Hiriart, Yolande

Martimort, David

Pouyet, Jérôme

English

Research Papers in Economics

On the Optimal Use of
Ex Ante Regulation and Ex Post Liability
Yolande Hiriarty David Martimortz Jerome Pouyetx
2nd March 2004
Abstract
We build on Shavell (1984)'s analysis of the optimal use of ex ante and ex
post interventions when a rm engages into activities potentially risky for the
environment or third-parties and has private information about the level of the
damage. The regulator enforces ex ante a standard of precautionary eort but
is uninformed about the harm level; ex post, in the event of an accident, the
judge may bring a lawsuit and discover the harm level. The social optimum can
be reached if, ex ante, the regulator oers the rm a menu of incentive contracts
(rewards, penalties and veriable standards). When the precautionary eort is
no longer veriable, the ineciencies generated by the moral hazard incentive
problem cannot be circumvented.
JEL Classication: K13, K32, L51.
Keywords: Ex Ante Regulation, Ex Post Liability.
1 Introduction
Shavell (1984) provides a pioneering analysis of two distinct and often-encountered
instruments in environmental policies: ex ante regulation and ex post legal inter-
vention. Three actors are involved: a rm with limited assets which undertakes an
This paper is part of a research program between IDEI and the French Ministry of Ecology and
Sustainable Development on the regulation of risky industrial activity. Financial and intellectual
support from the Ministry of Ecology and Sustainable Development are gratefully acknowledged.
We wish to thank the Editor, Eric Maskin, and an anonymous referee for their helpful comments.
yUniversity of Toulouse (IDEI, LEERNA). Address: LEERNA-IDEI, Manufacture des Tabacs,
Bat. F, 21 All ee de Brienne, 31000 Toulouse, France. E-mail: yhiriart@cict.fr.
zAuthor for correspondence. University of Toulouse (IDEI, GREMAQ) and Institut Universitaire
de France. Address: IDEI, Manufacture des Tabacs, Bat. F, 21 All ee de Brienne, 31000 Toulouse,
France. Phone: +33 (0)561128614. Fax: +33 (0)561128637. E-mail: martimor@cict.fr.
xCREST-LEI, University of Toulouse (IDEI), CERAS-ENPC and CEPR. Address: ENPC, LEI,
28 rue des Saints-P eres, 75007 Paris, France. E-mail: pouyet@ensae.fr
1environmentally risky activity, thereby potentially causing harm to third-parties; a
regulator, who intervenes ex ante and enforces a veriable standard of precaution-
ary eort for the rm which aects the probability of an accident; a judge who may
impose a ne on the rm after an accident has occurred. Shavell shows that the opti-
mal regulation consists in setting a standard of care which equals the rm's marginal
disutility with the expected damage. The benet of using the judge comes from the
possibility of discovering the value of this damage when a legal suit is undertaken and
to improve incentives conditional on this event. We extend Shavell (1984)'s analysis
by allowing ex ante regulatory transfers which are socially costly. The rst-best level
of care depends on the damage level and can now be easily implemented when care
is observable and a standard can be used. When care is non-observable, the opti-
mal precautionary care depends only on the expected damage and no longer on the
realized damage. It is no longer rst-best.
2 Setting the stage
Consider a rm which undertakes a risky activity. The probability of an accident is
1 e where e is a precautionary eort exerted by the rm at a cost  (e) ( 0; 00 > 0).
In the event of an accident, third-parties suer from a damage whose magnitude is
h. Possible levels of the damage belong to [h;h]. The rst-best eort level depends
on the size of the damage and is given by  0(e(h)) = h. At the margin, the optimal
eort level must trade o the gain associated with a smaller accident probability,
and consequently a lower expected damage on third-parties, with a larger cost of
precaution for the rm.
Assume that the rm has limited assets y < h and is privately informed about
h. When an accident occurs, the judge engages a lawsuit against the rm with an
exogenous probability given by q 2 [0;1]. The judge will be able to discover h only
if a lawsuit is engaged. The regulator can enforce a given standard of precautionary
eort s. In this context, Shavell (1984) studies the joint use of regulation and liability
by a merged regulatory entity. Since ex ante transfers to the rm are ruled out, the
merged entity obtains information on harm only when an ex post intervention is used
and an ex ante standard is useful otherwise. The level of care depends then on h only
because of the ex post intervention. With ex ante transfers, we show that the only
role for the judge is to make incentives to reveal information on h strict when care
is observable and a standard can be used. Using the judge is irrelevant when care is
non-observable. In this case, the optimal regulatory policy cannot be contingent on
the level of harm.
23 Observable precautionary eort
Invoking the Revelation Principle, there is no loss of generality in restricting the
merged entity to oer a direct and truthful menu of contracts to the privately in-
formed rm. This menu consists of a standard s(^ h), a transfer in case of an accident
(respectively, no accident) ta(^ h) (respectively, tn(^ h)), which all depend on the rm's
announcement ^ h of the value of the damage. This contract also stipulates a penalty
R(^ h;h) if the rm has announced ex ante ^ h to the regulator and the judge discovers
ex post that the true damage is h (with R(h;h) = 0).1
The following incentive constraints must thus hold: for all pairs (h;^ h)
U(h;h)  s(h)tn(h) + (1   s(h))ta(h)    (s(h)) 
U(^ h;h)  s(^ h)tn(^ h) + (1   s(^ h))
h
(1   q)ta(^ h) + q

ta(^ h)   R(^ h;h)
i
   (s(^ h)):
(IC)
Given the restricted liability of the rm, the following limited liability constraints
have to be satised by the contract: for all pairs (h;^ h)
ta(^ h)   R(^ h;h)   y; (LL1)
ta(^ h);tn(^ h)   y: (LL2)
Finally, the rm accepts the contract if its individual rationality constraints are
satised: for all pairs (h;h)
U(h;h)  0: (IR)
The regulator's objective2  (1   s(h))h   s(h)tn(h)   (1   s(h))ta(h) =  (1  
s(h))h  (s(h)) U(h;h) is maximized when the rm receives no rent (i.e., U(h;h) =
0) and the standard is set at the rst-best level of care, i.e., s(h) = e(h).
To relax incentive constraints under asymmetric information on h, the penalty
R(^ h;h) should be set at the highest value consistent with the limited liability con-
straints of the rm: (LL1) is binding at equilibrium. Is it possible to implement the
socially optimal standard while leaving the rm with no rent and ensuring incentive
compatibility? This amounts to nding a set of transfers such that, for all h
s
(h)tn(h) + (1   s
(h))ta(h)    (s
(h)) = 0; (1)
s
(h)tn(h) + (1   s
(h))[(1   q)ta(h)   qy]    (s
(h))  0; (2)
ta(h);tn(h)   y: (3)
1This game features adverse selection with ex post arrival of correlated information, as studied
in Riordan and Sappington (1988), with the following dierences: the probability of occurrence of
the ex post information depends on the contract itself and, more importantly, the adverse selection
parameter h does not aect directly the rm's utility.
2Note that regulatory transfers are costly.
3Simple algebra reveals that such transfers always exist. Indeed, taking into account
that (1) holds, the incentive constraint (2) becomes q(1   s(h))[ta(h) + y]  0 and
it is implied by (3).
To explain this result, consider rst the case of regulation alone, i.e., q = 0. In
this case, the true harm level is never discovered ex post. However, the regulator
can oer a menu of contracts such that, for each possible value of h, the standard
is rst-best and the transfers ta(h) and tn(h) are such that U(h;h) = 0. Faced with
this menu, the rm knowing h is exactly indierent between announcing h or ^ h 6= h
to the regulator since in both cases it gets no rent. This stems from the fact that the
rm's private information does not enter directly into its objective function but only
indirectly through the mechanism oered by the regulator. If this indierence could
be broken in favor of the regulator, then there would be no gain to complement ex
ante regulation with ex post liability rules. The joint use of ex ante regulation and
ex post liability ensures that the rm has a strict incentive to reveal its information.
Then, (2) is a strict inequality. Indeed, if it lies, the rm runs the risk of being caught
ex post if a lawsuit is engaged and the true harm level is revealed.3
4 Unobservable precautionary eort
Consider now that, on top of the adverse selection incentive problem, the joint entity
cannot observe the precautionary eort, which is now chosen by the rm in order
to maximize its utility. No standard can be imposed because care is non-observable.
In a truthful equilibrium, the following (rst-order) moral hazard constraint must be
satised
tn(h)   ta(h) =  
0(e(h)); (4)
where e(:) denotes now the eort level. When the rm has enough wealth (typically
y >  h), the regulator overcomes the moral hazard problem by creating suciently
large a wedge between the transfers in the event of an accident and of no accident.
Neither the nonobservability of the precautionary eort nor the adverse selection
problem create ineciencies.4
However, when y < h, the limited wealth constraint always binds and ta(h) =  y.5
Ex post legal intervention turns out to be useless. In the event of an accident, which
occurs with probability 1 e(^ h), ta(^ h) =  y and thus R(^ h;h) = 0 so that the rm not
revealing truthfully its information earns (1 q)ta(^ h)+q[ta(^ h) R(^ h;h)] =  y, which
no longer depends on the probability of the judge's intervention. The regulator must
3Note that it is possible for the regulator to oer the rm a transfer only if there is no accident
or only when an accident has occurred.
4The proof of this statement is immediate and left to the reader.
5It is standard to show that this is the relevant limited liability constraint.
4now give to the rm a socially costly liability rent U(h)   y+e(h) 0(e(h))  (e(h))
to induce care. The regulator can no longer choose transfers so that adverse selection
incentive compatibility constraints are satised at no cost. The adverse selection
constraint writes indeed as U(h)  U(^ h) for all pairs (h;^ h). This implies that the
same level of rent must be given to the rm6 whatever its information on the damage,
and that tn(h) (and thus s(h) from (4)) are independent of h.
Regulatory transfers are used to induce the rm to internalize the eects of its
actions and to partially realign the social and private incentives but do not allow for
information revelation.
In this context, moral hazard truly magnies the adverse selection problem and
leads to socially costly ineciencies. Under moral hazard for the precautionary eort
and adverse selection on the harm level, no information revelation occurs and ex post
intervention is useless. The eort level ep induced by an optimal regulation with ex
ante transfers depends only on the expected damage:
E(h) =  
0(e
p) + e
p "(e
p): (5)
5 References
Lewis, T. and D. Sappington, 2000, \Contracting with Wealth-Constrained
Agents", International Economic Review, 41: 743-767.
Riordan, M. and D. Sappington, 1988, \Optimal Contracts with Public
Ex Post Information", Journal of Economic Theory, 45: 189-199.
Shavell, S., 1984, \A Model of the Optimal Use of Liability and Safety
Regulation", RAND Journal of Economics, 15: 271-280.
6See Lewis and Sappington (2000) for a related model.
5

On the Optimal Use of Ex Ante Regulation and Ex Post Liability

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