This article was originally published as
C. W. Boyd, 1986. The Enforcement of Tax Compliance: Some Theoretical Issues. Canadian Tax Journal, 34, 3, May-June, 588-99.
--------------------------------------------------------------------------------------------------
THE ENFORCEMENT OF TAX COMPLIANCE:
SOME THEORETICAL ISSUES
{Article revised 17th February 1986. The original frontspiece reads as follows -* of the Edwards School of Business, University of Saskatchewan, and currently on leave at London Business School. The author wishes to thank Jack Dart of the University of Saskatchewan for his valuable assistance in the preparation of this article.}
ABSTRACT
The cost of tax evasion has been estimated to be between 5% and 20% of potential revenue. There are two main ways of fighting evasion : either through the improvement of taxpayers' attitudes to taxation, or through increasing the deterrence of tax authorities. This paper deals with the optimal management of one aspect of deterrence, namely expenditure on inspection.
As an aid to the evaluation of the optimal allocation of resources to inspection, the paper argues that the tax evasion problem is similar to the problems of evasion of payment for licences for televisions, vehicles, pets and bicycles, and evasion of payment for bus and train travel and for the use of metered parking spaces. In all these cases there exists the problem of deciding just how many inspectors to employ.
There are several theoretical ways of determining inspection resource levels. At the extremes lie a zero inspection rate, for systems where inspection is economically unjustifiable, and a full compliance inspection rate, for systems where evasion is intolerable. Interestingly, both these cases reveal distortions in the elasticity of compliance with respect to inspection.
Most payment collection authorities operate with some intermediate level of inspection resource. The prior literature on inspection resource administration suggests that an optimal level of resources should exist, although the mathematical analysis is difficult to follow. Up to a certain point, expenditure on additional inspectors produces extra revenue (both normal revenue and penalty revenue) but beyond that point further expenditure produces diminishing returns.
The paper describes the economic logic of several intermediate inspection resource rules: i.e. the inspection resource implications of "profit" or net tax yield maximisation, revenue maximisation, and quota-setting. It is also recognised that social and moral considerations may modify the pure economic determination of optimal inspection resources. In general the theoretical economic analysis of inspection resources is quite straightforward and intuitive, although the specific mathematics is complex.
The main circumstance in which the elasticity of compliance with respect to inspection would be evaluated to any degree would be when a tax administration manager is considering altering the level of inspection resources. The paper outlines the problems and opportunities inherent in the time-lag of response (hysteresis) to a change in the inspection resource level.
More importantly, the paper presents an argument that any change in inspection resource levels may produce a major unpredictable and irreversible change in compliance. Evidence from the enforcement of parking meter payments suggests that catastrophe theory may, under certain specific conditions, apply to the relationship between tax compliance and inspection. The paper concludes by expressing the need for empirical investigation of the theories outlined, and for discussion and analysis of the actual management of the inspection function in tax authorities such as Revenue Canada.
INTRODUCTION
Evasion of full payment of taxes by a portion of the population is a persistent problem faced by national, regional and local tax authorities. A recent review of the literature on tax evasion reveals estimates of the cost of evasion ranging between 5% and 20% of potential revenue[1].
In his further analysis, Lewis goes on to identify two major policy alternatives or initiatives available to deal with the problem of tax evasion. One initiative involves the improvement of taxpayers' attitudes and perceptions vis a vis the state and tax authorities, whereas the other involves increasing the deterrence of tax authorities. In relation to this second initiative, "the policy tools available ........ are the tax rates themselves, the penalty rates and the expenditure on investigation, which determines the probability of detection"[2].
This paper will discuss the problem of the determination of the optimal level of inspection expenditure in a tax collection authority. In particular it will be shown that while compliance levels may be determined by inspection pressure, it is theoretically possible that inspection pressure is itself determined by compliance level. If it exists, any feedback between these two variables would produce instability that frustrates the administration of tax collection
DETERMINING INSPECTION RESOURCES.
In order to discuss various administrative aspects of the determination of inspection resource levels in as simple a way as possible, we will make a number of assumptions which enable the elimination of factors which are tangential to the central theme. We will assume that the tax rate is fixed, as is the penalty rate applied to evaded tax, and we will also assume that the population is homogeneous on all relevant characteristics (e.g. income and profession). For the purposes of this discussion it is also helpful to consider the tax evasion problem as being similar to the problem of evasion of payment in a number of other domains. These related areas are as follows:
• licence payments for vehicles (common in Europe, for example), for televisions (Europe), and for the ownership of pets and bicycles. The evasion of licence payment takes the form of complete payment avoidance rather than under-payment[3], and any financial interaction with the collection authority is on an annual basis.
• Payments for bus and train travel, and for the rental of metered parking spaces. Evasion of payment consists of either non-payment, or else under-payment in the form of consumption in excess of the quantity paid for. The transaction frequency is high, often daily or twice-daily.
In virtually all of these domains the collecting authority invests in methods of monitoring payment and detecting payment evaders, and there exists a system for imposing financial penalties on those found guilty of evasion. The problem we address is common to all these domains, namely the question of how many inspectors to employ in a given context. If too few inspectors are employed, then the revenue loss from evasion is not balanced by the revenue generated by inspectors (which is made up of any captured evaded revenue plus the associated penalty revenue obtained from the detected evaders). It is also possible to employ too many inspectors, and to incur excessive costs in gaining a particular level of total revenue.
The tax collection manager is faced with several alternative theoretical methods of determining the optimal level of inspection resources. These are illustrated and discussed below:
Zero Inspection
A zero inspection rate is adopted when the allocation of resources to inspection is considered uneconomic in the light of the effects of redistributing taxes which would otherwise be evaded. Zero inspection, and hence the zero probability of detection of an evader, is found in domains such as the licensing of pets and bicycles. Certain transit systems with relatively low unit fares also operate on this basis. The range of attitudes in the population to the risks and morality of non-payment is such that the evasion rate does not equal 100%, for a proportion of the population pays up despite an absence of enforcement.
The payment of taxes in the absence of enforcement indicates a distortion in the relationship between evasion rate and inspection rate for low levels of inspection rate approaching zero. The elasticity of evasion with respect to inspection may therefore not be constant, with the elasticity across low levels of inspection being quite different from that across moderate levels of inspection.
Full Compliance Inspection
At the other extreme, it is possible to envisage a taxation system where full compliance is essential. Although it is difficult to imagine the specific circumstances in which this would apply, this is an interesting case to consider.
The intriguing aspect of full compliance systems regards the actual level of inspection that is required to ensure minimal evasion. Is 100% inspection, a complete client audit, necessary? Intuitively, it would seem that the inspection rate could be reduced to 95%, 90%, or even 80%, without producing any appreciable increase in evasion. It is plausible that there is some threshold level of high inspection above which further inspection activity produces hardly any deterrent effect. For example, the evasion behaviour of taxpayers who are audited 6 occasions out of every 7 should not differ significantly from those who are audited every single tax period. Again, this suggests that the elasticity of evasion with respect to inspection may not be constant, with the elasticity across higher levels of inspection differing from that across moderate levels of inspection.
Intermediate Inspection Rates
Most collection authorities subject to payment evasion operate with an intermediate inspection rate that lies between 0% and 100%. The determination of an optimal level of inspection resource has been the subject of a number of theoretical studies[4]. These studies, which are characterized by complex mathematical analysis, conclude that an optimal level of inspection should exist for any given system. At its simplest, the calculation of an optimal level of inspection resource in these studies involves the comparison and balancing of the following cost and revenue items[5]:
|
Item |
Dependence on inspection level |
|
The component of normally reported revenue that would be evaded in the absence of inspection |
As inspection level increases, the rate of evasion decreases, producing increased normal revenue |
|
Revenue captured by inspection |
As more inspectors are employed more evaders are discovered and hence captured revenue increases. Above a certain point the decrease in evasion is such that captured revenue decreases as the inspection rate goes up. |
|
Penalty revenue, calculated as a multiple of captured revenue or as a fixed penalty amount |
As above |
|
Inspection cost |
Assumed to be proportional to inspection level over an intermediate range |
The first of these items, namely the component of normal revenue that is attributable to the deterrence effect of inspection, may be difficult to measure and may therefore be a disregarded variable in the actual decision models used by some collection authorities. If it is excluded, then the inspection function can be managed like any other discrete business activity which collects direct revenue in return for direct cost expenditures. Alternatively, the effect of inspection on normally received revenue may be estimated by extrapolation of the rate of compliance, as revealed by inspection. Many collection authorities can be expected to operate within some arbitrary rule-of-thumb target range of compliance which has developed over time as an organizational norm, and which may or may not have been originally determined by systematic evaluation of the costs and benefits of alternative inspection resource levels.
The prior literature suggests the penalty rate and the inspection level are interchangeable deterrents. A tax system with a low inspection rate (i.e. with the probability of an individual being inspected being of the order of 0.05% - 5%), when coupled with penalty payments which are high multiples of the unit of revenue evaded, may experience the same compliance rates as a tax system with a high inspection rate and less extreme penalty fines. Since we have defined the penalty rate as being constant for the purpose of this paper, we will not persue the argument in favour of low-inspection-rate systems with draconian penalties as providing the lowest-cost solutions. It has been noted that such arguments lead to extreme conclusions (e.g. an optimal system would comprise very low inspection rates and punishments with infinite cost, such as hanging), and that most inspection systems operate within limits which are generally defined by the moral attitudes of the society which is allowing itself to be inspected[6]. It is possible that such moral considerations may be of such importance that they are overwhelming, and that inspection resources are subsequently set at a level (which may be high, or low) which appears unjustifiable on purely economic grounds.
We would anticipate though that systems with low inspection rates may be expected to have a high transaction frequency (e.g. daily in the case of transportation or parking facilities) in order for the low frequency of inspection to be at all observable by the population, and hence act as a deterrent to evasion. Conversely, systems with low transaction frequencies (e.g. for annual personal income tax declarations) might be expected to operate with reasonably high inspection rates if inspection is to have any widely dispersed deterrent effect.
'Profit' Maximising Inspection
One specific decision rule alternative available to the tax collection manager would be to set inspection resources at the level which maximises 'profit' or net tax yield, the difference between total inspection-related revenues and inspection costs. Inspection resources would be increased up to the point at which marginal revenue equals marginal cost, and thus the tax collector would authorise the expenditure of an additional dollar on inspection, provided it brought in at least another $1.01 in revenue. This kind of approach implies the toleration of moderate levels of evasion, otherwise inspectors would not find sufficient victims to justify their existence.
Under 'profit' or net yield maximisation there would have to exist a delicate balance between the number of inspectors and the number of evaders that would be similar to the relationship between predators and prey in the natural world. Equilibrium states in predator-prey relationships have been extensively studied, and would appear relevant to the management of tax authorities[7].
The profit maximisation approach would theoretically appear to be most applicable to situations where inspection costs can be readily identified (i.e. few joint costs with the normal revenue processing function), where the normal revenue unit is small (as with bus fares or parking meter charges), and the penalty revenue unit is a reasonably large multiple of the normal revenue unit. Under these circumstances penalty revenue would comprise a substantial proportion of total revenue or even sometimes exceed normally received revenue.
Revenue Maximisation and Quotas
As stated above, net yield maximisation implies a toleration of moderate levels of evasion, and it may be that a tax authority decides that these levels of evasion are higher than desired by society, and are hence morally unacceptable. An alternative decision rule would thus be to increase inspection resources above the point at which marginal revenue equals marginal cost and towards the point at which total revenue is maximised (marginal revenue equal to zero), regardless of the cost of the additional inspection resources required to achieve this.
In comparison to profit maximisation, this regime would employ more inspectors, each of whom would not now spend so much time dealing with evaders (e.g. time spent out writing out penalty tickets for a parking meter inspector), since a lesser number of evaders would now be spread across a larger number of inspectors. This method still allows for the existence of a degree of evasion, provided that the revenue obtained from captured evaders is greater than the payments they have attempted to avoid making. Any further increase in the number of inspectors would produce negative marginal revenue.
The revenue maximisation approach to the determination of inspection resource levels appears more applicable to income tax collection, where the question of the extent of compliance may be of more importance than an economic criterion such as yield maximisation.
In reality it is unlikely that marginal revenues and costs can be measured with such precision that the points at which MR = MC or at which MR = 0 could be identified with any confidence, and consequently modified versions of these marginal analysis models may evolve. Such decision models may incorporate a definition of a desired marginal revenue beyond which additional marginal costs would not be incurred. This type of rule could easily be adopted in the form of the specification of revenue quotas for individual inspectors. Such models would define an inspection resource which may range from somewhere below the level associated with profit maximisation through to the level associated with revenue maximisation. It should be noted that this kind of external basis for the setting of quotas is primarily market-driven (e.g. determined by estimates of client response to the 'selling' activity of inspectors), and that this must be distinguished from various other internally derived reasons for the use of quotas, such as for the purpose of motivation of individual inspectors or to facilitate the appraisal of inspectors' performances.
For any specific tax collection system, the actual number of inspectors defined by each of these decision rules depends on the elasticity of evasion with respect to inspection, in other words the degree to which a given level of inspection determines a given level of evasion.
INTERACTION BETWEEN INSPECTION AND EVASION
The decision of an individual to evade payment must incorporate consideration of the subjective probability of detection, evaluated according to the individual's attitudes to risk-taking and to the 'morality' of the tax. A tax authority can influence the perceived or subjective probability of detection in a number of ways, such as through the use of marketing techniques to convey an impression of a greater chance of being caught than actually exists, or through various schemes of deployment of inspectors in the field (e.g. block sampling techniques rather than random sampling). Fundamentally however, evasion behaviour must be related to the objective probability of detection, which is dictated by the number of inspectors employed[8].
The main circumstance in which a tax collection manager will consider the interaction between inspection and evasion is when a change in the level of inspection resources is being contemplated. What happens when such a change is made?
One obvious outcome is that there will be a time lag before the behaviour of the client population adjusts to the new level of inspection. This arises if an individual's decision to change behaviour is based primarily on observation and experiences of occurrences of inspection, both directly, and as reported through the individual's social network. If the number of inspectors is changed, then it will take quite some time for an observer to determine that the changed number of occurrences of inspection represents a different probability of detection, rather than being some statistical quirk associated with a constant number of inspectors being deployed randomly. As each member of the population identifies the new probability of detection through further observation, each will consider the risks involved and decide whether or not to change behaviour.
In systems with daily transactions, such as parking and transportation, the time lag may be such that it takes several months for the system to stabilize after a change in inspection level[9]. For income tax, the response time could be very long, and could even be such that incremental changes in inspection which are not publicized may have little deterrence effect.
This time lag would be frustrating to tax collection managers, but it is not necessarily bad. Although it implies that increased inspection will not produce immediate returns, it also implies that reduced inspection will not provoke an immediate reduction in revenue. Tax yields might be quite robust, for example, in the face of a temporary reduction in the number of inspectors, provided the cut-back receives minimal publicity.
A second outcome of a change in the level of inspection relates to the nature of the workload of individual inspectors, and is of great potential importance. It theoretically arises if the time taken by an inspector to discover and process an evader substantially exceeds the time taken to discover that a client has been honest, and is best explained by considering the activities of a parking meter inspector.
Suppose that it takes an average of 20 seconds to inspect and discover that a meter still has paid time showing on the clock, and that it takes an average of 3 minutes to inspect and discover a meter violation and to issue a penalty ticket. An inspector's working day of 420 minutes could be made up of any combination of these two activities. Some of the combinations are shown in the rows below, together with the notional evasion rate implied by each combination[10].
|
Number of penalty tickets issued (3 min. each) |
Number of valid meters inspected(20 secs.) |
Total number of inspections |
Notional rate of evasion |
|
0 |
1260 |
1260 |
0% |
|
20 |
1080 |
1100 |
2% |
|
40 |
900 |
940 |
4% |
|
60 |
720 |
780 |
8% |
|
80 |
540 |
620 |
13% |
|
100 |
360 |
460 |
22% |
|
120 |
180 |
300 |
40% |
|
140 |
0 |
140 |
100% |
The output of this constant inspection resource (as measured by the total number of inspections made) is not constant, and is determined by the number of evaders discovered. It can thus be seen that while inspection level may generally determine the rate of evasion, the enforcement pressure that this inspector is able to exert is itself a function of the evasion rate. The degree to which this two-way dependency exists in any given system is obviously dictated by the size of the ratio between the time taken to deal with an evader and the time taken to discover that a client has made honest payment.
A given level of inspection may not therefore define a unique level of evasion, and any particular equilibrium position in a payment collection system may have to be regarded as a temporary state which may not be subsequently reproducible. Some empirical evidence of this kind of instability has been reported in relation to parking enforcement in Central London[11]. It was observed that a reduction in the number of inspectors, which was followed by a return to the original number, produced a dramatic increase in evasion which could not be reversed. This collapse in the ability to enforce parking regulations in London was described by Elliott and Wright as being similar to a number of phenomena which are amenable to analysis using catastrophe theory[12].
An initial reduction in inspection may trigger a catastrophic increase in evasion, because the initial increase in evasion slows down the output of each inspector, which triggers further evasion, which further reduces output, which stimulates more evasion, and so on. Although this vicious spiral would represent a great frustration for the tax collection manager, there is also the possibility of utilizing this phenomenon to advantage. For example, a temporary burst of increased intensive inspection may provoke a catastrophic reduction in the level of evasion which may allow increased permanent output from the base number of inspectors[13].
DISCUSSION
This paper has presented an outline of the various theoretical methods of determining inspection resource levels in organizations subject to payment evasion, and has described theoretical aspects of interaction between inspection and evasion which may frustrate the effective management of such organizations.
It is hoped that this paper will stimulate discussion and analysis of the management of the inspection function in tax authorities such as Revenue Canada, which in recent years has been embroiled in controversy over the implementation of more effective enforcement techniques. The past academic literature on the topic of optimal enforcement has been of little relevance to the practitioner because of the impenetrability of the mathematical analyses used in these studies. The simplified interpretations and models which have been presented here should provide some foundation for the analysis of actual management practices.
Several of the theories put forward in this paper deserve empirical investigation. In particular, it would appear important to determine if the complex interdependency between evasion and inspection that has been observed in the enforcement of parking meter payments in Central London is also found to apply to tax collection. If it is found to apply, then much of the prior literature on optimal tax administration will have to be discarded, because of the universal adoption of an over-simplified assumption on the relationship between compliance and inspection.
FOOTNOTES
1. A. Lewis, The Psychology of Taxation (Oxford: Martin Robertson, 1982), 257, at 125.
2. M. G. Allingham and A. Sandmo, "Income tax evasion: a theoretical analysis" (1972), 1 Journal of Public Economics 323-38, at 338.
3. The prior literature frequently refers to tax evasion as the 'under- reporting' of income. We assume that the phrase 'under-reporting' connotes one or more discrete decisions to evade components of tax liability, utilizing some mixture of the under-statement of some sources of income and the non-reporting of other sources. This latter form of tax evasion may be validly compared with licence payment evasion.
4. For example, Allingham and Sandmo, supra footnote 2 ; V. Christiansen, "Two comments on tax evasion" (1980), 13 Journal of Public Economics 389-93 ; S. Kolm, "A note on optimum tax evasion" (1973), 2 Journal of Public Economics 265-70 ; M. Marrelli, "On indirect tax evasion" (1984), 25 Journal of Public Economics 181-96 ; A. Sandmo, "Income tax evasion, labour supply, and the equity-efficiency tradeoff" (1981), 16 Journal of Public Economics 265-88 ; and T. N. Srinivasan, "Tax evasion: a model" (1973), 2 Journal of Public Economics 339-46.
5. These cost and revenue items are defined respectively as administrative costs, and payments received or due. These definitions are arguably simplistic (see R. M. Bird, "The costs of collecting taxes: preliminary reflections on the uses and limits of cost studies" (1982), 30(6) Canadian Tax Journal 860-65, for an exploration of the variety of potential definitions of tax costs and revenues), but are sufficient to illustrate the general nature of the inspection resource problem.
6. Kolm, supra footnote 4.
7. For example, C. W. Clark, "Profit maximisation and the extinction of animal species" (1973), 81 Journal of Political Economy 950-61. Readers may also be interested to view the tax inspector as a type of mugger: see P. A. Neher, "The pure theory of muggery" (1978), 68(3) American Economic Review 437-45 for an analysis of the economic dilemmas faced by muggers.
8. For a full review of the literature on behavioural aspects of tax evasion, see Lewis, supra footnote 1.
9. In the physical sciences this kind of time lag is known as hysteresis, and the literature on this phenomenon may be of relevance to tax administration. If inspection resources are increased from x to y, and then reduced back down to x again some time later, then a graph of inspection rate against evasion rate should exhibit a pattern known as a hysteresis loop. The time lag, and the nature of the feedback between inspection and evasion may also be such that evasion could overshoot in response to a change in inspection, before settling back at a new equilibrium point. This phenomenon, if it exists, would be analagous to a process known as hunting, which is observed in under-damped servomechanisms.
10. The actual rate of evasion may differ from this notional rate if the frequency of inspection of each parking bay does not match the average frequency of turnover of vehicles in each bay.
11. J. R. Elliott and C. C. Wright, "The collapse of parking enforcement in large towns: some causes and solutions" (1982), 23(6) Traffic Engineering and Control 304-310
12. See E. C. Zeeman, Catastrophe Theory , (Reading, MA.: Addison- Wesley, 1977) for a full description of this theory.
13. In commenting on this paper, the Editorial Review Committee of this Journal expressed the opinion that the tax administration problem is predominantly one of deciding where best to apply a fixed auditing resource across a very heterogeneous set of taxpayers so as to get maximum revenue generation, and not one of deciding to vary the resources applied to a homogeneous crowd of meters (or taxpayers).
We would argue that the assumption of homogeneity that is made in this paper does not preclude the subsequent consideration of the allocation of inspection resources across a heterogeneous set of taxpayers, and that this resource allocation problem follows on from the problems described in this article. If such a set of taxpayers can be regarded as being comprised of various sub-sets of homogeneous groups, each with their own particular elasticity of compliance in relation to inspection, and each with their own particular average tax yield for a given level of inspection, then the allocation of inspection resources across these groups can be analyzed. It would appear to be a problem requiring exceptionally complex mathematical techniques - most probably various forms of dynamic linear (and non- linear) programming.
If catastrophe theory is found to apply when inspection resources are varied for one particular sub-group (e.g. waiters), then there is little point in utilizing such complex techniques for determining the optimal distribution of a fixed set of inspection resources until more is known about the elasticity of compliance at the level of homogeneous groups.