Tax Evasion and the Firm

1
Tax Evasion and the Firm

• Frank Cowell
• Encuentros de Economía Pública
• Almeria, February 2006

2
Purpose

• 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

3
William the Conqueror

• 1066 a date known to British schoolchildren
• But 1086 should be better known to tax
  researchers
• The Domesday Book
• 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

4
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?

5
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

6
TAG

• 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

7
Cat-and-mouse

• 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)

8
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?
• Lets see how well the models work
• Do they capture the essential features of tax
  compliance with firms?
• Start with TAG

9
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.

10
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 bat b t 1 a ft a 1
  a b 1ft
• Expected profits are
• p m c te q
• p price
• m marginal production cost

11
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 lt 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?

12
Generalisations

• Monopoly / imperfect competition
• 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)

13
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
• 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

14
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
• Dont 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?

15
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

16
Learning from the tax authority

• What will the TA do?
• 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

17
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

18
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?

19
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
• incorporates industrial organisation
  considerations
• again uses naturally arising information
• introduces an output-security tradeoff
• modifies standard IO equilibria in an interesting
  way

20
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?
• 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

21
Cut-off rule

• Well-known to be wasteful
• 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

22
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
• 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 TAs ability to estimate probability of
  firm i being an evader.
• Firms who declare relatively low are more likely
  to be evaders
• 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

23
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
• 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.

24
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

25
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

26
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

27
The role of firms beliefs

• Beliefs generate heterogeneity
• 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

28
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

29
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

30
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

31
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

32
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

33
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 ß for all firms
  
• Consider the use of a relative audit rule
• Audit probability for firm i is given as ß(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

34
Tax, profits and penalties

• Firm is 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

cost of concealment
probability of audit
gross profit if audited
gross profit if not audited
35
How the model works

• Timing in the model is intuitive
• 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

36
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
• 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.

37
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 is optimal output reflects
• the induced change in js declarations
• the indirect impact on is probability of audit

38
Role of information

• Announcement of audit regime is crucial
• If tax authority uses relative rule
• interdependence of firms declarations is common
  knowledge
• Each firms 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?

39
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 ß firms
  declare more profits than under independent
  audits with the fixed detection probability ß(i)
  ß.
• Second production efficiency
• A relative audit rule leads to outputs higher
  than in under the independent audit rule

40
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.

41
Changing the audit rule shifts the output
reaction function
42
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
• 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

43
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?
• 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

44
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

45
Changing the audit rule shifts the price reaction
function
46
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
• Whos in the game?
• firms versus the TA
• firms versus firms
• perhaps a little like William Is Domesday
  investigation
• How is the tax-base determined?
• profits created by firms
• firms in the context of an industry
• where TAs could learn something that king
  Williams investigators did not know

47
References

• 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.