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PRIVATIZATION AND INCENTIVES
Jean-Jacques Laffont
Jean Tirole
Number 572
June 1990
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
PRIVATIZATION AND INCENTIVES
Jean-Jacques Laffont
Jean Tirole
Number 572
June 1990
fV
>
pR o
1
19*1
PRIVATIZATION AND INCENTIVES*
by
Jean-Jacques Laffont** and Jean Tirole***
June 1990
*
Financial support from the National Science Foundation and the Center for
Energy Policy Research at MIT is gratefully acknowledged.
**
GREMAQ, Universite des Sciences Sociales de Toulouse, France.
***
MIT, USA.
1
-
INTRODUCTION.
more
public or private ownership
Is
ancient and
central
question
likely to
economics
in
has
promote social velfare
generated
a
?
This
amount
fair
of
conventional visdom on the benefits and costs of public production of goods and
Hovever the arguments underlying
services.
delicate.
The
first goal of this
the framevork of
this conventional
exploratory paper
modern agency theory
superficial as the conventional
visdom
recent research in agency theory
recast some of these
This
''.
criticizes
it
may
is to
visdom are often
and
arguments
in
paper vill remain almost
as
vill only try to suggest that
start offering clues for a
more
satisfactory
analysis of comparative ownership structures.
The second goal of
this
paper
is to
analyse a specific trade-off betveen a
public enterprise and a private regulated firm. In order not
the superiority of one ownership structure,
intrinsic
taste
ve
supervisors of
public
to
and private
different institutional arrangements and incentives. In our
to
model, the cost of public ovnership
is
a su boptimal in vestment bv the firm's managers
in those assets that can be redeployed to serve social
goals pursued bv
ovners While such a reallocation of investment avay from
.
be ex post socially optimal,
This expropriation
exogenously presume
trace differences in efficiency not
differences of managers and
enterprises, but rather
to
is less
it
profit
t
he public
enhancing uses may
constitutes an expropriation of the firm's investment.
likely to take place
under private ownership because the
shareholders, like the managers, derive their monetary revards from high profits.
The
cost of private
ow nership
in
our model
is
that the firm's managers must respond
to
tvo masters, the regulators and the shareholders Conflicts betveen the regulators and
.
the shareholders' goals have been perceived as a source of inefficiency in regulated
industries. In our model,
The multi-principal
ve
focus on the conflict over managerial incentive schemes.
situation dilutes incentives,
and yields lov-povered managerial
incentive schemes and lov managerial rents. This conclusion
fits
vith very anecdotal
evidence that US regulators complain about lov managerial incentives in public
[Technically, the multi-principal distortion
utilities.
double
marginalization
on
tvo
complementary
is
very similar
goods
sold
by
to
the classic
non-cooperative
monopolists.]
In the remainder of the introduction
structures,
ve
recall
and
criticize the
ve develop
a
taxonomy of ovnership
conventional visdom and ve recast the debate
a framevork of residual rights of control. Section 2 sets up a model vhich
in sections
3.
4
and
5.
Final remarks are gathered in section
6.
is
in
analyzed
i)
Public enterprise, private ret Dialed firm and unregulated
firm.
Government intervention
in
production gives rise
a continuum of
to
governance structures. For eipositional convenience, we distinguish between two
scopes of control
government can
obtain three stylized ownership patterns. The
to
exercice external and internal controls of the firm, or one of the two. or none.
External control
outsiders
the control of all variables that link the firm vith
is
consumers (regulation of prices, quality, product
:
(regulation of entry, access pricing.
Internal control
process
:
is
...),
competitors
selection,...),
taxpayers (cost auditing.
...).
the control of the firm's inputs and cost minimization
influence on managerial inputs through managerial incentive schemes,
intervention in the decisions concerning employment, level, location and type of
investments, borrowing,
We
etc...
define a public enterprise as a firm
whose
assets are in majority
by the government who therefore performs both internal and external
private regulated firm, ownership belongs to the private sector
rights over the firm's
management. So the government contents
control and the shareholders exercice internal control.
subject
to
A
who
itself
owned
control. In
has residual
with external
private unregulated firm
franchised firm
there
(e.g.
are
other
governance
structures.
the naval dockyards in the U.K.), the
and delegates operational tasks
to
For
instance,
government owns
in
Renault in France) whose market
may be
the private sector. Futhermore each of the above
is
relatively unregulated and in
for instance the
discretion. Last,
which internal
and the shareholders fluctuates across industries and
US supreme court has moved toward allowing more agency
one may argue that there
is
no such thing as a "private unregulated
firm". Most private firms are subject to antitrust laws,
subsidies and other
government
decisions.
thought off as a firm not subject
rules.
(e.g.
as important as external control. In the regulated sector, the division of
residual rights between agencies
;
a
the assets
governance stuctures admits several variants. There exist public enterprises
over time
is
neither external nor internal control by the government.
Clearly
control
a
to
and are affected by
tariffs,
A "private unregulated firm" must thus
"personalized regulation", but only
to
be
general
Another difficulty vith such a simplistic Uxonomy
nature of ovnership. After
all
government can change
the
distribution of control. For instance
legal
the lav ind affect the
common during vars
it is
relaxes to the
governments
for
to
intervene in the business of private firms. Because governments may change the
distribution of control, the relevant
governance structure does not depend only on the
formal allocation of residual rights of control, but also on the socio-political conditions
that determine the government's cost of breaching contracts, altering
ovnership
structures and interfering vith private property. For instance, in a country in
the cost for the
government of taking private property
and assume
that,
ovnership
small, public
From nov
litely to be the only efficient or viable structure.
issue
is
on,
ve
vhich
is
ignore this
viil
because of strong legal institutions and a high political cost of
altering ovnership structures, the
government
is
able
to
abide by
its
contracts
and
to
respect the ovnership structures once these have been determined.
ii)
Conventional visdom shout privatizations
While ve viil occasionally mention
interesting comparison for
that betveen
public
many
private
unregulated
firms,
the
instances of privatization in capitalist economies
enterprises and
private
regulated firms, henceforth
is
called
"regulated firms".
The conventional visdom (CF) has noted some analogies betveen a private
firm and a public enterprise. Both face agency problems associated vith the separation
of ovnership and control. Both have
some
sort of board of directors
dispersed ovnership. Boards of directors are fcnovn
the firm either because they receive too
because they collude vith
its
little
managers
to
meant
to
represent
exert insufficient control over
relevant information from the firm or
(see Stigler (1971) for a discussion of a
regulatory capture vhich although cast in a regulatory framevork
is
relevant for a
public enterprise and Mace (1971) for similar complaints about the control of private
firms by their board of directors). Last, in both cases, takeovers (in the private sector,
elections or administrative upheaval in the public sector) are
mechanisms
for controlling the firm
and
its
The conventional visdom has
ovnership
to
be imperfect
board of directors.
identified the folloving
costs
of public
(a "minus" indexes a cost, a "plus" a benefit).
C¥l~
enterprise
knovn
(
absence of capital market monitoring ). "The managers of a public
may mismanage
its assets.
First they invest too
little
as they are not given
the
and stocks opUons that vould encourage them
slocks
take
to
a
long-term
perspective Stock market prices contain information about the firm's future prospects
and thus about the managers's long-term decisions. By retiring the firm's
stock, a
public enterprise deprives itself of a measure of managerial performance and reduces
managerial incentives. Second, a public enterprise
managers are therefore
The
first
less
not subject
concerned about losing their
argument
in
government may. and sometimes
nationalizing.
is
CV1~
is
to
A further argument is needed
its
jobs."
not as straightforward as
does, retire
takeovers and
it
seems. First the
only a fraction of the firm's stocks vhen
to
explain
firm (in vhich the government vould hold 51
%
vhy
the stock price in a miied
of the shares, say) vould be less
informative about managerial performance at that of the same, private firm. Second,
economists have never demonstrated that the stock market
even the most efficient instrument
The
to
First,
little
in vhich. for legal or other reasons, takeovers
(soft
argument
clearer,
is
managers of public enterprises are
takeovers occur. Second, this argument has
CV2"
the only instrument, or
obtain outside information about a firm's health.
absence-of- financial-takeovers
conclusive either.
is
and
isn't
political
relevance in countries or in periods
have played a minor
budget constraint ) "A public enterprise
discipline of the bankruptcy
fired
but
is
role.
not subject
process because the government alvays bails
it
to the
out in
case of difficulty. This reduces managerial incentives".
One
difficulty vith
CV2"
is
that public enterprises
may
(although one vould expect that this vould occur less frequently than
private.)
Another
difficulty,
difficulty is that regulators do bail out
if
be shut
dovn
the firm
vere
private regulated firms in
by raising alloved prices for instance. Thus CW2"
does not distinguish
clearly betveen a public enterprise and a regulated firm.
C¥3" (expropriation of investements) "Managers of public enterprises
refrain from investing because once investments are sunk the government
these investments for purposes they
investments
may
vere not intended
to
serve.
may
use
Hence managerial
be expropriated."
The argument
in
CW3~
is
appealing in situations in vhich managerial
incentive contracts arc incomplete so that the government's residual rights of control
over the firm may help
it to
ex post expropriate the managers's investments. Hovever.
is
it
stands,
it
fails to
distinguish between public and private ownership.
¥hy
wouldn't
the shareholders of & private firm expropriate managerial investments in similar
situation ?
CW-T
The
(lack of precise objectives)
multiplicity, fuzziness
and changing
character of government objectives exarcerbates the problem of managerial control
in public enterprises."
CW4"
also fails to distinguish
goals that are complex
among ownership
and vary over time vill
structures. Governments'
also affect the
behavior of regulated
firms.
CWV
groups
to
(lobbying
:
"Governments are subject
direct the behavior of public enterprises
to
to
the pressure of interest
enhance
the velfare of these
groups."
An
governments
obvious objection
to
to
CV5"
is
that interest groups successfully lobby
control regulated firms to their benefit, as veil.
The main argument concerning the benefits of public ownership
CW1*
(social
velfare)
;
"Nationalizations give governments the
achieve social goals that include, but are not confined
Vhile this argument
is
is
veil-taken,
it
to
:
means
to
profit maximization."
does not explain
vhy
the
government
could not achieve the same social goals in a regulatory framevork.
CY2* (centralized control)
"By letting the government be responsible for
both internal and external control, a nationalization prevents conflicts of objectives of
the firm's regulators and ovners."
While CW2* suggests a potential inefficiency associated vith the multimasters feature of private regulated firms,
inefficiency.
it
remains vague about the nature of the
iii)
Residual rights considerations.
The previous section has discussed some
difficulties
vith the conventional
visdom. This section hardly scratches the superficies of the ownership puzzle but tries
to
point at vays
to
look at the issues. As emphasized by Williamson (1985) and Grossman
and Hart (1986), the ovnership structure does not matter
vritten
firms,
;
therefore, if
ve must point
ve
at
are
to
if
complete contracts can be
distinguish betveen public enterprises and regulated
some contract incompleteness. Our
goal
is to
examine vhere in
the logic of the arguments incompleteness arises.
Ve argue
in turn
that the
ownership structure matters
imply further distinctions.
First,
in tvo basic respects,
vhich
(even partial) public ovnership reduces the
acquisition of (non contractable) information about the firm's manaiers's activity bv
outsiders,
namely stock market participants Second, public and private ovnershios
.
imply ovners vith different objectives and therefore different behaviors in case of
contract in completeness.
a) Acquisition of infor mation about managerial activity.
The separation of ovnership and control creates a problem of managerial
One of the crucial roles of a stock market
is to
discipline.
give managers incentives beyond those
provided by revard schemes based on accounting data.
First,
stock
market participants
,
including investment bankers, lured by
the prospect of speculative gains, analyze the firm's health and, to the extent that their
knovledge
level
is
at least partly reflected in the stock price,
convey information about the
and quality of managerial investments. Stocks and stock options accordingly
induce managers
to invest.
value of the firm disappears
this respect,
The information conveyed by
vhen
the stock
is
the stock price about the
retired, as in the case of public firm. In
pure public firms have a hard time disciplining their managers. Hovever,
ve mentioned above
that the
government could take control only
of a majority of
shares and have an active stock market for the remaining shares, the information
value of 20
%
of the shares, say,
is
a priori the same as that of 100
%
of the shares. This
might suggest that managerial incentives are unaffected vhen the government takes
control, but does not retire the entire stock.
Holmstrom and Tirole (1989a) hovever
argue that the ovnership structure matters because market Liquidity
market participants have lov incentives
to
is
affected. Stock
acquire information in the illiquid market
created by high government stakes.
The
stock price
is
then a very garbled measure of
managerial performance.
A
limitation of the
that a stock market
is
HolmstrOm-Tirole analysis
is
that
an (approximately) optimal institution
it
to
takes for granted
induce outsiders
to
acquire information about the firm's prospects. No such proposition has ever been
proved, although the pervasiveness of the institution suggests that alternatives are
hard
come
to
by. Because the
information held by outsiders
(verifiable in the language of information economics),
given
it
is
often not contractable
is
likely that incentives
outsiders must be (positively or negatively) correlated vith the firm's future
to
performance,
as
vay
an incentive compatible
for outsiders
to
"prove" that they have
acquired relevant (favorable or unfavorable) information about the firm. This
exactly
vhat speculation
disconnecting
in the stock
and
shareholding
market
does. Hovever,
property
For
rights.
one could think about
instance,
absent
legal
The
constraints, a pure public enterprise could issue shares vith non-voting rights.
speculator could
supply useful information about the firm by buying and selling
still
such shares vhile leaving ownership
to
to
the government. Therefore the puzzle seems
find an explanation for the cost of depriving shares of their voting rights.
little to
offer on this issue beyond
tempted
to
is
Ve have
some superficial remarks. The government may be
expropriate shareholders vith non-voting shares (as veil as minority
shareholders vith voting rights). Expropriation, which may take the form of sales of
the firm's assets or products at artificially lov prices
favored by the government,
use of
may
firms or interest groups
to
entail deadweight losses
(e.g.,
result in suboptimal
the assets or excessive consumption of the products). Second,
value of the shares and thus the incentives for speculators
(think of the extreme case in vhich everything
consequences similar
to
those of a reduction in
Second, stock market participants
is
reduces the
search for information
expropriated)
market
may
to
it
;
in this respect
it
has
liquidity.
intervene in management through
a proxy fight or a takeover. Such interventions disappear under (pure or partial)
public ovnership.To be certain, there are also political takeovers. Ministry personnel
changes,
or,
more
drastically,
the
entire
takeovers hovever have tvo drawbacks.
change
of ministry officers or of
administration
may change.
Political
they tend
to
be "global" in that the
an entire administration
is
triggered by a vhole set
First,
of regulatory issues, and not by the regulation of a particular public enterprise
contrast, a financial takeover focuses
servants
may
not alv ays have
on
a specific,
enough incentives
to
mismanaged firm. Second,
;
in
civil
invest in acquiring information
mismanagement or potential synergies while corporate
about
raiders have financial
incentives.
b)
Owner's objectives,
A government naturally has other objectives than
prevent monopoly pricing
;
control quality
reduce negative externalities
;
and employment
sectoral policies, national independence, investment
etc...
The problem with many government objectives
hard
to
contract upon.
It
may
be costly for instance
to
the
may change between
objectives
power
to
:
encourage
;
in recessions,
that, unlike profit, they are
is
describe the state contingent
shadow price of employment in a contract with the firm.
among
profit maximization
Also, because the weights
successive administrations legal [imitations on
commit must be introduced
(this
concern does not arise in a private firm,
vhose objective-value maximization-stays the same over time). This may explain why
it is
often felt that regulators
have fuzzy and time-varying objectives (CV3).
This observation per se does not shed light on the privatization issue, as
pertains
difference
the
both
to
is
and regulation. Where ownership mares a
public ownership
when contingencies occur
that are not covered by the contract between
government and the firm. Residual rights of control determine who can
the assets in such contingencies.
it
dispose of
One should thus not expect the same response under
public and private ownership.
First,
a benefit from public ownership (CT1*)
impose socially desirable adjustments
to
is
that the government can
the firm in unforeseen contingencies while
it
must bargain with a private firm. ^
may
Second, public ownership
invesments (see the model in Section
non
2).
lead to an expropriation of managerial
Suppose that the manager invests today in
verifiable capital that permits cost reduction and profit
enhacement tomorrow.
Tomorrow, the government may reallocate
this
which
if
such a reallocation
to
invest and leads
the
optimal,
it
manager
is
not rewarded. Even
reduces the managers' incentive
private ownership (in
it
The
to
an alternative use for
to
is
ex post socially
a situation in which
which managers are induced by incentive schemes and
which shareholders have no reason
even though
investment
makes the
socially
ex post intervene
wrong
case against public
government does not maximize
to
to
reduce profit)
use of assets ei post (this
enterprise
may
social welfare. As is
is
is
in
superior
CW3").
be even stronger
when
the
well-known, government decision-
mating may be captured by
interest groups.
government's pover associated
ilh
An example
is
to
may
a nationalization
in
a non-benevolent
(CWO.
thus reduce eLfare
governments on public enterprises
the frequent pressure of
military sector not
The increase
in the
compete vith private firms on civilian markets, even
public enterprises have idle capacity and the
machinery and
the
if
expertise to produce the
civilian goods.
Last, the
may
explain
vhy
divergence of objectives betveen government and shareholders
the US public
utilities'
their managers' incentive schemes.
government and the shareholders
A
to
shareholders have the right of control over
possible explanation
is
agree contractually on the
incentive schemes and that a government
vhich has
to
yet another variant on
make
the
details of
managerial
to
properly maintain the
theme that expropriation might occur
offer than this conjecture, and
2 -
difficult for the
the profit maximizing investment decisions (this
shareholders leave residual rights of control
to
it is
residual rights of control over
managerial incentive schemes might not induce managers
shareholders' assets and
that
to
the government).
much more vork
We have
is
private
if
more
little
vill be required to explain the fact.
THE MODEL
A government rants to
realize
an indivisible project
-with social
value
S.
A
single firm can realize this project at cost
C-p-e
(2.1)
vhere P
knovn
F(.)
€
to
[jl
fJ]
,
parameterizes the firm's efficiency, and e
over P vith a
(
\
strictly positive density.
——
—
dp
d
F(P)
ftp)
Ye make
the usual monotone hazard rate
^
to
>
avoid
bunching
in
optimal
schemes.
incentive
J
Managerial effort creates a
>
disutility *P(e) in
monetary units vith
T
>
0,
is
X
H"
>
0,
0.
Moreover, managers can commit some non monetary investment, T
I
is
the firm's managers only. Other parties have prior cumulative distribution
assumption
T"
managerial effort. P
is
a non monetary cost for managers (vhich
is to
(I » 0) yields no benefit. If the investment is
alternative uses.
Its
€
(0,1).
be added to ¥(e)). Not investing
made (I
»
I),
it
has one of two
"internal use" yields private (non monetary) benefit D
>
I
to
the
10
firm's insiders (the
benefit
D'
D
>
managers) and
outsiders
to
and
to outsiders.
to insiders.
place during the single period of the model.
'external use" yields private
Its
Investment and accrual of benefit take
The
benefit, like the investment,
contractable (not verifiable) and therefore cannot be sold. Let
Last, the firm's outsiders
to a.
A
D
-
not
I.
bring a level of cost reductions or synergies equal
(For notational simplicity, ire do not include a in the cost function.)
more on
is
Ye
Till say
this shortly.
Tvo ownership structures vill be considered
Public ownership
:
:
The government ovns the firm and gives
incentive scheme based on the realization of cost,
the firm's managers an
to
Making
t(C).
convention that costs are paid by the government the managers'
U
Because
- t -
investment and
the
government cannot commit not
to
the accounting
utility level is
¥(e).
benefit
its
are
not
expropriate managers in order
the
contractable,
to
maximize ex post
public use of the investment^. Anticipating this behavior, the managers do not invest.
Let us give simple examples of such behavior.
firm Till be reluctant
or machines
if
to
invest in facilities
they knoT that access
population by the governement.
return on a
nev
to
The managers of a government-ovned
(e.g., cafeteria,
theater or holiday resort)
those Till be later granted
to
the general
More importantly, the government may reduce
plant by forcing to keep excess labor in bad states of demand or
may
domestically produced inputs. In all these examples, the government's action
post optimal but represents
Ye
an expropriation of the firm's investment.
to
the
buy
be ex
let Bp
denote the social value of the cost reductions or synergies coming from the firm's
outsiders (ministry, board of directors, intervenors,...). Bp is the
cost reduction,
evaluated at
There X
(1
X)
is
the shadov cost of public funds,
valued
X)a* of the
minus the agency
cost (also
per dollar spent) of inducing cost reduction a* from the
bureaucratic system. [Bp
is
difference]. For our purpose,
of course taken at the value a*
it is
that maximizes this
useful to preserve generality by not specifying the
process of monitoring of public enterprises by outsiders.
Aceordingly, the objective function of an utilitarian government
(2.2)
here
(t
Y
- S - (1
C) is total regulatory cost.
X)
(t
C)
B p *U,
is
Regulated private firm
regulates Lhe firm''.
firm
price p
it
Ve assume
:
Suppose nor that the government privatizes and
government regulates
the public. Second, the
to
government
the following timing. First, the
relevant project, and the shareholders offer an incentive scheme
tax rate T can be determined in either stage
on the
first stage.
the managers.
to
ve assume
to
chosen
it is
a regulaory
to
governemnt could commit
to
a regulatory
at the privatization stage, it could sell the social surplus associated
ovners' decisions
The
reflects the idea that privatizations are long-term decisions
effects cover several periods. If the
scheme
the firm for the
The assumption that the government does not commit
scheme vhen privatizing
hose
;
for concreteness,
sells the
them and multi-principal
Tith the
conflicts vould not arise. Privatization
vould alvays be optimal.
In a regulated firm, private shareholders select managerial incentive
schemes. Shareholders are taxed at rate
T
vhich
is
endogenous
by the stockholders. The
denote the managers' revard (including perks) provided
firm realizes the project and receives
Let Bt
(t)
its
income from the government.
denote the social value of cost reductions or synergies brought
Ve assume
about by the firm's outsiders (board of directors, stock market).
decreasing that
strictly
;
is,
benefits the firm. (Example
higher taxes reduce incentives
:
to
(1 -
l)a
-
elsevhere for
Ve
(t)
Bj
(T).
Bjj
(T)
-
a
»
1,
that B,(.)
is
information that
disutility of effort
a*(i) so as to mcTimira
g(a). In this eiample. B,(t) - (1 - T) a*(x) - g(a*(T))
alvays strictly decreasing in the neigborhood of T
Bj
to collect
suppose a single shareholder incurs
reduce the firm's cost by a. He viil choose a
g(a)
v
the model. Let
to
and
(1
XH
strictly
is
a*(x)
is
decreasing
sufficiently small).
vill use the decomposition of B, (T) into the stockholders' private gain
and the social value of additional taxes obtained from this cost reducing activity
(In the above example, B. (T) - (1
- (1
XYt a
-
t) a*(x)
-
g(a*(l)) and
#
(t).)
Ve assume
that the
government observes only
cost
C.
but not v. This
assumption makes particular sense in a multiproduct firm in vhich the government
observes only the cost of the product line
it is
interested in and
is
unable
to
measure
various components (including perks) of managerial compensation that enter the
firm's global accounting.
objective function
is
The government makes a transfer
again the sum of surpluses in society.
to
the firm ziC) and
its
12
¥
(2.3)
vhercU
v
-
-
-
S
-
(1
?(e)
Note that,
•
X) (z
C
-
T(z
-
))
B,(t)
U
•
(1- t) (z
)
-
Xp
.
A. 6 >
nov
reap net private benefits A.
no incentive
the shareholders have
knoving
benefits of the investment to outsiders and,
¥e assume
*
'
that the
this the
reallocate
to
the
managers invest and
'.
government and
the shareholders
mate simultaneous
contract offers. The government offers ziC) to the firm and the shareholders offer
v(C)
to
the managers.
The managers produce only
if
they accept both offers.
ovnership
Clearly, the advantage of private
is
to
commitment of non expropriation of managerial investments. The
the multiprincipal structure of regulation and the inability of the
male
the
credible
cost Till
come from
government
to
fully
tax stockholders^ profits.
Before studying optimal regulation under the different ovnership
structures let us determine the optimal allocation of ressources under complete
information
marginal
transfer
:
the investment should be
disutility of effort
to
made and
should equate
its
allocated ex post to outsiders.
marginal
managers should saturate their IR
utility, i.e. "r"(e
constraint. If S
is
large
#
)
-
1
The
and the
enough the
project should aivays be realized.
3 -
OPTIMAL REGULATIOM WITH PUBLIC 0¥ FEES HIP
Under public ovnership the managers do not invest. The manager's
level
utility
is
(3.1)
U
- t -
¥(e)
- t -
Incentive compatibility requires
(3.2)
vhere P^
is
(3.3)
u(p)
the largest value of P for
- -
-
*(P
:
v
?-(«<p))
vhich the
C(p) >
Using (32). the IR constraint. (u(P) >
V
project
P
V
«
p
C).
is
p
€ [a, p;]
undertaken, and
[{L Pr*]
€
[fL
P*] ) can be rewritten.
u(p;>
(3.4)
An
utilitarian
(3-3) (3.4). expected social
government maximizes, under the
elftr»,
(3.5)
under public ownership
1
is
:
IC
and [R contraints (32)
i.t
V
S
f
Proposition
> 0.
X)(p
(1
-
(Laffont-Tirole (19S6))
given by
e(p)
:
*(e(P)) )
*
-
XU(P)] dF(p)
The optimal regulatory outcome
:
(3.6)
T'(e p (P))
(3-7)
U(p) -
"i-TTY^^'U^)
T"(e p (P)) dP
f
(3.S)
^-(1
either
S
or
P*
X) [(p;
-
e^P,*))
<F(e,(p;))]
- f.
(37) defines the rent of asymmetric information captured by
efficiency p. (36) describes the optimal distortion from efficiency
t
firm vith
to mitigate
the rent
of asymmetric information. (3.8) defines the cut-off point P*.
From
Laffont-Tirole (19S6),
ve tnov
implemented by a menu of linear contracts defined by
KC.C)
here C
is
-
:
b(C) (C
a(C°)
mechanism can be
that the optimal
-
C)
the announced cost and C the realized cost. b(C°) defines the sharing of
overruns and
is
equal
to
T'(e p (&)). For p
selects a filed price contract
efficient types
-
^
F(g.)
•
and
and has the right incentive
have part of their
cost,
1
-
Y '(e p (g.))
to
-
minimize
1
;
type
cost.
ft.
Less
¥'(e*(p)), reimbursed by the regulator
TT
and consequently exert a socially suboptimal
enables
efficiency
regulator
the
effort.
decrease
to
Thb
the
distorsion in illocilive
costly
rent
of
asymmetric
information.
4 -
OPTIMAL REGULATIOM OF A PRIVATE FIRM
We assume
that the
government and the shareholders
simultaneously offer incentive schemes z(C) and r(C)
monetary revard
to
managers. The scheme
managers offered by the government and H.)
to
required by shareholders. Alternatively one can think of
shareholders
vho
(.)
offer
K.)
« z(.) -
of the private firm
z(.) as
is
a
a rental contract
being offered
managers. We look for a
to
z(.) is
to
the
diffe re n Liable
Nash equilibrium in these contracts.^'
Taxing
subject
We
to
z(.)
as given, the shareholders maximize their expected
the managers'incentive compatibility and individual rationality constraints.
ailov the shareholders
not vant
profit
to
to
offer incentive schemes such that some high
produce. Let $1 denote the "cut-off type",
i.e.
the type
vho
is
(3
types do
indifTerent
betveen producing and not producing.
Managers receive v(C)
as veil as the benefit of their investment. A,
incur a disutility ^(e). Their utility level
U(p)
(4.1)
-
and
is:
A-
v(c(p))
From the point of viev of the managers
<F(e(P)).
v(.) plays the
same
role as U.) in
Section 3 and therefore, incentive compatibility and individual rationality constraints
are as in
Section
(using v(c(p))
3-
Accordingly, the shareholders'
U(0)
-
A
?(e(P)))
optimization program
is
:
K
Max
(1 - T)
f[z(p
-
e(p))
-
U(p)
{•(>*;}
s.t
(4.3)
(J(p) -
-
r(e(p))
A
-
f(e(p))] dF(p)
Bjj
(t)
U(P K*)
(4.4)
The
first
-
0.
order conditions of this program ire (see appendix
l"(e.(P))
(4.3)
-z(P
-
-
MP>)
"
J^
1 )
:
*"(e.(p))
r(c{^))
(4.6) either[z(p;-e,(p;))*A-«F(e,(p;))]*^-f(p;)-F(p;)
orP,*
-
-
P
Note thai (4.3) differs from the formula (3.6) obtained in the case of public
ownership
(•which
is
in tvo vays. First, a unit reduction in cost
is
vhat the firm receives from the government)
of the cost of transfers
to
the cost of real expenditures
valued
(-z*)
instead of
is
equal
1.
to
by shareholders
Second the ratio
1
for the profit
X
for the velfare maximizing government.
maximizing shareholders instead of
1
The government chooses z(.)
X
to
maximize expected social velfare subject
to
the managers' incentive compatibility and individual rationality constraints, taxing
K.) as given. Ex post social welfare
is:
(4.7)S-(l«X)(p-e(P)*z(p-e(p))-Xr(p-e(p)))*U(p)*(M)r(p-e(p))*Bt (T)^p
-S-(l*X.)(p-«(p)*'P(e(p))-A)-XU(p)-X(l-T)r(p-e(p))*Bt (T)*Xp
Hence, ve have the following government's optimization program
(4.8) MaxrS-(l^)(p-e^(e(p))-A)-XU(P)-X(l-l)r(p-e(p))p-e(p)
MTWpldHp)
{eo.pr}
s.t.
:
10
-
(4.9)
tl(p)
(4.10)
U(p,"*)
The
first
¥'(e(p))
-
-
order conditions of this program are (see appendii
r(e„(P))
(4.11)
-
—
1
(1-T)
(4.12) either {s-(l*X)(pr-e„(P t**))
r(p-e„(P))
-
-
1 )
— j^
¥"(e B <p)).
A* f(e t (p;*))
v
-X(l-T)r(pr-e R (pD)*Bf (T)*Xp} np;
#
)
#
-xF(p;
orpr
From
r(e„(p;*))
)
= o
- p.
the managers' first order incentive compatibility condition
r(p-e(p))
-z(p-e(p))
(4.13)
Multiplying
(4.3)
by—r
adding
(1-T),
»
ve have
:
r(o(p)).
to (4.11)
and using
(4.13) yields
:
1«A
(4.14)
r(e,(p))
-
In equilibrium
(4.15)
An
1-^-
P^
-
(2-t)
P»**.
From
r(p-e,(P))-z(p-e,(p))
interesting observation
at the cut-off type p»V (The
^
-
is
r-(e t (p)).
(4.13)
and
Jf'(e ,(£)) (l-i,#))dP
that the shareholders
managers have no rent
case of a public enterprise).
(4.4)
The reason
is
obvious
vho brings them no
rent of better types by doing
'
From
(4.11)
ve obtain
:
make a
A-*(e t (p;)).
positive profit
at the cut-off type, just liie in the
nothing from shutting off a type
so.
*
:
the shareholders vould lose
problem, and vould reduce the
p;
(l-X)
(4.16)
r(p-e,<P))
X(l-T)
(l-e t (P))dP .r(p;-e t (p;)).
From
and using
(4.3)
and
ve
(4.12)
ve determine,
(4.4)
From
(4.6)
#
obtain the constants r(p«-e,(p t )) and z(p,*-e,(p,"))
PR
.
ve obuin
»;
(4.17)
*'(e»<P>)
z(p-e,(P))
•5||
,
!'"(e I (P))|(l-i r <P))dP
r
*2(p;-e«(pD).
Next ve must ask whether the second-order conditions for the agent
and the tro principals are sufficient. The second-order condition for the agent
t
- 1-e
>
0.
But (4.14) implies that efTort
is
decreasing vith
type
is
under our
assumptions
-X
F
d
(2-T)
!*,
T
f
Y"-^"
dp
—
*
T
F
(2-t)
7 T'
<
Hence the agent's global second-order condition
Before turning
of
independent
to
interest
concerning
?"
r"
l-e
(2-T)
ux
(4.19)
and
2'
is satisfied.
the principals' second-order conditions,
Differentiating (4.5), (4.13) and (4.14) yields
(4.1S)
0.
1—7
(2-T)
the
:
curvature
of
ve
derive results
re-rard
functions.
IS
X
f"
(4.20)
2"
-
-
r" -
-
—r
(2-T) r"> 0.
l.Jt
That
is,
the net
revard of the agent.
Tirole [19861. In the single-principal
the government,
t(.), is
equal
to v(.)
(i.e.,
and
is
therefore replace his revard scheme by a
concave in cost
if
X
<
l/(l-T),
v(.), is
cost as in Laffont-
public ovnership) case, the transfer from
therefore convex in cost
menu
;
the regulator can
of linear contracts. In contrast,
z(.) is
and the regulator cannot use a menu of linear contracts,
and the shareholders' revard function, -K.),
is
convei in cost Hovever,
imply that they can replace their revard scheme,
The regulator might vant
convex in
-r(.),
by a
change his ovn scheme
to
this does not
menu
of linear contracts.
take
advantage of the
to
sharehoders' linear sharing of cost by inducing large cost padding by the managers.
Ve can
the Hamiltonian in
there exists X 9
concave in
Last
turn
to
the principals" second-order conditions. First,
program
(4.2) is
such that X
>
effort.
-t
i
convave in
effort. Second,
ve determine
the optimal tax rate
T.
X
<
1/(1-1),
can be shovn that
it
implies that the Hamiltonian in
The second-order conditions are then
if
program
(4.8) is
satisfied.
Using p - E [(l-t)r(p-e(p))
J
P
ex ante social velfare
is
E[s-(l-X)(p-e* ,P(e)-A)
-
Xu]
B,(T).
9
vhere
e
depends on X as shovn in equations (4.14) and
(4.12).
For our purpose,
suffices to note that the tax rate that maximizes ex ante social velfare
than
equal
1.
The derivative of the
to
at T-l
shareholders
first
term in ex ante
by the envelope theorem (from
X(M)r and
social velfare
(4.12)
the distortion of effort due
vhenT-1).
Ve nov summarize our main
conclusions.
and
to
is
stricly
vith respect
(4.14),
it
lover
to X is
the ex post loss
to
multiple principals vanish
Proposition 2
:
The necessary conditions for the optimal regulatory outcome under private
ownership
sufficient
cost.
if
given by equations
X
4
min (X
.
(4.12). (4.14), (4.16)
to
the firm
(4.17).
These conditions are
is
concave in
.
There
Consider the folloving schemes
convex In
non
in
vhich
z
differentiable equilibria.
:
I
(4.21)
also exist
is
cost.
Non differentiable equilibria We have focused on the equilibrium
r are differentiate functions of C.
zZ
if
2(C)
-
r(C)
otherwise
oo
r
if
c£
=
-
oo
otherwise
The agent accepts those schemes
better than this simple cost target
satisfy
and
The managers' net revard function
1/(1-1)}.
The government's net transfer
.
and
is
scheme
?
iff
t-l > ¥(£-£). Can a principal do
For this not
to
be the case, f and Z must
:
(4.22)
f
-
arg max
¥" l (Z
(f(C
-
r))r}
and
t«Y~
(4.23) I
arg
max
l
(z-r)
f[s-(i*Ji)
(c~
y(P-C)-a)
-x[z-r-f(p-C)]
z
JUl-T)f
From
(4.23),
since transfers
society of these transfers
rationality) z
is
is
Xp]ftp) dp}
(T)
the firm are socially costly (the cost for
to
T<1 and z>r from
X(z- ir) vith
bounded above, say by z*
Br
.
Therefore, r
is
also
the agent's individual
bounded above by z*
zu
The existence
and
f(.)
of Lhe pooling equilibrium
bounded belov by a positive number. The function defined
concave in rand maps
from [¥ (fi.-C).z*l into
I
The function defined in
[0,z
10,
3
#
]
z*]
-
guaranteed
is
[¥($_-£). z*l
into
(-423)
10,
z*]
concave in
¥e can apply Brouver's theorem
.
)
in (4 22)
is
concave
is
strictly
and mans r from
z
in the
compact space
x [¥($.-£). z*l to obtain the existence of a solution.
COMPARISON OF OTNERSHIP STRUCTURES
The main result
is
that effort
lover in the regulated private firm
is
than in the public firm, as one can check by differentiating
and
F(
.
strictly
is
if
(4.14)
vith respect
to
t
Proposition 3
:
The
e t (p)
<
e p (p) for
any p€ (jLP'I.
intuition for the result is straightforvard. As
the existence of shareholders
and the fact that the tax rate
program
is less
(4.8)
than 100
shovs,
%
(to
preserve incentives for information acquisition), create an additional ex post rent.
iz
e
therefore more costly
It
the same effort level as in the public firm and the
to elicit
regulator settles for a lover level of effort.
For S large enough, P*-PiT- P
(|J-e«(|J))
r
r
v(p -e,(p )J
-
¥
r
(e t (p ))
-
A
:
furthermore,
from(4.1) but the decomposition of
betveenz((P-e»(|J)) and (minus) r^ff-e,^))
is
arbitrary at the Nash
equilibrium as long as the left-hand sides in (4.6) and (4.12) are non-negative.
For lover levels of S.
(5.1)
S-(l*X)(p;
-
differs
P»*
e,(p,*)
+
from P and
is
(uniquely) defined by
¥ (e,(p;>))
(l-X)A
Xp
:
B,(X)
F(B*)
-X(2-T)-^-r(e,(p;))
ftp,
#
In this case, z((P,*)
-
-
Bid)
)
e»(P,
))
and
r((P»*)
-
e,(P,*)) are uniquely
defined by (4.6) and (4.12). That the principals* transfers are either determinate or
defined up
to
a constant should not surprise the reader familiar with the theory of
public
goods.
la
cue
the
of a corner
responsible for mating sure thai type
fJ
solution (£,*
-
(J),
both
principals
produces, and reducing the transfer
to
are
the
agent by one principal and increasing the one by the other principal by an equal
amount preserves equilibrium
to
produce. There
more
is
is
as long as the second principal strictly prefers type
therefore a range of possible transfers
efficient types) for each principal.
off point P^,
type
(J
(and therefore
to
The transfer received by the agent hovever
determinate. In the case of an interior solution
transfer that a principal must pay for P«
to
(J
to
((}»
<
fj),
an increase
produce vould lead him
andvould induce the other principal
to
to
in the
reduce his cut-
raise his cut-off point, thereby
destroying equilibrium.
The
costs
and benefits of regulation in this model can be •summarized as
follows:
1.
Incentives
2.
A
to
reduce cost are lover in a regulated firm
regulated firm's managers invest more because they are
more
lirely to derive
private benefits from invesment
3-
Last, public
and private ownerships differ in their incentives for outsiders
collect information
about cost reduction
or
synergies.
Ve
left
the
values
to
of
information B p and B»(T*) general. Opening the black boxes of public and private
monitoring of firms
scope of this paper.
is
an important item on the research agenda, but
is
outside the
->->
APPENDIX
1
Proof of(4.6)
The Hamiltonian of program (42)
-
H(P)
From
(M) [z(p
e(p))
-
the Pontryagin principle
-
A
U(P)
ve have
-
the Hamiltonian vith respect
(1-T) [-
that
is to
(z(p
-
e(p)))
-
fl(p)?'(e(p))
HP)
|l(P) - (1-T) F(P).
Maiimization of
gives
T(e(P))l
-
a consUnt
¥(e(p))]f(p)
O.veget
-
p.(|J.)
to e(.)
to
:
[i(p) - (1-T)
Using the transversality condition
up
is,
ftp)
-
(1-T) F(p)
r'(e(P))
-
say, (4.0.
Proof of (4.11)
The Hamiltonian of program
H
-
{s-(l*X)(p
-
e(p))
(4.S)
is,
^(p))
up
to
A
-
-
a constant
XU(p)
-
X(l-T)r(p
-
e(p))} ftp)
|L(p)r(e(p))
-
|i(p)
- -
}t(BJ -
dH
—
-
«
jj
Xftp)
|L(p) -
=>
(UX) (r(e(p))
-
-
l)
XF(p)
it(l-T)r'(p
de
-
or
*-(e(p))
XF(p)r(e(p))
.
1
^
(1-T)
-
e(p))J ftp)
-
r(p
-
e(p))
-
± ^2 T ^)
-FoonorES
See Sappington-Stigiitz (1987).
1)
Rionkn
interesting discussions of the theoretical issues related
to
for
privatization.
In a recent case in point, regulators in Syracuse tried
2)
Yarrov (1983)
(1988). Vickers and
to
force a utility
to raise
managerial incentives.
In
3)
particular if bargaining
under asymmetric information,
place
takes
inefficiencies vill typically result, as pointed out in Milgrom-Rpberts (1987) and
Holmstrom-Tirole (1989b).
Here the investment yields higher benefits
A)
than
if
controlled by shareholders, because
expropriated by the government
is
it
controlled by the government
if
under public ownership. One can think of cases in vhich the incentives
invest are
to
higher under government ownership than under private ovnerhsip. This vould
occur for instance
if socially
conscious managers vere
be redirected by the shareholders
profits.
The
case
avay from
to
make investment that vould
their original purpose
ve consider seems hovever more
to
many situations.
realistic in
One could consider the converse experiment in vhich the firm
3)
private and
nationalized by the government.
is
Note that in equilibrium p
6)
-
E(l-T)
(z -
The analysis
is
v) Hovever
.
enhance,
is initially
unchanged.
it is
important
to
treat
it
P
as a
sunk revenue for the government That
today, the
7)
government does not
is,
by changing
affect the price that the public paid for the shares.
to
reallocate or not.
It
seems reasonable
favor their managers, vhich they vould strictly prefer
investment had any direct or indirect monetary value
costs
regulatory process
Under our assumption, the stockholders are actually indifferent betveen
ordering the managers
8)
its
By assuming
A
to
if
ve made
the internal use of the
ve completely
this section clearly
the assumption that the
assume that they
the firm.
be exogenous and not monetary
and the benefits of privatization. As
vould obtain
to
if
to
separate the
shovs the same model
government cannot commit not
to
expropriate managers vhereas stockholders can. Therefore a political theory of
differences in
commitment
theory ve relied upon here.
abilities could be substituted to the
incomplete contract
9)
In independent vork. Stole (1990) offers a general analysis of
design under
common agency, and shovs hov
mechanism
the lack of coordination betveen
principals aggravates or alleviates allocative inefficiences depending on whether the
principals' screening variables are
complements
(as
is
the case here) or substitutes in
the agent's utility function.
10)
This
is
the same
above his marginal
cost.
argument
as that
shoving that a monopolist charges a price
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50081
74
Date Due
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