MSc Public Economics 2008/9 darp.lse.ac.uk/ec426

1. 9 March 2009 MSc Public Economics 2008/9http://darp.lse.ac.uk/ec426 Fiscal Administration

2. Overview... Policy Design Background Objectives and constraints Locating the subject within public economics Optimal policy C&B Optimal policy Cat-&-Mouse Tax design

3. Issues in enforcement policy design Identify main policy rules based on utilitarian ethics using the principal model types Objectives reconcile with utilitarian goals? what guidance for tax agencies? Implications for tax policy what guidance for tax agencies? impact of level and structure of income tax on tax evasion? and vice versa? Feedback to tax design For overviews: Cowell (2004), Slemrod and Yitzhaki (2002)

4. The principal economic actors • The key players • Control & reporting, simple constitution • Delegation • Tax farming Government • Further delegation • Control & reporting, full delegation • Corruption model Tax Authority Inspector Inspector Inspector Taxpayers

5. Government Control? Government is denied direct information about citizens Is therefore denied some measure of control Multi-layered structure Different types of concealed information and control failure? Leads to different types of economic model Fundamental difference between types of “control failure” 1 Tax-evasion: Assumes effectively a two-level model Version 1 (Government, taxpayer). Assumes complete internal compliance; external non-compliance. Version 2 (Tax authority, taxpayer). A simplified model of delegation. 2 Corruption: focus on incentives facing the inspector level Taxpayer offers payment to inspector to reduce prob of punishment Inspector is monitored by authority.

6. Questions in enforcement policy Policy questions from previous lecture What is the optimum degree of enforcement? Can smart auditing improve efficiency? Move beyond this to broader questions Should we try to eliminate evasion? Often an implicit objective But on what grounds? Implications of devolution of function Not just lack of control Also the type of objective function Implications for tax design?

7. Connection with previous topic Related to compliance lecture Examine general issues of “breakdown” in fiscal relationships tax under-reporting is one example also black/shadow economy And the mechanisms that may act as insulation institutions social factors

8. Overview... Policy Design Background Objectives and constraints Limitations of standard utilitarian model Optimal policy C&B Optimal policy Cat-&-Mouse Tax design

9. Modelling issues What is the appropriate objective? Law enforcement? Eliminate evasion? Welfare of law-abiding citizens? Utilitarianism? What institutional structure? Direct government-taxpayer relation? Tax collection/enforcement agencies? What components of the enforcement problem? requires a multi-stage approach see Cowell (1989)

10. Utilitarian enforcement problem Basic behavioural model taxpayer maximises expected utility Eu(c) = Eu([1 – t] y + r te) y: taxable income t: proportionate tax rate e: concealed income r : rate of return to evasion (= – s with prob p, 1 with prob 1 – p) Outcome of basic model determines optimal evasion response e* = e(p, s, t; y, a) in general depends on both tax and enforcement parameters (p, s, t) and on personal characteristics (y, a) Welfare model Take expected utility of representative taxpayer as welfare criterion W = [1 – p] u([1 – t] y + te) + pu([1 – t] y – ste) where y = y , a = a (representative taxpayer) (so we can drop y, a from optimal evasion response)

11. Fundamental constraints Realities for the government / tax agency a fixed revenue requirement R cost of enforcement f(p) where f is an increasing function in utilitarian modelf may include private compliance costs Government budget constraint R R which implies ty –rte–f(p) R where r is the expected rate of return to evasion,1– p – ps zero evasion if p p0 where f(p0) =ty –R Welfare contour for utilitarianism [1 – p] u([1 – t] y + te) + pu([1 – t] y – ste) = const where e = e(p, s, t) Evasion eliminated where rate of return is zero: s = [1−p]/p gives zero-evasion contour where welfare is u([1 – t] y) = W0 so determines boundary of “honesty set”

12. Model types Problem essentially has three control variables, p, s, t Three stages in the approach to the solution Keep t fixed enforcement authority has considerable, but not total, discretion can trade off severity of penalty against probability of detection Keep s or p fixed unmovable penal system inflexible police system trade off tax against an enforcement parameter Vary p, s, t together Total flexibility

13. The problem if t is fixed • The feasible set s • The “enforced honesty set” W0 • A: The zero-evasion point R R • W0welfare contour through A • Welfare contours • B: the optimum zero-evasion line • f(p0) =ty –R s [1−p]/p • W0 satisfies s = [1−p]/p W • Welfare increases “South-West” • B • A p p0 0 1

14. Assessment of the fixed-t model Corresponds to the case where: enforcement decisions are separated from tax-schedule decisions government tries to maximise welfare welfare respects individuals’ utility Features of the model: there is a determinate welfare-maximising solution does not imply elimination of evasion Could appeal to non-EU model to justify this

15. The problem if p is fixed • Draw feasible set • The “enforced honesty” set s • A welfare contour • Welfare contours 1−p —— p • A • Optimum R R W t 1 0

16. Assessment of the fixed-p model Case of an inflexible enforcement infrastructure Again there is a determinate welfare-maximising solution But in this case utilitarianism does imply elimination of evasion Reason: Resource costs are fixed You can raise the surcharge and compensate with lower t For risk-averse people this increases welfare Danger is the problem of penalty structure “Might as well be hung for a sheep as for a lamb” Iyengar (2008)

17. Tax farming Farming involves delegating some action to an agency (Stella 1993) Suppose the agency’s remit is to use s and p to maximise revenue to ensure compliance Government may use revenue raised through reductions in p to reduce t To analyse this, transform the problem…

18. Transform optimisation problem from this… s objective constraint • A p 0 1

19. .…to this s constraint • A p objective 1 0

20. Tax farming: optimality? • Draw “enforced honesty” set s • A revenue contour “Enforced honesty” set • Revenue increases to North-East • Tax farmer moves this way? revenue R = constant p 0 1

21. “Tax farming” has no solution! Consider an arbitrary status quo where evasion is just deterred Consider the following process Increase the surcharge s Decrease the probability of detection p. Cost of enforcing honesty falls So revenue increases and tax can be cut Therefore welfare increases Steps 1-5 can be repeated indefinitely… …as long as p > 0 !

22. Should evasion be eliminated? The answer depends on the appropriate institutional background: Keep t fixed don’t eliminate evasion Keep p fixed: eliminate evasion Vary p, s, t together: no solution

23. Overview... Policy Design Background Objectives and constraints A utilitarian approach Optimal policy C&B Optimal policy Cat-&-Mouse Tax design

24. Take a standard welfare-economics approach fixed t fixed s Basic utilitarian model homogeneous population simple revenue target uses a paradigm adopted elsewhere in public economics a type of cost-benefit approach to enforcement Extended utilitarian model Heterogeneous population Public goods Optimal degree of enforcement?

25. Optimisation problem Individual income: y =wh consumption: c = [1  t]y + rte leisure: ℓ = 1 h utility: u(c, ℓ) Government/tax authority enforcement cost per taxpayer: f(p) revenue requirement: `R expected revenue leakage per tax dollar: `r =1 p ps budget constraint: twh [1 p ps]t e(t, w) f(p)≥`R / n Utilitarian model, homogenous population objective function: v(t, w) = max Eu(c, ℓ) Lagrangean: v(t, w) + l [twh [1 p ps]t e(t, w) f(p) `R / n ]

26. Choosing p for given (s,t) • Probabilities, costs and benefits • Marginal cost of audit fp • Marginal benefit of audit • Optimum investigation effort Bp • MC is monotonic increasing • MB may not be monotonic • MB may go to zero p* p 0 1 indirect yield from extra honesty supply side effect direct yield MC of audit effect of risk on utility

27. A cost-benefit approach: to policy? Model of enforcement assumes: fixed s, t uniform p Can be extended to heterogeneous population case where revenue is spent on public goods other interesting cases (non-utilitarian welfare) Can also be simplified down to a “tax-agency” rule ignore risk-aversion component in marginal rule But it relies on a “lucky dip” approach Where taxpayers and the authority are in a reporting relationship one may be able to do better than this

28. Overview... Policy Design Background Objectives and constraints Strategic approach to audit policy Optimal policy C&B Optimal policy Cat-&-Mouse Tax design

29. Policy: strategic interaction model Results of cat-and-mouse model: simultaneous move: no equilibrium in pure strategies leader-follower, get a simple outcome Build this into a richer policy model focus on tax-collector/tax-payer interaction what role is there for beliefs about others’ goals and actions? can tax authority precommit to an audit strategy? Model ingredients tax rates and penalties are exogenously determined tax enforcement powers are delegated, like contract farming there is a constant, universally known, cost of audit  there is a known distribution of attributes and incomes...

30. Tax-payer v. Tax-collector game (2) • Similar to earlier version of model, but now includes Dy • the difference between high and low income • Remember, there is no NE in pure strategies. • To find a solution we need to look more closely at: • the structure of taxpayer population • control that can be exercised by tax authority

31. Types of taxpayer Essence of model is taxpayer heterogeneity differ by income and by attitude to tax-paying authority does not know individual taxpayer attributes but does know distribution in the population Take a simple 2x2 version: type income attitude pop proportion poory0 ??? a0 honest rich y0 + Dy always pay a1 chancers y0 + Dy cheat if can a2

32. A mixed-strategy approach Each knows that there is no equilibrium in pure strategies Each expects the other to play probabilistically: tax authority investigates low incomes with probability p taxpayer cheats with probability p Expected net tax receipts DT = [a1 + a2 [1 – p] ] t Dy + a2pp [[1 + s]tDy –  ] – a0p Marginal impact on receipts from increasing p is: a2p [[1 + s]tDy –  ] – a0 This is positive if p is greater than a threshold value: a0 p > p* :=  a2[[1+s]tDy –  ]

33. Equilibrium concepts Taxpayers and tax agency each form beliefs about the other’s actions Equilibrium where each adopts a consistent set of beliefs What is the optimal “tailored” audit strategy? Two types of relationship between taxpayer and tax authority: tax authority precommits to a strategy tax authority does not precommit see Reinganum and Wilde (1985, 1986)

34. Precommitment: policy • If the tax authority were permissive, net receipts would be low: • DT|p=1,p=0 = a1t Dy • If authority can commit it ought to audit all low-income reports: • p = 0 if report is y0 + Dy • p = 1 if report is y0 • Tax receipts net of audit costs are • DT|p=0,p=1 = [a1 + a2] t Dy – a0 • This amounts to a “Punish the poor” policy • Is this in fact optimal? • viability • credibility

35. Precommitment: optimality? • Condition 1 for financial viability is: • DT|p=0,p=1 ≥ DT|p=1,p=0 • [a1 + a2] t Dy – a0p ≥ a1t Dy • a2t Dy ≥a0 • Condition 2 for financial viability is: • net return from investigating a false report must be non-negative • [1 + s] t Dy –  ≥ 0 • Combining the two conditions • [1 + s] t Dy –  ≥ [1 + s – [a2/a0]]t Dy • satisfied if • if audit cost is not too high • if there are not too many honest people • Credibility: • everyone sees that only the genuinely poor people are audited • no revenue is ever raised in equilibrium • policy may not be credible in a repeated setting

36. No commitment: outline • Tax authority: • believes probability that a chancer will cheat is p • perceived probability of catching an evader is q :=a2p/[a0+a2p] • expected net tax receipts can be written as: a0 const +  [ p / p* - 1] a0+a2p • p* is pivotal value of belief • Chancers: • believe that probability of audit is p • expected utility if cheat is: pu([1 - t]y0+[1- t– st]Dy) + [1- p]u([1 - t]y0+Dy) • expected utility if don’t cheat is: u([1 - t][y0+Dy]) • there is a pivotal probability satisfied p* which equates these two utilities • if u is risk neutral then p* = 1 / [1+s] • Solution: • tax authority’s best response given belief p defines reaction function p(p) • chancers’ best response given belief p defines reaction function p(p) • equilibrium where beliefs consistent – where reaction functions intersect

37. No commitment: Solution • The strategy space p • Tax authority’s strategy • Chancer’s strategy 1 • Equilibrium p(p) tax authority reaction • always audit if proportion of cheats is believed high p(p) p* • (p*,p*) • always cheat if probability of detection is believed low • p* = 1 / [1 +s] a0 • p* =  • a2[[1+s]tDy –  ] taxpayer reaction p 0 p* 1

38. What happens as tax-enforcement parameters change increasing the cost of audit increases equilibrium evasion increasing the tax rate decreases equilibrium evasion increasing the surcharge decreases equilibrium evasion

39. What happens as the population proportions change Increasing the proportion of the poor increases equilibrium evasion increasing the proportion of chancers decreases equilibrium evasion

40. Overview... Policy Design Background Objectives and constraints Another look at optimal taxation Optimal policy C&B Optimal policy Cat-&-Mouse Tax design

41. Implications for tax design How should presence of evasion affect tax progression? two approaches 1 Build evasion into optimal income tax model Will presence of tax evasion lower optimal marginal tax rate? Cremer and Gahvari (1994) 2 Fiscal administration model that involves multiple failures Tax evasion: false reports to government may involve more than one economic actor Corruption: corruptibility involves self-interested public agents usually involves bribery Extortion: threaten the taxpayer with an excessively high assessment Hindriks et al (1999) based on Mookherjee and Png (1995)

42. Model 1: Assumption and results Standard utilitarian optimal linear income tax disposable income function c = [1t]y +B where y=wh welfare W = ∫ u(u(w) dw individual can conceal income e spend k on concealment to reduce prob of audit p ∂p(e,y,k)/∂k< 0, ∂2p(e,y,k)/∂k2< 0 ∂p(e,y,k)/∂e ≥ 0, ∂p(e,y,k)/∂(e/y) ≥ 0 Theorem 1. The optimal tax must satisfy: cov (u', [1 `r] ) / Eu' = E([w + fp] dh/dt)E(dk/dt) Theorem 2. Given ∂p/∂(e/y) = 0and u'''< 0 then the optimal mtr is lower with evasion that without evasion Two problems: Theorem 1 does not give explicit formula for the mtr Theorem 2 applies to very few useful functional forms

43. Model 2: Objectives, Agents, Information • Government objectives: • raising revenue • concerns with tax evasion and corruption • distribution of tax payments • Tax inspector • government agent takes incentive schemes as given • is risk-neutral and corruptible • Taxpayer (citizen): • risk-neutral and willing to pay bribes • Information • At time of inspection: taxable income is private information • After tax inspection inspector also knows taxable income and taxpayer knows whether inspector has behaved corruptly • Government does’nt know if inspector has truthfully reported

44. Model 2: Timing • Inspector selects taxpayer: • made in ignorance of true income • only the distribution known • no additional signals available • Inspector meets taxpayer: • true income becomes known • assessment is made • bribe may be paid • Inspector reports to government • misreporting in two directions: • under-reporting (collusion in tax evasion ) • over-reporting (extortion) • Taxpayer may appeal • decided by an honest judge • random non-appeal cases investigated by an honest auditor

45. Model 2: Rewards and incentives • Tax inspectors can be rewarded several ways: • straight fee, related to tax revenue, related to nature of reports • payment scheme create incentive for zeal? • also create conflicting incentive effects? • Effect 1: Collusion: • defeats effectiveness of tax instruments, undermines deterrent effect of penalties • provide high-powered incentives to the inspector • commission payment to resist the temptation to collusion • Effect 2: Extortion: • discretion of inspector gives power: threat of extortion • to deter inspectors from abusing power need low-powered incentives • In Hindriks et al model: • extortion effect dominates • never any strict gain from paying positive commissions. • threat of extortion leads to low-powered incentives.

46. Model 2: Tax and penalty structure • Pay tax inspectors commission on low income reports? • can be counterproductive • a risk of inducing corruption • Heavy penalties on corrupt inspectors • ineffective if on collusion… • … raises equilibrium bribe • effective on extortion • A wage for inspectors? • if government just maximises revenue… • …and is averse to evasion and corruption • pay inspectors a fixed wage… • …with penalties proportional to misreporting • Argument for a flat tax? • if government just maximises revenue… • …and is averse to evasion and corruption • set a proportional tax schedule

47. Model 2: Distributional outcomes • Evasion is regressive • poor have less to gain from evading taxes • rich have more to gain from evading taxes • Extortion is regressive • poor are vulnerable to over-reporting of their incomes • rich are less vulnerable to over-reporting of their incomes • Collection of progressive taxes can be costly • conflicting temptations: • understate income to evade progressive taxes, • overstate income to raise the commission payments • inducing honesty requires additional resources • An additional aspect of the equity-efficiency tradeoff

48. Assessment Compliance is a central component of public economics Arises naturally from the issues concerning the provision of public goods Analysed using standard microeconomic techniques Incentives issues similar to those of labour supply Important to model the interactions involved in evasion Perceptions of others’ behaviour may be important. Also interaction between tax-payers and enforcement agencies Crucial issues on policy concern the institutional background What is the nature of the optimisation problem? Is a standard reporting model appropriate? What information should each party be assumed to have?

49. References Cowell, F. A. (1989) “Honesty is sometimes the best policy,” European Economic Review, 33,605-617 Cowell, F. A. (2004) “Carrots and Sticks in Enforcement” in Aaron, H. J. and Slemrod, J. (ed.) The Crisis in Tax Administration, The Brookings Institution, Washington DC, 230-275 Cremer, H. and Gahvari, F. (1994) “Tax evasion, concealment and the optimal linear income tax,” The Scandinavian Journal of Economics, 96, 219-239 Hindriks, J., Keen, M. and Muthoo A. (1999) “Corruption, Extortion and Evasion”, Journal of Public Economics, 74, 395-430 Iyengar, R. (2008) “I'd rather be Hanged for a Sheep than a Lamb:  The Unintended Consequences of 'Three-Strikes' Laws,” NBER Working Paper, 13784 Mookherjee, D. and Png, I. (1995) “Corruptible law enforcers: how should they be compensated?” Economic Journal,105, 145–159 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. Slemrod, J. and Yitzhaki, S. (2002) “Tax avoidance, evasion and administration,” Handbook of Public Economics, Volume 3, pp 1423-1470, North-Holland, Elsevier Stella, P. (1993) “Tax Farming: A Radical Solution for Developing Country Tax Problems?” IMF Staff Papers40, 217-225