Learning about Compliance under
Asymmetric Information
Carmen Arguedas
Universidad Autónoma de Madrid
and
Sandra Rousseau
HUBrussel
Center of Economic Studies, K.U.Leuven
Zaragoza, 13 December 2008
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Motivation (1)

Regulations aim to mitigate negative externalities arising from production
When do agents comply with them?

In theory (Becker, 1968):




When expected penalties of violating exceed compliance costs.
Otherwise, they do not comply.
In practise (Ogus and Abbot, 2002):
Environmental crime:



Only 23 % of major violations prosecuted
Low average fines (£6900 for firms and £1000 for individuals)
Still high compliance rates!!
Harrington’s paradox
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Motivation (2)

Aim of the paper:
Explain Harrington’s paradox by means of a
signalling game which incorporates dynamic
enforcement and learning
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Motivation (3)

Inspection agencies



have limited available budgets
learn about firms’ performance over time
In a dynamic setting, monitoring & enforcement
strategy based on:


Firms’ past compliance status
Firms’ performance relative to others
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Motivation (4)
If future regulations based on actual relative position of firms
with respect to externality levels, then:


Bad firms tempted to mimic good firms
Good firms tempted to prevent being mimicked by bad firms
UNDER
Actual external costs might be considerably lower
WHAT
than those expected in a static regulatory process!! CONDITIONS?
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Motivation (5)

Related literature:

Dynamic enforcement:



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Contract theory:


Greenberg (1984),
Landsberger and Meilijson (1982) and
Harrington (1988)
Laffont and Tirole (1988, 1990)
Avoidance:



Innes (2005),
Malik (1990),
Slemrod and Yitzhaki (2002)
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Model: Assumptions (1)

Industry with N firms with negative production externality (ei)
 Cost to control externality levels:
c  i , e 
with
 i   H ,  L 
ce  i , e  0
and
cee  i , e  0
and
ci ee




ci e  i , e  0
 
 , e   0
i
 NH high-cost firms and NL low-cost firms

Regulation (fixed by law):

Uniform limit on externality

Linear penalty
e 0
F  f max 0;  e  e ,
f  0.
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Model: Assumptions (2)

Inspection agency:

Minimize external costs produced by industry by selecting
inspection strategy pti



For given regulation
For given (yearly) budget B > 0
Budget constraint
with
B  m  NH ptH  NL ptL  .
m = cost per inspection
pti = probability that firm i is inspected in period t
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Model: Timing

Two period model:

Each period:

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Agency announces inspection strategy
Firms react by selecting optimal control level
After first period:


Agency can update inspection strategy
Update based on outcome of inspections
Law
Standard
+ Fine
Firm
Agency
Inspection
frequency
Firm
Agency
Externality Inspection
frequency
Period 1
Externality
Period 2
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Model: Information

Information:



Firms are fully informed about their type
Agency knows distribution of types
Agency can learn through inspecting firms only if they perform
differently (beliefs)
p2H
H
p2L
L
p1
1-p1
p2N
H
p2N
L
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Model: Objective functions

Firms



Decision: externality level
Minimize expected discounted costs associated with regulation
= control costs + expected fines for non-compliance
Agency


Decision: inspection strategy
Minimize total external costs in industry s.t. budget constraint
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Results: one-period regulation (1)

Timing
Law
Agency
Firm
Standard
+ fine
Inspection
frequency
Externality
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Results: one-period regulation (2)
Firm Behavior: minei c i , ei   pi f max 0, ei  e.
$
Marg. expected fine
pif
Marg. control
costs
Marg. control costs
e
e
e
e
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Results: one-period regulation (3)

There exists a threshold inspection probability for each type,
such that compliance is ensured above that threshold:
ce i , e 
pi  
f

pH  pL
Relation inspection probability and externality level:
ei
f

0
pi
cee i , ei 


and
ei
ei
 H , eH    L , eL 
pi
pi
Firms’ expected costs increasing in inspection frequency
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Results: one-period regulation (4)

Agency strategy:

No information: random inspections
B
p  p  p , where p 
.
mN
*
H

*
L
Perfect information: targeted inspections

Large budget: complete deterrence possible

Medium budget: only complete deterrence of high-cost firms

Small budget: incomplete deterrence of high-cost firms and low-cost
firms non-inspected
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Results: two-period regulation (1)
Law
Standard
+ Fine
Firm
Agency
Inspection
frequency
Firm
Agency
Externality Inspection
frequency
Period 1
Externality
Period 2
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Results: two-period regulation (2)

Period 2:
Agency’s inspection strategy depends on information
gathered during inspections in first period
1.
Firms’ externality levels are identical (pooling)
B
 Uniform inspection frequency: p 
mN
2.
Firms’ externality levels are different (separating)
 Perfect info about inspected firms
 Estimate of distribution of types over non-inspected firms
(Bayes’ rule)
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Results: two-period regulation (3)
Now:
ei
ei
N  nH ei
N  nL ei
 H , eH  
 H , eH  
 L , eL    L , eL 
pi
N  n pi
N  n pi
pi
Therefore, the optimal inspection policy in the second period is:

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Large budget: complete deterrence
Lower budget: complete deterrence of known high-cost firms and non-inspected
firms, incomplete deterrence of known low-cost firms
Even lower budget: complete deterrence of known high-cost firms, incomplete
deterrence of non-inspected firms, known low-cost firms uninspected
Even lower budget: Only incomplete deterrence of high-cost firms, non-inspected
firms and known low-cost firms non-inspected.
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Results: two-period regulation (4)

Period 1

Agency: random inspections

Firms:

High-cost firms can try to imitate low-cost firms reducing their
externality level:



Benefit: if successful, lower inspection probability in period 2
Cost: extra control costs
Low-cost firms can try to prevent imitation by high-cost firms
reducing their externality level also:


Benefit: if successful, lower inspection probability in period 2
Cost: extra control costs
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Results: two-period regulation (5)
Period 1
Period 2
Agency
Firms
Agency
Firms
Case (ia)
Uniform
Separating:
Differentiated
Separating:
e  eH  e1*L
inspections: p
e1H  e1*H  e1L  eH
inspections:
e2* HI , e2* LI , e2* HN , e2* LN
p2 H , p2 L , p2 N
Case (ib)
*
e  e1L
 eH
Uniform
Separating:
Differentiated
Separating:
inspections: p
e1H  e1*H  e1L  e1*L
inspections:
e2* HI , e2* LI , e2* HN , e2* LN
p2 H , p2 L , p2 N
Case (ii)
Uniform
Pooling:
Uniform
Separating:
e  eH
inspections: p
e1L  e1H  e
inspections: p
e2* H  e1*H  e2* L  e1*L
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Results: two-period regulation (6)
High-cost firms are more likely to mimic low-cost
firms and low cost-firms less likely to deter
mimicking (i.e., pooling equilibrium more likely):

the larger the budget

the lower the number of firms

the lower the monitoring costs

the lower the number of regulatory periods
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Conclusions

The agency can learn about firms through inspections only if it
discovers groups of firms performing differently

Learning has implications for the agency and firms’ strategies,
and also for social welfare

The targeting strategy can be detrimental for high-cost firms
but beneficial for low-cost firms.

Mimicking or the threat of mimicking can result (but not
always) in a lower level of the total externality

Mimicking is more likely the larger the regulatory budget, the
smaller the number of firms, the lower the monitoring costs,
and the smaller the number of regulatory periods
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Extensions

Other agency’s objectives

Other beliefs

Inspection errors

Imperfect knowledge of firms regarding future
regulations
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