Tài liệu Tax Compliance by Firms and Audit Policy∗ docx

First, the e¢ ciency considerations arise from the interaction among …rmswithin an industry as well as interaction of …rms with the tax authority.Bayer and Cowell 2009 have demonstrated

Tax Compliance by Firms and Audit

Policy ∗

University of Adelaide and London School of Economics

September 2010

Disciplines

Houghton Street London WC2A 2A

∗

We are grateful for comments from participants at the ESRC/HMRC International Conference on

Institutional Taxation, the 9th Journées Louis-André Gérard-Varet and the 2009 meeting of the

European Economic Association

Abstract

Firms are usually better informed than tax authorities about market conditions and the potential profits of competitors They may try to exploit this situation by underreporting their own taxable profits The tax authority could offset firms’ informational advantage by adopting “smarter” audit policies that take into account the relationship between a firm’s reported profits and reports for the industry as a whole Such an audit policy will create an externality for the decision makers in the industry and this externality can be expected to affect not only firms’ reporting policies but also their market decisions If public policy takes into account wider economic issues than just revenue raising what is the appropriate way for a tax authority to run such an audit policy? We develop some clear policy rules in a standard model of an industry and show the effect of these rules using simulations

• JEL: H20, H21

• Keywords: Tax compliance, evasion, oligopoly

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1 Introduction

Should a tax authority take into account the “real-economy” e¤ects of itscompliance policy? The actions of tax authorities are often perceived inpurely …nancial terms, perhaps as a kind of tax farmer that seeks to max-imise the revenue for the government or as a …scal police o¢ cer that seeks

to ensure enforcement of the law as e¤ectively as possible However, just as

a conventional police force may properly have objectives other than simplelaw enforcement (fostering good community relations for example) so thetax authority may be required to have concern for a broader range of eco-nomic objectives than simple revenue-raising and compliance Although it isconvenient as a modelling device to assume that an agency has a single …nan-cial target it would be unreasonable to insist that the government’s di¤erentpolicy objectives were located in separate watertight compartments In thispaper we suppose that a sensible tax authority is concerned about issues ofproductive e¢ ciency in the economy and about equitable treatment of tax-payers We develop a model of tax compliance by …rms and show how theiractivity in product markets is connected with the design and implementation

of enforcement policy by a tax agency

Some aspects of the real-economy issues associated with tax complianceare already well known For example in the case of the personal income taxand decisions made in the labour market the conventional Allingham andSandmo (1972) model can be extended to incorporate labour supply Theconventional welfare-economic analysis of deadweight loss as applied to in-come taxes and commodity taxes can be extended to take tax noncomplianceinto account (Cowell 1990) However the further considerations that apply

in the case of the taxation of …rms have not been worked out The case of

…rms is special in terms of both the e¢ ciency and equity objectives

First, the e¢ ciency considerations arise from the interaction among …rmswithin an industry as well as interaction of …rms with the tax authority.Bayer and Cowell (2009) have demonstrated that the e¤ectiveness of com-pliance policy depends on whether there is e¤ective competition or collusion

organ-isation and the design of compliance policy raises several policy questions.Should audit rules be designed in such a way that …rms will be induced to

1 See also Besfamille et al (2009) who show that with imperfectly competitive …rms increased enforcement of an output tax will reduce output and may reduce revenue.

act more e¢ ciently in product markets? Should a change in industry petitiveness change the design of compliance policy?

com-Second, the equity considerations arise precisely from the tailored auditrules that the tax-authority might employ to induce the behaviour in productmarkets that might be desirable on e¢ ciency grounds A “smart”compliancepolicy may give the appearance of treating equals unequally in a way thatdoes not arise in compliance models involving the personal income tax Thisimplies that in evaluating the desirability of compliance policy one needs to

go beyond the conventional individualistic welfare model in order to dealwith questions of tax equity

The paper is organised as follows Section 2 explains our approach andrelates it to the literature and Section 3 sets out the formal model Section

4 develops the simple welfare-analytics of this model examines its workingsusing a simulation; Section 5 discusses the special issues of equitable treat-ment that occur in the audit model with …rms; Section 6 draws the policyimplications from this Section 7 concludes

Before we specify the precise model that we shall use to establish resultsand to simulate behaviour let us describe the economic agents and theirinterrelationships

treated as no more than pro…t centres which can be tapped by the tax agency.More sophisticated approaches take some account of the …rms’role as produ-cers but in a naive fashion that does not yield much economic insight Thestandard assumption is either that each …rm is a price-taker without marketpower or that there is a perfectly-informed monopolist with almost completemarket power However, under conventional treatment of risk and taxation,each of these idealised market forms turns out to produce an analysis of tax

2 What happens is that under these special market conditions the production decisions can e¤ectively be separated out from the tax compliance decisions, reducing the tax- compliance problem to a minor elaboration of the Allingham and Sandmo (1972) model

each …rm is assumed to be in a particularly simple market environment,particularly simple results emerge.

To make the analysis interesting we need to think of the …rm also as

an information processor This involves analysing the behaviour of the …rmunder uncertainty The uncertainty comes from three sources:

1 exogenous uncertainty, such as demand shocks, cost shocks and ment errors

assess-2 uncertainty as to whether the …rm will be audited for tax purposes,

3 uncertainty about the behaviour of other …rms in a similar position toitself

All three types of uncertainty will be seen to have a role within our model.The third type makes it clear that it is important to consider the …rm withinthe context of an industry where the behaviour of other …rms is important

in determining its own behaviour

much on the physical characteristics of the outputs of the member …rms but

on the relationship among them In the light of the exogenous uncertaintymentioned as point 1 in the list above it makes sense to suppose that mem-bers of the industry are better-informed than other economic agents aboutmarket events that may a¤ect their pro…ts: they intimately know the eco-nomic conditions that apply to their industry and could, if they wanted to,make reasonable estimates of the performance of other industry members In

a sense the industry is an information network in which the insiders have anadvantage over an outside observer such as the tax authority If there were

no information advantage then the tax authority could work out the maximising decisions and the associated industry equilibrium for itself andaudits would become virtually irrelevant To keep the problem manageable

pro…t-we assume that the industry is assumed to have a …xed number of …rms: pro…t-we

do not attempt to account for entry into or exit from the industry In ourformal model it is su¢ cient to let the number of …rms be 2, although thissimpli…cation is not essential to the main point of the argument

(Cowell 2004, Lee 1998).

Tax authority We suppose that tax policy is entrusted to an agency thathas the responsibility for enforcement, control over audit policy, and, pos-sibly, over tax design but not over the structure or level of penalties for illegalnon-compliance (evasion) Its objectives may be wider than simple revenueraising: this is important in our discussion of e¢ ciency and policy design inSection 4 The tax authority will expect to …nd that di¤erent types of auditpolicy will have di¤erent types of impact on the …rms’behaviour Once againthe role of information is crucial because, although the tax authority will nothave as good information about an industry as the insiders it will …nd thatthere is some information that can be used to re…ne and improve the auditpolicy.

government that cares about the well-being of its citizens Accordingly policycan be evaluated in terms of welfare-economic criteria that are applied asstandard to other problems of public policy evaluation such as cost-bene…tanalysis

We begin with the factors that determine the …rms’ taxable capacity Werepresent the industry as a duopoly The essential insights can easily beextended to an arbitrary number of heterogeneous …rms: the two-…rm modeljust requires some interpretation: if we focus on the behaviour of …rm 1 then

“…rm 2”can be considered as a proxy for the rest of the industry in the eyes

of …rm 1’s decision makers

We assume that …rms make decisions about quantities of a good to produceand sell in a market Each …rm’s market opportunities are given by a linearinverse demand schedule:

where p is the the market price of the industry’s output given that …rm 1

are the production-cost functions of …rms 1 and 2 respectively, then pre-taxpro…ts are

In the standard industrial-organisation model this is almost the end of thestory There remains a type of endogenous uncertainty for each …rm aboutthe output decisions of the other; this is usually resolved within a standardgame-theoretic framework to capture the type of relationship between theeconomic agents in the industry; here we take each of two apparently standardcases:

Cournot: each …rm takes the other’s output as …xed while solving itsown pro…t-maximisation problem

Collusion: the …rms act jointly in their decision making

However, this is not almost the end of the story and, in the presentcontext, these two cases are not quite the standard ones of the industrial-organisation literature As we will discuss in Section 3.2, the introduction

of taxation and the possibility of non-compliance introduce new elements tothe pro…t-maximisation problem

authority is aware that …rms may perceive that their information about thepro…ts that they make in a given year is better than the tax authority’sinformation and that this may give them to under-report or to conceal Ifthe tax is proportional at rate t and there is full compliance by the …rm thenthe …rms’pro…ts net of taxes are simply

However, these pro…ts are not directly observable by the tax authority without

…rms and it may choose to undertake a costly audit in order to check the

truthfulness of the report If a …rm is found to have under-reported, it isrequired to make up the shortfall of the tax and also to pay a …ne F Thesize of the …ne is assumed to be outside the jurisdiction of the tax authority– we will assume it to be a …xed proportion of the under-reported pro…t,

Even with the presence of the …ne, less than complete compliance maystill be an attractive option for a …rm, as discussed in section 3.3 Howthe …rm may be expected to react will depend on the type of audit policy

in place and the consequent probability of being subjected to a …ne Weassume that the …rms are well informed about the audit strategy being used

by the tax authority although not about how it will be applied in their owncase In other words all in the industry know how the probability of auditingindividual …rms is determined but no …rm knows for sure that it will beaudited Clearly there is a wide range of possibilities for the structure ofaudits in the light of …rms’ behaviour However, we will focus on just twotypes of audit policy that are, perhaps, useful caricatures of actual practiceand that enable us to analyse the role of information

will use this primitive type of policy as a benchmark

information it has about the industry it could use this to tailor the auditrule for each individual …rm in the light of that …rm’s declaration relative

to declarations generally in the industry The reports from each …rm arefree information and we can imagine the situation where an intelligent taxauthority would use this to ‡ag suspicious behaviour If there were manysimilar …rms in the industry the tax authority might well concentrate itsinvestigations on individual …rms reporting substantially below the industryaverage In our two-…rm case this translates into a rule where, ceteris paribus,one always assigns a higher audit probability to the …rm reporting the lowerpro…t In the case where …rms 1 and 2 are indeed similar it is instructive tolook at the linear relative audit rule that generates detection probabilities

where a and b are policy parameters Parameter a re‡ects the total audite¤ort by the authority and is determined by its budget: it is the averagedetection probability for any pattern of declarations by the two …rms Para-meter b captures the authority’s reactivity: the higher is b the higher is the

0

We assume that …rms are concerned just about expected net pro…ts If the

pro…ts are, respectively,

we may reasonably suppose the marginal concealment cost to be increasing

in the amount being concealed Accordingly we let the cost of concealment

be represented as

for i = 1; 2 Drawing together expressions (6) to (12) this means that theexpected payo¤s for the two …rms, net of concealment costs, are

1(d1; d2) 1(d1; q1; q2) + [1 1(d1; d2)] 1(d1; q1; q2) C1( 1(q1; q2) d1);

(13)

2(d1; d2) 2(d1; q1; q2) + [1 2(d1; d2)] 2(d1; q1; q2) C2( 2(q1; q2) d2)

(14)

As we noted above, there is rather more to this analysis than a conventional

made by the other The …rm’s activities are carried out in two stages:production stage: This covers the generation of taxable pro…t and in-cludes production and sales of the product In the model …rms choose

…rst stage Furthermore, between the production stage and the declarationstage each …rm may experience a pro…t shock, which is observable to the

…rms in the industry but unobservable to the tax authority Because the

oc-curs, pro…t shocks that result from …xed-cost shocks, marginal-cost shocks,demand shocks or observation errors by the tax authority can all be expressed

in the same way We assume that the …rms are essentially identical exceptfor the pro…t shock; in particular they are perceived ex ante as identical bythe tax authority when determining its audit rule

The two stages and the two contrasting market assumptions, Cournotcompetition or collusion, lead us to consider four possible cases, which wewill brie‡y consider in turn

Case 1: Cournot competition at both …rst and second stages.Here the tax authority has a nice opportunity Consider the standard model

of a symmetric duopoly illustrated in Figure 1 where the two straight linesrepresent the reaction functions of the two …rms If …rms were perfectlycompliant on principle, or if the tax authority could perfectly observe mar-ket events so that there were no possibility of evasion, then equilibrium would

cannot observe events perfectly and just uses a …xed audit rule then thisdoes not a¤ect the product market so that the reaction functions and equi-librium remain unaltered (Marrelli and Martina 1988) In our model this isthe case when b, the reactivity of the rule in (6, 7), is zero Then …rms face adeclaration-independent detection probability of a: However, if the authorityswitches to a relative rule it creates an informational externality: each …rmknows that its probability of audit is going to depend on its declaration re-lative to the average declaration in the industry Two things then happen.First, the switch to the relative rule causes each …rm to increase the declara-tion for any given level of output, for reasons that are straightforward to seeintuitively The reactivity of the relative rule is of special importance here

the amount of taxes evaded:

Second, there is an e¤ect on the …rst-stage reaction curves in Figure 1

the pro…ts of …rm 2 to fall, which in turn reduces the optimal declaration of

…rm 2 Therefore, …rm one can indirectly decrease its audit probability byincreasing its production quantity A …rm wants to do this up to the point

the improved scope for evasion By this reasoning we can see that the switch

in the audit regime will move …rm 1’s reaction function out to the right asshown Of course the same e¤ect works for …rm 2 and so it is clear that

We can state this positive e¤ect of a relative rule on the quantity choicesmore formally

3 The result is general and does not depend on either the assumption that there are only two …rms or the assumption of linear reaction functions (Bayer and Cowell 2009).

Figure 1: E¤ect on reaction function of informational externality

Cournot quantity, while under a relative rule they produce more than theCournot quantity

Case 2: Cournot competition at the …rst stage, collusion at thesecond stage

If …rms are able to cooperate on tax returns then it is clear that they willaim at eliminating the externality introduced by a relative audit rule Bycoordinating their declarations they can avoid the dilemma that both …rmshave an incentive to increase their declarations in order to reduce the auditprobability Consequently, in the case of collusion at the declaration stage,

a relative rule loses its positive e¤ect on declared pro…ts and declarationsbecome the same as under a …xed rule (i.e the reactivity of the rule b is

reduce evasion

4 This is true in a symmetric environment, where both …rms have the same production and evasion cost In asymmetric situations the declarations may di¤er from the …xed rule outcome, as collusion provides an additional incentive to minimise aggregate evasion cost.

Proposition 3 If …rms collude on the declaration stage than in a symmetricequilibrium the reactivity of the rule b has no impact on the evaded tax.

Obviously, this raises the question how collusion at the declaration stageimpacts on production decisions The impact is not obvious One mightexpect that eliminating the externality of the relative rule on the second stagealso takes away any incentive to produce more than the Cournot quantity Oreven worse, one could conjecture that the collusion at the second stage mightspill over to the production stage leading to quantities even smaller thanthose under Cournot competition Luckily, these fears are unsubstantiated.Cooperation among …rms when they …le their tax returns does not fullyeliminate the externality on production quantities created by a relative rule.The intuition is subtle When …rms individually decide on their productionquantities they foresee already that they will collude on the declaration stagelater on The jointly optimal declarations will depend on the gross pro…ts

As in the case without collusion …rm i’s optimal declaration (now the one

pro…t For this reason –with the ultimate outcome in mind –a …rm wants

to reduce the pro…t of the competitor by increasing production even when itknows that they will cooperate when …ling the tax returns

(b > 0) still leads to quantities greater than the Cournot quantity

A relative rule loses its bene…cial e¤ect on evasion behaviour in the ence of collusive tax declarations but still delivers welfare gains in the productmarket through production quantities beyond the Cournot outcome

pres-Case 3: Collusion at the …rst stage, competition at the secondstage

Suppose the …rms can agree on total output and some allocation of outputand pro…t between them Since …rms are identical ex ante, assume furtherthat they can only agree on quotas that lead to the same gross pro…t for

5 This could be the outcome of Nash bargaining with identical bargaining power and wihtout side payments.

pro…ts Here the relative audit rule is obviously still e¤ective in reducing theamount of taxes evaded compared to a …xed rule, as the externality stemmingfrom the relative rule is still on operation in the declaration stage.

stage the rule’s reactivity b decreases the amount of taxes evaded:

It remains to be determined, which production quantities the …rms willagree upon on the …rst stage Intuition suggests that the relative rule oper-ating on the second stage does not play a role Since ex-post expected netpro…ts should increase with the gross pro…ts …rms should be able to agree on

a joint monopoly production plan The following Proposition con…rms thisintuition

quotas produce half the monopoly quantity each

Case 4: Collusion at both stages

It is clear that this combination results e¤ectively in monopoly behaviourthroughout; the distinction between the stages becomes arti…cial as does thedistinction between the two types of audit rule Under fairly weak conditions(e.g symmetric cartel agreements) we know that output and declaration

pro…t maximising entity with respect to both production and declarationdecisions then a relative rule loses all bite It is worth noting that a relativerule at least does no harm in this highly collusive environment

In the light of the diverse behaviour that will arise from auditor-…rm action under various competitive regimes there are some important policyimplications to be investigated We will do this in two stages in order to

inter-6 The proofs to Propositions 3 and 6 showing independence of declarations and ities from b if there is collusion on the respective stage still go through.

quant-separate out pure e¢ ciency objectives from equity considerations: …rst wewill examine the case where the pro…t shock is vanishingly small so thatthe …rms necessarily appear to the tax authority as identical if they makeidentical choices; then, in section 5 we will consider the impact of the pro…tshock.

In what follows we use a simulation to analyse how relative audit rulesa¤ect revenue, quantities and evasion cost

We …rst look at the non-collusion scenario, where we have established that

a relative rule increases tax declarations for given pro…ts, but also reducespro…ts by inducing higher production quantities, which in turn reduces de-clarations and revenue So the total e¤ect of a relative audit rule on revenuehas two con‡icting components: a positive declaration e¤ect and a negativepro…t e¤ect The declaration e¤ect is a …rst-order e¤ect, while the pro…t ef-fect is only of second order The declaration e¤ect is anticipated by …rms atthe quantity-choice stage and production quantities are adapted accordingly.Thus, we can expect that a more ‡exible rule provides a “double dividend,”which consists of an increased production quantity and an increased revenue

To investigate this we simulate the two-stage game using the model of tions (1)-(14) and the assumption that marginal production cost is a constantc

equa-First, if the authority uses a relative audit rule, what happens to outputand tax revenue as the sensitivity of the rule and the tax rate change? Figure

2 shows contour plots of the simulated equilibrium quantity and revenue for

the quantities and government revenue, respectively

It is apparent that a more reactive rule increases production quantitiesand revenue for a given tax rate The marginal quantity e¤ect of an increase

in the sensitivity is decreasing The marginal revenue e¤ect of the auditsensitivity increases with the tax rate We see that a more reactive auditrule might lead to higher welfare, as a higher reactivity does not lead to anapparent con‡ict between the revenue and industry output The tax ratehas an in‡uence on the quantity only if the detection rule is relative The

7 The calculation of the equilibrium is tedious and is available on http://darp.lse.ac.uk/taxcompliance…rms