HMRC-HMT Economics of Taxation 2011 darp.lse.ac.uk/HMRC-HMT

1. 14 December 2011 HMRC-HMT Economics of Taxation 2011http://darp.lse.ac.uk/HMRC-HMT 10.2 Policy design

2. Policy Design Overview... Background Objectives and constraints Locating the subject within public economics Optimal policy C&B Optimal policy Strategic 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. Policy Design Overview... Background Objectives and constraints Limitations of standard utilitarian model Optimal policy C&B Optimal policy Strategic

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. 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

15. The problem if p,s,t all variable • Optimisation problem again s • Transform the problem objective “Enforced honesty” set • Revenue increases to North-East • Tax authority moves this way? constraint revenue • A R = constant p 0 1

16. Policy Design Overview... Background Objectives and constraints A utilitarian approach Optimal policy C&B Optimal policy Strategic

17. Optimal degree of enforcement? Take a standard welfare-economics approach choose the optimal p, given fixed s,t Basic utilitarian model homogeneous population simple revenue target a type of cost-benefit approach to enforcement Individual (slightly extended) 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 ]

18. Choosing p for given (s,t) • Probabilities, costs and benefits • MC is marginal audit cost • is monotonic increasing • MB is marginal audit yields + supply side and risk effects • may not be monotonic • may go to zero • Optimum where MB = MC • fp= [1+s]te `r te/p  w0ℓ/pe(t, w) + vp/l • Marginal cost of audit fp • Marginal benefit of audit • Optimum investigation effort Bp p* p 0 1

19. Extensions – agent interaction Cost-benefit approach is essentially individualistic compute MB for each agent Social interaction models prevent epidemics? shift the equilibrium? manipulate expectations? Iyer et al 2010) raise search costs? Focus on smart use of information recognise that agents may have better market information than tax authority exploit information about all agents’ behaviour Example: tax compliance by firms use of information: compare simple auditing with relative auditing relationships amongst firms is essential to the impact of policy choice Cournot behaviour: get effect on output as well as tax receipts collusion amongst firms – smart auditing less effective (Bayer and Cowell 2009) Examine smart auditing further in a reporting model

20. Policy Design Overview... Background Objectives and constraints Strategic approach to audit policy Optimal policy C&B Optimal policy Strategic

21. Tax-payer v. Tax-collector game • Model ingredients • tax rate t, surcharge s, cost of audit  are exogenously determined • tax enforcement powers are delegated, like contract farming • To find a solution we need to look closely at: • the structure of taxpayer population • control that can be exercised by tax authority • Essence of model is taxpayer heterogeneity • differ by income and by attitude to tax-paying • authority does not know individual taxpayer attributes and incomes... • 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

22. A mixed-strategy approach Each side 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 –  ]

23. 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)

24. 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

25. 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 audit cost is not too high and 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

26. 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

27. 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

28. How the model works Response to tax-enforcement parameters: ∂p*/∂> 0 ∂p*/∂= 0 ∂p*/∂t < 0 ∂p*/∂t ≥ 0 ∂p*/∂s < 0 ∂p*/∂s < 0 Changing population proportions: ∂p*/∂a0> 0 ∂p*/∂a0= 0 ∂p*/∂a2< 0 ∂p*/∂a2= 0

29. 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?

30. 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 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 Iyer, G.S. , Reckers, P.M.J. and Sanders, D.L. (2010) “Increasing Tax Compliance in Washington State: A Field Experiment,” National Tax Journal, 63,7-32, 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