Transcript No Slide Title

Frank Cowell: HMRC-HMT Economics of Taxation
14 December 2011
HMRC-HMT Economics of
Taxation 2011
http://darp.lse.ac.uk/HMRC-HMT
10.2 Policy design
Frank Cowell: HMRC-HMT Economics of Taxation
Policy Design
Overview...
Background
Locating the
subject within
public
economics
Objectives and
constraints
Optimal policy
C&B
Optimal policy
Strategic
Tax design
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Frank Cowell: HMRC-HMT Economics of Taxation
Issues in enforcement policy design
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Identify main policy rules
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Objectives
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reconcile with utilitarian goals?
what guidance for tax agencies?
Implications for tax policy
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based on utilitarian ethics
using the principal model types
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)
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Frank Cowell: HMRC-HMT Economics of Taxation
The principal economic actors
The key players
Control & reporting, simple constitution
Delegation
Tax farming
Further delegation
Control & reporting, full delegation
Government
Corruption model
Tax Authority
Inspector
Inspector
Inspector
Taxpayers
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Frank Cowell: HMRC-HMT Economics of Taxation
Government Control?
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Government is denied direct information about citizens
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Multi-layered structure
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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
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Is therefore denied some measure of control
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
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Taxpayer offers payment to inspector to reduce prob of punishment
Inspector is monitored by authority.
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Frank Cowell: HMRC-HMT Economics of Taxation
Questions in enforcement policy
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Policy questions from previous lecture
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Should we try to eliminate evasion?
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Often an implicit objective
But on what grounds?
Implications of devolution of function
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What is the optimum degree of enforcement?
Can smart auditing improve efficiency?
Move beyond this to broader questions
Not just lack of control
Also the type of objective function
Implications for tax design?
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Frank Cowell: HMRC-HMT Economics of Taxation
Connection with previous topic
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Related to compliance lecture
Examine general issues of “breakdown” in fiscal
relationships
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tax under-reporting is one example
also black/shadow economy
And the mechanisms that may act as insulation
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institutions
social factors
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Frank Cowell: HMRC-HMT Economics of Taxation
Policy Design
Overview...
Background
Limitations of
standard
utilitarian model
Objectives and
constraints
Optimal policy
C&B
Optimal policy
Strategic
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Frank Cowell: HMRC-HMT Economics of Taxation
Modelling issues
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What is the appropriate objective?
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What institutional structure?
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Law enforcement? Eliminate evasion?
Welfare of law-abiding citizens?
Utilitarianism?
Direct government-taxpayer relation?
Tax collection/enforcement agencies?
What components of the enforcement problem?
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requires a multi-stage approach
see Cowell (1989)
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Frank Cowell: HMRC-HMT Economics of Taxation
Utilitarian enforcement problem
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Basic behavioural model
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Outcome of basic model
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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)
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
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Take expected utility of representative taxpayer as welfare criterion
W = [1 – p] u([1 – t] y + te) + p u([1 – t] y – ste)
where y = y , a = a (representative taxpayer)
(so we can drop y, a from optimal evasion response)
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Frank Cowell: HMRC-HMT Economics of Taxation
Fundamental constraints
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Realities for the government / tax agency
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Government budget constraint
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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
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a fixed revenue requirement R
cost of enforcement f(p) where f is an increasing function
in utilitarian model f may include private compliance costs
[1 – p] u([1 – t] y + te) + p u([1 – t] y – ste) = const
where e = e(p, s, t)
Evasion eliminated where rate of return is zero:
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s = [1−p]/p
gives zero-evasion contour where welfare is u([1 – t] y) = W0
so determines boundary of “honesty set”
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Frank Cowell: HMRC-HMT Economics of Taxation
Model types
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Problem essentially has three control variables, p, s, t
Three stages in the approach to the solution
Keep t fixed
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Keep s or p fixed
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enforcement authority has considerable, but not total, discretion
can trade off severity of penalty against probability of detection
unmovable penal system
inflexible police system
trade off tax against an enforcement parameter
Vary p, s, t together
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Total flexibility
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 The feasible set
 The “enforced honesty set”
s
W0
 A: The zero-evasion point
R R
 W0 welfare contour through A
Welfare contours
zero-evasion line
Frank Cowell: HMRC-HMT Economics of Taxation
The problem if t is fixed
B: the optimum
f(p0) = ty –R
s [1−p]/p
W0 satisfies s = [1−p]/p
W
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Welfare increases
“South-West”
B

0
A
p0
p
1
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Frank Cowell: HMRC-HMT Economics of Taxation
The problem if p is fixed
 Draw feasible set
 The “enforced honesty” set
s
 A welfare contour
 Welfare contours
1−p
——
p

 Optimum
A
R R
W
t
0
1
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Frank Cowell: HMRC-HMT Economics of Taxation
The problem if p,s,t all variable
Optimisation problem again
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“Enforced
 objective
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honesty” set
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s
Transform the problem
Revenue increases to North-East
Tax authority moves this way?
constraint
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R = constant
0
A
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p
1
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Frank Cowell: HMRC-HMT Economics of Taxation
Policy Design
Overview...
Background
A utilitarian
approach
Objectives and
constraints
Optimal policy
C&B
Optimal policy
Strategic
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Frank Cowell: HMRC-HMT Economics of Taxation
Optimal degree of enforcement?
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Take a standard welfare-economics approach
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Basic utilitarian model
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income: y = wh
consumption: c = [1  t]y + rte
leisure: ℓ = 1  h
utility: u(c, ℓ)
Government/tax authority
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homogeneous population
simple revenue target
a type of cost-benefit approach to enforcement
Individual (slightly extended)
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choose the optimal p, given fixed s, t
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
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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 ]
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Frank Cowell: HMRC-HMT Economics of Taxation
Choosing p for given (s,t)
Probabilities, costs and benefits
Marginal cost of audit
fp
Marginal benefit of audit
Optimum investigation effort
Bp
p*
0
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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 r te/p  w0ℓ/p e(t, w) + vp/l
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Frank Cowell: HMRC-HMT Economics of Taxation
Extensions – agent interaction
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Cost-benefit approach is essentially individualistic
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Social interaction models
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recognise that agents may have better market information than tax authority
exploit information about all agents’ behaviour
Example: tax compliance by firms
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prevent epidemics?
shift the equilibrium?
manipulate expectations? Iyer et al 2010)
raise search costs?
Focus on smart use of information
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compute MB for each agent
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
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Frank Cowell: HMRC-HMT Economics of Taxation
Policy Design
Overview...
Background
Strategic
approach to
audit policy
Objectives and
constraints
Optimal policy
C&B
Optimal policy
Strategic
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Frank Cowell: HMRC-HMT Economics of Taxation
Tax-payer v. Tax-collector game
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Model ingredients
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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
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Take a simple 2x2 version:
type
poor
honest rich
chancers
income
y0
y0 + D y
y0 + D y
attitude
???
always pay
cheat if can
pop proportion
a0
a1
a2
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Frank Cowell: HMRC-HMT Economics of Taxation
A mixed-strategy approach
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Each side expects the other to play probabilistically:
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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]t Dy –  ] – a0p
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Marginal impact on receipts from increasing p is:
a2p [[1 + s]t Dy –  ] – a0

This is positive if p is greater than a threshold value:
a0
p > p* := 
a2 [[1+s]t Dy –  ]
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Frank Cowell: HMRC-HMT Economics of Taxation
Equilibrium concepts
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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:
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tax authority precommits to a strategy
tax authority does not precommit
see Reinganum and Wilde (1985, 1986)
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Frank Cowell: HMRC-HMT Economics of Taxation
Precommitment: policy
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If the tax authority were permissive, net receipts would be low:
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If authority can commit it ought to audit all low-income reports:
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p = 0 if report is y0 + Dy
p = 1 if report is y0
Tax receipts net of audit costs are
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DT|p=1,p=0 = a1 t Dy
DT|p=0,p=1 = [a1 + a2] t Dy – a0
This amounts to a “Punish the poor” policy
Is this in fact optimal?
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viability
credibility
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Frank Cowell: HMRC-HMT Economics of Taxation
Precommitment: optimality?
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Condition 1 for financial viability is:
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Condition 2 for financial viability is:
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net return from investigating a false report must be non-negative
[1 + s] t Dy –  ≥ 0
Combining the two conditions
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DT|p=0,p=1 ≥ DT|p=1,p=0
[a1 + a2] t Dy – a0p ≥ a1t Dy
a2t Dy ≥ a0
[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:
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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
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Frank Cowell: HMRC-HMT Economics of Taxation
No commitment: outline
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Tax authority:
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Chancers:
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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
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:
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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
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The strategy space
 Tax authority’s strategy
p
 Chancer’s strategy
 Equilibrium
1
p(p)
p*
•
p(p)
tax authority
reaction
Frank Cowell: HMRC-HMT Economics of Taxation
No commitment: Solution

 always
cheat if probability of
detection is believed low
(p*,p*)
taxpayer
reaction
0
p*
always audit if proportion
of cheats is believed high

p* = 1 / [1 +s]

a0 
p* = 
a2 [[1+s]t Dy –  ]
p
1
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Frank Cowell: HMRC-HMT Economics of Taxation
How the model works
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Response to tax-enforcement parameters:
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∂p*/∂ > 0
∂p*/∂t < 0
∂p*/∂s < 0
∂p*/∂ = 0
∂p*/∂t ≥ 0
∂p*/∂s < 0
Changing population proportions:
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∂p*/∂a0 > 0
∂p*/∂a2 < 0
∂p*/∂a0 = 0
∂p*/∂a2 = 0
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Frank Cowell: HMRC-HMT Economics of Taxation
Assessment
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Compliance is a central component of public economics
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Analysed using standard microeconomic techniques
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Incentives issues similar to those of labour supply
Important to model the interactions involved in evasion
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Arises naturally from the issues concerning the provision of public
goods
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?
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Is a standard reporting model appropriate?
What information should each party be assumed to have?
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Frank Cowell: HMRC-HMT Economics of Taxation
References
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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 principalagent 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, 739760.
* Slemrod, J. and Yitzhaki, S. (2002) “Tax avoidance, evasion and
administration,” Handbook of Public Economics, Volume 3, pp 1423-1470, NorthHolland, Elsevier
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