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? • Let’s 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 – 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

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 < 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 • 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?

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 • dibe 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 • 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  diand 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 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

34. 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: 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) = 0and 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 i’s optimal output reflects • the induced change in j’s declarations • the indirect impact on i’s 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 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?

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 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

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 • 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

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.