The Costs of Taxation and the Marginal Efficiency Cost of Funds
  • 1 0000000404811396 Monetary Fund
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It is argued that taxation causes deadweight losses—from substitution, evasion, and avoidance activities—and direct, administrative and compliance, costs. Some of these social costs tend to be discontinuous and/or nonconvex. Because most models of taxation ignore some components of the social costs of taxation, their conclusions cannot be considered all-encompassing. An alternative approach to policy evaluation is to rely on a marginal efficiency cost of funds rule that can indicate appropriate directions of reforms. The paper discusses the merits, applicability, and limitation of this rule, as well as its relationship to other concepts,


It is argued that taxation causes deadweight losses—from substitution, evasion, and avoidance activities—and direct, administrative and compliance, costs. Some of these social costs tend to be discontinuous and/or nonconvex. Because most models of taxation ignore some components of the social costs of taxation, their conclusions cannot be considered all-encompassing. An alternative approach to policy evaluation is to rely on a marginal efficiency cost of funds rule that can indicate appropriate directions of reforms. The paper discusses the merits, applicability, and limitation of this rule, as well as its relationship to other concepts,

A casual survey of the public finance literature reveals an interesting pattern. Until the mid-1950s, almost all textbooks devoted a considerable amount of space to the problems of tax administration, compliance, and enforcement.1 Beginning in the 1960s, though, administration and compliance issues almost disappeared from the literature, excluding that on developing countries.2 The interest of economists shifted to deadweight losses and formal normative models, known generally as optimal taxation. In the early 1970s, before optimal taxation literature reached its peak, Allingham and Sandmo (1972) marked a turning point with their choice-based model of tax evasion; a large theoretical and empirical literature followed. In the mid-1980s, the problem of tax administration regained some attention, but mainly in verbal as opposed to technical presentations.3 However, little effort has been made to integrate these aspects of tax analysis into a coherent normative framework.

We begin this integrative task in this paper. We argue that excess burdens, administrative costs, and compliance costs are all components of what we shall refer to as the social costs of taxation: the costs incurred by society in the process of transferring purchasing power from the taxpayers to the government. The social costs include the cost of enacting and administering the law, involuntary compliance cost, and the deadweight losses and expenditures caused by taxpayer activities undertaken to reduce the tax burden, such as evasion, avoidance, and switching to more lightly taxed, but otherwise less attractive, consumption. All these components of social cost should be included in a proper model of the costs of taxation, and they should affect the design of an optimal tax system. Hence, it is a bit puzzling that the interest of economists has tended to focus on only one or two components of the costs.4

One possible interpretation of this stylized fact is that the focus of the literature reflects the issues that economists are able to solve at a given time. Until the introduction of the concept of excess burden in the 1960s, the public finance literature was mainly verbal and descriptive. Hence, the range of issues was not limited to what could be solved by tractable mathematical models. With the emergence of mathematical models, however, the literature began to emphasize those elements of the social cost that could be easily modeled and analyzed, that is, the excess burden. This led to the optimal taxation literature, in which the main target was to find optimal rates of tax, and tax administration issues were set aside as technical matters that had no substantial bearing on the problem at hand.5

The pathbreaking paper by Allingham and Sandmo (1972) added another dimension that could be analyzed by mathematical models—the issue of tax evasion. Following the Allingham and Sandmo paper, hundreds of papers dealing with different aspects of evasion, most of them theoretical, were published.6 Relatively fewer books and papers have attempted to estimate empirically the magnitude and determinants of evasion.

The realization that tax evasion is a serious problem faced by many industrial countries has led economists to raise the issue of tax administration; the mere fact that tax evasion exists often implies administrative inability to enforce tax laws. However, relatively little analytical work incorporating tax administration has been done, mainly because administrative issues are hard to analyze with continuous differentiable functions and, therefore, they require complex modeling.

In this paper, we argue that the problem of designing a tax system is much broader than that presented in the optimal taxation problem, although the target is still to maximize social welfare or, alternatively, to minimize social costs subject to given targets. The most important component missing from models of optimal taxation is the administration of the tax law, which includes not only the process by which tax bases are determined, but also the tax process itself—the procedure that determines and transfers tax revenue from the individuals to the government.

Enacting a tax law does not by itself raise revenue. It is the enforcement of the tax law by the administration that transfers the tax from the individuals to the government. This was already well understood 50 years ago. Note the following quote from Blough ((1952), p. 146):

It is tax policy in action, not simply the wording of the statute, that determines how much the taxpayer must pay, and the effects of the payment. Knowledge of the statute is only a start in knowing a tax system. The interpretations placed on language by administrators and courts, the simplicity and understandability of tax forms, the competence and completeness of audit, the vigor and impartiality of enforcement, and the promptness and finality of action all influence the amount of revenue collected, the distribution of the tax load, and the economic effects of the tax.

One expert has even declared that in developing countries “tax administration is tax policy” (Casanegra de Jantscher (1990), p. 179). Although one may judge such a statement to be too extreme, most public finance experts would probably agree that the way the laws and regulations are administered affects the economic implications of the tax laws.7 Therefore, administrative issues should not be ignored.

The aim of this paper is to present the social cost of taxation in a broad context that includes administration, evasion, and optimal taxation issues so that one can fit the various components of the tax problem into one framework. One theme of the paper is that the problem of taxation may be too complicated to be solved in the general case, so that one has to rely on models that cover only certain parts of the problem. But if an essential part of the problem is overlooked, partial models may give incorrect answers. We explore an alternative approach that is limited to identifying desirable marginal changes, without a claim of optimality. The less ambitious objective enables us to use the concept of the marginal efficiency cost of funds. This methodology is less demanding than alternative methods in terms of data, as its application revolves around forecasts of marginal tax revenue.

The paper proceeds as follows. In Section I we identify the major actors of the tax system, and in Section II we discuss the costs associated with each actor. In Section III we derive the marginal efficiency cost of funds concept in a simple model. In Section IV we extend the analysis to include distributional issues, and in Section V we discuss the problems that arise in analyzing nonmarginal changes. Some conclusions are offered in Section VI.

I. The Cast of Characters

We begin this task by laying out a stylized framework of the important actors in a tax system. The simplest framework has a social planner and two sets of agents—the tax administrators and the taxpayers. The social planner, which encompasses the legislative branch, the spending branch, and the judicial system, aims to maximize social welfare. The tax administrator acts as an agent on behalf of the social planner, while the taxpayers pay taxes.8 It is important to distinguish the tax administrator from the social planner because the tax administrator is only an agent, and the planner must therefore take into account the possibility of self-serving behavior by the administrator, including rent seeking, corruption, abuse of power, and disloyalty. Hence, it must limit the power delegated to the administrator, for example by requiring a lengthy and detailed prosecution process, including tax courts and provisions to allow the taxpayer to appeal. These hurdles increase the administrative cost (see Virmani (1987), Chander and Wilde (1992), and Tanzi (1994) on corruption).9

The Social Planner

For our purposes, the only objective of the social planner is to raise a given amount of revenue while keeping the social cost of raising revenue at a minimum level. Provision of public goods and any other services provided will be ignored. Also ignored are the motives of the social planner in governing, which could be the maximization of a social welfare function, the maximization of the tax revenue (Levi (1988)), rent seeking, or acting “… like a discriminating monopolist, separating each group of constituents and devising property rights for each so as to maximize state revenue” (North (1981), p. 23). All those targets are consistent with the aim of keeping the social cost of taxation as low as possible. At this stage, we do not consider other targets of (or constraints on) taxation, such as horizontal equity and redistribution of income. We will return to these issues in Section IV. However, some equity issues could be perceived as enhancing cost minimization, and therefore could be included in the analysis, for example, because it is easier to collect taxes when they are viewed by the taxpayers as fair, or when the tax law is simple and unambiguous.10 In this case, the value attached to fairness is the reduction in cost that it causes.

Since the tax administrator and the social planner are different entities, the social planner must set not only the tax law, but also the rules of the game being played by the administrator and the taxpayers. It determines the rights and the duties of each party, including possibly the duties of the taxpayers to collect information or taxes on behalf of the tax administrator.

The Tax Administrator

Roy Blough ((1952), pp. 388–9) defines the target of the administration as “to collect every dollar due the government—and no more,” He continues: “In tax administration the problem of equity or equal treatment is whether everyone is being required to pay the amount of tax due under the law.… But a more important source of inequity is the failure of administrators to collect taxes from those who owe them. Such taxpayers receive a financial subsidy, while the tax loads of other taxpayers must be increased to make up the resulting revenue deficiency,”

Definitions of the target of tax administration used in modern analytical models focus almost entirely on revenue maximization. (See, for example, Reinganum and Wilde (1985).) Such a target, if taken seriously, implies ignoring overpayment by taxpayers and any other activity whose objective is not to raise short-term revenue. On the other hand, tax administrations, like any other bureaucracy, are not subject to competition and can set their own agendas, which have nothing to do with the intentions of the social planner.11 Two issues arise here: what should be the targets of tax administration, and how does one devise a framework so that the administration adheres to those targets, which include both cost minimization and equity?12 The first target can be defined quantitatively, and requires simply that administrative effort, like any other economic activity, be subject to cost considerations. The other target, equity, can be interpreted as pursuing justice regardless of its cost implications. We return in Section IV to the issue of how to combine justice and efficiency in an analytical model.13

The Taxpayer

Taxpayers can minimize the impact of the tax system by engaging in three kinds of activities, all of which involve a substitution effect:14

1. A shift to other activities. Taxation makes the tax base more expensive, so one way to avoid its impact is to divert the derivation of utility to other, cheaper sources. The importance of this factor depends on the substitutability and/or complementarity between the tax base and the untaxed commodities. The distortion that results from this activity is measured by the standard deadweight loss.

2. The taxpayer may try to avoid the tax by investing time and other resources into finding legal ways not to pay the tax. This activity is usually referred to as avoidance, and is considered a component of compliance costs. However, as will be argued later, one has to differentiate between two kinds of compliance costs—those that are imposed on the taxpayer by the social planner or the tax administrator, and those that the taxpayer voluntarily makes in order to reduce the tax paid. In this paper, the term avoidance will be restricted to voluntary compliance costs that are intended to reduce the tax paid.

3. The taxpayer may evade tax liability illegally. By imposing a tax with evasion opportunities, the relative price of being honest is increased. The substitution effect that is causing evasion is the change in relative price of honesty and the increase in the return to risk bearing through tax evasion.

All in all, we have encountered five components of the cost of taxation: administrative costs—the cost of establishing and/or maintaining a tax administration; compliance costs—the costs imposed on the taxpayer to comply with the law; the regular deadweight loss—the inefficiency caused by the reallocation of activities by taxpayers who switch to nontaxed activities; the excess burden of tax evasion—the risk borne by taxpayers who are evading; and avoidance costs—the cost incurred by a taxpayer who searches for legal means to reduce tax liability.

In some cases the classification of a particular activity into one category of cost or another is arbitrary, and may depend on one’s interpretation of the agents’ intentions. Taxpayers can spend money to conceal the tax base or they can spend it to comply; similarly, they may try to avoid taxes but end up evading them. Because of this overlap, some investigators use the term “aversion” to refer to both avoidance and evasion (Cross and Shaw (1982)). The separation of the costs borne directly by taxpayers into avoidance costs and involuntary compliance costs requires knowledge of the intentions of the taxpayers. However, as demonstrated below, this classification is important in avoiding double counting of social costs. These distinctions present a challenge when constructing optimal models of a tax system.

II. The Components of the Cost of Taxation: Properties and Modeling Problems

In this section we describe the five components of the social cost of taxation and basic problems in modeling systems.

Administrative Costs

Tax administrations deal, among other things, with information gathering. But this is a difficult element to model because information varies in quality. There is a qualitative difference between an auditor “knowing” that a given taxpayer is evading and having sufficient evidence to sustain a court finding to that effect. Also, the cost of gathering information depends on how accessible the information is, and whether it can be easily hidden. The advantages of taxing a market transaction relative to taxing an activity of the individual such as self-consumption result from several properties. First, in any market transaction there are two parties with conflicting interests. Hence, any transaction has the potential of being reported to the authorities by one unsatisfied party. A second property is that the more documented the transaction, the lower the cost of gathering information on it. For this reason it is easier to tax a transaction that involves a large company, which needs the documentation for its own purposes, than to tax a small business, which may not require the same level of documentation. Administrative cost may also be a function of the physical size and the mobility of the tax base (it is harder to tax diamonds than windows), whether there is a registration of the tax base (e.g., owners of cars; holders of driver’s licenses), the number of taxpayer units, and information sharing with other agencies.15 It is also an increasing function of the complexity and lack of clarity of the tax law.

Administrative costs possess two additional properties that complicate the modeling of tax administration issues: they tend to be discontinuous and to have decreasing average costs with respect to the tax rate. To see the first property, consider two commodity tax rates, denoted by t1 and t2. If t1 = t2, then only the total sales of the two commodities need be reported and monitored. If, however, the two rates differ even slightly, then the sales of the two commodities must be reported separately, doubling the required flow of information. There are decreasing average costs because the cost of inspecting a tax base does not depend on the tax rate (except to the extent that people are more inclined to cheat with a higher tax rate). Hence, a higher tax rate reduces the administrative cost per dollar of revenue collected (see Sandford (1973)). Administrative cost may also be a function of the combination of taxes employed and their rates, because the collection of information concerning one tax may facilitate the collection of another tax (e.g., inspection of value-added tax (VAT) receipts may aid the collection of income tax). Because of these properties of administrative costs, it is not surprising that economic modeling, which more easily handles continuous and differentiable variables, tends to be scarce in this area.

Compliance Costs

As far as we know, there is only one formal normative model that addresses compliance costs (Mayshar (1991)), although one can find estimates of its magnitude (Sandford (1973); Sandford, Godwin, and Hardwick (1989); Slemrod and Sorum (1984); Blumenthal and Slemrod (1992)). As an example of the modeling difficulties this topic poses, consider the following problem: when is it optimal to delegate to employers the authority to collect taxes and convey information about employees, thus requiring the administration to audit both the taxpayer agent and the taxpayer himself, and when is it optimal to deal only with the employee? Clearly, given that the employer already has the necessary information, it would save administrative costs to require him to pass it along to the tax administrator. This might also reduce total social costs if the cost of gathering information by the administration is higher than the increase in cost caused by imposing a two-stage gathering system.16

However, the potential efficiency of involving taxpayers in the administrative process must be tempered with a practical consideration. Administrative costs must pass through a budgeting process, while compliance costs are hidden. Hence, there may be a tendency to view a decrease in administrative cost accompanied by an equal (or greater) increase in compliance costs as a decrease in social cost, because it results in a decrease in government expenditures. We return to this point later.

Regular Deadweight Loss

Any tax that creates a wedge between the relative prices that any two taxpayers face entails an efficiency loss. The deadweight loss created is an increasing and continuous function of the tax rates, but it is also a function of the combination of taxes employed. If one abandons the assumption that the set of taxed commodities is given, one cannot assume that the deadweight loss is a continuous function.

Excess Burden of Tax Evasion

In the Allingham and Sandmo model of a taxpayer who maximizes his expected utility, tax evasion occurs only if the taxpayer expects to increase his expected income by evading taxes, including the expected fines that he would have to pay if he were caught. Hence, a taxpayer who evades taxes increases both his exposure to risk and his expected income. This additional exposure to risk is a deadweight loss to society. In principle, the taxpayer could be better off under an agreement whereby the taxpayer pays at least as much as the government currently collects, while the government ceases to audit. Assuming a risk-neutral government, the excess burden of tax evasion is equal to the risk premium that the taxpayer would be ready to pay in order to eliminate the exposure to risk (Yitzhaki (1987)). Depending on the other assumptions about the probability of detection, the penalty structure, and risk aversion, the excess burden of evasion may be a continuous function that increases with the tax rates.

Avoidance Costs

We distinguish between compliance costs, which are imposed on the taxpayer by the tax agency, and avoidance costs, which result from voluntary action carried out by taxpayers whose intention is to reduce tax payments. Clearly, any activity to reduce the tax is a pure loss from the social point of view, and therefore creates a deadweight loss. In practice it is hard to distinguish between avoidance and compliance costs because the distinction between the two depends on the intentions of the taxpayer. It will be made evident later in the paper that it is important to distinguish who controls each activity. The taxpayer controls activities that produce excess burden (including avoidance), while the tax administrator controls compliance and administrative costs.

Basic Problems in Modeling Tax Systems

Slemrod (1990) distinguishes between the theory of optimal taxation and optimal tax systems. Optimal taxation is usually restricted to the optimal setting of a given set of tax rates, ignoring administrative costs, compliance costs, avoidance, and evasion. When optimizing tax systems one has to consider all the elements of the problem. Clearly, any general solution that ignores components of the problem is doomed to fail if the omitted part of the problem is an important issue. For example, minimizing the classical excess burden requires (in the general case) unequal commodity tax rates, and the finer the classification of commodities, the lower the excess burden. But this solution ignores the administrative costs of differential commodity taxes.17

Another example concerns normative models of enforcement of tax evasion, which, with a few exceptions, imply that it is optimal to impose a penalty severe enough to abolish all evasion.18 The main idea is simple. A rational taxpayer will never evade if the costs to him are too high, and the tax administrator can make the private cost as high as he wishes by increasing the penalty to infinity. In this case no one will evade and it will be possible to reduce costly monitoring almost to zero. But this kind of model ignores the possibility of a corrupt tax administrator who abuses the system or, alternatively, harshly punishes someone who commits an honest mistake. The harsher the penalty, the more damage that can be inflicted by a corrupt administrator or. in the case of an honest mistake, the more cruel and unfair the system is. Hence, the harsher the penalty, the more detailed and cautious the prosecution process should be, although this may increase its administrative costs. In the absence of modeling the interaction between the penalty rate and administrative costs, analytical models usually assume a ceiling on the penalty rate.

A final example is that optimal tax models, which ignore administrative costs, if taken literally, generally imply that lump-sum taxation is the first-best solution. However, in real life lump-sum taxes rarely exist and when they do, they are for the most part connected with military service (i.e., the draft, reserve duty, national service); an exception is jury duty.19 The main reason that lump-sum taxes do not exist is the cost of their administration. The problem in enforcing a lump-sum tax is how to proceed if the taxpayer declares he is unable to pay it. If the administrator has to prove that the taxpayer can afford to pay the tax, it is not a lump-sum tax. The advantage of taxing a market transaction is that the transaction itself reveals an indication of both the ability to pay the tax and the liquidity that enables the taxpayer to pay without excessive damage.

III. Marginal Efficiency Cost of Funds

Listing the basic components of social costs in a taxation problem, together with their unfriendly nature, is a reminder that the quest for an optimal tax system is far from being complete. No model can both cover all the important issues and provide important insights. Nor can we provide such a model here. Instead, in what follows, we offer a tractable methodology that can evaluate marginal changes in tax systems and take account of all five components of the cost of tax systems. The methodology is based on the concept of the marginal cost of public funds.

Marginal Efficiency Cost of Funds with Only Regular Deadweight Loss

The concept of marginal cost of public funds that we will be using is based on Mayshar (1990) and Wildasin (1984), as refined by Mayshar and Yitzhaki (1995) to distinguish between distributional issues and efficiency issues. We first discuss the concept in the absence of administrative costs, evasion, or avoidance, and extend the application to these issues in later sections. We will show that being able to forecast the revenue from each tax allows us to calculate the relevant marginal excess burdens. Furthermore, knowing these marginal excess burdens allows us to identify a revenue neutral marginal change that will improve the tax system by lowering its total social cost.

Consider a representative taxpayer with a well-behaved utility function u(), and an observed allocation of its budget that satisfies y = ΣiqiXi, where qi is the price of the ith commodity the household faces, Xi is the quantity consumed, and y is given income.20 Assume that the vector of producers’ prices, p, is given and that ti = qipi are the tax rates. Then, the marginal burden of a marginal tax reform on the household is21


The marginal burden is the income equivalent of the effect of the reform. Equation (1) shows that MB is a function of the quantities (tax bases) consumed and the changes in prices.

Tax revenue is


where Xi (q, y) is the demand for commodity i, y is income, and consumer prices are q = p + t, where t is a vector of specific taxes. Revenue neutrality requires that


where MRi = ∂R/ti is the change in total tax revenue due to a small change in the tax rate on commodity i.

It will turn out to be convenient to work with dollars of revenues rather than with tax parameters. Denote by δi the change, measured in dollars of tax revenue, that results from a change in the tax rate on commodity i, dti so that


Then the marginal tax reform, dt, can also be characterized by the vector of tax receipts δ, and the change in tax revenue would then be MR = Σiδi.

Substituting expression (4) into (1), while taking into account that dti = dqi, yields


subject to the constraint Σiδi = 0.

The term in the parentheses is the marginal efficiency cost of public funds (henceforth MECF),22 interpreted as the cost to the society of increasing tax revenue by a dollar, through a change in the ith tax rate or other fiscal instrument.23

Let us illustrate the implications of equation (5) by concentrating on a revenue neutral tax reform that involves only two taxes, in which case, because δ1 = –δ2,


As long as MECF1 does not equal MECF2, a tax reform can reduce the burden of taxation and therefore increase the welfare of the representative taxpayer. If MECF2 > MECF1, the reform must feature δ1 > 0, that is shifting revenue toward t1; if MECF2 < MECF1, a welfare-improving reform should decrease reliance on t1 to raise revenue. Thus, promising directions for tax reform are indicated by comparing the MECFs. To estimate the MECFs, one has to be able to estimate only two parameters for each instrument—the marginal change in revenue, MRi, and the tax base, Xi, equal to the expected change in tax revenue if the tax base is inelastic.24 Xi is the burden imposed on the taxpayer at the margin.

Note that the above interpretation is not limited to reforms involving tax rates. One may define the marginal cost of funds with respect to any parameter of the tax system (e.g., income brackets, exemption levels, penalties for tax evasion, etc.). Nor does its application rely on an assumption that tax policy has been set optimally. The only assumption is that the taxpayer is a utility maximizer.

Having established the relevance of the MECF in a simple setting, we next discuss how it can be extended to other issues involving evasion and avoidance.

Extensions of the Marginal Efficiency Cost of Public Funds to Include Other Cost Components

The concept of marginal efficiency cost of public funds presented above was derived in a model that ignored administrative and compliance costs as well as evasion and avoidance. It can. however, be applied and used in a tax system framework. To see that, let us start with an intuitive explanation of the concept.

Recall that the potential change in tax revenue (assuming an inelastic base) is Xi but, because of taxpayers’ response, the government collects only MRi. We can divide the potential tax Xi into two components as follows:


where MRi dollars are collected and (XiMRi) “leaks” outside the tax system. The critical question is how to evaluate, from a social point of view, the leaked dollars. To do this one must ask how much a taxpayer is ready to expend (on the margin) to save a dollar of taxes or, alternatively, how much utility loss he is willing to suffer to save a dollar of taxes. The answer is that a rational taxpayer will be ready to sacrifice up to, but no more than, one dollar in order to save a dollar of taxes. Hence, on the margin the private cost, which is equal to “leaked” dollars multiplied by their cost per dollar, is XiMRi. Hence, the collection of MRi dollars results in a loss of (XiMRi) to the taxpayer over and above the taxes paid. If we assume that the private marginal cost of the leaked tax revenue is also a social cost, then the cost to society of transferring a dollar to the government is (XiMRi)/MRi = Xi/MRi – 1. The total marginal cost to the individual taxpayer, including the taxes paid, is Xi/MRi.

Consider now a taxpayer who also has the option to evade part of the additional tax. On the margin, he would be ready to sacrifice the value of one dollar (in additional risk bearing due to evasion and/or due to substitution to cheaper but less rewarding activities) in order to save a dollar of taxes. Hence, we do not have to know whether the “leak” was through evasion or substitution to evaluate the costs to society.

The same rule applies to avoidance activity and, in fact, to any activity under taxpayer control, including substitution and evasion. Therefore, all one needs to know is the potential tax (i.e., assuming an inelastic tax base) that will be collected from a change of a parameter of the tax system, and the actual change (taking into account all behavioral responses) in order to evaluate the marginal efficiency cost of raising revenue.

In constructing the MECF we have made use of two critical assumptions that deserve further attention. The first of these is that the taxpayer is not constrained. (That is, he is not at a corner solution. An example of such a taxpayer is one who is unable to evade additional taxes simply because he has evaded all the tax due.) If there are corner solutions, it is not appropriate to presume that at the margin the taxpayer is giving up a dollar’s worth of utility to save a dollar of taxes; thus the “leak” in tax revenue may have a private cost that is less than the revenue cost. As an example, consider the MECF of raising the tax rate on labor income in a situation where, in an economy with two taxpayers, one taxpayer reports no labor income at all and, at that corner, is bearing risk valued at 20 cents to evade one dollar; the other taxpayer, with identical labor income, reports all of it. Assuming no substitution or avoidance response and zero compliance and administrative costs, the economy MECF with respect to an increased tax rate is 1.2, even though the potential tax base is exactly twice the revenue collected.

To take account of the possibility of the taxpayer being at such corner solutions, we generalize the expression for the MECF by introducing a parameter γ, the marginal value to the taxpayer of a dollar of tax saved is multiplied by XiMRi, the leaked revenue. Introducing γ reduces the simplicity of the MECF expression because its value varies depending on the situation under study. Empirical investigation is required to determine whether it is reasonable to assume that γ = 1.

The second critical assumption is that the cost borne by taxpayers in the process of reducing tax liability is equivalent to the social cost. This is certainly true in many situations, such as when the private cost takes the form of a distorted consumption basket. But in some cases the private cost is not identical to the social cost. A straightforward example is when the taxpayer hires an accountant to search for legal reductions in taxable income, and these costs are deductible from taxable income. In this case the social cost is 1/(1 – t) higher than the private cost, where t is the taxpayer’s marginal tax rate.

Fines (but not imprisonment) for tax evasion bring up a more subtle example of divergence between the private and social costs of tax-reducing activities. The possibility of a fine for detected tax evasion is certainly viewed as a cost by the taxpayer, but from the society’s point of view it is merely a transfer. Thus the leak of revenue resulting from evasion has a lower social value than the private value; in the extended MECF below, we subsume this issue into the γ parameter. Note that if the fine itself is the ith policy instrument, this argument implies that its MECF could be close to zero, and almost certainly less than one, making an increase in fines look like an attractive policy option indeed. As discussed above, there are reasons unrelated to cost minimization for which increasing fines for tax evasion without limit is not desirable.25

We turn now to application of the MECF rule to administrative and compliance issues. Earlier normative models of taxation that address administrative costs have formed the problem as follows.26 There are two ways to raise revenue. One way is to increase a set of tax rates, and by so doing to increase excess burden. The alternative involves increasing administrative costs (e.g., by broadening the tax base as in Yitzhaki (1979), or by increasing the probability of a tax audit, as in Slemrod and Yitzhaki (1987)). On the margin, it is optimal to equalize the marginal costs of raising revenue under the two alternatives. Hence, in order to incorporate administrative cost all we have to do is to define the costs of taxation as deadweight loss plus administrative costs. At an optimum, the MECF of each tax rate should be equal to the MECF of administrative improvements that raise revenue. In calculating the MECF of administrative improvement, it is important to account for the fact that these expenses come out of funds that were presumably raised with tax instruments that have a MECF in excess of one.27 In other words, administrative improvements that raise net revenue decrease the excess burden; hence, on the margin and for given revenue, the saving in excess burden should be equal to the increase in administrative costs. In this way, the MECF criterion can be applied to tax administration, too.28

Compliance costs are additional costs imposed on the taxpayer. Therefore, they should be added to the burden imposed on the taxpayer. They serve as a substitute to administrative costs, but the expenses are borne directly by the taxpayer rather than through the government budget.

Having described all the components of the MECF, we have to define what are the relevant MECFs for society. Clearly, one has to sum the excess burden of the tax to compliance and administrative costs to reach the total cost to society. But should we sum the marginal costs of substitution, compliance, and administration to come up with the social marginal costs to society of raising revenue? First, note that if optimal policy prevails, all policy instruments yield the same MECF, and hence it is sufficient to calculate one MECF to know them all. In reality, the MECF of different instruments can differ, and it is feasible to raise revenue utilizing only those policy instruments with a relatively low MECF,29 In either case, one should not add the MECF of administrative costs to the MECF of the other costs (excess burden and compliance costs) to get the overall MECF. because administrative costs are “factors of production” in the process of taxation and their role is to reduce the excess burden of the tax system.

The revised MECF that includes all components is


where γ is the value that the taxpayer is sacrificing at the margin in order to save a dollar of tax, Ci is the marginal compliance cost associated with the ith instrument, Ai is the marginal administrative cost, and MRiAi is the net revenue collected at the margin. The intuitive interpretation of the expression is the same as before, with some qualifications. The potential tax is Xi. XiMRi is leaked at a social cost of γ per dollar, MRi is collected by the government, and Ci is the additional involuntary compliance cost. Hence, the total burden on society is the sum of those components. Of the MRi collected by the government, Ai is spent on administration, leaving MRiAi in the coffers. The MECF is the burden on society divided by what is collected after subtracting the cost of doing business. This yields the marginal costs of a dollar collected.

Because in equation (8) Ci is added in the numerator and Ai is subtracted in the denominator, the key conceptual difference between the two is explicit—only the latter uses revenue raised from taxpayers. To illustrate this difference, consider that a tax for which Ci = MRi (with Ai and Xi – MRi = 0) might conceivably be part of an optimal tax regime (if the MECFs of other instruments exceed 2), it would never be optimal to have Ai = MRi, for at the margin this instrument has social cost but raises no revenue.30

IV. Distributional Issues

In this section we introduce distributional considerations into the analysis. Distributional issues can be divided into two separate issues: vertical equity and horizontal equity. Vertical equity deals with the treatment of individuals that are identical in all properties except income. Horizontal equity deals with the treatment of individuals with different characteristics.

Vertical Equity

The MECF concept ignores differences in the distributional patterns of different taxes. When distribution matters one cannot continue to treat all dollars alike, but instead each dollar of potential marginal revenue (whether collected or leaked) should be weighted by the social evaluation of the marginal utility of income of the taxpayers. In other words, one should take into account what Feldstein (1972) calls the distributional characteristics of the burden on the taxpayers. There are three different approaches to incorporating distributional concerns: an explicit assumption of a social welfare function; an implicit assumption of a social welfare function; and an assumption of a broad class of social welfare functions.

Using an explicit social welfare function, one should weight the X (the burden on the taxpayer) by the social evaluation of the marginal utility of income. For example, using an Atkinson-type (Atkinson (1970)) social welfare function implies that the marginal burden is weighted by the marginal utility of income

article image
, so that instead of Xi/MRi as the basic expression of the MECF (in the simple model) we get the marginal cost of funds (MCF) as


where xih is the marginal burden of the tax on taxpayer h. Optimal tax theory implies that one should equate all the MCFi.31 For a sophisticated application of this approach, see Ahmad and Stern (1984 and 1991).

The main problem with assuming a specific social welfare function is that it is difficult to defend such a strong assumption. Hence, Ahmad and Stern consider whether a reform is suitable under a range of social welfare functions. An alternative approach is based on inequality measures (or a poverty index) such as the Gini coefficient. Then the investigator implicitly assumes a social welfare function. In some cases one can recover the (implicit) social evaluation of the marginal utility of income. Those marginal utilities can be used to estimate a weighted income elasticity that summarizes the distributional characteristics of the tax base. For example, Yitzhaki (1994) uses μ(1 – G), where μ is the mean income (e.g., consumption per capita) and G is the Gini index of income inequality, as a social welfare function. In this case, MCFi becomes


where ηi is the Gini income elasticity of the tax base.32 In essence, equation (10) adjusts the MECF by the appropriate income elasticity to take distributional issues into account. Note that, other things being equal, the higher the income elasticity of the tax base, the lower will be the MCF of raising a given amount of revenue. The attractiveness of this kind of methodology is that it separates the estimation of the income elasticity from the estimation of the MECF. Hence, it can be useful for first-order approximations, where one can rely on a conjecture concerning the income elasticity and the Gini measure of income inequality.

Implicitly assuming a social welfare function does not, however, eliminate the need to defend it. Hence, an attractive alternative is to investigate whether an assumption of a specific social welfare function is really needed to determine the direction of a tax reform. Under certain conditions one may find a reform that improves upon a large set of social welfare functions. For an illustration, see Mayshar and Yitzhaki (1995).

Horizontal Equity, Fairness, and Justice

Objectives related to horizontal equity or the fairness of the tax process itself are more difficult to incorporate into the analysis, and we do not attempt that task here. Yet we believe that these issues are fundamental to understanding the design of tax systems. Because the interpretation of fairness is influenced by cultural setting, ideology, prejudice, and propaganda, it cannot be generalized over time or across countries. For example, one’s view of whether the rich accumulated their wealth by theft or by hard work, and whether the poor are poor because of lack of opportunities or because of laziness, leads to different interpretations of fair taxes. However, it seems to us that there are some widely accepted characteristics of fair taxes. Among them are that (1) taxes should not be arbitrary, that is, they must be imposed either on a tax base that indicates an ability to pay or on benefits derived from the provision of public goods;33 (2) taxes should not be imposed retroactively, that is, the taxpayer should be given advance notice, so that he has a chance to adjust his activities to the tax; and (3) the tax should not serve the specific interest of any person and should be general in the sense that equal taxpayers are treated equally.34

These arguments were contained in the four canons of taxation of Adam Smith. Bastable (1895), in his interpretation of Smith’s canons, points out that others have considered those rules as “partly ethical … and partly economical” and recommends that one “regard them not as economic, ethical, or constitutional, but as essentially financial; they therefore rightly combine the different elements that must enter into problems connected with that subject” (pp. 385–86).

If these important objectives cannot be quantified, all one can do is calculate the cost to society of adhering to those targets, and then discuss whether it is worthwhile to pay this price in the name of fairness. Alternatively, changes in the tax law that do not conform with constraints related to these objectives may simply be discarded.

V. Evaluating Nonmarginal Changes

Although marginal analysis can be helpful for evaluating small changes in the tax system, it cannot handle the grand design of the tax system. Because of the nature of the system—namely, the noncontinuity of administrative costs, nonconcavity of the revenue constraint, nonconcavity of deadweight loss, and increasing returns to scale in tax administration—changes to it cannot be evaluated by deriving marginal conditions in a well-behaved optimization problem. In order to compare the actual level of the social welfare function under different tax regimes, one may have to resort to simulation models.

Presumptive Taxes

One interesting example, which involves both non-cost-related targets and nonmarginal changes, is presumptive taxation. Presumptive taxes involve tax bases, or indicators, that can serve as proxies for ideal tax bases, but which are less easily manipulated and more easily monitored than the otherwise ideal tax base. Although the main motivation of presumptive taxes is to save administrative and compliance costs, the use of a proxy means that achievement of other targets will likely be adversely affected. The use of the term presumptive can be interpreted as including an apology for the fact that other targets (such as fairness) are sacrificed. In the sense that all taxes make design sacrifices for administrative reasons, all taxes are presumptive; after all, if there were no information gathering costs, an ability tax would arguably be optimal.

Consider the following tax design issues in the context of presumptive taxation. Most economists would agree that the household, and not the family, is the appropriate unit for capturing economies of scale in measuring economic well-being. However, actual income taxes and transfer payments are related to the family, where individuals are connected by relationships that cannot be manipulated easily. The choice of the family as the appropriate unit of taxation can be explained by administrative costs. One may be able to evaluate the cost saving in taxing the family instead of the household, but a proper evaluation of this issue requires the knowledge of the harm done—in terms of mismeasuring ability to pay—by not taxing the household.

Presumptive taxation is usually applied to income taxation. Most economists recognize that ability to pay is a function of full income, which includes the value of leisure. However, it is difficult to value leisure and therefore all tax systems are based on income and not on full income or the return to ability. Thus, taxes based on income are in a sense presumptive taxes on full income. Furthermore, one can interpret the provision existing in many countries allowing spouses to file separately as a presumptive recognition of the fact that two working spouses have less leisure than one working spouse. Whether this is a reasonable approximation depends on the value attached to the deviation from horizontal equity caused by separate filing.

One can add to the list of presumptive taxes depreciation schedules, the standard deduction, and a long list of what are explicitly labeled as presumptive taxes (see Tanzi and Casanegra de Jantscher (1987), Sadka and Tanzi (1992), and Slemrod and Yitzhaki (1994)). In our opinion, the issues involved in presumptive taxes cannot be easily handled by the MECF concept nor by simple optimization, because they involve cost saving at the expense of another target (horizontal equity) that is analytically intractable. Numerical simulation combined with evaluation of the cost attached to deviations from justice principles may be necessary (see, for example, Stern (1982)).

VI. Conclusions

In this paper, we explore the usefulness of the marginal efficiency cost of funds (MECF) as a guiding principle in the formation of tax policy recommendations. We argue that the MECF concept is useful for analyzing minor tax reforms. For any change in the tax system that is considered,35 one has to evaluate the expected tax revenue and the expected leaked tax revenue. In the simplest case, the sum of the two, divided by the former, is the MECF. One can calculate the MECF for alternative ways of raising revenue, and other things being equal, the one with the lowest MECF is the one that should be recommended.

How relevant is the concept of MECF to the International Monetary Fund? Our argument is that policy recommendations that are derived from abstract models (or, in some cases, experience) tend to be almost identical for all countries, simply because differences in culture, ethics, technological development, market structure, or any other country-specific difference, such as the level of income, are missing in those models. To overcome the complexity of the tax problem, there is a tendency to concentrate on one component of the problem, which leads to policy guidelines that are only correct under certain conditions, and those conditions tend to be forgotten. For example, the aims of “tax neutrality” and “optimal tax rates” are correct conclusions from disparate models, but they contradict each other. Careful application of the MECF concept can begin to sort out which component of the tax problem is most relevant to a particular country because country-specific properties, such as corruption, administrative capabilities, and an inability to enact simple tax laws, are all captured in the MECF.36

Consider the following example. The effectiveness of a VAT depends, among other things, on the validity of bookkeeping records in the country, which in turn depends on whether taxpayers need the records for running their own businesses. Excluding multinational corporations, it seems safe to assume that the larger the business, the higher the reliance on records for in-house management, and the more costly manipulations would be. Hence, one can expect the efficiency of a VAT to increase with the size of the business. Therefore, we should expect a crucial level of development that is required for a VAT to be efficient. We do not know what this crucial “level of development” is and how to measure it. But clearly, the MECF of having a VAT may differ among countries, and comparing the MECF of a VAT to the MECF of other taxes within a country may shed some light on whether a VAT is the appropriate tax for a country. The challenge, then, is to measure the MECF. Calculations similar to those performed by Silvani and Brondolo (1993) can be viewed as a first step toward doing so.37

We are not offering the MECF concept as a replacement for traditional analysis of efficiency of tax systems, nor as a substitute for an expert’s analysis of the weaknesses of a tax system. We do suggest, though, that it can be useful in making the choice between competing alternative approaches.


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Joel Slemrod graduated from Harvard University. He is a Professor of Business Economics and Public Policy and Director of the Office of Tax Policy Research at the University of Michigan Business School. This paper was written while Shlomo Yitzhaki was a visiting scholar in the IMF’s Fiscal Affairs Department. He is now Director of the Falk Institute for Economic Research in Israel and a Professor of Economics at Hebrew University of Jerusalem. He received his Ph.D. from Hebrew University. The authors thank Vito Tanzi, Howell Zee, and Louis Kaplow for many helpful discussions and comments; the FAD staff for providing a stimulating environment; and the FAD librarians for their help.


See, for example, Blough (1952); Shoup, Blough, and Newcomer (1937).


Musgrave (1959) does not mention the terms. Atkinson and Stiglitz (1980) do mention tax administration as an important subject, but no analysis is offered. In contrast, Bird and Casanegra de Jantscher (1992) stress the importance of tax administration.


Rosen (1985) devotes four pages (pp. 319–22) to the subject.


Administrative costs of taxation are fundamentally different from market transaction costs. In a market transaction, both parties willingly engage in the transaction. Hence, in a market transaction, the demand price exceeds the price received by the seller by the amount of transaction costs. Such costs can be viewed as being embodied in the utility or production functions, and they do not affect the stability of the equilibrium. In the case of taxation, one party may not be interested in participating in the deal and one role of the administration is to force the other party to participate. Since one partner may be trying to escape from the deal, tax transactions, unlike market transactions, are not stable. The administrator’s ability to gather information and exert his power on the taxpayer depends on the amount of resources budgeted for the administrator’s activities. The more public the information, the lower the administrative costs needed to retrieve it. One of the targets of compliance costs is to force parties that are engaged in market transactions to reveal the information to the tax authorities. This would reduce administrative costs.


Sec the survey by Cowell (1990), and Tanzi and Shome (1993).


Note that whether a tax is feasible is determined only by administrative issues.


One way to interpret tax withholding is to view it as drafting some taxpayers (e.g., employers) into the tax administration. They are not empowered to act fully as tax administrators but this kind of hierarchy is typical of any bureaucracy.


There are many instances in which one has to resort to a wider classification of actors. For example, the assumption of one social planner implicitly assumes that the social planner is interested in collecting the tax revenue. But whenever the planner is composed of several agents, as is the case in a democratic society, they may hold different opinions or represent different interest groups. In order to reach a decision about the tax system, compromises must be made. The result may be a blurred tax law that is hard to administer or to comply with. We refrain from extending the problem of taxation in this direction, not because it is an unimportant issue, but because it is difficult to analyze a tax law with a social planner who, in effect, undermines his own proposals.

Another case that is not captured in this framework is one in which the social planner, that is, the government itself, undermines the implementation and administration of the tax law. When the government consists of several branches, if some of the spending branches are relatively strong, they may use their influence to increase their budget by allowing contractors to evade taxes. Such a situation undermines the ability of the tax administrator to collect taxes. As we will argue later, these kinds of issues, which are country specific, are difficult to model. On the other hand, they are captured by the marginal efficiency cost of funds.


The term “simple” is not well defined. Slemrod ((1985), p. 71) defines complexity in terms of the amount of resources needed to operate the law. Blough ((1952), pp. 430–1) makes a direct attempt to define it by arguing: Tax simplification has been a loudly demanded objective. A good deal of discussion of simplification reflects a misunderstanding of what makes a tax complex. Emphasis is often placed on cumbersome and complicated language. The most important quality of a well-drafted statute is that it shall not be open to more than one interpretation. The ordinary taxpayer does not need to read the tax statute. More simple statements are available for his use. The language of the law is for administrators and courts. Wherever possible, the language should be simple rather than complex, but the matter is relatively unimportant. Lack of clarity, on the other hand, is of very great importance. Simple language, which proves to be ambiguous, may result in great complexity and uncertainty.


Note the following statement: “Unfortunately, tax administrations do not function optimally. In some cases, they can be so inefficient as to distort completely the intention expressed by the tax laws” (Tanzi and Pellechio (1995), p. 2). See also Bird (1989).


Tanzi and Pellechio (1995) differentiate between “effectiveness” and “cost minimization,” where effectiveness is defined as attaining a high level of compliance among citizens and cost minimization for a given revenue is identical to revenue maximization for a given cost. Interpreting “high” as “equal” would make their target similar to the targets referred to in this paper.


One can argue that activities that are directed toward equity establish confidence between taxpayers and administration, which may lead to a long-run increase in revenue.


We consider a one-period model. In a multiperiod model one would have accounted for such taxpayer behavior as deferral of taxable income to future periods.


A good description of the properties of administrative cost can be found in Shoup, Blough, and Newcomer (1937), pp. 337–51.


Note that a withholding system requires two information gathering systems and creates an opportunity for the withholding agency to evade the taxes it collects (Yaniv (1988 and 1992)). In a period of rapid inflation, the gain to the agent from withholding may exceed the cost.


For additional examples, see Tanzi (1992).


For example. Christiansen (1980) argues that a large fine and a small chance of detection are the most powerful deterrent in the case of tax evasion. This result is due to Becker (1968).


See Hahn (1973) for existence of lump-sum taxes during the U.S. civil war.


The “commodities” may include factors of production such as labor. In this case the quantity of the commodity is nonpositive.


One can derive this relationship under two alternative sets of assumptions:

(1) That the taxpayer is a utility maximizer and by Roy’s identity ∂v()/∂ti = – λ Xt, where v is the indirect utility function and λ is the marginal utility of income. The marginal burden is the income equivalent of the change caused by the reform.

(2) No optimization is carried out by the taxpayer and we are only interested in a Slutsky compensation to the household. That is, the question asked is what compensation would enable the taxpayer to continue to consume the basket he consumed before the reform.


The term MECF is slightly different from marginal cost of funds because efficiency considerations are separated from distributional issues. We will return to this point later.


This cost does not net out any benefits that arise because of the expenditure of the funds collected.


In many practical estimations, Xi is also used as an estimate of MRi (see Sutherland (1991)). The interpretation in those cases is that all MECFs are assumed to equal one or, alternatively, that all taxes are lump-sum taxes.


This result is due to the fact that we did not distinguish between the administrator and the social planner. Raising fines increases the possibility of corruption on behalf of the administrator.


Most of the models that incorporate administrative costs restrict the analysis to a subset of the types of cost related to taxation. For example. Yitzhaki (1979) and Wilson (1989) deal with excess burden and administrative cost, while Sandmo (1981), Slemrod and Yitzhaki (1987), and Mayshar (1991) deal with evasion, administrative costs, and labor supply. The main drawback of the first type of model is that it relies on specific utility functions (Cobb-Douglas in Yitzhaki (1979); CES utility in Wilson (1989)) to overcome the discontinuity created by having different commodities. The latter set of models do not allow for more than one tax in the system.


This means that it is not optimal for a tax administration to behave like a tax farmer, that is, setting marginal revenue equal to marginal costs, ignoring the fact that it spends tax dollars. Hence, privatization of tax collection may lead to over-enforcement. See Slemrod and Yitzhaki (1987) and Mayshar (1991).


Yitzhaki and Vakneen (1989) use the term “the shadow price of a tax inspector,” which is the revenue collected by adding another tax inspector. Note that the MECF is actually the reciprocal of the shadow price of a tax inspector.


MECFs may differ even in an optimal taxation model if one includes other targets in addition to cost minimization. We return to this point in the next section.


To formally see the point, assume that MECF > 1 and ask what would be the changes in compliance costs and administrative costs that will keep MECF constant. It is easy to see that — dCi/dAi = MECF, which means that Ci, should increase more than Ai decreases while keeping MECF constant.


Note that we use MCFi rather than MECFi when we take into account both distributional and efficiency issues.


The (Gini) income elasticity is a weighted average of the income elasticities of the potential marginal tax. weighted by the (implicit) weighting scheme of the Gini index. The term in parentheses is always positive (provided that the tax base is always positive).


One can point out that random taxes, such as a draft lottery or random auditing, do exist but, in practice, random taxes are often imposed in the presence of indivisibilities or increasing returns to scale.


See the discussion in Lambert and Yitzhaki (1995) on horizontal inequity.


It is argued by Bird and Casanegra de Jantscher (1992 p. 3) that “it seldom makes sense to try to reform tax administration without simultaneously reforming the tax structure,” One can generalize the argument by saying that it is rarely ideal to change only one tax parameter. Rather, an optimized combination is necessary.


Morag (1965) argued that taxes should be changed from time to time simply because it takes lime lor the taxpayers to learn how to “adjust” themselves to a new tax. This argument means that one cannot expect the same tax to be “the” appropriate tax for a long period of time. Recalculations of MECFs can indicate when to abolish a tax.


Silvani and Brondolo (1993) calculate the compliance rate of the VAT by estimating actual and potential tax revenues. They find that such revenues vary from 90 percent to 33 percent. Restricting their analysis to the margin (or assuming that the marginal and average compliance rates are equal), adding compliance and administrative costs enables the calculation of the MECF of the VAT for different countries, which should be compared to the same calculations for alternative taxes. Note that a compliance ratio of 33 percent implies an MECF of 3, ignoring administrative and compliance costs.

IMF Staff papers, Volume 43 No. 1
Author: International Monetary Fund. Research Dept.