Tax Compliance and Firms Strategic Interdependence

Tax Compliance and Firms’ Strategic Interdependence Ralph Bayer University of Adelaide and Frank Cowell London School of Economics Tax Compliance: Background • Typically on the personal taxpayer • Simplified information structure • Broadly two categories  TAG models  Cat-and-mouse models • Neglects some important features and information  Production  Creation / disappearance of taxable units  Structure of industry TAG • • • • • • Taxpayer as Gambler: Individual has fixed income Conceals a part of this income Knows the penalty and probability of audit Audit probability is fixed Takes a risk on whether he is audited Cat-and-mouse • • • • • Audit probability depends on report Generates strategic interaction Known distribution of income and types Condition audit on report Alternatively can use information from history Firm: competitive model • Assume expected profit maximisation  Only source of randomness is due to audit.. • 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].     Proportional tax rate t. Probability of audit b. Penalty rate for concealed output f. te = [1 – b]at + b [t + [1 – a ]ft ] = [a + [1 – a ] b [1+f]]t • Compute expected effective tax rate te • Behaviour driven by two things  Concealment cost model  Conditioning of audit probability and penalty Competitive model: result • Expected profits are [p – m – c – te ] · q  p: price  m: marginal production cost • 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 • Optimal output satisfies  [1 – a ]g'(1– a) = t – te.  “MC concealment equals reduction in expected tax”  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? Generalisations • Monopoly / imperfect competition     Determinate demand curve Replace q with q(p) Little changes: replace "price" with "MR" in FOC Separation result persists. • 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 (NTJ 1998) Standard approach – assessment • Tax neutrality argument is artificial  Not robust to different tax base • Audit rule is naive  Does not make full use of industry information • Tax-neutral policy, no effect on output?  Seems to run counter to experience Model setting • Allow for multiple firms • Make better use of information  On part of firms  On part of tax authority • Compare with  Naïve audit rules  Simple models of compliance 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 • Simple reporting models may be in appropriate  There is no fixed income to uncover • May be a natural way to model output and evasion linkage Assumptions: firms • • • • • Identical cost structures Details of these subsumed within profit function Opportunities to evade are common knowledge Firms are risk-neutral Objective function is expected profits Assumptions: evasion • • • • Specify cost-of-evasion function C() Argument is concealed output Increasing, convex C(0) = 0 Taxation and enforcement • Conventional tax/enforcement regime  Could be generalised  But focuses on the main action of the model • Linear profits tax • Simple fine structure for noncompliance • Two types of audit regime  independent audits  relative audits Assumptions: 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 Tax and profits • Firm i’s profits gross of tax and depend on output vector of industry • Profits form base of tax • Given linearity, firm i should pay • The tax it actually pays is • Assume there is no audit • Profit net of tax is Profit and penalty • Assume a fixed proportional fine f. • Total fine is therefore • Assume a fixed proportional fine f. • Given the linear tax function, profits after audit are Objective function • Risk-neutrality implies that firm i maximises expected net profit: • Expanding this probability of audit gross profit if audited gross profit if not audited cost of concealment Relative audit rule • Audit probability depends on i's declaration relative to the rest. • Each firm knows that: • ...own declaration may reduce the probability • ...others' declaration may increase the probability • Normalisation: Timing • The government announces taxes and an audit regime • Firms choose quantities • Firms observe gross profits of the others • Firms choose profit declarations Declaration decision • First-order condition: • Second-order condition: <0 <0 = f+t >0 >0 • Sufficient condition for 2ndorder condition: FOC conditions • To get an interior solution we need two conditions • If marginal concealment costs are high for extensive tax evasion • Low level of detection probabilities and C'(0) = 0 gives • Second condition corresponds to usual TAG case. Output decision • Changes in quantity affect optimal declarations of others • Changes in others' declarations affect i's audit probability • So first-order condition is: • The * indicates that i takes into account the interdependences • Substitute in from declaration decision FOC: 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. • Imagine starting with simple independent audits. • Would there be a “dividend” in refining and announcing the refinement? First "dividend" Proposition • Under the relative audit rule with mean equilibrium detection probability β* firms declare more profits than under random audits with the fixed detection probability β(i) = β*. Second "dividend" Proposition • A relative audit rule leads to outputs higher than in Cournot competition without taxes. Second dividend: analysis (1) • What is interdependence effect? • We need the sign of • This can be found from <0 • where D is <0 >0 <0 • So the interdependence effect is positive Second dividend: analysis (2) • Use the FOC • Expression (a) is negative • Expression (c) is positive • Therefore expression (b) is positive Independent auditing • Here each firm faces a fixed audit probability Proposition • Under an independent audit rule output is independent of the evasion decision and equals the Cournot quantities. Independent auditing: analysis • Substituting the FOC for declaration into the FOC for output choices gives • This only holds if • Gives the Cournot outcome Other developments • Similar results for Bertrand model with differentiated products. • Entry/exit of firms