Tax Compliance Frank Cowell: MSc Public Economics 2011/2 http://darp.lse.ac.uk/ec426 Overview... Tax Compliance Introduction How compliance fits into public economics Basic model Extensions Policy 13 February 2012 Frank Cowell: EC426 2

Tax compliance and PE In tax problems usually focus on margin of individual choice labour supply the demand for particular consumption goods Could consider tax-compliance analysis as just another margin compliance/noncompliance in reporting work above/below ground But: its related to a core problem of public economics public goods will not be provided efficiently by private initiative usual response is to say let government do it Useful to reinterpret the basics of this type of problem provision of collective goods pure public goods and others involving externalities focus on relations between citizens and state 13 February 2012 Frank Cowell: EC426 3 Agenda Outline main approaches to tax compliance 1 TAG 2 Strategic models

3 Social interaction Consider some important variants public goods and the public sector the role of firms Analyse implications for policy Literature overviews: Andreoni et al (1998) Cowell (1990, 2004) Slemrod (2007) Slemrod and Yitzhaki (2002) 13 February 2012 Frank Cowell: EC426 4 Overview... Tax Compliance Introduction Individual behaviour and the public sector

Basic model Individual taxpayer Multiple taxpayers Extensions Policy 13 February 2012 Frank Cowell: EC426 5 TAG model Standard model is essentially one of Taxpayer As Gambler based on Allingham and Sandmo (1972) The gamble involves a bet with the tax authority Individuals make bets on whether they will be caught concealing income or not reporting at all or working in underground economy Appropriateness relies on a special set of assumptions about motivation of individuals about the way that the government is perceived

13 February 2012 Frank Cowell: EC426 6 TAG: taxes, penalties, returns Tax payer/evader has true income y is supposed to pay tax on all of this at rate t chooses to conceal an amount e, pays tax on the remainder Tax authority audits: if evader is caught, pays a surcharge s on the evaded tax te perceived probability of this happening is p Parameters determine returns to evasion: consider rate of return to $1 of evasion activity... r = s with probability p r = 1 with probability 1 p expected rate of return is 1 p ps Consumption (disposable income) is a function of: income y and tax rate t random rate of return r evasion choice e c = [1 t] y + rte (a random variable) 13 February 2012

Frank Cowell: EC426 7 TAG: budget constraint c" [1t]y A ct fr e pe f o ty e

n lin rtai ce c': consumption if not caught c'': consumption if caught A: Payoffs if absolutely honest B: Payoff if blatantly dishonest Consumption possibilities for all e 1 A cut in the surcharge rate s 2 A cut in the tax rate t 3 Increase in income y c' = [1 t] y + te if not audited / convicted B c'' = [1 t] y ste if audited and convicted [1tst]y c' [1t]y 13 February 2012 y

Frank Cowell: EC426 8 TAG: Preferences and beliefs Tax payer has von-Neumann Morgenstern preferences gets no intrinsic pleasure from evasion and feels no shame correctly perceives probability of detection p assumes that it is exogenously given Consumers welfare is expected utility of consumption: Eu(c) = [1 p] u(c' ) + p u(c'' ) Eu(c) = [1 p] u([1 t] y + te) + p u([1 t] y ste) Cardinal utility function u has the usual properties: uc() > 0 (first derivative) ucc() 0 (second derivative) Both u and p determine shape of ICs in (c', c'' )-space curvature of ICs depends on risk aversion ucc()/uc() slope of ICs where crosses 45 line is [1 p]/p 13 February 2012 Frank Cowell: EC426 9

Equilibria of the tax-evader Feasible set A: corner solution (honesty) B: corner solution (dishonesty) c" C: Interior (partial honesty) E: Expected payoff solution depends on tax parameters t:= (p, s, t) income y personal attributes a e* = e(t, y, a) E A C 0 13 February 2012

E(ruc(c)) 0 if e* = 0 E(ruc(c)) 0 if e* = y E(ruc(c)) = 0 if 0 < e* < y B c' Frank Cowell: EC426 10 Comparative statics Focus on the interior solution what happens when tax / enforcement parameters change? do this graphically or analytically differentiate the first-order condition E(ruc(c)) = 0 Effect of increased p: indifference map rotates for given budget constraint, tangency moves closer to A Effect of increased s: point B moves down for given utility function, tangency moves closer to A Effect of increased t: assume decreasing absolute risk aversion (DARA) amount invested in a risky asset increases with resources

so in this model, given DARA, evasion rises with y but this will also imply that evasion falls with t 13 February 2012 Frank Cowell: EC426 11 Overview... Tax Compliance Introduction How to assemble the whole economy Basic model Individual taxpayer Multiple taxpayers Extensions Policy

13 February 2012 Frank Cowell: EC426 12 Forward from simple TAG model Obvious difficulty with isolated individual model reacts to exogenously given risk situation no perceived effect of his behaviour on this situation no interaction with other aspects of public sector no interaction with other agents Start to put this right in this section 1 aggregate individual risk-taking behaviour 2 introduce public sector Then, later in the lecture: 3 focus on interaction with tax agency 4 focus on interaction amongst agents 13 February 2012 Frank Cowell: EC426 13

Components of model Government budget constraint: R `R revenue actually raised required target revenue Define economy-wide aggregates aggregate income: Y := y dF(y, a) aggregate nominal tax receipts: tY aggregate leakage from evasion: re(t, y, a) dF(y, a) cost of enforcing probability p across economy F(p) Composition of revenue R = tY t re(t, y, a) F(p) So budget constraint becomes tY t re(t, y, a) F(p) `R But this ignores how the government revenue may be used 13 February 2012 Frank Cowell: EC426 14 TAG model: Public Sector Taxes are used to pay for a public good z Government budget constraint in this extended model is: R yz where y is the (constant) marginal rate of transformation

Individuals benefit from provision of the good but they prefer that someone else pay for it so there is still a motive for tax evasion and expected utility is now Eu(c,z), where uz(c,z) > 0 FOC for an interior maximum is: E(ruc(c,z)) = 0 essentially as before Response of e in this model is much the same for some cases: Surcharge Probability of detection But for the tax rate t we have new insights 13 February 2012 Frank Cowell: EC426 15 The effect of a rise in the tax rate There are still the conventional income and substitution effects But t also affects amount of public good available Increasing t will: reduce private consumption c

increase availability of public good z Desirable to increase t? depends on amount of public good already available Expect a hump shape: Eua for t close to 0 we have z close to 0: raising t is desirable for t close to 1 we may have satiation in z: lowering t is desirable underprovision z < z*a overprovision z > z*a t 13 February 2012

Frank Cowell: EC426 16 Preferences for public and private goods How is z* determined? Optimal provision uses standard SMRS = MRT rule Because of the risk component general formula is unwieldy So take a simplified set of preferences c ua(c, z) = c + va(z) ma := uza(c, z)/uca(c, z) = vza(z) m := Sma = MRT Evasion erodes effectiveness of tax in providing z... feeds back into effect of tax on evasion change in (et) has sign of m y / zt a simple criterion for determining under / over provision slope = m 13 February 2012

Frank Cowell: EC426 z 17 Effect of a rise in the tax rate If the public goods are under-provided: a rise in t increases the amount of evasion over-provided: a rise in t decreases the amount of evasion Cowell and Gordon (1988) te ty But individuals differ in: risk aversion taste for public goods income So, different responses: constrained by e y high marginal evaluation t low marginal evaluation Get a more complex relationship between t and evasion overall 13 February 2012

Frank Cowell: EC426 18 Overview... Tax Compliance Introduction An alternative model of the individual agent Basic model Extensions Firms Interaction Policy 13 February 2012

Frank Cowell: EC426 19 Firms and non-compliance Individuals or firms? fine line status of self-employed? Two major issues in setting up the model how to model market interaction how to model the output decision Several types of market situation captured in one model just need a determinate demand curve. Output decision based on an expected-profit criterion 13 February 2012 Frank Cowell: EC426 20 Firms: a model Conventional (non strategic firm) marginal production cost m demand (sales) given by x(P) P is market price

Tax t payable on sales Firm conceals a proportion b of sales concealment costs per unit of output G(b) Expected tax rate p and s have same interpretation as before effective tax if not caught: [1 b]t effective tax if caught: [1 + sb]t so Et := [1 p][1 b] t + p [1 + sb]t Expected profits are: EP = [P m b G(b) [1 p][1 b] t + p [1 + sb]t ] x(P) EP = [P m g(b) Et] x(P) where g(b) := bG(b) 13 February 2012 Frank Cowell: EC426 21 Firms: solution Maximise EP w.r.t. b and x. From FOC for a maximum: dg(b) = [1 p ps] t db marginal concealment cost = expected return For competitive firms:

P = m + g + Et price = expected augmented marginal cost We have a separation result Output and evasion decisions are taken independently a neutrality argument applies to both competitive and monopolistic firms result depends on risk-neutrality (Lee 1998) 13 February 2012 Frank Cowell: EC426 22 Firms: predictions Effect of penalty surcharge is conventional b/s < 0 Et/s > 0 P/s > 0 So is effect of detection probability b/p < 0 Et/p > 0 P/p > 0

Effect of nominal tax increase: ...raises proportion not declared b/t > 0 ...may or may not raise expected tax Et/p K 0 ...raises price 0 < P/t <1 13 February 2012 Frank Cowell: EC426 23 Overview... Tax Compliance Introduction Alternative model of rational behaviour. Climate of evasion and social sanction Basic model Extensions

Firms Interaction Policy 13 February 2012 Frank Cowell: EC426 24 Strategic interaction Based on a application of game theory Two players: tax authority and taxpayer Tax authority chooses whether or not to investigate Taxpayer chooses whether or not to cheat Intuition of simple strategic model: simultaneous move if tax authority plays audit best response of taxpayer is report if taxpayer plays report best response of tax authority is not audit etc, etc. no equilibrium in pure strategies Intuition of simple strategic model: leader-follower if tax authority moves first, perhaps get a simple outcome Develop 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? 13 February 2012 Frank Cowell: EC426 25 Climate: motivation Different countries, different types of compliance behaviour? develop a model of a compliance climate? (Cummings, et al. 2009) others evasion choices affect my evasion decision (Fortin et al. 2007) several possible foundations 1 Symmetric consumption externality if you evade maybe I feel less pain if caught behaving antisocially social stigma (Benjamini and Maital 1985, Kim 2003) 2 Technological (production) externality the more others evade the easier to find a corrupt accountant leads to reduction in noncompliance costs 3 May also be induced by tax authority auditing rules may induce a perceived interdependence creates a co-ordination game Alm and Mckee (2004) Develop the first of these variants 13 February 2012

Frank Cowell: EC426 26 Climate: model background Evasion decisions affect outcomes in two ways each persons outcome affected by own choices (as before) also affected by evasion of others (independently of public goods) Nature of the consumption externality aggregate evasion affects utility moral climate? Utility of an a-type is Va(e,E) where e: Own evasion activity E: aggregate evasion In principle there are two subcases: 1 where aggregate E increases utility 2 where aggregate E reduces utility Focus on case 2 13 February 2012 Frank Cowell: EC426 27 Interaction: model behaviour

utility The Evasion-Utility Space Payoffs if act honestly Payoffs if act dishonestly Check incentive to switch Dominant behaviour Find equilibrium V (0,E) a Va(y,E) 0 13 February 2012 Y

E* aggregate evasion E Check stability min E = 0, max E = Y low E : individual switches to 0 high E: individual switches to y E < E*: switching decreases E E > E*: switching increases E Three equilibria: E = 0 (stable) E = E* (unstable) E = Y (stable) Frank Cowell: EC426 28 Overview... Tax Compliance

Introduction A utilitarian approach Basic model Extensions Policy Basic model & extensions Strategic interaction 13 February 2012 Frank Cowell: EC426 29 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) depends on tax parameters (p, s, t) and personal characteristics (y, a) Welfare model Take expected utility of representative taxpayer as welfare criterion W = [1 p] u([1 t] y + te) + p u([1 t] y ste) Should evasion be eliminated? t fixed : dont eliminate evasion p fixed: eliminate evasion p, s, t all variable: no solution 13 February 2012 Frank Cowell: EC426 30 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: = 1 h

utility: u(c, ) 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, ) Lagrangean: v(t, w) + l [twh [1 p ps]t e(t, w) f(p) 13 February 2012 `R / n ] Frank Cowell: EC426 31 Choosing p for given (s,t) fp Probabilities, costs and benefits Marginal cost of audit Marginal benefit of audit Bp Optimum investigation effort

p* 0 p 1 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 13 February 2012 `r te/p w0/p e(t, w) + vp/l Frank Cowell: EC426 32 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 13 February 2012 Frank Cowell: EC426 33 Overview... Tax Compliance Introduction Strategic approach to

audit policy Basic model Extensions Policy Basic model & extensions Strategic interaction 13 February 2012 Frank Cowell: EC426 34 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 poor y0 ??? a0 honest rich y0 + D y always pay a1 chancers y0 + D y cheat if can a2 13 February 2012 Frank Cowell: EC426 35 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 = [aa1 + a+ + aa2 + a[a1 p] + a] + at + aDy + a2pp + a[[1 + s]t Dy + a] a0p Marginal impact on receipts from increasing p is: a2p + a[[1 + s]t Dy + a] a0 This is positive if p is greater than a threshold value: + a + a + a + a + a + a + a + a + a + a + a + a + aa0 + a + a p + a> + ap* + a + a:= + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + aa2 + a[[1+s]t Dy + a] 13 February 2012 Frank Cowell: EC426 36 Equilibrium concepts Taxpayers and tax agency each form beliefs about the others 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) 13 February 2012 Frank Cowell: EC426 37 Precommitment: policy If the tax authority were permissive, net receipts would be low: DT|p=1,p=0 = a1 + at + aDy 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 = [aa1 + a+ + aa2] + at + aDy a0 This amounts to a Punish the poor policy Is this in fact optimal? viability credibility 13 February 2012 Frank Cowell: EC426 38

Precommitment: optimality? Condition 1 for financial viability is: DT|p=0,p=1 DT|p=1,p=0 [aa1 + a+ + aa2] + at + aDy a0p + a a1t + aDy a2t + aDy a0 Condition 2 for financial viability is: net return from investigating a false report must be non-negative [a1 + a+ + as] + at + aDy + a 0 Combining the two conditions [a1 + a+ + as] + at + aDy + a + a [a1 + a+ + as [aa2/a0]]t + aDy 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 13 February 2012 Frank Cowell: EC426 39 No commitment: outline Tax authority: believes probability that a chancer will cheat is p

perceived probability of catching an evader is q + a:= a2p/[a0+a2p] expected net tax receipts can be written as: + a + a + a + a + a + a + a + aa0 + a + a + a const + + a[a + ap + a/ + ap* + a + a + a + a1] + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + aa0+a2p + a p* is pivotal value of belief Chancers: believe that probability of audit is p expected utility if cheat is: pu([a1 + a + at]y0 + a+ + a[a1 + at + a st]Dy) + a+ + a[a1 + ap]u([a1 + a + at]y0 + a+ + aDy) expected utility if dont cheat is: u([a1 + a + at][ay0 + a+ + aDy]) there is a pivotal probability satisfied p* which equates these two utilities if u is risk neutral then p* = 1 / [1+s] Solution: tax authoritys 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 13 February 2012 Frank Cowell: EC426 40

No commitment: Solution p The strategy space Tax authoritys strategy Chancers strategy Equilibrium 1 p* (p*,p*) p(p) tax authority reaction p(p) always audit if proportion of cheats is believed high always cheat if probability of detection is believed low

+ ap* + a + a= + a 1 / [1 +s] 0 13 February 2012 taxpayer reaction p* p 1 + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a + a a0 + a + a + ap + a + a= + a + a Frank Cowell: EC426 * 41 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 13 February 2012 Frank Cowell: EC426 42 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? 13 February 2012 Frank Cowell: EC426 43 References (1) Allingham, M. and A. Sandmo (1972) Income tax evasion: a theoretical analysis, Journal of Public Economics, 1, 323-338

Alm, J. and Mckee, M. (2004) Tax compliance as a coordination game, Journal of Economic Behavior & Organization 54, 297-312 Andreoni, J. Erard, B. and Feinstein, J. (1998) Tax Compliance, Journal of Economic Literature, 36, 818-860 *Bayer, R.-C. and Cowell, F. A. (2009) Tax compliance and firms' strategic interdependence, Journal of Public Economics, 93, 1131-1143 Benjamini, Y. and Maital, S. (1985) Optimal tax evasion and optimal tax evasion policy: behavioral aspects, in Gaertner, W. and Wenig, A. (eds) The Economics of the Shadow Economy, Springer Verlag, Berlin Cowell, F. A. (1990) Cheating the Government, MIT Press, Cambridge MA *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 Cowell, F. A. and Gordon, J. P. F. (1988) Unwillingness to pay: tax evasion and public good provision, Journal of Public Economics, 36, 305-321 Cummings, R. G., Martinez-Vazquez, J., McKee, M. and Torgler, B. (2009) Tax morale affects tax compliance: Evidence from surveys and an artefactual field experiment, Journal of Economic Behavior and Organization, 70, 447-457 13 February 2012 Frank Cowell: EC426 44 References (2)

*Fortin, B., Lacroix, G. and Villeval, M.-C. (2007) Tax evasion and social interactions, Journal of Public Economics, 91, 20892112 Kim, Y. (2003) Income distribution and equilibrium multiplicity in a stigma-based model of tax evasion, Journal of Public Economics, 87 15911616 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, Lee, K. (1998) Tax evasion, monopoly and nonneutral profit taxes, National Tax Journal, 51, 333-338. 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 Slemrod, J. (2007) Cheating Ourselves: The Economics of Tax Evasion, Journal of Economic Perspectives, 21, 25-48

Slemrod, J. and Yitzhaki, S. (2002) Tax avoidance, evasion and administration, Handbook of Public Economics, Volume 3, pp 1423-1470, North-Holland, Elsevier 13 February 2012 Frank Cowell: EC426 45