# Tax Compliance Frank Cowell: MSc Public Economics 2011/2

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- Slide 1
- Tax Compliance Frank Cowell: MSc Public Economics 2011/2 http://darp.lse.ac.uk/ec426 http://darp.lse.ac.uk/ec426
- Slide 2
- Overview... Introduction Basic model Policy Tax Compliance How compliance fits into public economics 2 Frank Cowell: EC426 2 Extensions 13 February 2012
- Slide 3
- 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 2012Frank Cowell: EC426 3
- Slide 4
- 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)2004 Slemrod (2007) Slemrod and Yitzhaki (2002) 13 February 2012Frank Cowell: EC426 4
- Slide 5
- Overview... Introduction Basic model Policy Tax Compliance Individual behaviour and the public sector 5 Frank Cowell: EC426 5 Extensions 13 February 2012 Individual taxpayer Multiple taxpayers
- Slide 6
- TAG model Standard model is essentially one of Taxpayer As Gambler based on Allingham and Sandmo (1972)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 2012Frank Cowell: EC426 6
- Slide 7
- 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 2012Frank Cowell: EC426 7
- Slide 8
- TAG: budget constraint A B c" c' [1 t]y [1 t st]y y [1 t]y line of perfect certainty c': consumption if not caught B: Payoff if blatantly dishonest c'': consumption if caught A: Payoffs if absolutely honest Consumption possibilities for all e c' = [1 t] y + te if not audited / convicted c'' = [1 t] y ste if audited and convicted 1 A cut in the surcharge rate s 2 A cut in the tax rate t 3 Increase in income y 13 February 2012Frank Cowell: EC426 8
- Slide 9
- 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: E u(c) = [1 p] u(c' ) + p u(c'' ) E u(c) = [1 p] u([1 t] y + te) + p u([1 t] y ste) Cardinal utility function u has the usual properties: u c () > 0 (first derivative) u cc () 0 (second derivative) Both u and p determine shape of ICs in ( c', c'' )-space curvature of ICs depends on risk aversion u cc ()/u c () slope of ICs where crosses 45 line is [1 p]/p 13 February 2012Frank Cowell: EC426 9
- Slide 10
- c"c" c'c' 0 Equilibria of the tax-evader Feasible set A: corner solution (honesty) B: corner solution (dishonesty) C: Interior (partial honesty) E: Expected payoff B A E E(ru c (c)) 0 if e* = 0 E(ru c (c)) 0 if e* = y E(ru c (c)) = 0 if 0 < e* < y C solution depends on tax parameters := (p, s, t) income y personal attributes a e* = e( , y, a) 13 February 2012Frank Cowell: EC426 10
- Slide 11
- 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 (ru c (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 2012Frank Cowell: EC426 11
- Slide 12
- Overview... Introduction Basic model Policy Tax Compliance How to assemble the whole economy 12 Frank Cowell: EC426 12 Extensions 13 February 2012 Individual taxpayer Multiple taxpayers
- Slide 13
- 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 2012Frank Cowell: EC426 13
- Slide 14
- 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( , y, a) dF(y, a) cost of enforcing probability p across economy (p) Composition of revenue R = tY t re( , y, a) (p) So budget constraint becomes tY t re( , y, a) (p) R But this ignores how the government revenue may be used 13 February 2012Frank Cowell: EC426 14
- Slide 15
- TAG model: Public Sector Taxes are used to pay for a public good z Government budget constraint in this extended model is: R z where 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 E u(c,z), where u z (c,z) > 0 FOC for an interior maximum is: E (ru c (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 2012Frank Cowell: EC426 15
- Slide 16
- 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: 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 13 February 2012Frank Cowell: EC426 16 EuaEua t z > z* a z < z* a underprovisionoverprovision
- Slide 17
- Preferences for public and private goods How is z* determined? Optimal provision uses standard MRS = MRT rule Because of the risk component general formula is unwieldy So take a simplified set of preferences u a (c, z) = c + v a (z) m a := u z a (c, z)/u c a (c, z) = v z a (z) m := m a = 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 / z t a simple criterion for determining under / over provision 13 February 2012Frank Cowell: EC426 17 c z slope = m
- Slide 18
- 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) But individuals differ in: risk aversion taste for public goods income So, different responses: constrained by e y high marginal evaluation low marginal evaluation Get a more complex relationship between t and evasion overall te t ty 13 February 2012Frank Cowell: EC426 18
- Slide 19
- Overview... Introduction Basic model Policy Tax Compliance An alternative model of the individual agent 19 Frank Cowell: EC426 19 Extensions 13 February 2012 Firms Interaction
- Slide 20
- 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 2012Frank Cowell: EC426 20
- Slide 21
- Firms: a model Conventional (non strategic firm) marginal production cost demand (sales) given by x(P) P is market price Tax t payable on sales Firm conceals a proportion of sales concealment costs per unit of output G( ) Expected tax rate

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