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Lecture 6: Tax administration and its problems
Andreoni, J, B. Erard, J. Feinstein (1998), Goodin, R.E. (1996), Kay, J.A. (1990)
Economics of taxation
dr Grzegorz Kula, [email protected]
Problems of tax administration
For Adam Smith taxation is efficient if, among other things, the costs of collecting taxes are low.
Problem: how can we have low costs of tax administration and collection, and at the same tax efficient mechanism for collecting taxes?
In models analyzing tax administration “the probability of audit is a function of reported income and is determined jointly with cheating as part of an equilibrium.” (Andreoni, p. 825)
Two types of models:
• The tax agency can commit to its audit rule before taxpayers file returns – principal-agent problem.
• The tax agency cannot commit to its audit rule but instead decides which taxpayers to audit after all returns have been filed – game-theoretic equilibrium.
dr Grzegorz Kula, [email protected]
Basic model, Andreoni et al. (1998)
Assumptions:
1. Large population of potential taxpayers and each of them possessing true income y owes t(y) in taxes.
2. True income is distributed along a continuum between and . f(y) is the density function, F(.) – the distribution function associated with f(.).
3. The tax authority can learn a household's true income y only by performing a costly audit.
y y
dr Grzegorz Kula, [email protected]
The tax collection system consists of two stages:
1. Each taxpayer is asked to report his taxable income to the authority and to pay the taxes he claims to owe.
x – a taxpayer's report, where generally x ≤ y.
2. The authority audits a subset of cases.
c – the costs of one audit, B – a budget for audits
When the authority audits a taxpayer:
1. It learns his true income y,
2. Collects the additional tax t(y) – t(x),
3. Assesses additional penalties and interest charges in the amount θ[t(y) – t(x)], where θ[0]= 0 and θ'[q]> 0 for all q.
Basic model, Andreoni et al. (1998) dr Grzegorz Kula, [email protected]
For a taxpayer with true income y the expected utility from a report x is given by
(2)
where p(x) is the probability of audit associated with report x.
Additional assumptions:
1. Audit imposes no costs on a taxpayer beyond those related to the underreporting of income.
2. Both the tax rate and the penalty function are linear.
3. Taxpayers are assumed to be risk neutral.
4. The tax authorities objective is to maximize expected net revenue.
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Basic model, Andreoni et al. (1998) dr Grzegorz Kula, [email protected]
Principal-agent model
Tax authorities can commit to an audit rule
1. Principal-agent problem.
2. The strategy that maximizes audit revenue involves a "cut-off” rule.
3. Cut-off rule consists of a threshold value w and a policy to audit any report below the threshold with some probability p.
4. When the tax and penalty schedules are linear and taxpayers are risk neutral, the optimal value of p is 1/(1+ θ).
5. When p takes this value, taxpayers with true incomes above w choose to report exactly w, paying tw in taxes and bearing no risk of an audit.
dr Grzegorz Kula, [email protected]
The simple cut-off rule is the optimal audit strategy, if:
1. tax payers are risk neutral;
2. the penalty schedule is linear;
3. the expression t’(y)γ(y) is decreasing in y, where t'(y) is the derivative of the tax schedule at income level y and γ(y) is the hazard function
The optimal audit rule is a nonincreasing function of income.
yf
yF1
Principal-agent model dr Grzegorz Kula, [email protected]
Principal-agent model
Modifications of the cut-off rule:
1. Reduce the probability of audit below 1/(1+ θ) for reports beneath the threshold value w.
Taxpayers would strictly prefer to report if:
- their true incomes are below w,
- their true incomes are between w and some value q above w.
2. Introduce a two-step rule: p = 1/(1+ θ) between and some report z , z < w, and a lower audit probability between z and w.
Taxpayers with true incomes between z and w report z rather than their true incomes,
Taxpayers with true incomes between w and some higher value r report z rather than w.
y
y
dr Grzegorz Kula, [email protected]
Game-theoretic approach
Tax authorities cannot commit to an audit rule
1. A sequential move game.
2. Taxpayers correctly forecast the probability of audit for each income value.
3. The tax and penalty functions are linear.
4. All taxpayers are willing to cheat "if the price is right”.
5. Many possible equilibria. We focus on the fully separating equilibrium, in which each observed report x is associated with a single true income level y(x).
dr Grzegorz Kula, [email protected]
Each taxpayer underreports by the same amount:
where c is the audit cost and λ is the shadow value associated with the audit budget constraint.
Reported income lies between and , where
The audit function p(x) • takes the value zero over the half-strip • nonincreasing in x, • strictly between zero and one over the range
t
c
1
x x
t
cyx
1 t
cyx
1
yx,
xx,
Game-theoretic approach dr Grzegorz Kula, [email protected]
It is an equilibrium of the game, because:
1. if taxpayers report as specified, then when the tax authority observes a report x, it knows that the report corresponds to true income
2. The tax authority is indifferent between auditing and not auditing the return, since the cost of the audit λc is exactly equal to the revenue that can be earned by performing it, (y - x)(1 + θ)t.
3. The authority is willing to follow a mixed strategy and audit with some probability between zero and one.
t
cx
1
Game-theoretic approach dr Grzegorz Kula, [email protected]
The function p(x) is chosen so that:
• The first-order condition associated with the maximization of expected utility is equal to zero when
• The value of λ is chosen to satisfy the budget constraint.
• To sustain the equilibrium, p(x) is assumed to equal one for all reports below .
Apart from the fully separating equilibrium, there are many alternative pooling and partially pooling equilibria in this model. There is no universally accepted criterion for determining whether the fully separating equilibrium or one of the pooling equilibria will be played.
Game-theoretic approach
t
cyx
1
x
dr Grzegorz Kula, [email protected]
Assume now that there are some honest taxpayers: • At each income level y a fraction Q of taxpayers
always reports truthfully. • The remaining fraction 1 – Q of taxpayers is willing
to cheat and reports the value x that maximizes expected utility.
• The tax authority does not know a taxpayer's true income prior to conducting an audit.
• Expected tax revenue now depends on two factors: - the magnitude by which dishonest taxpayers
reporting at x cheat, y(x) – x, - the fraction of dishonest taxpayers reporting at x.
Game-theoretic approach dr Grzegorz Kula, [email protected]
In the principal-agent models: • All audited taxpayers will be found to have reported
honestly, at least if a cut-off rule is adopted. • The agency knows the true incomes of all individuals
who will be subjected to audit prior to conducting any audits.
In the game-theoretic models: • It seems unrealistic that in equilibrium the tax
authority is just indifferent between auditing and not auditing taxpayers over much of the reporting range.
Many tax agencies apparently do establish cut-off points and focus their audit resources on returns falling below the cut-offs. However:
• They usually select only a subset of the total number of returns below their cut-off points.
• Theory implies that they select them randomly, but in practice they may use additional rules.
Main criticism of the models dr Grzegorz Kula, [email protected]
Problems with assumptions: • Taxpayers can correctly deduce the audit rule. - In the real world asymmetry of information -
taxpayers seem to possess quite poor knowledge of the audit function.
• Taxpayers only experience a cost from being audited if they are found to have underreported their income.
- Audits can be costly even for honest taxpayers (overreporting of tax liability?).
• Taxpayers report only a single piece of information, i.e. taxable income.
- In practice taxpayers make rather detailed reports. • Taxpayers are certain of their true tax liability. - Many taxpayers do not know their actual tax
obligations.
Main criticism of the models dr Grzegorz Kula, [email protected]
In the principal-agent model there are two sides to taxation problems:
1. The interaction between tax administration and taxpayers - one is trying to ensure that taxes are paid honestly, while others are trying to pay as little as possible or not to pay at all.
2. A problem of tax officials and their principals, i.e. the state, politicians in power. Bureaucracy can act in their own interest and be corrupt.
Two problems which can affect a tax collector: 1. Shirking – the basic moral hazard problem. 2. Corruption – how to ensure that a tax collector
passes along information uncovered in his investigative activities, instead of using it to his own benefit?
Corruption and motivation of tax authorities dr Grzegorz Kula, [email protected]
Question: what wages should be offered to the tax administration?
- Wages are the most significant component of the administrative costs of taxation.
- Each government would prefer to cut the costs of administration.
- We need good and honest specialists in tax administration and their services are expensive.
- Wages or bonuses? Administrative costs and compliance costs can be both
substitutable and complementary: • Substitutability works through the way in which
taxes are collected – who is more involved? • Complementarity arises because avoidance activity
by taxpayers causes compensating responses by the revenue authorities and (perhaps) vice versa.
Corruption and motivation of tax authorities dr Grzegorz Kula, [email protected]
Rational choice theory explains the problems of institutional compliance by possible gains from deviations.
Two strategies: 1. The deviant-centered strategy: • With most norms of behavior there are some deviants
and noncompliers. • If self-interest makes people to deviate, then we
should design institutional rules to make compliance the self-interest option for them (the knave strategy).
• Problems: - Who will guard the guardians? - Many people often act in nonegocentric way. Do we
need to have extreme sanctions, as if we were all knaves?
- If we are treated as knaves, we may start behaving as ones.
Rational institutional design dr Grzegorz Kula, [email protected]
2. The complier-centered strategy: • Focuses on the ordinary individuals, who are
usually complying and nonegocentric in their actions.
• First try to strengthen the compliant behavior, and only afterwards guard against the deviations.
• Helping honest taxpayers may encourage others to comply with the rules.
• We need a hierarchy of sanctions, especially punishments.
• The problem of guarding against guardians is weaker:
- Screening mechanisms applied to the choice of people in power.
- Multilevel sanctions on the people in power.
Rational institutional design dr Grzegorz Kula, [email protected]
