Tax Evasion and the Firm
Frank Cowell
Encuentros de Economía Pública
Almeria, February 2006
Purpose
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This talk is about modelling in public economics
I want to focus on a puzzle
Then a suggestion for answering the puzzle
But first: a history lesson
 an English history lesson
William the Conqueror
• 1066: a date known to British schoolchildren
• But 1086 should be better known to tax researchers
• The Domesday Book
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a detailed audit of the kingdom
what is the place that I have conquered worth?
who owns what?
where are the resources?
• A thorough operation
 extensive teams of investigators
 multiple information sources
 penalties for wrong information
Lessons from the Conqueror
• Not just a system of national accounts
• Clearly concerned with revenue raising
 Note questions on valuation
• An early example of a tax audit problem
 But questions are about assets rather than income
 A forerunner of the Allingham-Sandmo problem?
Tax Compliance: Background
• Typically focus on the personal taxpayer
 exogenous income
 isolated economic agent
• Simplified information structure
• Since Allingham and Sandmo lots of specifications
 But broadly two categories
• TAG models
 Taxpayer As Gambler
• Cat-and-mouse models
 The main economic actors play games with each other
TAG
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The individual taxpayer behaves just as a gambler:
Taxpayer has fixed income
Conceals a part of this income
Knows the penalty and probability of audit
Audit probability is fixed
Taxpayer takes a risk on whether he is audited
Cat-and-mouse
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Audit probability depends on report
Generates strategic interaction
Known distribution of income and types
Condition audit on report
 Get a “cut-off” rule
• Alternatively models use other forms of
information
 Reinganum and Wilde (1985,1986)
A modelling strategy
• Is the analysis well suited to analysing
taxpayer behaviour…
 …when the taxpayers are producers?
 …when the taxpayers are grouped in an industry?
• Let’s see how well the models work
• Do they capture the essential features of tax
compliance with firms?
• Start with TAG
TAG: competitive firms
• Assume expected profit maximisation
 Only source of randomness is due to audit..
• Behaviour driven by two things
 Nature of concealment costs
 Structure of audit probabilities
• Tax evasion incurs resource costs
 Firm declares proportion of output a.
 Incurs total concealment cost C(1 – a).
 Average cost c(1 – a) := C(1 – a) / [1 – a].
TAG model structure
• Can treat this as modified Allingham-Sandmo
• Tax-enforcement parameters:
 Proportional tax rate t.
 Probability of audit b.
 Penalty rate for concealed output f.
• Compute expected effective tax rate te
 te = [1 – b]at + b [t + [1 – a ]ft ] = [a + [1 – a ] b [1+f]]t
• Expected profits are
 [p – m – c – te ] · q
 p: price
 m: marginal production cost
Competitive model: results
• Only c and te depend on concealment
 increasing marginal cost of concealment
 reduced effective expected tax rate
 Firm always conceals if te < t
• Optimal concealment satisfies
 [1 – a ]g'(1– a) = t – te
 “MC concealment equals reduction in expected tax”
• Optimal output satisfies
 p = m + g + te
 “Price = (adjusted) marginal cost”
• Essentially a “separation” result
 Makes it easy to get comparative statics
 But does it survive more generalised modelling?
Generalisations
• Monopoly / imperfect competition
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Determinate demand curve
Replace q with q(p)
Little changes: replace "price" with "MR" in FOC
Separation result persists. (Marrelli 1984, Marelli and
Martina 1988)
• Risk aversion
 max Eu([p – m – g – t ] · q)
 Separation result is preserved
• Change the tax/penalty regime.
 b not only a function of over-reported cost?
 b or penalty not constant?
 No longer get the separation result – Lee (1998)
TAG and firms – a puzzle
• The puzzle is that the firm seems to have disappeared
 write out FOC
 solve for output and profits
 back into an “Allingham-Sandmo” world
• Tax-neutrality argument is central
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but it appears artificial
not robust to different tax base
seems to run counter to experience
zealous enforcement has no effect on output?
• Perhaps the answer is in the audit rule?
 Audit rule is naïve
 Does not make full use of industry information
 Consider cat-and-mouse
Cat-and-mouse: firms
• The cat-and-mouse model is a reporting game
 tax-payer and tax authority (TA)
 With or without precommitment
• Is cat-and-mouse a suitable for firms?
• Simple reporting models may be inappropriate
 There is no fixed income to uncover
 Don’t have independent estimate of distribution
• May omit some of the key strategic aspects of the
game
 Do we have the right players?
 What do the players know?
William the Conqueror again
• How does the modern tax-audit differ from the Domesday book?
 production
 nature of report
 nature of reporting process
• We need to address a key practical question
 how would we expect the TA to act?
 clearly depends on the type of tax…
 …corporation tax? VAT?
• Recognise the contrast with the situation of personal taxpayers
 who knows what the taxable profit is?
 how handle of heterogeneity of firms?
 how handle inter-relations amongst firms?
• Design an audit strategy that
 uses the available information
 recognises its own ignorance
Learning from the tax authority
• What will the TA do?
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sort firms by industry grouping
sort firms by size
monitor over time
adapt audit procedure accordingly
• Can we adapt the standard approaches…?
• Neglect some important features and information
 Production
 Creation / disappearance of taxable units
 Structure of industry
 This provides an answer to our puzzle of the vanishing
firm
Taking the firm seriously
• What makes the firm “special”?
 Internal organisation
 Interrelation with other firms
 The role of information
• Internal organisation
 Not a single decision-making entity
 Role of Chief Financial Officer?
 Effective separation of functions within the firm?
• Interrelations
 Several models that deal with this – for example Benjamini-Maital
 But why should firms care about each other?
 Not “stigma” but “profits”
• Information…
 …needs closer examination
Information
• What does the firm know about itself?
 incomplete information may lead to agency problems
 Crocker and Slemrod (2005)
• What does the tax authority know about the firm?
• What do firms know about each other?
A way forward
• How to capture the essence of the tax-compliance problem
with firms?
• We will focus on two main features:
• 1. “Industry-group typing”
 incorporates interrelations among taxpaying firms
 arises naturally from informational structure of the problem
 results in a well-behaved equilibrium in a minimalist model
• 2. “Production and industry”
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incorporates industrial organisation considerations
again uses naturally arising information
introduces an output-security tradeoff
modifies standard IO equilibria in an interesting way
Approach 1: Industry-group typing
• Consider the cat-and-mouse model
 simple versions use a “cut-off” rule Reinganum and Wilde (1985)
 ignore income declarations greater than d*
• But this based on a particular strategic interaction…
 …TA “versus” representative taxpayer
• Can the model be made richer?
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In some cases yes
see tax-payers as a group
allow natural group interaction (Sánchez 2006)
particularly important for firms
• Role of the industry
 classify according to broad observable characteristics
 enough information to condition audit policy
Cut-off rule
• Well-known to be wasteful:
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the cut-off rule wastes ammunition: auditing “genuine” taxpayers
but what if firms in an industry are subject to common shocks…
…unobserved from the outside?
problem gets worse
• Negative shock:
 more firms than expected by the TA have profits below the cut-off level
 more firms declare low
• Positive shock:
 more than expected by the TA have profits above the cut-off level d*
 but each successful firm will declare only d*, thus increasing the number
of evaders that go undetected.
• Result: more resources wasted
 find systematic mis-targeting by the TA
 under-auditing in good years
 over-auditing in bad years
Policy with shocks
• Can the TA do better than a cut-off rule?
 Suppose TA is concerned about “wasted ammunition”
 resources spent on audits of compliant taxpayers
 TA better off if policy is contingent on the industry information
• Use the industry typing
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form fairly homogeneous audit class
let D be average declaration for the class
di be declaration for firm i within the class
condition on D  di
• Changes nature of the compliance game
 the D component induces interaction among firms (Alm and McKee 2004)
 improves TA’s ability to estimate probability of firm i being an evader.
• Firms who declare relatively low are more likely to be evaders
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homogeneity within a given industry category
since firms share characteristics expect to have similar profits
consequently expect similar income declarations.
declaration significantly below the class average seen as “suspect”
How interaction works
• Consequences for TA policy :
 knows relationship between D  di and probability that i is an evader
 so make auditing intensity for low declarers increase with D.
• Introduces an externality among taxpayers
 fundamental nature of the tax compliance problem
 each firm has to interact strategically with other firms
 not just with TA as in conventional cat-and-mouse
• Firms forced to participate in a coordination game
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if the average declaration is high (most firms comply)…
…probability of detection is also high too
if the average declaration is low (so most people evade) …
the probability of detection is low
• Each firm always has incentive to join the majority.
A paradox?
• Auditing intensity increases with the average declaration?
 A waste of resources…?
 …most firms would have declared truthfully.
• Will this policy harm the goal of discouraging evasion?
 Low auditing intensity when D is low…
 …means TA lets evaders get away undetected.?
• But auditing intensity applies only to low di
 those who declare high are never audited
 the greater is D the greater is the TA's belief that the class faces a
favourable shock
 the greater is its belief that a low di means i is an evader.
 So – no paradox
The contingent rule…
• Contingent policy slightly resembles the cut-off rule
 non-increasing in true income
• But there is a big difference:
 probability of detection for those who declare low…
 …an increasing function of the class-wide average declaration.
• Why the contingent rule?
 not a consequence of new elements added to the model
 simply an application of common sense
 making efficient use of all the available information.
• Implications for TA
 take advantage of strategic uncertainty it generates
 manipulate this by imposing severe penalties in the case of a
coordination failure
Fundamental uncertainty
• But how do firms view the government?
• A second element of uncertainty
 the type of the government
 value it puts on resources wasted on auditing compliant
taxpayers
 this information is private to the government
• Firms do not know this type
 faced with a the probability distribution
 need to estimate it
 results in a system of beliefs
The role of firms’ beliefs
• Beliefs generate heterogeneity
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expectations over type of the government differ among taxpayers
eliminates all but one equilibrium
the presence of different signals…
…leads to different taxpayers to make different decisions
• Simplifies the model
 each firm has a unique optimal strategy
 unlike a coordination game without heterogeneity...
 …get multiple solutions (one for each possible equilibrium)
• Sánchez (2006) model yields unique, interior equilibrium
The industry-typing model
• Presence of two kinds of uncertainty
 strategic: generated by the coordination game
 fundamental: firms’ imperfect information about government type
 …makes the tax evasion problem well suited to be modelled as a
global game.
• Global game captures the interaction among its actors
 firms in an industry a bit like subjects in the kingdom of William I
 leaves open scope for manipulating beliefs
• Capture stylized facts missing in other models
 Unique interior equilibrium where some comply, some evade
 TA's comprehensive and efficient use of all available information
• But incomes (profits) are still exogenous
 consider the second approach
Approach 2: production and industry
• Explicitly model the industry
 Make the multi-firm setting essential
 Model differential information of insiders and outsiders
 Bayer and Cowell (2005)
• Make better use of information by the TA
 On part of firms
 On part of tax authority
• Compare with
 Naïve audit rules
 Simple models of compliance
Model motivation
• How much does the tax authority know about
firms?
 May be reasonably well informed about a specific
industry or sector.
 But firms probably have better information about their
own industry
 This information may concern both production and
financial performance
• Yields a natural way to model output and evasion
linkage
Firms
• Production
 Identical cost structures
 Details of these subsumed within profit function
• Evasion
 Opportunities to evade are common knowledge
• Specify cost-of-evasion function C()
 Argument is concealed output
 Increasing, convex
 C(0) = 0
• Objectives
 Firms are risk-neutral
 Objective function is expected profits
Industry
• Fixed number of firms n.
• Firms compete
 Cournot style
 Bertrand style
• Firms make profit declarations
d := (d1, d2, ..., dn )
• New possibilities for tax authority
 independent audits
 use information from all declarations in audit rule
Taxation, audit and enforcement
• Conventional tax/penalty regime
 linear profits tax
 simple fine structure for non-compliance
 both could be generalised
• But a variety of audit regime
• Instead of considering a policy of independent audit…
 …given a fixed audit probability β* for all firms
• Consider the use of a relative audit rule…
 …Audit probability for firm i is given as β(i, d)
 depends on firm i's declaration relative to the rest.
 Again we could use the D  di rule
• Under the relative rule each firm knows that:
 ...own declaration may reduce the probability
 ...others' declaration may increase the probability
Tax, profits and penalties
• Firm i’s profits gross of tax and depend on q
 output vector of industry
• Profits form base of tax
 assume linear tax function
• The tax it actually pays depends on evasion decision
 assume a fixed proportional fine f.
• Risk-neutrality: firm i maximises expected net profit:
probability
of audit
gross profit
if audited
gross profit if
not audited
cost of
concealment
How the model works
• Timing in the model is intuitive:
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The TA announces taxes and an audit regime
Firms choose quantities
Firms observe gross profits of the others
Firms choose profit declarations
TA audits and punishes where appropriate
• The solution is found as usual…
 by working backwards
 start with the declaration stage
Declaration decision
• At this stage, outputs have been determined
 profits are determined…
 …and known within the industry
• Declaration problem for each firm is simple
 driven by the known audit rule
• To get an interior solution need two conditions
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1 If marginal concealment costs are high for extensive tax evasion…
then, near di = 0, expected payoff increases with di
2 If C'(0) = 0 and detection probability is low…
… then, near full declaration, expected profits decrease with di.
Latter condition corresponds to usual TAG case.
Output decision
• Changes in quantity are known to affect optimal declarations
of others
 there is the usual Cournot interdependence
 and the audit rule is common knowledge
• Changes in others' declarations affect i's audit probability
 the audit rule is common knowledge
• Decisions on output will reflect this interdependence
• Condition for i’s optimal output reflects
 the induced change in j’s declarations
 the indirect impact on i’s probability of audit
Role of information
• Announcement of audit regime is crucial
 If tax authority uses relative rule…
 …interdependence of firms’ declarations is common knowledge
• Each firm’s declaration creates an externality
• Tax authority can use this in selecting the type of audit rule
 can influence the “climate” of the industry
• Imagine starting with simple independent audits.
• Would there be a “dividend” in refining and announcing the
refinement?
A double dividend
• Bayer and Cowell show that there are two
“dividends” from refining the audit policy
• First: audit efficiency
 Under the relative audit rule with mean equilibrium
detection probability β* firms declare more profits than
under independent audits with the fixed detection
probability β(i) = β*.
• Second: production efficiency
 A relative audit rule leads to outputs higher than in
under the independent audit rule
Audit rules and output
• Independent audit rule
 fixed audit probability
 output is independent of the evasion decision and
equals the Cournot quantities.
 rather like the simple competitive model
• Relative audit rule
 audit probability depends on D  di
 outputs are higher than in Cournot competition without
taxes.
Changing the audit rule shifts the
output reaction function
Another paradox?
• What is gained from increasing output beyond the Cournot
level?
 Surely a firm reduces its own profit…
 …as well as its competitors’ profits?
 A loss rather than a gain?
• Informational externality
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As qi increases, profits of other firms fall
Optimal declarations of the other firms fall
Given the relative audit rule…
…probability of audit of firm i decreases
This gives firm i more scope for evasion
• So it is rational for the Cournot firm to operate in this way
The non-paradox again
• A tradeoff
 by increasing output beyond the Cournot quantity…
 …a firm loses some gross profit
 but gets a better environment for evasion.
• A malicious incentive?
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other firms decrease their declaration if their profits fall
but this decreases firm i's audit probability
firm i has an incentive to sabotage other firms' profits
…by producing more than under the usual Cournot
Changing the industry rules
• The result is not special to quantity competition
• Similar results for Bertrand price-competition
model
 you need differentiated products…
 …and a regularity condition on demand curves
• The intuition is the same
 forgo some gross profits
 for a better evasion environment
Changing the audit rule shifts the
price reaction function
Conclusions
• We can suggest an answer to our puzzle
 can we find an approach to the topic…
 …where the firm does not vanish?
 two main components to the answer
• Who’s in the game?
 firms versus the TA
 firms versus firms
 perhaps a little like William I’s Domesday investigation
• How is the tax-base determined?
 profits created by firms
 firms in the context of an industry
 where TA’s could learn something that king William’s investigators
did not know
References
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Allingham, M. and A. Sandmo (1972). Income tax evasion: a theoretical analysis. Journal of Public
Economics 1, 323-338.
Alm, J. and M. Mckee (2004). Tax compliance as a coordination game. Journal of Economic Behavior
& Organization 54, 297-312.
Bayer, R.-C. and F. A. Cowell (2005). Tax compliance and firms’ strategic interdependence.
Distributional Analysis Discussion Paper 81, STICERD, London School of Economics, London WC2A
2AE.
Crocker, K. J. and J. Slemrod (2005). Corporate tax evasion with agency costs. Journal of Public
Economics 89, 1593.1610.
Lee, K. (1998). Tax evasion, monopoly and nonneutral profit taxes. National Tax Journal 51, 333-338.
Marrelli, M. (1984). On indirect tax evasion. Journal of Public Economics 25, 181.196.
Marrelli, M. and R. Martina (1988). Tax evasion and strategic behaviour of firms. Journal of Public
Economics 37, 55.69.
Reinganum, J. F. and L. L. Wilde (1985). Income tax compliance in a principal-agent framework.
Journal of Public Economics 26, 1.18.
Reinganum, J. F. and L. L. Wilde (1986). Equilibrium verification and reporting policies in a model of
tax compliance. International Economic Review 27, 739.760.
Sánchez, M. (2006). Divide and conquer: Tax evasion as a global game. Distributional Analysis
Discussion Paper 80, STICERD, London School of Economics, London WC2A 2AE.