income earned by that factor in both sectors. A partial income tax would tax incomes earned by both factors in just one of the sectors. A partial factor tax would tax income of that factor in just one of the sectors.

Tax-equivalence relations

Certain combinations of the taxes listed above are equivalent in their effects to other taxes, or combination thereof. These are mostly straightforward.19 Excise taxes on both goods at the same rate is equivalent to a broad-based sales tax, at the same rate. A broad-based sales tax is equivalent to an income tax, since on the consumer side, income equals consumption expenditure, and because factor supplies are fixed and the sales tax does not directly alter relative goods prices. Obviously, partial factor taxes on use of a factor in both industries at equal rates is equivalent to a factor tax at the same rate. A partial factor tax on both inputs in one industry is equivalent to a partial income tax in that sector, which is equivalent to an excise tax in that industry. Factor taxes on both factors at the same rate are equivalent to a general income tax, at the same rate.

Tax incidence results

The most technically complex and interesting incidence question involves a partial factor tax; this is analyzed in the next subsection. The incidence of other taxes are the following:

• A factor tax is not shifted if the supply of the factor is fixed. (In this case, the tax is borne completely by owners of that factor.);

• A general income tax is not shifted if all factor supplies are fixed. The tax is borne by the two factors in proportion to their shares of income;

• A general factor tax is borne by the two factors in proportion to shares of income; and

• An excise tax on one of the goods will in the first instance tend to cause costs and hence the price of that good to rise. As a consequence, demand and production in this industry will decline. As output declines, firms in this industry will release quantities of both inputs of production. These released inputs must be absorbed into the other sector. The functional incidence of the tax depends importantly on the terms under which firms in the untaxed sector are willing to absorb the released inputs. This depends in turn on the ratio of capital to labor being released by the taxed industry relative to the capital-labor ratio in the untaxed industry. For example, if capital and labor are being released in a ratio less than that currently employed in the taxed industry, then the relative price of labor must fall to induce that industry to absorb all of the released labor as well as the capital. The general result is that the price of the factor that is used relatively intensively in the taxed industry, falls. How much the relative price of the factor falls depends on the total quantities of factors released and reabsorbed (determined by the elasticities of demand for the two goods), and the substitutability of capital and labor in production of the goods (the elasticities of substitution in production, which indirectly describe relative elasticities of factor demands by firms).

Incidence of a partial factor tax

The effect of the imposition of a tax on the use of one factor in one industry can usefully be decomposed into two effects, called the output effect and the factor substitution effect. The output effect arises because the price of the good in the taxed sector will tend to rise and quantity fall, thus releasing resources from that sector. The output effect is thus equivalent to the effect of the imposition of an excise tax on this sector. As indicated above, the sign of the output effect depends on relative factor intensities, with the price of the factor used relatively intensively in the taxed sector falling. The magnitude of the effect depends on demand and factor substitution elasticities. The factor substitution effect arises from the partial factor tax in the first instance changing relative factor prices in the taxed industry, making the taxed factor relatively more expensive. Thus, even without a change in output, firms in the taxed sector would wish to substitute the untaxed factor for the taxed factor, releasing the taxed factor and demanding more of the untaxed factor. These changes in factor demands represent a second category of influences determining equilibrium factor prices. This effect always has the effect of lowering the relative price of the taxed factor, as long as some factor substitution is possible. The magnitude of the effect depends on relative factor intensities and the degree of substitutability of factors in production.

Adding the two effects gives the incidence of the tax. If the taxed sector is intensive in the taxed factor, then there is no ambiguity; the relative return to the taxed factor falls. If the taxed sector does not use the taxed factor intensively, the two effects offset and the result is ambiguous, depending on relative factor intensities and elasticities of demand and factor substitution. Thus, any outcome is possible. The value of the analysis is in indicating what information is important in determining the incidence of the tax. For example, the results indicate that only if the taxed sector is relatively intensive in the untaxed factor, can the tax be shifted to that factor.

Two aspects of the analysis should be noted. First, since after-tax factor returns are equalized across sectors by competition after the imposition of the tax, the incidence of the tax falls on factor owners in all industries, not just the taxed industry. Second, it is possible that total returns to owners of the taxed factor can fall by more than the amount of tax revenue raised. In this case, owners of the untaxed factor actually benefit from the imposition of the tax. Conversely, it is possible that the tax is more than 100 percent shifted, that is, net incomes of owners of the taxed factor actually rise in response to the tax. Thus, the introduction of the tax may have an effect opposite of the intended effect.

Extensions and Limitations of the Model

The robustness of the results to model structure

The theoretical results discussed above rely on the assumptions made, and in this section, we investigate how those results are altered when some of the assumptions concerning technology and factor fixity and mobility are relaxed.

The effects of adding additional factors. The model assumes only two factors, capital and labor. Certain sectors of the economy, however, particularly agriculture and real estate, employ not only labor and capital but also a third significant factor, land, which is relatively unimportant in the more highly taxed manufacturing sector.20 This suggests, at the minimum, the introduction of a third, specific factor into the model. Shome (1981) shows that the qualitative properties of many of the two-factor results are preserved when such a third, specific, factor is added. The quantitative results differ, however, because with a third factor, factor substitutions generated by the switching of taxes are more complicated. The functional incidence results now depend on the elasticities of factor substitution among all three factors. It is possible that all mobile factors lose as a result of the imposition of a partial factor tax in the two-factor sector, with the specific factor in the nontaxed sector benefiting from the imposition of the tax.

Factor immobility. The model assumes that capital and labor are equally productive in both sectors, and can costly migrate between sectors whenever factor returns are not equal. While such an assumption is appropriate for some factors, for example, unskilled labor, it is inappropriate for others. If the model is changed to allow for immobility of one of the factors, it is straightforward that a partial factor tax on that factor is borne entirely by owners of the factor in that use. The analysis of the incidence of an excise tax is also altered. As the mobile factor is released from the taxed sector and absorbed in the untaxed sector, the return to the fixed factor in the untaxed sector rises. In this case, the burden of the tax is shared between the mobile factor and the immobile factor in the taxed industry.

Technological uncertainty. The model assumes that all economic decisions are made in the presence of complete certainty regarding tastes, technologies, and prices. Uncertainty, however, pervades all aspects of the economy in developing as well as developed countries. It is a common observation that individuals act to avoid risk so that the presence of uncertainty materially affects behavior. Taxation, by altering the distribution of payoffs from an action, affects the will-ingness of individuals to take on risk (see section on taxation and risk taking). Thus, incidence in an uncertain world would differ from that in an environment of certainty. If the standard two-sector model is altered, for example, by introducing technological uncertainty into one sector, the functional incidence of a variety of taxes would depend on attitudes toward risk.21 To indicate the nature of the results, consider the case of the replacement of a general income tax by an equal yield broad-based sales tax. In a certain world, these taxes are equivalent. In an uncertain world, however, the substitution of taxes makes the more intensive factor in the uncertain industry better off when absolute risk aversion is decreasing. Similarly, with certainty, an excise tax on a good is equivalent in its effects to a partial factor tax on both inputs into that good. With uncertainty and risk aversion, the more intensive factor gains from the replacement of partial factor taxes by an equal rate commodity tax on the uncertain sector.

Endogenously determined aggregate factor supplies. It has been assumed that the aggregate supplies of the two factors, capital and labor, are fixed to the economy Clearly, however, these are endogenous in the long run, determined by labor supply and human capital investment decisions, and saving decisions of households. Feldstein (1974) extended the analysis of the incidence of a tax on capital in a growing economy by assuming that the supply of capital is determined in the long run by the savings behavior of households in the economy. He showed that if saving is depressed by the lower after-tax return on capital, the long-run burden of the tax may be shifted to labor due to the reduced capital-labor ratio in the economy In fact, in a central case, the tax is completely shifted to labor, as the capital stock falls sufficiently to restore the after-tax return to capital to its pretax level.

The functional incidence of the corporate income tax

The incidence of the corporate income tax is among the most researched of tax incidence questions. It is with this tax that the distinction between statutory and economic incidence is most apparent: the company itself remits the tax to the government, but it could be the owners of the firm, its workers, its customers, capital owners in general, or workers in general, or some combination, that actually carry the burden. An important advance in the analysis of the tax was made by Harberger (1962), who enunciated the two-sector model described previously. He divided the entire economy into two sectors—the corporate sector and the noncorporate sector (mainly unincorporated, professional and self-employed businesses, and housing). Both sectors employ capital and labor to produce their output, and factors are mobile between sectors. The corporate income tax is then interpreted as a tax on the return to capital employed in the corporate sector, that is, it is a partial factor tax in the terminology of this chapter.

To determine the incidence of the tax, the model was parameterized to accord roughly with the U.S. economy of the 1950s. Harberger found that for several reasonable sets of demand and factor substitution elasticities, the corporate income tax was not shifted, but was fully borne by the owners of capital. Similar results have been derived for a variety of developed countries.

The two-sector model has also been applied to analyze the incidence of corporate taxation in developing countries. An application of the two-sector general equilibrium model to corporate taxation in India partially reversed previous empirical results for that country by showing that the tax is not completely shifted to labor and consumers, but is borne in part by capital owners.22 The corporate income tax is also an important revenue source in many east Asian economies, providing a share of total tax revenue approximately as large as in several developed countries. Using the best available estimates of elasticities of demand and factor substitution, general equilibrium incidence calculations for these countries have indicated that in two central cases, capital bears almost all or more than all of the tax, depending on the value of the elasticity of substitution in the noncorporate sector.23

Subsequent analysis has addressed a number of problems with Harberger’s approach. Shoven and Whalley (1972) solved numerically for the general equilibrium of a more disaggregated model of the economy than Harberger used, adding more sectors, but found that his incidence result was approximately maintained. Another criticism has brought out the importance of firms’ financial structure for the incidence of the tax. Some have questioned the assumption that the corporate tax was correctly modeled as a tax on the use of capital in the corporate sector. Specifically, since under most tax systems, interest expense is deductible in determining the tax base, only equity financed capital is taxed (see section on corporate income tax). In this case, since the marginal investment can always be financed with debt, the corporate tax does not change the cost of capital, and does not lead to the resource reallocations analyzed by Harberger. Thus, the tax falls solely on corporate rents and is borne by the claimants of those rents rather than by capital owners.

Relatedly, it is worth noting that the incidence of the corporate tax depends on other specific provisions of the tax law. For example, corporate tax codes often allow investment tax credits and other incentives to investment. Some tax reforms, for example, the 1986 corporate tax reform in the United States, have reduced the investment tax credit at the same time that the corporate tax rate was reduced. Because this package of changes has offsetting effects on the taxation of capital, the net effect is that there is no change in the effective tax rate to new investment in the corporate sector, so that the output and factor substitution effects do not arise on account of the tax reform. In this case, the only effect is that the tax burden has decreased on previously invested corporate capital, on account of the reduction in the corporate tax rate. Since previous investments cannot be reversed, owners of this capital at the time the tax becomes apparent are the beneficiaries of the tax reform. This benefit would become capitalized into the value of their ownership claims.

The incidence of preferential tax treatment of investments in targeted industries

By altering the perspective in the analysis of a partial factor tax above, we can gain some insight on the incidence of policies that give preferential treatment to investment in particular industries. Consider the untaxed sector in the model of the incidence of a partial factor tax. It is favored relative to the taxed sector; that is, it is as if investment in this sector is subsidized. Examples would include land, real estate, and household durables, as well as investment in certain favored manufacturing industries. What is the “functional incidence” of this preferential treatment? Clearly, that depends on the magnitudes of output and factor substitution effects. From the analysis above, it can be seen that to the extent that capital owners benefit, capital owners in all industries benefit. Similarly, it is not impossible for labor to benefit from the subsidy to capital.

Open-economy considerations

New considerations arise if the economy under study is open to international trade and international capital movements. First, if the country is small, in that it cannot influence by its choices the world prices of tradeables, including the price of internationally mobile capital, then capital cannot bear any of the burden of a tax on capital, whether levied on all uses or only on some uses of capital. This is because the supply of capital to the economy is perfectly elastic. Second, when a country attracts foreign investment, the home country of the investor may offer a tax credit for taxes paid by its resident firms to host country governments. In this case, host country taxes do not alter the cost of capital at the margin to the firm and have no effect on investment. The tax levied on foreign-controlled companies are effectively paid by residents of the home country, through a transfer from the home to the host treasury, at least up to the limit of creditability. Third, if the country imposing the tax is large, in that it can affect world prices, it has the ability to export part of the burden of domestic taxes by altering through its tax policy the terms of trade in its favor.

Judgmental Studies of the Incidence of the Tax System

The approach

There have been a number of major studies of the distributive impact of the tax system.24 These studies begin with a distribution of annual family income by ranges, and then allocate taxes paid under each of the major taxes to each of these income groups, relying on what seem reasonable assumptions (judgments) regarding the incidence of the taxes. The allocations of tax depend on available data on patterns of the distribution of types of income by income group, in particular the distribution of labor income, components of capital income (for example, dividends and interest income), and transfer income. Data on consumption patterns by income group (obtained, for example, through surveys of consumer expenditure) are also used to allocate tax burdens that are judged to be borne by families as consumers. The effective tax rate of each income group is then determined as the ratio of the taxes deemed paid by that group to the income allocated to that group. Using these calculations, the studies permit a judgment about whether the burden distribution of the tax system is progressive, proportional, or regressive.

Shifting assumptions

The incidence calculations focus on five key taxes: personal income, corporate, sales and excise, property, and payroll. The taxes under each of these are assumed to be paid in some combination by consumers and factor suppliers, based on judgments of demand and supply elasticities and on other factors. The personal income tax is usually treated as paid by income recipients, and is progressive due to increasing average tax rates. Labor income itself is observed to be more or less proportionally distributed throughout income classes, so that a proportional payroll tax is regressive due to the ceiling on contributions (see Chapter IV). A variety of assumptions characterize the treatment of taxes on capital income, with different assumptions leading to different burden distribution estimates. Corporate taxes are regressive if judged to be shifted forward to consumers, on account of the observed declining propensity to consume with income, but progressive if assumed to be paid by recipients of dividends or alternatively by all recipients of capital income, which is heavily concentrated in the upper tail of the income distribution (although it is also an important income source at the bottom of the distribution because of pension income). Intermediate positions are also considered, with the tax split between consumers and capital income recipients. The residential and commercial property tax is progressive if paid by capital recipients, but less so if split among capital recipients and consumers, including consumers of the services of residential capital. Using similar reasoning, sales and excise taxes are regressive if borne by consumers, and progressive if borne by recipients of factor incomes used in production of the taxed good, as well as the pattern of exemptions and incentives.

The proportionality hypothesis

Statistical exercises such as the judgmental studies are useful in giving a broad view of the shape of the tax system. The studies suggest that the total tax burden is close to being proportionally distributed, and definitely less progressive than an analysis of the tax law would suggest. Thus, annually, the tax system by itself changes the distribution of income in the economy to an imperceptible degree, except perhaps at the two extremes of the income distribution. This “proportionality hypothesis” is the consequence of the progressivity of income taxes being offset by regressivity in sales and excise taxes, and payroll taxes.

Limitations of the approach

The strength of the judgmental approach is its detail and the relatively high quality of the data. While studies of this form offer useful insights into the incidence of the tax system, the following three shortcomings should be kept in mind.

Implicit modeling of the working of the economy The results are sensitive to shifting assumptions. Reasonable variations in judgments on incidence of particular taxes can lead to different estimates of the distribution of the burden of the entire tax system, appearing either sharply progressive or regressive.25 For example, since much of the progressivity in these studies arises from the taxation of capital, greater regressivity can be achieved by assuming that a greater share of the taxes levied on capital are shifted.

Lack of general equilibrium interactions. Related to the first point above, judgmental studies lack fully articulated behavioral responses by households. While data on household behavior in the presence of the current tax system is available, such data are unavailable in the absence of the taxes. One cannot correctly judge the impact of the tax without knowing the behavioral responses of the economy’s participants. Nevertheless, the studies for the most part assume that relative producer prices are constant and that there is no behavioral response by households, and calculate tax burdens accordingly.26

Problems in measuring income. In these studies, a hypothetical, or “counterfactual” before-tax position must be specified, to be compared with the observed posttax position. The incidence results are sensitive not only to the shifting assumptions chosen, as indicated above, but also to the hypothetical income position chosen. Several problems arise.27 The most important shortcoming relates to the studies presenting a point-in-time picture of the effect of taxes, a snapshot of incidence for a particular year. Using annual income at a point in time as a measure of the position of a household in the income distribution ignores that there is significant mobility across the income distribution through the life cycle of a household; that is, a given household would show up in different income classes at different times. Under these conditions, ultimate interest should lie in the longer-term tax burden of households, which relates to the whole path of tax burdens over the life cycle.

Lifetime tax incidence is the appropriate concept to examine. This shift in perspective may have a significant effect on the conclusions about the progressivity or regressivity of the tax system. For example, payroll taxes that finance social security measured at a point in time indicate substantial redistribution from the relatively higher-income working population toward the lower-income retired population. However, in lifetime terms, there may be no redistribution, as tax payments during employment are repaid as social security benefits. Similarly, estimates of the incidence of consumption taxes may be greatly altered when a lifetime perspective is adopted. For most countries, consumption as a proportion of income varies much less in life-cycle terms than on annual terms. Then consumption taxes that appear regressive from the annual viewpoint would appear less regressive if measured over the lifetime. Under these circumstances, annual consumption may provide a more accurate proxy for lifetime income than does annual income. Thus, the result of Shome (1986) that the domestic indirect consumption tax system in Bangkok is more progressive with respect to annual consumption than with respect to annual income can be interpreted to mean that the indirect tax system is more progressive when measured relative to lifetime income.

Computable General Equilibrium Models of Tax Incidence

The next innovation, which is still evolving, in the calculation of the distribution of tax burdens consists of constructing and simulating a complete general equilibrium model that reflects the observed structure of the economy.28 This model is then made to respond to the introduction of particular taxes, and the resulting changes in households’ positions are observed. The major advantage relative to the Harberger analysis and related empirical work is the ability of the approach to derive empirical results at a much greater level of disaggregation. The introduction of more than two sectors and factors allows a wider number of interactions to be examined. Similarly, a number of household types can be introduced to more closely match the distribution that prevails in the economy under study. In addition, the approach can yield the exact impact of taxation at finite rates (and not extrapolations of results derived from linearizations and infinitesimally small taxes). For the same reason, the approach allows an estimation of the distribution of the deadweight loss of the tax system in addition to the distribution of the direct tax burden. The advantage of the approach relative to the judgmental studies discussed in the previous section arises from replacing implicit modeling assumptions with explicit assumptions on values of important parameters. That is, judgments about forward or backward shifting for any tax are replaced by a fully specified general equilibrium model through which the full implications of assumptions can be traced.29

Most of the applied work in this area has been for developed countries. Early work focused on the incidence of the corporate income tax, where Harberger’s casual result that capital bears the full burden of the tax was confirmed in a more complex model,30 allowing a greater number of substitutions. Other empirical work has investigated incidence of the entire tax system, incidence in an open economy environment, lifetime tax incidence, capital allocation, and risk. Future developments of numerical general equilibrium analysis, for both developing countries and developed countries, will incorporate more complete modeling of intertemporal substitutions and intergenerational effects, and risk; a more careful modeling of effective tax rates, taking into account the detailed provisions of the tax law; a richer structure of the financial sector, capturing interasset substitutions; greater detail on the consumption side, allowing for more types of household groups; modeling of incomplete markets, unemployment, and other market imperfections; and an expanded scope for sensitivity analysis of the results. Thus, these models capture a wide variety of interactions among different markets. The models, however, still require improvement in their treatment of inter-temporal issues, different market structures, foreign trade, public expenditures, and the detailed provisions of the taxes under study.31

Static Versus Intertemporal Effects of Taxation

Julio Escolano

  • What do we gain from considering a time dimension in the analysis of tax policy?

  • Does the timing of tax burden matter?

  • What are the intertemporal effects of taxes on income?

  • Can tax policy increase the rate of economic growth?

The theory of public finance was developed within a static analytical framework, abstracting from the inter-temporal consequences of government actions. Many issues in the theory of taxation can be successfully analyzed from a static standpoint, either because they are static in nature or because the insights gained carry over to a dynamic framework with only minor modifications. To name only one example, David Ricardo’s analysis on the effect of tariffs on welfare was developed in terms of comparative statics. Still, it remains at the core of the current view on the subject. A static analysis is not necessarily inferior to a dynamic viewpoint.

Nevertheless, some issues in tax policy are intrinsically intertemporal. This is often the case when the problem at hand involves the effects of taxation on interest rates, savings, capital accumulation, or economic growth, among others. In these cases, a naive application of conventional wisdom, based on a static approach, may be misleading. Furthermore, there are cases in which the goal is not only to identify the final consequences of a given policy—which often can be accomplished with the tools of statics—but to assess the temporary effects of such policy and to determine the path of the relevant economic aggregates during the transition between the present and final states of the economy. To tackle those problems, it is necessary to consider explicitly economic interactions that take place over time. Thus, for example, an inefficient tax may initially increase revenue at the expense of a subsequent reduction in savings and investment, causing a slowdown in economic growth and, ultimately, in revenue.

Dynamic considerations have always been an important part of economic analysis and policy design. The development of theories of economic growth32 and general equilibrium33 expanded the scope of available tools and fostered more rigorous and quantifiable evaluations of the dynamic consequences of tax policies. Recent developments in the theory of endogenous growth have further expanded these possibilities. The intertemporal approach emphasizes connections between present and future tax and fiscal measures and between expectations of future events and present behavior of households. These interrelations may be essential to the analysis of tax policies and would go unnoticed under a static analysis. The present section covers a few selected topics in the dynamic analysis of tax policies. Since the dynamic approach currently pervades virtually all areas of the theory of public finance, no attempt at exhaustive coverage is made here. Yet, the issues included here have important tax policy implications by themselves and illustrate the potential of an intertemporal approach.

Timing of Taxes and Ricardian Equivalence

A frequent topic of policy interest is the effectiveness of temporary tax cuts in increasing output and reducing unemployment. According to the traditional static approach, the substitution of tax revenue by government debt would, on the one hand, stimulate the economy by making households feel wealthier. On the other hand, public debt would compete with private investors for loanable funds, driving interest rates upward and crowding out private investment. Although, under the incentive of higher interest rates, households would save more than before, the total amount of domestic savings—that is, private savings less public deficit34— would be lower. Moreover, the decrease in total domestic savings—public and private—would be matched by a corresponding imbalance in the external sector.

When the same policy problem is recast in a dynamic framework, the possible outcomes and underlying forces may be very different. A tax reduction without a corresponding cut in government expenditures means an intertemporal rearrangement in the timing of the tax burden while holding constant its discounted present value. Thus, a current tax cut implies an increase in future taxes with a discounted present value equal to the newly issued debt. The economy’s reaction to this policy will depend on the way households anticipate the higher future tax burden and on the form in which they will be affected by it. During the last 15 years, economist R.J. Barro35 has revived an old theory, first proposed by David Ricardo, called Ricardian equivalence. According to this view, a current tax cut financed by government debt has no real effects and does not change either the present or the future path of the economy. Rational agents, anticipating higher future tax liabilities (needed to service the debt) with a discounted present value equal to the current increase in their wealth induced by the tax cut, will proceed as if the debt and the tax cut had never taken place. They will match the debt issue with an increase in their savings, financed with the tax cut, to face anticipated future taxes. Consequently, interest rates, private investment, consumption, and the balance of payments will remain unchanged.

There is very little doubt that the necessary conditions for Barro’s theory are far too restrictive for this theory to hold in all circumstances. Nevertheless, despite its near certain invalidity as a literal description of the role of public debt, Ricardian equivalence seems to approximate the actual behavior of the economy in many instances.36 Empirical studies are still inconclusive about the theory as a whole, but there is already enough factual evidence to infer that the effect that it predicts is an integral part of the reaction of the economy to increases in public debt and changes in the timing of taxation. The intensity of Ricardian equivalence effects will depend on a number of factors, some of which are mentioned below.

A first factor is the planning horizon of economic agents. According to the life-cycle hypothesis, individuals save during the first part of their life to finance their retirement and dissave during the second part of their life.37 If this is the main motive for private savings, a current tax cut financed by public debt that will be repaid with taxes far into the future does have real effects and Ricardian equivalence breaks down. The policy effectively transfers income from future genera-tions—which will pay the taxes needed to redeem the debt—to current generations. The lifetime income of current generations is increased by the amount of the tax cut. Only a portion of this increase will be saved. Thus, the increase in private savings predicted by Ricardo will not be enough to absorb the issue of debt, which equals the tax cut, and public debt will tend to crowd out private investment. As a result, subsequent generations will inherit a lower stock of capital, and higher debt and interest rates.

In contrast, if there are altruistic intergenerational links and the desire to leave bequests is the main motive for private savings, Ricardian equivalence effects will be stronger. In this case, the relevant economic agent is not only the individual but also includes his progeny. Owing to altruistic intergenerational links, anticipated future tax increases will prompt current savings with the same discounted present value. As a consequence, increased individual savings will sterilize the effects of debt-financed tax cuts, as predicted by the Ricardian equivalence theory.

A second factor is the existence of liquidity constraints. Households are liquidity constrained if they would like to borrow to enjoy a higher level of current consumption at the expense of their future income but, owing to constraints in the credit markets, are unable to do so. If some households are, in fact, liquidity constrained, a tax cut will increase their present consumption. The policy allows them to sidestep the constraint they face in the credit market by spending the tax cut in higher present consumption and paying higher taxes in the future. From the point of view of the liquidity constrained households, the government, when issuing debt to finance the tax cut, is borrowing on their behalf. Thus, a tax cut financed by issuing government debt will have real effects, in opposition to the Ricardian equivalence theory.

Finally, a third factor that makes debt financing non-neutral, in opposition to the Ricardian equivalence, is the existence of distortions created by taxation. Changes in outstanding government debt can be expected to change the timing and level of average and marginal tax rates, thereby increasing or reducing the overall efficiency loss. A concentration of the tax burden in any particular period will increase the inefficiencies created by distortionary taxation. It is known, for example, that under most conditions, intertemporal tax smoothing minimizes the efficiency loss. This is because the efficiency loss grows more than proportionally with the tax rate. A current tax cut financed by future increases in taxes may decrease present efficiency losses at the expense of creating higher inefficiencies in the future, with the effect of increasing the overall efficiency losses in the economy. Thus, the policy under consideration will alter the future path of the economy and Ricardian equivalence will not hold.

Debt and Inflation Financing

Changes in the timing of the “inflation tax” can be subject to a dynamic analysis similar to that used to evaluate the effect of debt financing.38 This analysis would primarily apply to countries where money creation plays an important role in financing the fiscal deficit.

The government may attempt to reduce inflation by switching from inflation to debt financing without reducing the fiscal deficit, that is, by maintaining the current and prospective values of its real expenditures and tax receipts. In this case, the decrease in seignorage financing must correspond to the increase in government debt. This decrease in the growth rate of the money supply, however, is not sustainable. Since the time paths of real tax revenue and expenditure are left unchanged, future debt service will have to be financed by resorting eventually to money creation. In other words, the government is just rearranging the timing of increases in the money supply

Under these conditions, the current contractionary policy will have no effect on the long-run rate of inflation. In fact, due to the anticipation of future increases in the money supply, it is likely that the policy will fail to reduce inflation significantly even in the short run. The initial slowdown in the money supply will possibly be matched by a parallel shift downward in the demand of money—or an increase in its velocity of circulation— leaving current and future inflation rates essentially unchanged. Therefore, a plan to curb inflation, even temporarily, will be unsuccessful unless it comprises a permanent real reduction of the fiscal deficit.

Taxes on Capital Income and Private Savings

The traditional view on the effects of capital income taxation on savings was based, in the 1950s and 1960s, on the Keynesian static model of consumption demand. In the best-known version of this model, individuals save and consume constant fractions of any increase in their after-tax income (constant marginal propensity to consume).39 As a consequence, returns to capital were predominantly treated as rent. That is, the taxation of capital income was not considered to have consequences on the allocation of resources, and the stock of capital could be taken as approximately fixed. Since intertemporal substitution effects were not taken into the analysis, taxation of capital appeared optimal.

This viewpoint came to be increasingly challenged in the 1970s. Feldstein (1978) and Boskin (1978) argued that the tax treatment of capital income had major effects on accumulation and growth. Boskin (1978) and others pursued the issue empirically and showed that savings were not inelastic with respect to the interest rate. It became clear that changes in the after-tax interest rate, prompted by capital income taxation, could have important dynamic effects, and that savings could not be represented as a stable function of the contemporaneous return on capital.40

Recently, many economists have studied the effect of capital income taxation on savings, capital accumulation, and welfare in an intertemporal framework.41 Empirical evidence as well as analytical considerations point to a larger welfare cost of capital taxation than had previously been thought.

One objective of current savings is to increase future consumption. If successive generations are related by altruistic links, and bequeathing is an important motive for saving, the deferral of consumption can extend far into the future. Under these conditions, current savings will depend on the relation between the price of current consumption and a long sequence of prices of possible future consumptions. The relative price between future and present consumption is the amount of consumption that would be attainable on a future date by forgoing one unit of consumption today. Therefore, this relative price between consumption on any given future date and current consumption is the result of compounding the successive interest rates corresponding to the years in between.

A tax on capital returns creates a wedge between the pretax and after-tax return rates lowering the aftertax interest rate. Consequently, after the introduction of a tax on capital income, forgoing one unit of current consumption affords a lower amount of future consumption; that is, future consumption becomes more expensive in terms of present consumption. The tax induced distortion of relative prices becomes larger the farther into the future is the intended consumption that motivates current savings. This is due to the compounded effect of many periods of reduced interest rates. Thus, a tax on capital income discourages long-term saving more than short-term saving.

The short-term supply of capital may be relatively inelastic to changes in the after-tax rate of return, as postulated by static analyses. The supply of capital in future years, however, is indeed increasingly elastic with respect to permanent changes in after-tax returns. This is due to the accumulated effect that period after period of lower savings have on the stock of capital of an economy.42 Since at least part of the growth in productivity is achieved through the introduction of technological changes embodied in new capital goods, high taxes on capital may prompt a slowdown in productivity, hinder economic growth, and ultimately cause a lower level of both savings and consumption.

Taxation, Human Capital Accumulation, and Economic Growth

The classical theory of economic growth was primarily concerned with the accumulation of physical capital. Technological change, human capital accumulation, and other growth-inducing factors, although analyzed, were generally considered beyond the reach of economic policies.43 The new theory of growth, which has been developed in recent years, focuses on those factors that can produce long-term increases in the growth rate of an economy. Much attention has been paid to the study of ways in which the economic environment and government policies affect the rate of human capital accumulation. Although it is still early for conclusive results, these recent studies shed new light on the effect of taxation on the long-term growth prospects of an economy.44

Income taxation affects the accumulation of human capital in many ways. The taxation of capital income reduces the net rate of return on physical capital and makes human capital a relatively more attractive investment. Capital taxation causes savings to fall, thus reducing physical capital over time. As a result, the wage rate will tend to decrease owing to the relative abundance of labor vis-à-vis physical capital. Future lower wages imply a lower return to the current investment in human capital. These two effects operate in opposite directions and therefore, from purely analytical grounds, the consequences of capital income taxation on human capital accumulation are ambiguous.

If the primary input in the accumulation of human capital is time, its main cost will be forgone wages during the time necessary to acquire human capital. This cost may take the form of longer schooling or a higher age when entering the labor market. Thus, the taxation of labor income, by lowering wages, reduces the cost of investing in human capital. It also reduces, however, the future return to current human capital investment, that is, future wages, in the same proportion. In other words, labor taxation lowers both the return and the cost of human capital by the same proportion.

The taxation of labor income also has a negative effect on human capital through general equilibrium effects. A tax on wages will permanently reduce the supply of labor45 and thus, the rate of utilization of human capital. This utilization effect is also produced by capital income taxation through the lower capital-labor ratio and the corresponding decrease in wages that it causes in the long run.

Nevertheless, time is not the only input in human capital accumulation. Physical capital or past investments of society in the form of infrastructure—schools, universities, laboratories—are necessary for the efficient accumulation of human capital. Thus, taxation of capital income, by reducing the available physical capital, can limit the ability to accumulate human capital.

Quantitative and statistical studies tend to confirm the positive role that human capital plays in economic growth.46 They also indicate that the overall effect of taxation of either capital or labor income can substantially hamper human capital accumulation.47 Consequently, from the point of view of development and growth, consumption taxation seems preferable to income taxation. Consumption taxation does not alter the relative price of consumption between different dates, and therefore it is neutral with respect to the intertemporal allocation of resources. Moreover, it encourages the accumulation of human and physical capital by reducing their relative cost—their price in terms of consumption. As a result, it has the potential to increase, relative to other forms of taxation, the long-term stock of productive resources of an economy and its growth rate.

Taxing Consumption/Expenditure Versus Taxing Income

Julio Escolano

  • What is a personal expenditure tax?

  • Is an expenditure tax more efficient than an income tax?

  • What are the equity implications of an expenditure tax?

  • Is an expenditure tax equivalent to a payroll tax?

  • How could an expenditure tax be implemented?

The possibility of a direct tax on personal consumption expenditures has attracted the attention of many economists, at least since John Stuart Mill. Almost always, it has been proposed as an alternative to income taxation or, more specifically, as a substitute for the personal income tax.48 The critical difference between the “expenditure” or “personal cash-flow” tax and the more conventional income tax is that the former exempts that part of personal income which is saved (i.e., invested). Since income is either saved or consumed, the expenditure tax falls on consumption, which is determined by subtraction. Unlike indirect consumption taxes, such as the VAT or sales taxes, the expenditure tax is a personal tax. Therefore, tax liability can be tailored to the economic circumstances of the taxpayer. In particular, a direct tax on personal consumption can be made progressive.

Until now, the expenditure tax has remained in the economists’ drawing board with very few instances of practical implementation. Only India and Sri Lanka actually introduced an expenditure tax around 1960 under the advice of the economist Nicholas Kaldor and abandoned it shortly afterwards. Sri Lanka reintroduced the tax in 1976, but abandoned it once more in 1977. Both countries implemented the expenditure tax as a complement to the personal income tax. More recently, the possibility of adopting an expenditure tax has received attention in the United States,49 the United Kingdom,50 and Sweden.51 The widespread implementation and success of the VAT in many industrial and developing countries during the last decade has had a mixed impact on the perception of the expenditure tax by policymakers and economists. On the one hand, the popularity of the VAT has revived interest in consumption as a base for taxation. On the other hand, the versatility and achievements of indirect consumption taxes raise questions on the need for an additional tax instrument that targets the same macroeconomic aggregate directly. It can be said that the future of direct consumption taxation will hinge on the shortcomings of income taxes as tools for income redistribution, rather than on the relative advantages of consumption as a base for taxation.

Why an Expenditure Tax?

Efficiency and neutrality

Economic efficiency is commonly regarded as one of the main advantages of a consumption tax vis-à-vis an income tax. The difference between the two taxes arises from the “double taxation” to which investment returns are subjected by the income tax. Under a conventional income tax, income is taxed first when it is originally earned. Additionally, if a portion of that income is saved for later consumption, the return on savings will be taxed each year, effectively reducing the interest rate received on savings. Therefore, given any amount of pretax income earmarked for savings, the income tax reduces the return that could be obtained from it in two different ways: (1) through the levy on the original earnings, it diminishes the amount of funds initially available for saving; and (2) through subsequent levies applied on the income from savings when it accrues, the income tax lowers the yield obtained from any initial amount of savings. The first effect would, by itself, reduce the future flow of income in proportion to the tax rate by reducing the amount originally saved. The second effect reduces the future income flow further by lowering the after-tax interest rate.

These two effects reinforce each other when there is a long lag between the original saving decision and the eventual consumption of the proceeds. This is because the combined effect of many periods of lower after-tax interest rates can amount to a substantial “wedge” between the compounded pretax and after-tax rates of return. The effect is particularly relevant because most household saving decisions are made for motives—such as bequests, retirement, eventual medical expenses, etc.—that involve long-term deferral of consumption. For example, if the pretax annual interest rate on savings is 10 percent and the income tax rate is 30 percent, the one-year after-tax return will be 7 percent (30 percent lower than the corresponding pretax return). Under the same assumptions regarding interest and tax rates, however, the 20-year after-tax compounded interest rate is 50 percent lower than the corresponding pretax rate. Summarizing, the income tax reduces the amount of income available to allocate consumption among different dates, and it also penalizes at increasing rates the allocation of consumption to future dates.

Both income and consumption taxes reduce the flow of consumption that can be attained with any given lifetime income,52 thus lowering real income. The consumption tax reduces real income by increasing the price of any given amount of consumption by the extent of the tax liability. The income tax does that by directly taxing away a portion of earnings. Moreover, an income tax alters the relative price of future consumption with respect to present consumption by decreasing the after-tax interest rate. That is, the income tax makes it necessary to forgo more present consumption to obtain any given future consumption. In contrast, a consumption tax is neutral with respect to the intertemporal allocation of consumption because it taxes consumption expenditures independently of their timing.53 In particular, a consumption tax does not create a wedge between the pretax and after-tax interest rates and therefore, deferral of consumption (i.e., saving) is not penalized.

Although all taxes distort prices, thereby prompting a loss in efficiency, the specific distortion which income taxes introduce is generally considered particularly damaging. By penalizing savings and placing an even heavier handicap on long-term saving, income taxation might permanently reduce the amount of funds available for productive investment in an economy. Lower saving and investment rates will, in turn, hamper economic growth. Consumption taxation, on the other hand, can be expected not to have a similar negative effect. First, consumption taxes do not reduce after-tax interest rates and thus, they do not create a disincentive to save. Second, consumption taxes lower the price of investment goods relative to consumption goods. Consequently, whereas the distortions introduced by an income tax are biased against savings and investment, the opposite is true of the distortions introduced by a consumption tax.


Perhaps the most controversial issues concerning the choice of consumption as a base for direct taxation are related to its equity implications. The fundamental question is whether the tax burden should be distributed across individuals according to their ability to pay or according to the degree in which they make use of the output of society. Proponents of the income tax rely on the Haig-Simons definition of income as accretion of power to consume. According to this view, income, which by definition implies capacity to pay, should be the criterion for taxation. In contrast, proponents of the expenditure tax follow Hobbes’ assertion that it is fairer to tax an individual according to what he takes from the common pool (consumption), rather than according to what he contributes to it (income). This view relies on the consideration that factors of production are remunerated in proportion to their marginal productivities. Thus, total income measures the economic value of the resources that constitute the contribution of an individual to society. Higher income indicates a contribution with higher economic value while higher consumption reveals a more intense use of goods and services provided by society. Reaching a verdict on the correct criterion for the distribution of tax burden is perhaps, ultimately, beyond the purview of economics. At most, economic analysis can clarify the implications of different choices.

Neither income nor consumption taxes can accurately target, in practice, their intended bases. The sources of income that can be taxed are not a perfect indicator of the ability to pay. A complete inventory of the potential to contribute should include the use of time and productive resources in leisure and other nonmarket activities. Since these resources could have been employed in remunerated activities, they are part of an individual’s ability to pay. Similarly, direct use of time and resources directly owned by the consumer cannot always be effectively taxed by a consumption tax.

Another problem concerns the treatment of gifts and bequests under an expenditure tax. If they are regarded as consumption of the donor, they should add to the donor’s tax liability. Alternatively, since the mere transfer of property does not reduce the amount of goods and services available, bequests and gifts could be considered exempt from tax implications. The first treatment would be consistent with an individualistic definition of the unit of taxation. The second treatment could be based on the choice of the dynasty as the subject of taxation.

It has often been argued that, from a lifetime perspective, an expenditure tax is equivalent to a payroll tax. Therefore, it is claimed that an expenditure tax would place an unduly heavy burden on wage earners. Nevertheless, this equivalence only holds under very restrictive conditions. These conditions are that there be no initial wealth when the expenditure tax is introduced, that no one be allowed to bequeath wealth in the future, and that neither tax have a progressive rate structure. Under these conditions, the only primary source of lifetime income for an individual is labor, and all income must eventually be spent in consumption. Thus, the discounted present value of expenditures has to be equal to the discounted present value of labor income. Yet, if the existence of an initial stock of wealth is taken into account, an expenditure tax is, in fact, equivalent to a one-time levy on initial wealth combined with a payroll tax. Moreover, when gifts and bequests are taxed as consumption, the initial levy on existing wealth is repeated each time wealth is transferred. Finally, if tax rates are progressive, the discounted present value of tax liabilities will depend on the distribution of consumption across time. If consumption is concentrated in some periods, it will generally create a higher total tax liability than if it is evenly distributed across time. Thus, in the presence of progressivity, the equivalence between consumption and labor taxes—even if they have the same rate structure—will not hold if the time distribution of labor earnings differs from that of consumption expenditures. Therefore, when properly implemented, a consumption tax does not necessarily discriminate between labor and other sources of income.

Implementation of a Personal Consumption Tax

Different possibilities of implementing a direct tax on consumption have been proposed. The three tax models presented below represent proposals which have received attention from economists and policy-makers. The first proposal is the personal expenditure tax, which would be similar to the conventional income tax but would allow a deduction for net deposits placed in qualified savings or investment accounts. The second design allows intertemporal averaging of tax liabilities to target lifetime consumption. The third approach involves a payroll tax coupled with an enterprise cash-flow tax. This approach has a more ambitious objective since it is intended to replace the corporate income tax as well as the personal income tax.

Personal expenditure tax

This tax is also known as personal cash-flow tax. The idea underlying the expenditure tax is to measure consumption by subtracting net savings from income. Essentially, this involves aggregating all cash inflows such as wages, transfers, cash returns on past savings, and any dissaving (e.g., sales of property). From this total are deducted all outlays for the acquisition of qualified assets. Thus, under this method, consumption is measured by cash flow.

The treatment of savings and investment is the central feature that distinguishes this tax from a conventional income tax. Practical implementation requires the definition of qualified personal accounts, which should encompass any savings or investment that is intended to be excluded from the tax base. These accounts could be opened with stock brokers, banks, pension funds, etc. The treatment of these accounts for tax purposes would be conducted on a reverse cash-flow basis.54 That is, any deposits would be tax deductible and any withdrawals would be taxable. The treatment of loans or other forms of credit would follow the same cash-flow principles. The drawing of a loan would be taxable and repayment of principal and interest would be tax deductible. Cash-flow accounting bypasses many practical problems of an accruals-based income tax. Thus, accrual of interest, dividends, and capital gains would not have direct tax implications. They would be considered as operations taking place within the accounts and would not need to be monitored by the tax administration.

Entrepreneurial income and unincorporated enterprises pose problems similar to those encountered under a conventional income tax. Nevertheless, their treatment might also follow the cash-flow method.55 Net contributions to the business during the year would be deducted, whereas any cash received would be included in the tax base (see Chapter IV).

Another problem, shared with the income tax, is the definition of an adequate treatment of consumer durables, such as houses and automobiles. Ideally, a consistent treatment would call for an initial deduction of the amount initially spent in durables and subsequent inclusion in the base of the flow of services obtained from them. Nevertheless, owing to practical and administrative difficulties, a special treatment would probably have to be granted to expenditures in consumer durables. A possible approach is the tax-prepayment method. This means disallowing the deductibility of expenditures in durables, that is, treating them as current consumption. Correspondingly, the ulterior flow of consumption obtained from durables would not be taxed. In particular, if they were sold later, the proceeds of their sale would be exempted from tax.

If the expenditure tax has a progressive rate structure, however, special treatment would have to be accorded to exceptionally large expenditures in household durables. Financing the purchase of some durables, such as a house, usually involves a combination of loans and personal savings. Under an unmitigated cash-flow treatment, both sources would be fully included in the taxable base, which would result in an unusually high tax rate. Two methods could be used to alleviate this problem. The first method allows some form of intertemporal base averaging, such as carry-forward provisions. The second method is to accord also tax-prepayment treatment to the financing sources. Thus, in the case of selected loans, their undertaking would not create a tax liability and their servicing would not be deductible. Similarly, savings earmarked for selected purchases would not be deductible and withdrawals from those accounts would not be taxable.

The “Blueprints” cash-flow tax (BCT)

The proposal for this tax is contained in “Blueprints for Basic Tax Reform”56 under “cash-flow tax.” Its main difference with respect to the previously described expenditure tax is the extensive use that it makes of the tax-prepayment method. In the context of a cash-flow tax, using the tax-prepayment method of accounting for assets of any kind would generally be considered a flaw. Under the tax-prepayment method, the purchase of an asset is not a deductible expense and the subsequent stream of receipts generated by the asset—including returns and sale proceeds—are not taxable. Nevertheless, the BCT turns this inconsistency with cash-flow accounting into a useful feature. By giving individuals a wide latitude to choose between standard cash-flow and tax-prepayment treatment of savings, the BCT allows intertemporal smoothing of tax liabilities.

Since the rate structure of the BCT is progressive, individuals will choose the cash-flow treatment of savings when their consumption expenditures are relatively high. Conversely, when taxable consumption expenditures are comparatively low, taxpayers will choose the tax-prepayment treatment of savings. A key characteristic of the system is that the deferral of tax liabilities can only be attained at a cost. When the taxpayer chooses tax-prepayment treatment of an asset, the tax base is the initial purchasing cost. When the method chosen by the taxpayer is the cash-flow treatment, however, tax liabilities will eventually be assessed on the consumption stream financed with the asset, which includes returns as well as principal. Therefore, the deferral of tax payments carries a cost given by the taxes paid on the yield of the asset. In this way, the base of the BCT is the discounted present value of the taxpayer’s lifetime consumption. The BCT can be thought of as a program that imposes a progressive tax on the amount of wealth that an individual would need to fund his consumption for the rest of his life. By allowing intertemporal averaging of tax liabilities, the BCT is unaffected by differences in the patterns of lifetime earnings and consumption across taxpayers. Given two different time profiles of consumption with the same discounted present value, the BCT will tend to produce similar time profiles of tax payments.

Two-tiered cash-flow tax

This implementation was originally proposed by Hall and Rabushka (1983 and 1985) with a flat rate and has been later defended by Zodrow and McLure (1988) in a version with a progressive rate schedule. The principal feature of this tax is the simplicity of its administration. The system consists of two different taxes: (1) an individual tax on labor earnings that can be made progressive; and (2) a business cash-flow tax similar to an accounts-based VAT, but that allows the deduction of wages. The two-tiered cash-flow tax is meant to replace both the individual and corporate income taxes.

The base of the business tax is value added, calculated on a cash-flow basis, less payments to employees. This tier of the proposal is, therefore, similar to an R-based corporate cash-flow tax.57 Alternatively, it can be seen as an accounts-based VAT with an additional deduction for payments to employees. The base of the other tier, the personal tax, is labor income. Thus, although payments to employees are deducted from the base of the business tax, they are taxed under the personal tax. The combination of these two taxes is, therefore, similar to a tax on consumption, such as a VAT.

Although this version of a consumption tax possesses clear advantages in terms of its simplicity and low administrative costs, its rationale has been undermined by the widespread success of invoice-based VATs. Moreover, the discriminatory treatment it accords to labor income would, most likely, be seen as unfair. Whereas labor income would possibly be taxed at progressive rates, consumption financed by other sources of personal income would have to be taxed through a flat rate.

Taxation and Risk Taking

Russell Krelove

  • Does taxation of the return to a risky investment increase or decrease the amount of investment undertaken?

  • How does the effect of taxation depend on the specific provisions of the tax law, including the provision for loss offsets, the progressivity of the rate structure, and whether the investment or the return to the investment is taxed?

  • Why should private risk bearing be distinguishedfrom social risk bearing?

Profitability is in part compensation for bearing risk, so that a tax on the return from an undertaking taxes in addition the return from risk taking. There has long been a concern that the taxation of capital income leads to a reduction in risk taking. The concern arises from the belief that entrepreneurship is central to the development and growth of the economy, and that entrepreneurship involves risk taking in an essential way. If entrepreneurs are discouraged from undertaking new risky ventures, the growth rate would suffer.

In this section, we examine the effects of tax policy changes on the allocation of savings to risky assets.

• Taxing the return on risky assets can actually increase risk taking, if the tax system shares sufficiently in the risk of an investment as well as in the expected return. In particular, the provision under the tax law of full loss offsets will tend to increase risk taking.

• When loss offsets are partial, taxation may or may not decrease risk taking, depending on the relative strengths of income and substitution effects. Loss offsets are restricted under the tax system when losses from investments are not subsidized, or when losses cannot be completely carried forward at unchanged present value.

• Firms face two types of risk: income and capital. Even when there is effective full loss offset for income risk, tax systems as they are designed imply that government rarely shares completely in capital risk.

• When risky returns are taxed, so that the government is sharing in the risk, tax revenue is uncertain. A distinction should be made between private risk and social risk.

In the following paragraphs, we consider a simple example of investment decisions in conditions of risk, and show how taxation of the return to the investment can increase risk taking. Late in this section, we also consider a number of limitations and extensions of this simple model.

The main message of this section is that taxation of risky returns can materially affect behavior. It follows that tax incidence in an uncertain world will differ from that in an environment of certainty. The effect of the presence of technological uncertainty in the standard two-sector model has been discussed above, in the section on general equilibrium tax incidence. Computable general equilibrium simulation analysis of the effect of taxation on portfolio choice in the United States has been undertaken in Slemrod (1983), and in Galper, Lucke, and Toder (1988). This type of research is at an early stage of development, but the empirical results do indicate that the treatment of risk can make a substantial difference to the estimated effects of taxes.

Proportional Taxation with Full Loss Offset58

Suppose individuals make decisions about whether to invest in an asset based on two characteristics: the expected return on the asset and how risky that return is. Other things being equal, investors prefer assets that are expected to yield high returns. At the same time, investors are assumed to dislike risk; other things being equal, investors prefer safer assets.

Suppose there are two assets. The first yields a perfectly safe return. The second is a risky asset that has a positive expected rate of return greater than that on the safe asset. The investor can control the amount of risk he bears by choosing the amount to be invested in the risky asset. As the proportion increases, the risk borne increases, but the expected return on the portfolio also increases.

Now assume that a proportional tax is levied on the return to capital assets in excess of the risk-free rate.59 Assume also that the tax allows for full loss offset—individuals can deduct all losses from other taxable income.60 The tax lowers the expected rate of return to the risky asset, thus making it appear less attractive, compared to the safe asset. At the same time that the tax lowers the return, however, it lowers its riskiness as well. The government becomes in effect a partner in the investment. If the investment is successful, the government shares in the gain. But because of the loss offset provision, if the investment fails, the government also shares in the loss. That is, the tax lowers the risk borne by the investor. Thus, there are two effects that offset. If the second effect dominates, taxation can make the risky asset more desirable.

Consider the following simple numerical example. In the absence of taxation, an investor would be willing to invest 1 in an asset that has only two possible payoffs per unit invested, either 0 or 2, after deducting opportunity cost of the funds and the cost of the investment. The investor’s ex post wealth is risky, and equal to either 2 or 0. Now introduce a tax at the rate of 50 percent on the return to the asset, with full loss offset. Then by doubling the investment in the risky asset, that is, by investing 2 rather than 1, the investor can attain the same distribution of after-tax returns as in the no-tax situation. For by investing 2, the total return after deducting the cost of the investment and the opportunity cost, is either 4 or 0 before tax, and either 2 or 0 after tax. But this after-tax distribution is identical to what could be attained without taxation of the return. In this example, the tax has induced the individual to double investment in the risky asset.61

Note that in this example, although the amount invested in the risky asset increases, the risk actually borne by the investor, after tax, is the same as in the no-tax situation. That is, private risk bearing has not increased, although total, or social, risk bearing has increased.

The main principle of the example generalizes when the assumptions on which it is based are relaxed: taxation, when it shares in both the losses as well as the gains, lowers both risk and return, so that it is possible to increase risk taking by taxing it.62

Empirical Verification

Empirical verification of the result is difficult for a variety of reasons. First, taxation affects portfolio choices for reasons unrelated to risk taking, the most important being the differential effective tax treatment of different types of assets that also have different risk characteristics. Second, the unambiguous result above is blunted somewhat when the assumptions are relaxed (see below). Third, it is difficult to obtain reliable information on individuals’ actual asset holdings. One reasonably robust empirical result is that higher-income individuals (facing higher tax rates) tend to hold a larger share of their wealth in corporate equity, which is usually considered to be relatively risky.63 This can be interpreted as support for the hypothesis that, when all dimensions are accounted for, taxation in fact increases risk taking.

limitations and Extensions

Wealth effects of taxation

It has been assumed so far that the safe rate of return is not taxed. If it is in addition taxed, then there will be an income effect associated with the taxation on the return. This income effect can be of either sign, depending on how risk taking responds to wealth. If preferences for bearing risk increase with wealth, then the income effect tends to reduce the demand for risk.

Progressive rate structures

When the tax structure is progressive, returns to a successful investment are taxed more heavily than losses are subsidized. There is thus a bias against risk taking. To help reduce the impact of the graduated rate structure, the tax could allow taxpayers to smooth their tax base over time, either through forward or backward averaging of income. This allows the taxpayer to effectively pool risks that are resolved over time, giving the system more of the characteristics of a proportional tax.

Partial loss offsets

Most tax systems do not allow full loss offsets, either because tax on losses does not earn a credit when there is not sufficient other income to set against the loss, or because carry forwards do not accrue interest. Moreover, if the company closes, the value of tax loss carry forwards is eliminated.64 When loss offsets are not total, then the government shares in the risk only by taking part in any gains, while the losses are carried more than proportionately by the investor. Risky activities would tend to be discouraged under these circumstances, but conceptually the effect is ambiguous, as there are conflicting income and substitution effects, as discussed above.

There may be good reasons for limiting loss offsets in the tax system. For example, under a realization income tax, where the taxpayer can control the realization of income, the taxpayer with many risky projects can avoid taxes by realizing just the losses. In this case, appropriate tax policy must balance the restriction of abuses of the provisions with the cost of limiting loss offsets in terms of discouraging risk taking.

Income risk and capital risk

Two types of risks should be distinguished when discussing the extent of loss offsetting in actual tax systems.65 These are income risk and capital risk. Income risk refers to uncertainty regarding future net revenues. It is typically viewed as arising from uncertainty regarding the future price of the firm’s output or the future cost of variable factors of production, for example, for resource inputs. Capital risk, on the other hand, arises from uncertain future capital goods values, owing either to an uncertain physical rate of depreciation or future replacement cost of capital. Both types of risk are empirically significant in most countries, and the same set of economic considerations apply to both income risk and capital risk. The two types of risks, however, are often asymmetrically treated in the tax law. In particular, tax systems as they exist are inadequate in treating losses arising from capital risk. Most corporate income taxes allow for the deduction of depreciation, based on the original cost of the asset, from taxable income. The true cost of depreciation, however, is based on the current rather that the original cost of the investment. If replacement cost is uncertain, capital cost allowances based on the original cost of the asset fail to take into account the changes in capital values that occur when capital goods prices change. That is, since the deduction for depreciation is fixed ex ante, the government shares none of the capital risk. Thus, the government does not share capital risk with the private sector, although it does take some of the return, thereby penalizing investments made in projects facing capital risk. To share capital risk, depreciation must be based on replacement cost depreciation, an ex post concept. The practical problem is in determining the replacement value of thinly traded assets in secondary markets. An alternative is to allow a deduction of a risk premium for capital risk in addition to ex ante (expected) depreciation.66 Once again, it is uncertain how to measure the risk premium.67

Taxing the investment versus taxing the return to the investment

The example above dealt with ex post taxation of investments where the investor can choose the amount to invest in the asset. There is a tax equivalence in this situation from the point of view of the investor, between ex ante taxation and ex post taxation. Ex ante taxation taxes the act of investment itself, rather than the realized profit of the investment. For example, taxing the amount invested at a rate of 50 percent is equivalent to taxing the return to the investment (with full loss offset) at 33 percent. There is, however, a difference between the two taxes in terms of social risk bearing (see below); in the case of ex ante taxation, the government (i.e., taxpayers in general) bears no risk. The result continues to apply for risks that are not reproducible, but for which good insurance markets exist.

Private risk and social risk

When reproducible risks are taxed with full loss offset, the investor can attain any combination of risk and return that was possible in the absence of taxation. Thus, while total (or social) risk taking increases in response to the imposition of the tax, private risk taking, that is, the risk actually borne by the investor after tax, does not change. The increased risk is borne by taxpayers in general, through uncertain tax revenue. That is, all individuals in the economy are now bearing a new risk, through uncertain taxes on other transactions, to maintain tax revenue (or through uncertain interest rates because of uncertain public sector borrowing requirements) or through uncertainty in the level of public expenditures.

The importance of having the government share in risk depends on how well the private market achieves efficient risk sharing. For risks that are already widely spread throughout the economy, the government cannot significantly improve risk sharing. If risk-sharing markets are imperfect, or for risks borne by smaller firms that find it difficult to spread risk, the government may, however, be able to provide risk-sharing opportunities that the market cannot provide. If insurance markets are not complete, a tax system that bears some risk may compensate in part for missing insurance markets, spreading the risks among taxpayers in general. In many instances, a government will be in a position to insure an individual’s risk with very little risk to itself.

The Effects of Taxation in Imperfect Markets

Russell Krelove

  • How are competitive-economy tax incidence results altered when imperfect competition is present in the economy and when markets do not clear?

  • How do the effects of a tax depend on interactions with other aspects of the regulatory environment, such as price and quantity controls?

The effects of taxes depend upon the structure of markets and the concept of equilibrium. Thus, incidence of a tax varies as the concept of the market varies. Earlier sections in this chapter considered the incidence of taxes in markets characterized by perfect competition and market clearing, and in the absence of other distortions in the economy. In this section, we consider incidence in a variety of circumstances that deviate from the perfectly competitive, market-clearing paradigm. First, we consider incidence when the market is not competitive, but dominated by one or several firms. Second, payroll or wage income taxation is analyzed in a developing-country setting where there is migration between the urban labor market and traditional production in the rural areas, with urban unemployment generated by a wage differential. Third, we consider three examples of the interaction of taxes and other aspects of the regulatory environment. One way that the functioning of markets is altered is by government itself, through a variety of regulatory measures. Developing countries typically have a much different nontax policy and regulatory environment from developed countries, with higher protection, rationed foreign exchange, price controls, parallel markets, credit rationing, and other features. These features can alter the standard tax incidence results.

Taxation with Imperfect Competition

The effect of an excise tax on a monopolized market

It is often suggested that an excise tax on a monopolized market would automatically be shifted forward in higher prices to consumers. While it is possible for the monopolist to raise the price by the amount of the tax, it turns out that such a strategy is not generally optimal. Previously, the case of a competitive market was analyzed, and it was shown that incidence depended on supply and demand elasticities. In the alternative polar case of monopoly (or when an industry is cartelized by a group of colluding firms), the incidence of the tax again depends on elasticities of demand and cost (in particular marginal cost) curves, but the analysis is more complex. In particular, it is possible for the price to rise by more than the amount of the tax, depending on the elasticity of the demand curve. Regardless of the change in output price, however, the pure profit of the monopolist falls with the imposition of an excise tax, so that claimants to this profit bear some of the burden of the tax.68

In the absence of a tax, it is well known that production of a commodity by a profit-maximizing monopolist occurs at an output level where marginal revenue is set equal to the firm’s marginal cost. If the tax is considered a cost to the firm, then the imposition or increase in the tax has the same effect as an increase in the firm’s costs, and in particular its marginal costs. As a result, at the new equilibrium, marginal revenue rises by the increase in marginal cost. The implication for the change in consumer price depends on the shape of the demand and marginal cost curves. At one extreme, if marginal cost is infinite, then output and consumer price do not change, and the tax is borne entirely by claimants to the monopoly profit. At another extreme, if marginal cost is constant across different output levels, then consumer price will rise by more than the amount of the tax for many commonly employed forms of demand function.69 This contrasts with the competitive case, where consumer price rises by the amount of the tax when the market supply curve is perfectly elastic.

Finally, specific and ad valorem taxes can have different effects under monopoly, unlike the competitive case. In an equal-revenue comparison of two taxes in a given market, one specific and one ad valorem, it can be shown that the monopolist’s output will be higher with the ad valorem tax (and so the consumer price is lower). This is because the specific tax increases marginal revenue by more than the ad valorem tax does.70 The implication for policy is that the ad valorem tax is superior to the specific tax, since it induces a monopoly output level closer to the socially efficient level.

Payroll and wage income taxes under unionization

Wages are often determined in markets that are not perfectly competitive, but subject to bargaining and collective agreements. If the supply of a certain type of labor is monopolized through a union, then a tax on payroll or on wage income can have the characteristics of the excise tax on the supply of a monopoly discussed above. The analogy may be incomplete, however, for several reasons. First, for the analysis of union behavior, there is no appealing concept analogous to profit of the firm to act as maximand. The incidence of the tax will depend on the objective of the union, for example, whether the goal is to maximize total before-tax payroll, or after-tax wages, or employment, or some combination. Second, union power in many cases exists in conjunction with monopsony power on the part of employers of labor. Then the decision, and the effect of the tax, is determined by a process of bargaining, and there is no generally accepted theory of bargaining outcomes. Third, in certain countries, wages are determined as a matter of national policy, in centralized collective bargaining. In these cases, the level of taxation on wage income becomes part of the bargaining process itself, so that the exogenous properties of the tax structure (usually assumed in incidence analysis) are undermined.

Taxation and oligopoly

The analysis of tax incidence under oligopolistic conditions is undeveloped, as price determination in such market structures depends on the nature of expectations, on the strategic interactions among firms (both actual and potential) in the industry, and on the solution concept adopted. There is no generally accepted model of oligopoly that resolves the ambiguity, but a collection of models that can be applied in different circumstances. Generally, however, the extent to which the tax is passed forward by a firm depends on its expectations about whether other firms in the industry will follow its price increase. On the one hand, if the firm expects others to take its price increase as a signal for all firms to increase the price, the tax will more likely be shifted forward. On the other hand, if a firm expects its price increase not to be matched by its competitors, it will avoid the price increase to prevent losing market share.

Payroll and Income Tax Incidence with Unemployment

A prominent feature of many developing countries has been a rapid increase in both rural and urban migration.71 In models of this phenomenon, the urban wage is rigid, urban employment is controlled, and an urban-rural wage differential is maintained in equilibrium by unemployed labor in the urban sector, where a lower probability of being employed has the effect of equalizing expected wages. A tax on urban wages in this model can affect migration decisions, the amount of unemployment, and wages in the rural sector. Thus, part of the burden of the tax on urban labor is shifted to rural workers, even though employment or the before-tax wage does not change in the urban sector.

Interaction Between a Tax and Other Aspects of the Regulatory Environment

The interaction of taxes with other policy interventions that are important parts of the economic environment in developing countries can alter the standard incidence results in significant ways. In this section, three instances are considered: the effect of an excise tax when price controls exist that have encouraged the development of a parallel market; the effect of tariffs when there are quantity controls on imports; and the effect of a company tax when firms are credit rationed. In all three cases, the incidence results differ from the incidence when such non-tax controls on markets are absent.

Price controls and excise tax incidence

The widespread use of price controls for many items subject to sales and excise taxes can change the incidence of the tax. If the price-controlled firm is legally allowed to pass the tax through, then the price will rise by the amount of the tax, regardless of supply and demand elasticities. If there is no legal provision allowing the tax to pass through, then the tax is shifted backward to recipients of factor incomes.

A more complete analysis would consider that price controls also often encourage the emergence of parallel (or black) markets.72 When this is so, the imposition of a tax may also change the relative volumes of trade on regular and parallel markets, will affect the amount of time spent queuing to obtain white market goods, and will also affect parallel market prices. Thus, the tax can be borne in part by transactors on the parallel market, as well as by purchasers on the formal market.

Incidence of an import tariff under quantity restrictions

The usual incidence assumption for import taxes (or for the import component of VAT) is that they are fully shifted forward. An assumption of forward shifting implies that tariffs are treated in a similar manner to sales taxes, and hence, tend to be viewed as regressive. The results would be different, however, if, as in developing countries, there are, in addition, quantitative restrictions on imports, whether directly imposed through quotas, or arising indirectly through rationed foreign exchange or prior import deposit requirements, or other forms of quantitative control. When quantitative controls are binding, the tax will be borne by recipients of the quota rents, with the tax having no effect on domestic consumer prices. Since rights to quotas are usually allocated to higher income groups, tariffs with such incidence would be more progressive than in the situation without controls.

Credit rationing and corporate tax incidence

Credit rationing, whether undertaken by government or practiced by private lending institutions, is common in many developing countries. Such rationing acts as a quantity control, and just as with import quotas, can affect the incidence of a tax, in this case, of the corporate income tax. With credit rationing, rents are generated, and the corporate tax will primarily take rents away from those who qualify for rationed credit, lowering the return to their own investment of time and money. To the extent that those with access to credit are in the upper tail of the income distribution, the tax may be more progressive than under freer access to capital markets.

The Theory of Second Best

Russell Krelove

  • When the conditions ensuring full efficiency are not attainable in one or more sectors of the economy, how should the conditions for efficiency be amended in the other sectors of the economy?

  • Under what conditions are uniform taxes or uniform tariffs second-best optimal?

  • What is the potential role for quantity controls, in-kind transfers, queuing, and similar policies in a second-best environment?

The theory of second best addresses the following question: When the conditions ensuring full efficiency are not attainable in one or more sectors of the economy (that is, when irremediable distortions exist among relative prices), how should the conditions for efficiency be amended in the other sectors of the economy? The constraints in the uncontrolled sectors often arise from institutional, observability, and information problems that are usually assumed away in the standard “first-best” analysis, where the government possesses complete information and, through its policy instruments, has control over the allocation of resources in the economy. The problem of the second best applies beyond public finance, to all areas of economic policy.73 The purpose of this section is to consider its relevance for tax policy recommendations.

Through argument and example, the following four major points concerning tax policy in second-best environments may be established:

• If a tax distortion exists in one market (i.e., there exists some constraint that prevents the first-best optimal conditions from being satisfied in this market), adding another tax distortion can be beneficial;

• Conversely, if several tax distortions exist, removing one distortion may not be beneficial;

• Optimal policy in second-best situations may conflict with the usual intuition accompanying first-best policy advice. In particular, policies that would not be desirable in a first-best environment may have a role to play in a second-best environment. For example, rationing may increase welfare when tax distortions are unavoidable; and

• Policy design in second-best environments is complex, depending on the nature of the objective and on the instruments assumed available. In general, distortions should be introduced at all margins in the economy with the second-best optimal policy. Thus, the informational demands on tax policymakers are enormous. Nevertheless, some constructive, simplifying results are available. In particular, in certain circumstances, conditions familiar from first-best analysis may persist in second-best optimal policy. For example, in a wide class of second-best situations, it is not desirable to introduce distortions into the production sector of the economy. Further, when additional constraints, other than constraints on available instruments, are introduced, for example, political constraints and constraints on administrative capability, the analysis may sometimes support the use of first-best type policy recommendations, on account of the simplicity and informational parsimony of first-best rules.

By its nature, second-best policy involves an investigation of the interactions between markets. For this reason, the analysis is inherently general equilibrium.

An Instructive Example: Nonuniform Indirect Tax Rates to Increase Welfare

The deadweight loss of a set of distortionary taxes depends on the whole set of tax rates and the demand relations among the goods. Thus, to consider the combination of taxes that raise a given revenue, complementarity and substitutability among all goods, taxed and untaxed, must be considered. The example in this section brings out that there is no reason for these relations to yield optimal taxes that are uniform across all taxed goods.

Suppose we wish to raise a certain amount of revenue from an individual. A lump sum tax levied on the individual, that is, a tax the size of which cannot be influenced by the individual’s market behavior, can raise the revenue costlessly, in the sense that the welfare loss to the individual is equivalent to the government’s gain. A lump sum tax does not distort relative prices of goods. Equivalently, indirect taxes at a uniform rate on all goods that the individual consumes, including leisure, can raise the required revenue without distorting the relative prices of goods. Now, introduce the constraints on policy that lump sum taxes are unavailable and that leisure cannot be taxed, perhaps because its consumption cannot be observed. Suppose, however, that all other goods can be taxed freely. The question is whether it is still optimal to tax all other goods at a uniform rate. Such a tax policy would not distort the relative prices of all taxable goods, so that they preserve the usual first-best conditions on the relation between marginal rates of substitution and marginal rates of transformation. This tax structure would, however, make all taxable goods more expensive relative to leisure, so that it is distortionary if labor supply is not perfectly inelastic.

Corlett and Hague (1953) showed that such uniform indirect taxation is not optimal. Beginning with uniform taxation, a move that raises taxes on goods that are complementary to leisure (e.g., tennis rackets) and lowers taxes that are substitutes for leisure (work clothes) while maintaining the revenue yield, would be beneficial. The intuition is that by taxing complements to leisure, leisure is indirectly made more expensive, offsetting to some extent the encouragement to leisure arising from its relative price falling as other goods are taxed. Thus, in general, uniform indirect taxation is not optimal.

Examining this conclusion from another perspective illustrates a second important principle of second-best tax analysis. The result shows that if there are constraints on taxation, and if taxable goods are not taxed uniformly, then moving toward uniformity, that is, removing the distortions among taxed goods, is not necessarily beneficial. Only if all distortions are reduced proportionately can improved results be shown.

These results were interpreted as negative because they imply that policy advice firmly rooted in careful economic analysis is much more informationally demanding in second-best environments. This was too pessimistic, however; as the next subsection indicates, a variety of results exist to guide the design of second-best tax policy.

Constructive Second-Best Results

In this section, selected examples of second-best analysis and policy design are discussed. Three types of results are illustrated. First, the second-best rationale for low taxation on as broad a base as possible is presented. Second, an example of attempts at identifying important cases where simple first-best optimum conditions are valid for a subset of policy decisions in a second-best environment is illustrated. Third, the question, under what conditions does the introduction of extra constraints besides standard second-best constraints on the tax instruments available actually support first-best type recommendations is asked. Finally, an example shows that when there are constraints on taxation, there is scope for additional policies, for example, rationing and queuing, that are usually ruled out as inferior in first-best analysis.

The case for many small taxes

The deadweight loss of an excise tax on a good increases geometrically with the rate of tax. If cross-price demand elasticities are sufficiently small—relative to own-price elasticities—to be ignored, then the tax system that raises a given revenue with the least efficiency loss would tax as many goods as possible, all at a low rate. This result has to be tempered for equity considerations, administrative feasibility, and because many substitutability and complementarity relations among goods are important.

Production efficiency in a distorted economy

It is straightforward that production efficiency is desirable in a first-best world: when production is not efficient, it is possible to increase the output of all goods, with the surplus distributed to increase welfare. An important question that arises in second-best situations is under what conditions should production efficiency be preserved? That is, when the government can induce distortions in production through differential taxation of factors in different uses (e.g., by taxing capital services in the corporate and noncorporate sectors at different rates), when is it optimal to do so? It turns out that under certain conditions, it is not optimal to induce production inefficiency.74 When the government possesses enough flexibility in taxation so that it can place any desired wedge between producer and consumer prices in each market, and when the government can flexibly tax all firms’ pure profit, then production efficiency is desirable. When these conditions are not met, then taxation of inputs used in the production of the untaxable goods is desirable, as an indirect method of taxation of those goods.

When the conditions for production efficiency hold, the result has some strong implications. First, there should be no taxation of intermediate goods. Second, in an open economy, trade with the rest of the world can be considered as another production possibility. The production efficiency result implies that when the country is small in world markets, then optimal tariffs are zero, that is, all indirect taxation should be on final goods only, irrespective of origin.

The conditions necessary for production efficiency are strong, and are unlikely to be satisfied in any economy. The lesson to be derived, as Stern (1987) argues, is that in any situation, care needs to be taken to justify departures from production efficiency in terms of specific and well-defined arguments. For example, tariffs on imports at rates in excess of the rates of tax on domestic production would have to be justified by identifying final goods that are difficult to tax, or profits that cannot be taxed away directly.

When are optimal tariffs and optimal taxes uniform?

An important question in developing country tax policy is whether and when a case can be made for a uniform tariff structure. At a general level, the standard optimal second-best taxation arguments suggest that when tariffs are appropriate, differential tariff rates would constitute the optimal policy, with different rates across final goods and also across imports of raw materials and other business inputs. That is, in general, effective protection would not be uniform over commodities (see Chapter V). A variety of other constraints, however, support the argument for uniform effective protection.75 Political economy considerations, inadequate information on elasticities, and administrative convenience all support a minimally differentiated tariff structure. Thus, by introducing new constraints and transactions costs, the second-best policy may be uniform.

A similar set of considerations arise with regard to the implementation of domestic indirect taxation.76 There, the support for uniform indirect taxation, for example a VAT with a single rate, is based on constraints on policy arising from weaknesses in the information needed to calculate optimal differentiated taxes, and constraints arising from administrative capability and political constraints. The first two of these are particularly important in developing countries.

An important issue for growth in developing countries is taxation of capital income, and in particular, whether it is best to target specific types of investment for preferential treatment or whether it is best to adopt neutral taxation, thereby “leveling the playing field” by taxing all types of capital income uniformly. Some simulations for the United States77 suggest that while, for standard second-best reasons, a neutral tax would not be the optimal policy, the cost of adopting a uniform taxation policy would be small. Thus, the increased administration costs of discriminatory policy would more than offset the gain. In addition, other empirical work on a large sample of developing countries has found no empirical evidence to suggest that there are identifiable social externalities accruing to certain types of investment that would support preferential tax treatment of such investment.78

In these and other similar cases, the debate about the place of uniform versus nonuniform taxation in real-world tax policy will revolve around issues of observability of the relevant parameters of tastes and technology (including the stability of those parameters), the technology of administerability of taxes, and the nature of other constraints on policy, including political and fairness.

Quantity controls, in-kind transfers, and queuing as second-best policies

The rationing of certain commodities and the provision of free goods are obviously deleterious to efficiency in an economy satisfying the assumptions of the first-best model. To introduce such policies would create distortions. However, if distortions already exist, for example because taxes exist, their introduction may be beneficial. Nevertheless, not any rationing, in-kind transfer, or queuing policy results in an improvement. These policies must be carefully designed and calibrated to have their intended effect. In general terms, the arguments are economically intuitive. What is established here is that the potential exists, that is, what are normally considered nonstandard policies—rationing, in-kind transfers, and queuing—may serve as useful welfare-enhancing policies in second-best environments.

Quantity controls. Quantity controls can play a role in welfare enhancement as an accompaniment to commodity taxation. For instance, if a tax is placed on a commodity, say milk, consumers place a higher marginal evaluation on an extra liter of consumption than the cost of production of that liter. If consumers are forced to buy (at the consumer price) and consume one more liter, it is straightforward to show that they are made better off by this policy. Paying for and consuming an extra unit has only a negligible effect on welfare,79 but since there is a positive tax, the government receives extra revenue, permitting it to lower other taxes, which makes consumers better off. Conversely, rationing of products that are being subsidized by government can be beneficial.

In-kind transfers. It is a common first-best assertion that the redistribution of wealth among individuals is always done more efficiently by means of cash transfers than by transfers in kind. This may not be true, however, when it is difficult for the government to identify those to whom it wishes to distribute. In this case, by providing goods (which cannot be costlessly resold) that are relatively more preferred by the favored groups, the government can target its policy to those that it wishes to help. That is, by supplying specific goods, it induces these groups to reveal their characteristics by their choices. Cash transfers, being valued by all groups, including nonfavored groups, would not so readily induce such self-selection.

Queuing. Queuing as a rationing device imposes a pure deadweight loss in a first-best environment, as there is no gain to offset the lost time spent waiting. In a second-best environment, however, there is a rationale for queuing, which is closely related to the previous argument supporting the use of in-kind transfers. If it is difficult for the government to identify the members of the favored groups, when these groups have a lower marginal valuation of time, they can be induced to reveal themselves if they are required to queue for a period of time to receive a transfer. Since their valuation of time is lower, they are more likely to stand in line, thus revealing that they belong to the favored groups. It is important to note that the government is not requiring queuing to be mean-spirited; by using this method of inducing the favored groups to reveal themselves, the government is able to better target the transfer policy, actually making the favored groups better off than if queuing is not used.

The targeting principle in second-best policy environments

An important principle of first-best policy advice is the principle of targeting, which argues that a distortion is best offset by a tax instrument that acts directly on the relevant margin. Thus, the best response to an externality, for example pollution, is a Pigouvian tax on the polluting activity, rather than, say, a tax on consumption of the commodity, or a tax on the use of inputs into the production of the commodity. The extent to which the principle is useful in second-best analysis is an important but difficult question, with the answer depending on the nature of the objective and the constraints on policy. Two results are available, however, that suggest in many circumstances the targeting principle may apply. First, it has been shown80 that when complete commodity taxation is available, at possibly different rates, if it is desired (for whatever reason) to increase domestic production of a tradable good, the best way to accomplish this is by direct subsidies to producers, rather than tariff protection from imports. Second, the problem of international tax harmonization that arises when countries are constrained in the use of optimal lump-sum taxes to raise revenue is best addressed by a policy that directly alters countries’ marginal incentives to attract mobile capital from other countries.81

Concluding Remarks

There persists a large gap between normative tax theory and practical tax policy. This is particularly true in second-best environments. Nevertheless, as this section has indicated, the theory provides some insights into the design of policy. The challenge for practitioners is to identify conditions under which the insights are applicable and to adjust their prescriptions to cohere with the wide variety of real-world constraints on policy, arising from politics, information, and incentives.82


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See, among others, Auerbach (1985), Harberger (1978), and Mackenzie (1983) for general treatment of this subject.


For simplicity, it will be assumed throughout the discussion that the producer (i.e., tax-exclusive) prices are constant and not affected by the tax. Implications from relaxing this assumption are discussed in the section on optimal commodity taxation in Chapter III.


The excess burden of a tax is also commonly known as the dead-weight loss of the tax.


The expression in equation (5) gives an exact measure of the excess burden only when the demand curve is linear, as drawn in Figure II.1. For a nonlinear demand curve, the exact area of the “triangle” can only be found by integration. For a sufficiently low tax rate, however, the error involved in using equation (5) to approximate the excess burden under a nonlinear demand curve would be small.


Readers who are familiar with the construction of index numbers, such as the consumer price index, would immediately recognize that the difference between the compensating and equivalent variations is conceptually akin to the difference between the Laspeyres and Paasche index formulae.


The Engel curve depicts the relationship between the income levels and the quantities demanded of a commodity.


Technically, this special case is known as the case of homothetic demands.


A classic treatment of various aspects of equity is available in Mus-grave(1959).


Hence, it is common to regard an income tax system that treats different types of income differently (e.g., applying differential tax rates or granting exemptions on the basis of different income sources) as one that violates horizontal equity.


In conformity with the general practice adopted by the literature on this topic, it is assumed from now on that inequality is measured with reference to the distribution of income over some given period of time.


If ε = 0, equation (8) is not well defined. This equation, however, approaches a well-defined expression as ε approaches zero. The significance of this case is discussed below.


Some additional technical assumptions, whose treatment is beyond the scope of this Handbook, are needed to prove these results formally.


Readers who are familiar with the literature on risk and uncertainty would immediately recognize that (1 - e) corresponds to the coefficient of relative risk aversion (a constant in the present formulation). Hence, e could be interpreted as a parameter measuring the intensity of the policymaker’s aversion to inequality: the lower the value of e, the higher his aversion intensity.


Rawls’ argument for the max-min justice is rich and complicated. A simple explanation is as follows. Imagine all individuals of a society at the beginning of time (the “original position”), with no foreknowl-edge about their endowments, opportunities, and wants (they are behind a “veil of ignorance”), are to agree to a binding social contract that would guarantee their subsequent well-being according to the contractual terms. Rawls argues that, under such circumstances, rational and egoistic individuals would agree to a contract guaranteeing an egalitarian outcome.


Some mixedary calculus, omitted here for simplicity, is required to demonstrate the last two results.


The analysis of the effects of an excise tax can be found in any public finance text. See, for example, Musgrave and Musgrave (1989), or Stiglitz (1988). A classic treatment of incidence issues can be found in Brown (1979) (reprint of 1924).


For a fuller discussion, see Bradford (1986).


For the United States, see Pechman and Okner (1974) and Musgrave, Case, and Leonard (1974). Similar studies have been carried out for other countries. In the United Kingdom, the Central Statistical Office publishes results annually in Economic Trends. Studies for other countries include Dodge (1975) and Gillespie (1976) for Canada; Cazenave and Morrisson (1974) for France; and Franzén, Lövgren, and Rosenberg (1975) for Sweden. In developing countries, studies besides those already mentioned include Malik and Saqib (1989).


For a recent survey, see Whalley (1988).


The results of Devarajan, Fullerton, and Musgrave (1980) suggest that the results of the judgmental studies are fairly close to those of the conventional general equilibrium simulations.


See Whalley (1988) for an assessment of the contribution of these models.


For a strict interpretation of the concept of public dissaving, the relevant deficit is the current public deficit—current expenditure less current revenue. Correspondingly, the deficit of the capital budget should be considered part of total domestic investment. Under a static point of view, whether the capital budget deficit is classified as investment or negative saving does not alter its effects on private investment and interest rates. In a dynamic framework, in contrast, public investment may expand the growth potential of the economy. From this point of view, whether the public deficit corresponds to a current or capital deficit is not just a definitional issue but a distinction between two policies with very different long-run implications.


See Barro (1974).


A current survey of empirical and theoretical evidence for and against the Ricardian equivalence hypothesis can be found in Seater (1993). Another comprehensive survey on this topic is found in Bernheim(1987).


This is the case, for example, in Solow (1956). More sophisticated versions incorporated the influence of present wealth, current interest rates and, occasionally, lagged values of some variables.


See also Tanzi (1991).


See, for example, Summers (1981 and 1984), Auerbach and Kotlikoff (1987), and Lucas (1990), among others.


Empirical evidence of the high correlation between domestic savings and domestic investment, even in open economies with international capital flows, can be found in Feldstein and Bacchetta (1989).


Some recent analyses that pay particular attention to the relation between taxation and growth are Barro and Sala-i-Martin (1990), King and Rebelo (1990), Lucas (1990), Jones, Manuelli, and Rossi (1993), and Trostel (1993).


The effect discussed assumes an upward sloping supply of labor in the long run.


See Knight, Loayza, and Villanueva (1993) for recent evidence and an assessment of other studies.


See W.D. Andrews, “A Supplemental Personal Expenditure Tax,” in Pechman (1980) for a defense of the expenditure tax as a complement to income taxation.


The lifetime income is the discounted present value of the stream of present and future income flows of an economic agent.


It is worth noting that a direct tax on annual consumption with a progressive rate schedule can distort the intertemporal allocation of consumption. Progressive tax rates on annual consumption expenditure would encourage consumption smoothing across years in order to avoid higher tax rate brackets. This effect, however, is due to the disparity between the annual character of the tax base and the longer horizon of consumption-saving decisions. If the tax base were the present value of lifetime consumption instead of annual consumption, the incentive to smooth consumption expenditure across years to avoid higher tax rate brackets would disappear. A similar effect also occurs under an annual income tax with progressive rate structure, which creates an incentive for income smoothing.


Under the personal consumption tax, the taxation of the operation of the qualifying accounts is the reverse of that under a standard cash-flow tax. Outflows (to the accounts) are deducted from the base while inflows (from the accounts) are included in the base.


As with the qualifying investment accounts, the taxation of cash flows between the business and the taxpayer is the reverse of that under a conventional enterprise cash-flow tax. Inflows (from the taxpayer to the business) are exempt while outflows (from the business to the taxpayer) are taxed.


See Chapter IV of this Handbook. A recent and exhaustive treatment of business taxation based on cash-flow can be found in Shome and Schutte (1993).


The demonstration is initially due to Domar and Musgrave (1944). The modern version of the argument is due to Mossin (1968) and Stiglitz (1969). Textbook treatments include Stiglitz (1988).


The traditional exposition assumes that the risk-free rate is zero. It is assumed here that only the return to risk is taxed, that is, the return in excess of the risk-free rate. This is achieved, for example, if the investment is financed by borrowing (at the riskless rate), and interest expense is deductible from income to arrive at taxable income.


This implies that when the tax base is negative, a credit is paid equal to the tax rate multiplied by the amount of the loss. Equivalently, the taxpayer can be allowed to carry losses backward, or forward (cumulative with interest) to achieve full loss offset.


That is, to increase total risk bearing by the proportion l/(1-t), where t is the proportional tax rate.


The case of many risky assets has been analyzed by Sandmo (1977). He shows that the results are similar in essential respects.


One example is the recent study using U.S. data in Hubbard (1985). For a U.K. study, see Shorrocks (1982).


This is especially important for start-up companies.


That is, for neutrality of corporate taxation with capital risk, the allowable depreciation deduction should equal the certainty equivalent of replacement cost depreciation. This certainty equivalent exceeds the expected depreciation, for risk averse individuals.


In models of portfolio allocation, for example, the capital asset pricing model, the risk premium depends on the risk-free rate of return, the return on the market portfolio, and on the covariance structure of the asset.


Part of the tax can also be shifted backward to other factors of production, through reductions in input prices, lessening the negative impact on profit of the firm.


Marginal revenue is related to price according to mr - p(l - 1/ eD) where mr is marginal revenue, p is price, and eD is the (positive) elasticity of demand, assumed constant in the relevant range. eD is greater than 1 at a monopoly optimum (since marginal revenue is set equal to marginal cost, and marginal cost is positive). Then, if mr rises by the amount of the tax, p must rise by more than that amount to maintain the equality. It should be noted that this result relies on the assumption of a constant elasticity demand curve. By way of contrast, if the demand curve is linear, consumer price rises only by half the amount of the tax.


For the proof of this assertion, see Musgrave (1959), pp. 287–311.


See Harris and Todaro (1970). Various aspects of the problem are also discussed in the survey by Burgess and Stern (1993)


The problem wasfirstsystematically treated by Meade (1955). Definition of the problem was significantly advanced by Lipsey and Lancaster (1956–57).


See Diamond and Mirrlees (1971).


See Auerbach, Hassett, and Oliver (1993). The full sample comprises 88 countries including OECD countries, and developing countries on almost all continents, but excluding high-income oil-exporting nations.


Technically, since any consumer is initially consuming an optimal bundle of commodities, a small move along the budget constraint is also a move along the consumer’s indifference curve.