• Aucun résultat trouvé

Competition and the Reform of Incentive Schemes in the Regulated Sector

N/A
N/A
Protected

Academic year: 2021

Partager "Competition and the Reform of Incentive Schemes in the Regulated Sector"

Copied!
35
0
0

Texte intégral

(1)

Montréal

Série Scientifique

Scientific Series

2000s-58

Competition and the Reform

of Incentive Schemes in the

Regulated Sector

(2)

CIRANO

Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le

financement de son infrastructure et de ses activités de recherche provient des cotisations de ses

organisations-membres, d’une subvention d’infrastructure du ministère de la Recherche, de la Science et de la Technologie, de

même que des subventions et mandats obtenus par ses équipes de recherche.

CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and

research activities are funded through fees paid by member organizations, an infrastructure grant from the

Ministère de la Recherche, de la Science et de la Technologie, and grants and research mandates obtained by its

research teams.

Les organisations-partenaires / The Partner Organizations

•École des Hautes Études Commerciales

•École Polytechnique

•Université Concordia

•Université de Montréal

•Université du Québec à Montréal

•Université Laval

•Université McGill

•MEQ

•MRST

•Alcan Aluminium Ltée

•AXA Canada

•Banque Nationale du Canada

•Banque Royale du Canada

•Bell Québec

•Bombardier

•Bourse de Montréal

•Développement des ressources humaines Canada (DRHC)

•Fédération des caisses populaires Desjardins de Montréal et de l’Ouest-du-Québec

•Hydro-Québec

•Imasco

•Industrie Canada

•Pratt & Whitney Canada Inc.

•Raymond Chabot Grant Thornton

•Ville de Montréal

© 2000 Marcel Boyer et Jean-Jacques Laffont. Tous droits réservés. All rights reserved.

Reproduction partielle permise avec citation du document source, incluant la notice ©.

Short sections may be quoted without explicit permission, provided that full credit, including © notice, is given to

the source.

Ce document est publié dans l’intention de rendre accessibles les résultats préliminaires

de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions.

Les idées et les opinions émises sont sous l’unique responsabilité des auteurs, et ne

représentent pas nécessairement les positions du CIRANO ou de ses partenaires.

This paper presents preliminary research carried out at CIRANO and aims at

encouraging discussion and comment. The observations and viewpoints expressed are the

sole responsibility of the authors. They do not necessarily represent positions of CIRANO

or its partners.

(3)

Competition and the Reform of Incentive Schemes

in the Regulated Sector

*

Marcel Boyer

, Jean-Jacques Laffont

Résumé / Abstract

Nous analysons dans un modèle principal-agent avec sélection adverse et

contrats complets comment les incitations dans une entreprise réglementée sont

affectées par la concurrence externe à travers son effet sur l’information et la

fonction objectif du principal d’une part et les contraintes de compatibilité

incitative et de rationalité individuelle de l’agent d’autre part. Nous considérons

plus précisément les sources suivantes de pressions concurrentielles accrues : une

meilleure structure d’information, une menace plus forte de liquidation, une

concurrence plus intense pour le talent, un secteur privé plus efficace, et

l’existence de meilleurs substituts. Nous caractérisons dans chaque cas les

conditions sous lesquelles l’effet sur les incitations est positif.

We consider a regulation problem with complete contracting in a

principal-agent model with adverse selection and review within this model the

various channels by which external competition parameters affect incentives

within the regulated firm. The channels are: the principal’s information, the

principal’s objective function, the agent’s incentive constraint, the agent’s

participation constraint. We consider in particular a better information structure,

a threat of liquidation, a fight for talent, a more efficient private sector, and the

existence of better substitutes. We characterize in each case the conditions under

which the effect on incentives is positive.

Mots Clés :

Incitations secteur public, concurrence

Keywords:

Public sector incentives, competition

*

Corresponding Author: Marcel Boyer, CIRANO, 2020 University Street, 25

th

floor, Montréal, Qc, Canada

H3A 2A5

Tel.: (514) 985-4002

Fax: (514) 985-4035

email: boyerm@cirano.umontreal.ca

We thank participants in the Canadian Economic Theory Conference (Ottawa) and in the microeconomic seminar at

Rutgers University for their comments. Financial support from the SSHRC (Canada) and CNRS (France) is

gratefully acknowledged.

(4)

Theglobalizationofnationaleconomiesandthepaceoftechnologicalprogressincreasethe

over-alllevelofcompetitionlocallyandglobally. Thisinturnraisesquestionsregardingtheeconomic

role of the State as a regulator of economic activities. Demands for profound reforms of the

regulated sectorand governmentinstitutionsareexpressedinnumerouscountries. Indeedmost

countrieshave designedand begun implementingreforms aimed at increasing theperformance

of their regulated sector. The OECD public management service (PUMA) provides

numer-ous examples of national policies towards that goal. A signi cant exampleamong manyis the

implementation in England of Compulsory Competitive Tendering (CCT) procedures at the

municipalandregionallevels. Thelocalauthoritiesmustcallfortendersforanincreasingarray

of government servicesbeforedeciding whetherthose serviceswillbeo eredbyadirect

munic-ipal service organization ora private companyunder di erent forms of delegated management

contracts withthelocalauthorities. 1

Theunderlyingleitmotifsareperformance, incentivesand

competition of one kindor another. 2

The preferred pathof public sector reform has generally

beento privatizeand liberalizeformer publicsectors. 3

However, manyactivities willand must

remain under government's direct control for natural monopoly or national interest reasons.

How incentives, within public rms and institutions or within regulated private rms, should

respond to thismore competitiveenvironment ? 4

In this paper, we study a regulation problem with complete contracting and a benevolent

regulator (the principal) in a principal-agent model with adverse selection. We analyze the

comparative statics e ects on the power of incentives in the regulated rm or administration

(the agent)ofvariousparameterchangesusuallyassociatedwithgreatercompetitivepressures.

Thisisanecessarysteptoexplorehowgreatercompetitivepressuresmaya ectincentiveswhen

1

SeeLeGallo(1998). 2

There exists also an important literature which has investigated Machlup's (1967) claim that there is no

managerialslackwhena rmoperatesinaperfectlycompetitiveoutputmarket. Leibenstein(1966)hasprovided empiricalevidencefromcasestudiessupportingthecommonviewthatincreasingcompetitionreducesslack.

3

It is often accompanied by sizable downsizing. See Jeon and La ont (1999) for a study of the incentive problemscreatedbydownsizing.

4

Onepossibility issometimestointroducecompetitionwithintheregulatedsector itself. However,thisoften requires wasteful duplications so that competition will remain limited for example to duopolies or restricted oligopolies. AuriolandLa ont(1992)haveinvestigatedthechangesonincentivesbroughtaboutbythisduopoly

(5)

there is nosingle de nitionofwhat increasedcompetition means.

The level of competitive pressures exerted on thepublic sector may be directly decided by

the government when activities which were monopolies are liberalized. We want to explore a

more indirectnotionofincreasedcompetitivepressures. Thelevelofcompetitionitselfisnotan

exogenous parameter asemphasized by Blissand DiTella(1997) who criticizethemodeling of

greater competition bythe increaseinthenumberofcompetitorswhich isan endogenous

vari-able at theindustry level. They suggest thatmore fundamentalparameters, such as transport

costs, cost uncertainty, distribution and overhead cost, should be used. We recognize the

im-portanceofthispointand we willfollowtheirsuggestionasmuchaspossible. However, forour

purpose,apartialequilibriumanalysiswhichconsiderschangesinparametersoftheenvironment

(which are indeed endogenous in a more general analysis) is suÆcient to understand some of

the linksbywhichincreasedcompetitiona ects incentivesintheregulated sector. We consider

suchparameters,namelytheinformationstructure,thethreatof bankruptcy,theopportunities

availableto agents, thetechnologies andthequalityofsubstitutes.

Thepaperisorganizedasfollows. WediscusstherelevantliteratureinSection2followedby

the presentation of the basicmodel inSection 3. We study the informational e ect in Section

4. We devoteSection5 to thethreatof liquidatione ect whileSection6examines competition

in talent. Theimpactsof a more eÆcientprivatesector and ofimprovementsinsubstitutesfor

the regulated productareinvestigatedinSection7. We then concludeinSection8.

2 COMPETITION AND INCENTIVES.

Toreviewtheliteratureoncompetitionand incentives,wecan regroupthearticlesaccordingto

severalcriteria. Twosuchcriteriaarethetypeofagencyproblemconsideredandthechannelby

whichcompetitiona ects incentives. According to the rstcriterion,papers di eraccordingto

thetypeofmodelwhichformalizestheagencyproblemwithinthe rm,moralhazardoradverse

selection. According tothesecondcriterion,papersdi erbythechannelthroughwhichgreater

(6)

rationalityconstraint e ect. Theinformationale ect referstothefactthatgreatercompetition

mayincreasetheinformationoftheprincipalabouttheagentand thereforedecreasethecost of

asymmetric information. The incentive constraint e ect isthat greater competition maya ect

directly theagent's incentive constraint forexample bymaking it easier or more diÆcultfor a

good type to mimic a bad type agent. The principal's objective function e ect is that greater

competition maya ect directly thevalue of production forthe principal and consequentlythe

value forhimofcreating incentivesfortheagent: thedesirablechangeinproductionmaythen

a ect or not the incentive constraint of the agent. The individual rationalityconstraint e ect

conveys the idea that greater competition may increaseor reduce theoutside opportunities of

the agent and thereforeher reservation utilitylevel.

We canillustratethisclassi cationinthefollowingmatrix. Ineachcell, weplacethepapers

dealing withasimilaragency problemand asimilarchannelbutdealingpossiblywithdi erent

institutional contexts. As indicated in Table 1, our paper ts into four cells. In Holmstrom

(1982),relativeperformanceevaluation,orcompetitionamongagents, isusedinordertoexploit

the valuable informationconveyed bythe other agents' outputsregarding the e ortof a given

agent. InNalebu andStiglitz(1983)andShleifer(1985), theprincipalcaninfer,fromobserving

the outputs of all agents, some information on the level of e ort chosen by a given agent and

therefore competition enables the design of more eÆcient reward structures. 5

In Hart (1983)

andScharfstein(1988),competitionbetweenentrepreneurial rmsandmanagerial rmsmakesit

more diÆcultformanagers to shirk. Hart(1983) shows thatthemarketsystembyitselfmakes

the actions and utilities of di erent managers interdependent via prices. 6

Scharfstein (1988)

showsthatthenete ectofcompetitionon managerialslackdependsonmanagerialpreferences

and thenumberof statesand therefore,incentiveproblemsarenotalwaysmitigatedbygreater

competition. Increasingthenumberofbiddersinanauctionof contractswithadverse selection

5

Theyardstickcompetitionargumentwas furtherextendedtoagentswithdi erentbutcorrelated

character-istics by Cremerand McLean(1985,1988)for aprincipalwho is adiscriminatingmonopolist oranauctioneer, and byRiordanand Sappington(1988)whenregulating a rmwithanexpostsignalcorrelatedwiththe rm's

characteristics. 6

Competitionmakestheperformanceofdi erent rmsinterdependentbuttheimpactonincentivesworksin a di erent wayfromHolmstrom(1982). Whilethelatterassumedthat theperformancesofsimilar rms could

(7)

TABLE 1 Moral Hazard Adverse Selection Information structure Holmstrom(1982) Hermalin (1992)

Nalebu and Stiglitz (1983)

Shleifer(1985)

this paper (prop:1;2)

Incentive constraint Hermalin (1992) Schmidt(1997) Hart (1983) Scharfstein(1988)

La ontand Tirole (1987)

this paper (prop:3)

Principal 0 s objective function Hermalin (1994) Schmidt(1997)

this paper (prop:5;6)

Participation

constraint

this paper (prop:4)

In Hermalin (1992), the manager makes an o er to the owner-shareholder through a contract

satisfyingaparticipationconstraintfortheshareholdersandanincentiveconditionfortheagent.

More competition mayreduce theagent'sexpectedutilityorincome,therebygeneratinga

neg-ative directincome e ect bywhich theconsumption of perksor slackarereduced. But amore

competitive environment means better informed shareholders regarding the actions taken by

the agent, increasing the agent's net-of-risk-premium income and generating a positive income

e ect infavoroflesse ort. Thecompetitione ect istherefore ambiguous. InHermalin(1994),

principal-agent hierarchies compete inthe same market. Weak incentives may be the best

re-sponse to strong incentives because the value of incentives is proportional to the rm's lower

(8)

to the rm'slowercost. Hence,more competition hasanambiguouse ect. Finally,inSchmidt

(1997), competition a ects incentives through a positive threat-of-liquidation e ect, inducing

the manager to work harder, and a negative pro t-reduction e ect making it less valuable for

the principal to implement strong incentive schemes. He obtains that increased competition

mayincreaseorreduce managerialslackgiven theoppositesignsofthetwo maine ects

identi- ed. Moreover, increasingcompetitionmaylowermanagerialslackwhencompetitionislowbut

increasemanagerial slackwhen competitionis already intense.

3 THE MODEL

We considera naturalmonopoly 7

which realizesa publicproject valuedS at acost of

C = e (1) where  2 n ; o

is a parameter of cost eÆciency which is privately known by the manager,

where  = > 0; let  =Pr 

= 

be the common knowledge probability that

the rm isalowcost rm;wewillreferto a rmasagoodtype rmand toa rmas

a bad type rm;

 eis themanager'se ort levelwhich hasa disutility ( e) with 0 >0, 00 >0, 000 0; let ( x)= (x) (x  ) ;

 Cisobservablebythepublicregulator;wetaketheaccountingconventionthatitisdirectly

paid by theregulator.

The rm's utilitylevelis then

U =t (e) (2)

7

(9)

socialopportunitycost of1+with>0: Consumers'welfareis

S ( 1+)(t+ e) (3)

and social welfareistaken to be

W =S ( 1+)(t+ e)+U =S (1+)( (e)+ e) U: (4)

Undercompleteinformationtheregulatorwouldmaximizesocialwelfareundertheindividual

rationalityconstraintofthe rm,thatis,U 0. OptimalregulationwouldleadtoeÆciente ort

levels 0

( e)=1 ore=e 

forbothtypes,and no rentsU =0forbothtypes. Underincomplete

information, the regulator maximizes expected social welfare under the usual incentive and

individualrationalityconstraints,that is,solves(with obviousnotations)

(MP) max  h S ( 1+)  e+ (e)  U i +(1 ) h S (1+)  e+ (e)  U i subjectto U U +( e); U U ( e+ ); U 0; U 0

forwhichthe solutionis

0 ( e)=1; 0 (e)=1  1+  1   0 (e )<1 (5) U =(e ); U =0 (6)

The regulatormakestheoptimaltrade-o betweeneÆciencyandrents. He decreasesthe

incen-tivesofthe badtype(e<e 

) to decreasetherent ofthegoodtype(e ).

Such a mechanism can be implemented by an incentive compatible menu of transfer-cost

pairs f(t ;C); (t;C)g: the good type rm chooses the rst pair, implying the eÆcient level of

e ort (C= e 

) and apositive rent U =t C =(e );thebad type rmchoosesthe second

pair, implyingan ineÆcientlevel ofe ort(C = e)and no rent.

>From (5), incentives of the bad type decrease with increases in ,  and . When  is

(10)

reduces thisexpected cost. However, if  is larger than some value  

, it is better to give up

productionbythebadtypeando eracontractwithnorenttothegoodtype. Theincentivesof

theonlyactive rmarethenmaximal,asalways. Thevalueof 

isdeterminedbytheequality

of expectedwelfarewithand withoutthebad type rm,thatis,using(5):

(1   ) h S (1+)  e(  )+ ( e(   )) i =  (e(  ) ) (7)

We want to study the e ect of competition on this optimal trade-o between eÆciency and

rents. We startbyconsideringtheinformational e ect of competition.

4 THE INFORMATIONAL EFFECT OF COMPETITION

It has often been suggested that competition generates information. Competition allows

com-parisons and beingable to compare isbeing better informed. Rather than lookingdeeperinto

how exactly more competition means more information for the principal or the regulator, we

considerinthissectionhowthemenuofcontractso eredchangeswhentheregulatorhasaccess

to abetterinformationstructure. Weprovideageneraldescriptionofthisinformatione ect on

the powerof incentivesbeforelookingat specialcases.

We modelthisbetter informationstructureas thepossibilityforthe regulatorto observe a

signal correlated withthetrue type of the rm beforedesigningthe contractsand determining

in particular the e ort level to be induced from the bad type rm. However, contrary to the

literature reviewed inthe introduction,we assumethat thissignal isnon veri able and cannot

be used to condition the contract. It is the way yardstick competition works in practice, for

exampleinthetelecommunicationandelectricitysectors. Wethenproceedwiththecomparative

statics analysisof abetter informationorsignal.

4.1 Competition as a better information structure

Aninformationstructurefortheregulatorisasetofsignals=f 1 ; 2 ;:::; I gandconditional probabilities Pr( i j ); i =1;:::;I. For each signal  i

(11)

^  i =Pr( j i ); i=1;:::;I

and an associatedstrength ofincentivesde ned by thelevelof e ortofthe badtype

0 (e i )=1  1+ ^  i 1 ^ i 00 (e i ) (8)

when the regulatorwants to keep bothtypes of rms. Let e i = Z( ^  i 1 ^ i ) = ^ Z(^ i ) denote the solutionof (8). 8

Proposition1: If Z isconcave and^ i

< 

forall i,then theregulator wishes tokeepboth

types of rmsand theexpected power ofincentives decreases whenthe regulator has access

to an informativesignal on the privateinformation of the rm.

Proof: Byde nition, E  i ^  i =E  i (E1 f g j i )=E1 f g = :

>From Jensen's inequality, E  i e i  e() i ^ Z is concave. Since 00 > 0; 000 > 0, then Z is

a decreasing function. Let h(^ i ) = ^  i 1 ^ i

, then h() is increasing and convex. Hence, ^ Z 00 = Z 00 h 02 +Z 0 h 00 . Therefore ^ Z isconcave ifZ 00 0. Q:E:D:

Weshowedabovethat ^

Z isconcaveif ()isquadraticorifissmallenough. Notealsothat

ifwede neasignal i

asbeingfavorable[unfavorable]if^ i > i [^ i < i

],thepowerofincentives

8

Di erentiating(8)twiceandsubstituting,weobtain

^ Z 00 (^)= ^ Z 02  000 +  1+ ^  1 ^ 0000  +2 ^ Z 0  1+ 1 (1 )^ 2 000 +  1+ 2 (1 )^ 3 00 00 +  1+ ^  1 ^ 000 :

Therefore,if (e)isquadratic( 00

= ,where isapositiveconstant; 000 =0),weobtain ^ Z 00 (^)=  1+ 2 (1 )^ 3 <0: Similarly,if!0,weobtain ^ Z 00 (^)= 2 (1 ^) 3 00 1+  00 + ^  1 ^ 000 <0: Therefore, ^

(12)

theregulator,observingafavorablesignal,keepsonlythegoodtype rm,thatis,where^ i

> 

for all favorable signals, it is obvious that the expected power of incentives increases since it

increaseswhen thesignalisunfavorableandsincethebadtype rmisdroppedwhenthesignal

is favorable.

Proposition2 : The expected power of incentives of the active rms increases with the

availability of a signal correlated with the true i , for all favorablesignals (^ i > i ), we have ^ i >  .

Between the two extreme regimes de ned by propositions 1 and 2, the expected power of

incentives mayincreaseordecrease dependingon theprobabilitiesofthe signalsleadingto the

liquidation of the bad type rm. We now illustrate these two propositions with four relevant

cases.

4.2 Four Special Cases

Case 1: A generalnon-degeneratesignal.

We rstassumethatcompetitionallowstheregulatortoobtainimperfectbutvaluable

informa-tion on the cost function of the rm. We model thisform of yardstickcompetition as follows:

the regulatorcanobserve aninformativesignal 2f; g correlatedwiththetrue typeof the

rm, thatis, Pr  j  =Pr  j  = 1 2 Pr  j  =Pr  j  =1 :

As  increases, the informativeness of the signal increases, that is, the regulator's con dence

in the signal increases. We want to investigate the e ect of an increase in  on the power of

incentives. For reasons of simplicity, let us considerthe special case where (e) = 1 2

e 2

with

 =1. Aslong astheregulatorwants to keepbothtypes of rms, we ndthat:

dEe

d

(13)

adirectillustrationofProposition1. Inasense,thecostofimplementingalargere ortfromthe

bad type rm increases [decreases]with followinga favorable [anunfavorable] signal because

 isthena morereliablepredictoroftheeÆciencyofthe rm. Observing []impliesahigher

[lower]probabilitythataninformational rentwillbecapturedbythe rm,henceanincrease[a

decrease] inincentives. Thereis avalue   de nedby     +(1 )(1   ) =  ; where 

isde nedby(7), beyondwhichthebad type rmisshutdownafterafavorablesignal

 butremains active after an unfavorable signal . >From then on, the expected e ort of the

bad typeincreaseswithand reachestheeÆcientlevelwhen=1(SeeFigure1). Proposition

1 holdsfor< 

and Proposition2 holdsfor> 

.

With more signals, we have the following situation, illustrated in Figure 2. For  <  1

,

Proposition 1 holds and expected incentives decrease. When  reaches  1

, the bad type rm

is dropped after signal  4

. When  reaches  2

, the bad type rm is dropped after signal  3 . Between 1 and 2

theexpectedincentivescandecreaseorincreasedependingontheprobability

of 4

. For> 2

,Proposition2holdsandexpectedincentivesincrease. Thetransitionbetween

the two extremecases depends nelyon thespeci cs oftheproblem.

9

Letandbetheposteriorprobabilitiesthatthe rmisofthegoodtypeafterobservingandrespectively. Wehave  1  =  1   1  and  1  =  1  1  

Thee ortlevelofabadtype rmafterafavorablesignalisthen

e()= 1  1+  1   1  ; de() d <0; d 2 e() d 2 <0

Similarlyafteranunfavorablesignal

e()= 1  1+  1  1   ; de() d >0; d 2 e() d 2 <0

SincePr()=(1 )+(1 ),Pr ()=+(1 )(1 )andEe=e()Pr()+e()Pr(),weobtain

dEe d <0; d 2 Ee d 2 <0:

(14)

-FIGURE 1  0.5 e 1 e () 1  1+  1  Ee              e () 1   -FIGURE 2  6 0.5 e 1 1  1+  1   1  2 Ee         *          4  3 1  1  2  3

(15)

We nowconsider anotherexample wherethe regulatordiscovers thetrue type of the rm with

probability  and nothing with probability 1 . 10

This case refers to the possibility that a

benchmarking studythe regulatorcan conduct willreveal either thetrue eÆciency of the rm

(with probability)ornothinguseful(with probability1 ). The uninformative signalislike

a signal  1 such that Pr( 1 j ) = Pr( 1 j ) = 1 . Observing  1 gives no informationto

the regulator and the power of incentives is unchanged. The favorable signal  2 is such that Pr( 2 j )= and Pr( 2 j )=0. Observing 2

,we knowforsure that the rm isof thegood

type: e ort is eÆcient and no rent is captured bythe rm. The unfavorablesignal  3 is such that Pr( 3 j ) =0 and Pr( 3 j ) =. Observing  3

, theregulator knows forsure thathe is

facing abad type rm: e ort is eÆcient and no rent is leftto the rm. Globally,theexpected

e ort of thebad type(conditionally onbeing used)increases with: eitherthere is no change,

if  1

is observed, ore=1 if 3

isobserved. We are indeedin thespecialcase ofProposition2.

Case 3: Onlygoodtype rmsarediscovered.

If onlygood rmscan be identi edfollowingthebenchmarkingstudy,thenPr( 1 j )=1 , Pr( 1 j ) =1, Pr( 2 j ) =, Pr( 2 j ) =0, and Pr( 3 j ) = Pr( 3 j ) =0. If the study

reveals no new information,thenitis an unfavorablesignalsince

^  =

(1 )

1  < ;

and incentivesincrease.

Case 4: Onlybad type rmsarediscovered.

If onlybad type rms can bediscovered, thenPr( 1 j )=1,Pr( 1 j ) =1 . Pr( 2 j )= Pr( 2 j ) = 0, Pr( 3 j ) =0, Pr( 3

j ) = , The power of incentivesincreases when a bad

type rm is observed. When the type of the rm is not observed, it is a favorable signal. As

longas^=

 1 (1 )

< 

,bothtypesof rmarekeptand weareinthecaseofProposition

1 andincentivesdecrease. If^> 

,weareinthecase ofProposition2 andincentivesincrease.

10

(16)

To thispoint, we consideredthe valueof as given. But thisvalue is theshadow priceof the

government budgetconstraintand therefore willingeneralvary withthelevel ofexpenditures.

We considerinthis section thegeneral equilibriume ect of an improvement of informationon

thepowerofincentivestakingintoaccounttheinducedchangein. Asincreases,theregulator

has access to a better informationstructureand therefore can leave a smaller rent to the rm,

thus reducing thepressures on the budget constraint and decreasing its shadow value. 11

This

enables him to provide more incentives. The interesting questionis then whether this positive

e ect on incentivesdominatesthenegative e ect identi edinProposition1. Thefollowingcase

showsthatindeedthegeneralequilibriume ect,throughthechange intheshadowpriceofthe

budget constraint may be strongenoughto changethesign of thepartialequilibriume ect.

Let us considercase 4 above where Pr( = j ) = and  =; otherwise; we know that

in thiscaseincentives decrease withan increasein when thetype of rmis notdiscovered, a

favorablesignal leadingto ^==[1 (1 )]>. Thegeneral welfareproblemis

max E[ (S t)+( t ( e) (e))]=S   e+ ( e)  (1 )  e+ (e )  subject to Et=  e+ (e)  +( 1 )  e+ ( e)  +(e )K : We obtain 0 (e)=1  1+  1  1 1   0 (e ) (10)

that is,inthequadraticcase  where (e )= 1 2 e 2 and (e )= (e 1 2 )   e= 1  1+  1  1 1  (11)

where isnowthe (endogenous)multiplierofthe budgetconstraint. The budget constraintis

[ e  + (e  )]+(e ) +(1 )[ e  + (e  )]+(1 )(1 )[ e+ (e)]=K (12) 11

The general equilibrium e ectis related to the government global nancialneeds and becomes signi cant

when someformofbenchmarkingorCCTisavailableandimplementedfor mostifnotallgovernmentactivities orexpenditures.

(17)

E +[(+(1 ))( 1 2 e 2 e  )]+ (e 1 2 )+(1 )(1 )( 1 2 e 2  e )=K : (13) We obtain de d = (1 )( 1 2 e 2  e ) (1 )( 1 2 e 2 e  ) +(1 )(1 )(e 1) >0 (14) d d <0 (15)

Thepartialanalysisofcase4above(consideringas xed)ledto de d

<0;wethereforeconclude

that the general equilibrium e ect of d (through d d

< 0) is, in this case, of a sign di erent

from that of the partialequilibrium e ect of d. The power of incentives increases because a

larger  implieson average a less stringent budget constraint. However, it is not always true

that the general equilibrium e ect will overcome the partial equilibrium e ect. We illustrate

thisin Appendix1.

Abetterinformationstructurea ectstheregulator'swelfaremaximizationproblemandthe

levelofincentivesinthreeways. Ita ectstheexpectedcostoftheproject, 12

theleveloftherent

(e ) throughits e ect on the e ortlevele, and theprobabilitythat thisrent willbe captured,

that is, the posterior probability that the rm is a good type rm. Those e ects modify the

budget constraint and thereforeits shadowvalue.

5 THREAT OF LIQUIDATION AND INCENTIVES

Adi erentchannelthroughwhichmoreintensecompetitionisthoughttoa ectincentivesisthe

threat of bankruptcy or liquidation. For private non regulated rms, liquidationwould follow

fromthedecisionofthe nancierstorefusetore nancea rmwithliquidityconstraintsbecause

of its low expected payo . For regulated or publicly owned rms or projects, \liquidation"

would follow from a political decision to stop subsidizing the rm or project orto change the

management team. Forinstance,it isreasonableto assumethat politicianscannotcommitnot

to useamuchbetteralternativetechnologyifandwhenitbecomesavailable. Henceatthetime

12

Inour context,thereis noquantitye ectsince weare consideringthe realizationofagivenproject. More

(18)

of the contract, the current rm faces a probabilityof being dropped or liquidated. We are

discussing a kind of auctionwhich reduces the rent of the rm and induces higher e ortas in

La ont and Tirole (1987). The lack of correlation betweenthe rm's type and thealternative

technology explains why the full extraction of the surplus, as in Cremer and McLean (1985),

does not occur. We can suppose for instance that the alternative technology would allow the

realization of the public project at some cost C, a random variable with prior distribution

function G(C) and density g(C). If C < (e ) + e , then the switch to the alternative

technologywouldtakeplace,thatis,anew rmormanagement teamwouldbechosentorealize

theprojectand thecurrentone wouldbe\liquidated". Hence,theprobabilityofno liquidation

is given by Pr h C > (e )+ e i = 1 G  (e )+ e  an increasing function of e. 14 We

wantto characterize theimpact ofsucha liquidationruleon theintensityofincentives.

For reasons of simplicity and speci city, we willassume that the liquidation rule takes the

followingreduced form: when the rm is of type , there is a probabilityof liquidationwhich

increases withthecostof the rmand therefore decreaseswiththee ortlevele. Let1 kÆ(e)

denote thisprobabilityof liquidation whereÆ 0

(e ) >0 and k is a positive parameter. Incentive

compatibilityimpliesthattherentoftheeÆcient rmnowtakestheformU =kÆ(e)(e ). 15

Ifwe

denote byS thesocialwelfarewhen liquidationoccurs,that iswhen thealternative technology

is usedto pursuetheproject, expected socialwelfare is

 h S (1+)  ( e)+ e  kÆ(e )(e) i +(1 )kÆ(e) h S (1+)  ( e)+ e i +(1 )(1 kÆ(e))S: 13

Strictosensu,onedoesnotexpectthatapublicquasi-monopoly rmsuchasastate-ownedpowergenerating rm,telecomsorrailormarinetransportation rmswouldsimplybeshutdown. Butthemanagementteamcould

bereplaced ifit wereperceivedas ineÆcientand the rmcould facesigni cant restructuring, withdownsizing andoutsourcing,ifitsoperatingcostsweredeemedtoohigh.

14

Theexperienceof theCompulsoryCompetitiveTendering (CCT)process inthe U.K.isaninteresting real example. Beforeo eringapublicservicedirectlytothecitizens,throughapubliclyownedDirect Service Orga-nization(DSO),amunicipalgovernmentmustinviteprivate rmstobidfortheprojectorservicetogetherwith

the DSOwhomustact thenasaseparateentity. If aprivate rmoutbidsthemunicipalDSO,thenitwinsthe contractandtheDSOis\liquidated". Ifnot,theDSOisawardedanincentivecontractfortheserviceorproject.

The U.K.experience shows that DSOswonabout70% ofthecontractsandweretherefore\liquidated" witha probabilityof0.3.

15

Choosingthecontract(t;C),theeÆcient rmfacestheriskoflosingthecontracttothealternativetechnology;

(19)

0 (e ) = 1 0 (e ) = 1  1+  1   0 (e)  1+ Æ 0 (e )(e ) Æ(e) + Æ 0 (e ) (1+)Æ(e)  S (1+)( (e)+  e)  S  : (16)

A marginalincreaseinthethreat of liquidation(increaseof k) hasno e ect, because ithas

no e ect ontherent extraction-eÆciencytrade-o (sincetheinformationrentdecreasesexactly

asthe gainfromhavingtheineÆcient rmactive decreases), andit hasnoe ect on therate of

increaseof theprobabilityof liquidationÆ 0

(e )=Æ(e).

Proposition3: The power of incentives is insensitive to a marginal increaseof the

proba-bility of liquidation, as long as the regulator's optimization program remains concave.

Note howeverthat with amore general formulationÆ(k;e), we would getresults depending

on thecross derivative @ 2 Æ(k;e) @e@k . 6 COMPETITION IN TALENT

Analternativechannelthroughwhichcompetitionoperatesisthatitincreasesthe`market'value

ofgoodagentsintheprivatesector. Itwillthenbenecessarytoo erhigherpayo stogoodtype

agents in thepublicsector inorder to meet theirparticipation constraint. Thischannelbrings

into focustherelationshipbetweenthepublicsector wage structureand theprivatesectorone.

There aregoodreasons whyone may expectthat thewage structureis more egalitarianinthe

publicsector. Onesuchreasonistheredistributionobjectiveofthegovernment. Inthiscontext,

public authoritiesact asif they were usinga modi ed utilitariansocial welfarefunction where

a weight 

<1 isassociatedwiththe pro torinformational rent of thegoodagent. Thiswill

lead tolargeroveralleÆciencydistortionsinorder tolowerthelessvaluableinformationalrent.

Using thesocialwelfarefunction

S (1+)(t+ e)+ 

(20)

  S (1+)  e+ (e )  (1+  )(e )  +(1 )  S (1+)  e+ (e) 

we obtainthe rst-ordercondition

(1+  ) 0 (e ) (1 )(1+) 0 (e ) 1  =0

that is,for=1  , 0 (e )=1  1  + 1+ 00 (e)

implying, since>0,areductionine and(e), thatis,lowerincentivesand a smallerrent for

goodtypeagents.

The trade-o between eÆciencyand rent minimizationis in a sense solved infavor of rent

minimization: eÆciency is lower, that is, incentives are weaker but the good types capture

a smaller informational rent. In the private sector, the absence of a redistribution objective

together withcompetitivepressuresmake the rmsbehave asif, inorderto avoidbeing

cream-skimmed on the labor market, a utilitarian objective function with 

> 

were used and

therefore bringouta solutionmore inlinewith eÆciency: stronger incentivesareimplemented

and larger rentsare capturedby thegood type. Ascompetition intheprivatesectorincreases,



increases, generatingmore intense competition for thepublic sectorwhich isimplicitly led

to increase the value of 

in order to avoid the loss of the more capable, good type agents.

Hence, although there may not be a perfect alignment of incentives between the public and

privatesectors,theemergence of a more competitiveenvironmentwoulda ect both.

In our model thiscompetition intalent phenomenon can be modeled as an increasein the

reservationutilitylevelofagoodtypemanagerwhich wassofarnormalizedat zero. LetU 0

be

thisnew reservation utilitylevel. The maximizationprogram of theregulator(MP) isas given

above exceptfortheparticipation constraint ofthe goodtypewhichbecomes

U U 0

:

(21)

-U 0 0 (e) (e  ) (e  + ) AslongasU 0

( e) ,withede nedby(6)andobtainedforU 0

=0,theoptimalregulationis

unchangedsincetheinformationrentislargeenoughtosatisfythenew participationconstraint

of thegood typeagent. However, when U 0

becomes largerthanthisinformationrent(e )but

is stillless than (e 

), therelevant bindingconstraints become thetwo IR constraints and the

incentive constraint of thebad type. E ortlevel eis stillde ned by 0

(e)=1 and eis simply

de ned by ( e) = U 0

: So the e ort level of the bad type is increased (incentives increase) in

order tocreate asuÆcientlylargerent(butnotlargerthannecessary)forthegoodtypeto stay

in thepublicorregulated rm.

When U 0

becomes larger than ( e 

) but still less than ( e 

+ ), there is no point in

increasingfurtherewhichhasreachedtheeÆcientlevele 

. OnlytheIRconstraintsarebinding

and bothe ortlevels areeÆcient.

Finally, if U 0

becomes larger than ( e 

+ ), the incentive constraint of the bad type

agent becomes binding. A rent must be given up to the bad type. To mitigate this rent, the

e ort leveleis increasedbeyondthe eÆcient level. Itis de nedby

0 ( e)=1+  1   1+  0 ( e+ )

Competition from the unregulated sector obliges the public sector to select incentive schemes

which are even more powerfulthan the eÆcient ones to keep the good type within the public

sector.

Proposition4: Competition in talent always favorsstronger incentives.

7 A MORE COMPETITIVE ENVIRONMENT

Another meaning of increased competition is that theunregulated (private) sector which

(22)

goods which have become better substitutes. We consider the e ect of those changes on the

powerof incentivesintheregulated sector.

Letusassume thatthesocialvalue ofproductionfrombothsectors isnowgiven by

S(q 1 +q 2 )+q 1 q 2 where q 1

isthe variable output of the regulated sector and q 2

is the output of the competitive

sector and where   0 is a measure of how complementary the products of the two sectors

are. As  increases [decreases], the goods become more complementary [substitute] 16

and the

demandof each good increases[decreases]asusual.

Assuming thatC(q 2

) =cq 2

, that theoutput of theregulated rm is \sold"at its marginal

value level, that theproceeds go into thepublic budget and are therefore generating an extra

value ofp 1 (q 1 ;q 2 )q 1

,andthatthebenevolent regulatorcares abouttotal welfare, we canwrite

the regulator'sobjective functionas

S(q 1 +q 2 )+q 1 q 2 +U ( 1+)(t+( e)q 1 ) cq 2 +p 1 (q 1 ;q 2 )q 1 ;

where U =t ( e) is the regulated rm'sutility. Underfullinformation, theregulator wants

the rmto exerttheoptimallevelofe orte  characterized by 0 (e  )=q 1

forbothtypesofthe

regulated rm whileoperating a transfert leavingno rent to theregulated rm,U =U =0.

We assume that 2 n

; o

is private information of the rm while the private sector

technology, that is c, is common knowledge. This simplifying assumption can be justi ed by

the yardstick competition in the private sector which generates a perfect informative signal

makingcknowntotheregulator. Theregulatormaximizestheexpectedsocialwelfareunderthe

usual individualrationalityand incentive compatibilityconstraints of bothtypes and balances

eÆciency and rents by determining the output and e ort levels of the regulated sector as a

functionof . We obtain(seeAppendix2): 0 ( e)=q 1 and 0 (e)=q 1  1+  1   0 (e )<q 1 :

We can modelan increaseincompetitivepressures bymaking theprivatesectormore eÆcient,

that isreducing c,orbymakingthe twogoodsbetter substitutes,that isreducing.

16

The cross derivative ofsocialwelfare withrespect toq 1 and q 2 is S 00 +;if S 00

+ >[<]0, thegoods are

(23)

Let us rst consider a reduction in c. We can show (see Appendix 2) that, whatever the

eÆciency of the regulated sector, a reduction in production cost c increases the output of the

privatesectorbutmayincreaseordecreasetheproductionoftheregulatedsector. Letusassume

that the products are demand substitutes, that is S 00

+ < 0. 17

If the products are demand

substitutes and strategic substitutes, 18

then the production of the regulated sector decreases

when c decreases, implyinga reductionin incentives (no change in e ort e buta reduction in

e ort e) and in therent of the eÆcient type rm. If the products are demandsubstitutesand

strategiccomplementswithlargeenough,thentheproductionoftheregulatedsectorincreases

when c decreases, implyingan increase in incentives (no change in e ort e but an increase in

e ort e )and intherentof theeÆcient type rm.

The intensityof incentives, measuredby 19 k = 0 ( e) C e = 0 (e) q 1 ;

remainsconstant(atk =1) fortheeÆcient typebutmayincreaseordecreasefortheineÆcient

type,dependingon thevalue of. Forsmall,thee ect ofa reductionincon theintensityof

incentives is of thesame sign as thee ect on the productionlevel of theregulated sector. But

for suÆcientlylarge, we can have an oppositesign: 20

ifthe products aredemandsubstitutes

but strategiccomplementsand the value of is largeenough, a reductionin themarginal cost

c increases both production and e ort in the public sector, but nevertheless the intensity of

incentives decreases,asshown inAppendix2.

Proposition5: Iftheregulated productq 1

andtheprivatesectorunregulatedproductq 2

are

strategicsubstitutes,thenareductioninmarginal costcreducesincentivesfortheregulated

17

Thereadercanadapttheanalysistothecaseofdemandcomplements. 18

The products are strategic substitutes[complements]if themarginal social revenuefrom good idecreases

[increases] withtheproductionofgoodj,thatis,ifS 000

qi+S 00

+< [>]0. Ifthegoodsaredemandsubstitutes,

wehaveS 00

+<0;hencewhetherthegoodsarestrategic substitutesorstrategiccomplementsdependsonthe

signandmagnitudeofS 000

qirelativetoS 00

+. SeeAppendix2fordetails. 19

Theintensityofincentivescorrespondstothat partk oftherealizedcostwhichisborneby the rmat the

margin: ifU =t kC( ;e;q) (e)=t k( e)q (e),thenU e =kq 0 (e)=0impliesk= 0 (e) q 2(0;1]: 20 Unless 00

=0,asforthequadraticcase (e)= 1 2

e 2

(24)

cincreases incentives for the regulated rm.

So if greater competition means lower cost competitors, strategic complementarity and a high

socialcostof publicfundsare thekeys to greater productionof thepublicsector and therefore

to greater e ortandlarger rents. Whenislargebutnottoolarge, greatere ortis equivalent

to higherpowerof incentives. 21

7.2 Improved substitutes for the regulated rm's product

Let usnow consideran increasein substitutability,that is, a reduction in . We can show

(see Appendix2) forboth and thatthe e ect of a change in onthe productionleveland

e ort levelin thepublicsectorare of thesame sign. Iftheproductsare strategic complements

withlargeenough, thentheproductlevelsq 1

andq 2

aswellasthee ortleveleareallreduced

as  decreases. Indeed, a reduction of  increases substitution but also reduces the value of

bothcommoditiesto consumers. Ifon theotherhandtheproductsarestrong enoughstrategic

substitutes, thesubstitutione ect maydominate and q 1

mayincreaseaswellase.

Proposition6: If the regulated product q 1

and the private sector unregulated product q 2

are strategic complements with  large enough, then the incentives of the regulated rm

decrease with an increase in the degree of substitution. If the products are strong enough

strategic substitutes, then the incentives of the regulated rm increase with the degree of

substitution.

When more competition means better substitutability between the public and private sectors

products (andan increaseintheir globaldemand), then strategicsubstitutabilityis the keyto

higher production, e ort and rent in the public sector (unlessthe social cost of publicfund is

low). 21 Weneed >maxf (S 00 +) S 00 ++S 000 q 1 and 00 00 +  1+  1   00 > 0 q 1 ;

(25)

cost functionC =( e)q which yieldsthe rst orderconditionof thebad type 0 (e)=q 1  1+  1   0 (e )

from which the e ects of competition can be tracked. Clearly these e ects work through q 1

by changingthe social pro tability of e ort. Witha more general cost function satisfyingthe

incentivedichotomypropertyC=C(( ;e);q 1

)thechannelwouldremainsimilar, @C

@e

replacing

q 1

. If we drop the incentive dichotomy assumption, competition can a ect more directly the

incentive constraint and the rent. The marginal rent is now given by  0

(e)E

( ;e;q) where

E( ;e;q) is the solutionin e of 

C =C( ;e;q), thatis, the e ortlevel which enablesa rm of

type to produceq witha cost of 

C. Furthermore, thepricingequation requiresan incentive

correction and the e ect of a change in theproductionlevel, dueto increased competition, on

the e ortlevelis obtainedbydi erentiating thewhole system

 p 1 C q1  p 1 =  1+ 1 ^  1 +I 0 (e )= C e ( ;e;q)  1+  1   0 E ( ;e;q): 8 CONCLUSION

We characterized thee ects ofstronger competitivepressures on publicsector incentives,more

preciselyon thelevelofincentivesinan optimallyregulatedsector. Maybe contrary to

conven-tionalwisdomora rst intuition,greatercompetition doesnotalwayscallforhigherincentives.

We identi ed di erent channels through which competition a ects the powerof incentives.

First, we looked at the information channel, namely the idea that more competition provides

theprincipal,theregulator,withinformationabouttheagent, theregulated sector. We showed

in propositions1 and 2 thatthe e ect of better informationon thepower ofincentivesmaybe

positive or negative. If the quality of the competition signal is suÆciently high to induce the

regulatortodropthepublicprojectfollowingafavorablesignal,thepowerofincentivesincreases;

(26)

is quadratic and when the social cost of public funds  is small. Moreover, we characterized

the general equilibrium e ect of a better information structure, considering  as endogenous,

and we showed that its sign may be di erent from that of the partial equilibrium e ect. The

mainreasonfortheambiguousresultsisthatgreaterinformationprovidedbyamorecompetitive

environmentmayalterthedesirabletrade-o betweeneÆciencyandrentextractiontowardsless

rent extraction on average. However, when the competition signal is better, that is, becomes

veryinformative,theexpectedresult obtains.

Second, we looked at the threat of liquidation e ect and we showed that the power of

incentives isinsensitive to localincreases of thisthreat. Third,we analyzedthe competition in

talent e ect and weshowed thatthise ect increases also thepowerofincentives.

Fourth,weconsideredamodelofamorecompetitiveenvironmentandweshowed(i)thatthe

e ectofacostreductioninthecompetitiveunregulatedsector,producingasubstituteproductto

thatoftheregulated rm,onthepowerofincentivesisnegative[positive]whentheproductsare

strategicsubstitutes[strategiccomplementsandislarge],and(ii)thatthee ectofanincrease

insubstitutabilitybetweentheproductsispositive[negative]ifthedegreeofdemandsubstitution

isstrongenough[iftheproductsarestrategiccomplementsandislarge]. The mainreasonfor

theambiguousresultisthatthedesirablechangeinthepowerofincentivesisrelatedtothelevel

ofactivityoftheregulated rmandtotheinteractionbetweene ortandproductionlevelinthe

cost function. Dependingon thenatureand strengthofthesubstitutabilityorcomplementarity

betweentheregulatedproductandthegoodsproducedbytheunregulatedcompetitors,greater

competitive pressures from the latter may call for a shrinkage or an expansion of the public

sector, and that determinesto alargeextent the desirablechange inthepowerofincentives.

A next step in the analysis would be to recognize that, for political economyreasons,

reg-ulation is notoptimized and study to which extent the increasein competition disciplinesthe

regulators. 22

22

Thiswouldrequireanexplicitpoliticaleconomymodelas inBoyerandLa ont(1999)oranexplicit

(27)

A Non-Reversing General Equilibrium E ect

Weconsiderthegeneralequilibriume ect forthefollowinginformationstructureof case1. We

have e()= 1  1+  1   1  (17) e()= 1  1+  1  1   ; (18)

hence e()e (),and thebudget constraint

[ e  + 1 2 e 2 + (e () 1 2 )]+(1 )(1 )[ e ()+ 1 2 (e ()) 2 ] +(1 )[ e  + 1 2 e 2 + (e () 1 2 )]+(1 )[ e ()+ 1 2 (e ()) 2 ] = K (19)

Totallydi erentiatingthe systemof equations(17), (18) and (19)with respect to e(), e(),

and , we obtain de () de() d d 1 0 B 1 C 1 0 1 B 2 = C 2 A 1 A 2 0 where =[ (e () 1 2 ) (e () 1 2 )]+(1 )[( 1 2 (e ()) 2 e()) ( 1 2 (e()) 2 e())]<0,

with e () ande() given by(17)and (18), and

B 1 = 1 (1+) 2  1   1  >0; B 2 = 1 (1+) 2  1  1   >0 C 1 =  1+  1  1 (1 ) 2 <0; C 2 =  1+  1  1  2 >0 A 1 =  1 1+ <0; A 2 = (1 ) 1 1+ <0

with the determinant = A 2 B 2 A 1 B 1 >0. Observingthat A 1 <A 2 <0, jC 1 j>jC 2 jand B 1 >B 2 >0,weobtain d d / + C 2 A 2 C 1 A 1 < 0

(28)

d / B 1 A 2 C 1 B 2 +A 2 B 1 C 2 < 0 de() d / B 2 +A 2 C 1 B 2 A 1 B 1 C 2 > 0: Thesignof de () d

maybepositiveornegative. Itdependsontwoe ects: thepartialequilibrium

e ect ( xed)and thegeneralequilibriume ect through d d <0,namely de () d / @e () @ d=0 + B 1 B 2  A 2 C 2 

where the rst termisnegative [equal to C 1

<0] andthesecond termis of thesignof

+A 2 C 2 =  (1+) 2  2 1  1   2 : Indeed, for = 2 9 ;  = 1 3 ;  = 3 4 , we have de () d = 1:31 if  = 2 3 , and de() d = +0:49 if = 3 4 . Appendix 2

Increases in Competitive Pressures from the Private Sector

We wish to maximizesocialwelfare

W = h S  q 1 +q 2  +q 1 q 2 (1+)  ( e)+  e  q 1  cq 2 +p 1 (q 1 ;q 2 )q 1 U i +(1 ) h S(q 1 +q 2 )+q 1 q 2 ( 1+)  (e )+  e  q 1  cq 2 +p 1 (q 1 ;q 2 )q 1 U i subjectto IR: U 0 IR: U 0 IC: t ( e)t ( e)+( e) IC: t ( e)t ( e  ) with ( e)= (e) (e  )

(29)

dq 1 dc = 1 D 00 S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i ! dq 2 dc = 1 D " 00 S 00 + h @ 2 p 1 @q 2 1 +2 @p 1 @q 1 i ! (1+) # <0 de dc = 1 D S 00 ++  @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2  ! dq 1 dc = 1 D "  00  1+  1+  00  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i # dq 2 dc = 1 D "  00  1+  1+  00  S 00 + h @ 2 p 1 @q 2 1 +2 @p 1 @q 1 i (1+) # <0 de dc = 1 D S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i ! leading to dq 2 dc <0 sign  dq 1 dc  = sign  de dc  = sign " S 00 ++ " @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 # !# = sign   S 00 ++ @MR(q 1 ) @q 2  = sign  S 00 ++  S 000 q 1 +S 00 +  = sign  (1+) S 00 +  S 000 q 1 

As fortheintensityof incentivesk,we have

dk dc = 1 q 1 00 de dc + 0 1 q 2 1 ! dq 1 dc : Since de dc 00 = dq 1 dc and de dc h 00 +  1   1+  00 i = dq 1 dc ,we obtain dk dc = 1 q 1 " 1 0 (e ) q 1 # dq 1 dc =0 dk dc = 1 q 1 2 6 6 4 00 (e ) 00 (e )+  1   1+  00 (e) 0 (e) q 1 3 7 7 5 dq 1 dc :

(30)

 00 6=0, sign dk dc ! = sign  dq 1 dc  :

Regarding thee ect of a change in,we nd:

dq 1 d = 00 D " q 1  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i  +q 2  S 00 + h @ 2 p 1 @q 2 2 q 1 i # dq 2 d = 1 D " 00  S 00 + h @ 2 p 1 @q 2 1 +2 @p 1 @q 1 i q 1 00  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i q 2 +( 1+)q 1 # = 1 D " q 1 h S 00 + h @ 2 p 1 @q 2 1 +2 @p 1 @q 1 i ( 00 ) (1+) i +q 2  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i ( 00 ) # de d = 1 D " q 1  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i  +q 2  S 00 + h @ 2 p 1 @q 2 2 q 1 i  # dq 1 d = 00 +  1+  1+  00 D " q 1  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i +q 2  S 00 + h @ 2 p 1 @q 2 2 q 1 i # dq 2 d = 1 D " q 1 h S 00 + h @ 2 p 1 @q 2 1 +2 @p 1 @q 1 i 00  1+  1+  00  (1+) i +q 2  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i  00  1+  1+  00  # de d = 1 D " q 1  S 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i  +q 2  S 00 + h @ 2 p 1 @q 2 2 q 1 i  # where S 00 + h @ 2 p 1 @q 2 2 q 1 i

<0 bythe secondorder conditions,leadingto:

sign  dq 1 d  =sign  de d  : Therefore, { ifS 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i >0,then dq 2 d >0; dq 1 d >0; de d >0 { otherwise, if jS 00 ++ h @ 2 p 1 @q 1 @q 2 q 1 + @p 1 @q 2 i

j is large enough relative to j S 00 + h @ 2 p 1 @q 2 2 q 1 i j ,

the substitutione ect dominatesand

dq 2 d <0; dq 1 d <0; de d <0

(31)

have dk d = 1 q 1 00 de d + 0 1 q 2 1 ! dq 1 d : Since de d 00 = dq 1 d and de d h 00 +  1   1+  00 i = dq 1 d ,we obtain dk d = 1 q 1 " 1 0 (e ) q 1 # dq 1 d =0 dk d = 1 q 1 2 6 6 4 00 (e ) 00 (e )+  1   1+  00 (e) 0 (e) q 1 3 7 7 5 dq 1 d :

The intensity of incentivesfor thegood type remainsconstant but, for suÆcientlylargeand

 00 6=0, sign dk d ! = sign  dq 1 d  :

(32)

[1] Anton,J.andYao,D.(1989), \SplitAwards,Procurement,andInnovation",RandJournal

of Economics30, 538-552.

[2] Anton,J. andYao,D. (1992), \CoordinationinSplitAwardAuctions",QuarterlyJournal

of Economics107,681-708.

[3] Auriol, E. and La ont, J.J. (1992), \Regulation by Duopoly", Journal of Economics and

Management Strategy1, 507-533.

[4] Bliss,C.andDiTella,R.(1997),\DoesCompetitionKillCorruption?",JournalofPolitical

Economy105, 1001-1023.

[5] Boyer, M. and La ont, J.J. (1998), \Towarda Political Theory of theEmergence of

Envi-ronmental Incentive Regulation," RandJournal of Economics30, 137-157.

[6] Cremer, J. and McLean, R. (1985), \Optimal Selling Strategies under Uncertainty for a

DiscriminatingMonopolistwhenDemandsareInterdependent,"Econometrica53,345-361.

[7] Cremer, J.andMcLean, R.(1988),\FullExtraction oftheSurplusinBayesianand

Domi-nant Strategy Auctions,"Econometrica 56, 1247-1258.

[8] Dana, J. and Speir,K. (1994), \Designinga Private Industry: Government Auctions with

EndogenousMarketStructure", Journalof Economic Theory53, 127-147.

[9] Hart,O. (1983), \The Market asan Incentive Mechanism",BellJournal ofEconomics14,

366-382.

[10] Hermalin, B. (1992), \The E ects of Competition on Executive Behavior", Rand Journal

of Economics23, 350-365.

[11] Hermalin, B. (1994), \Heterogeneity in organizational Form: Why Otherwise Identical

Firms Choose Di erent Incentives for their Managers", Rand Journal of Economics 25,

518-537.

(33)

Bank Economic Review13, 67-88.

[14] La ont, J.J. and N'Guessan, T.T. (1999), \Competition and Corruption in an Agency

Model,"Journalof Economic Development 60, 271-295.

[15] La ont, J.J. and Tirole,J. (1987), \Auctioning Incentive Contracts," Journal of Political

Economy95, 921-937.

[16] La ont,J.J.andTirole,J.(1993),A TheoryofIncentivesinProcurementand Regulation,

MITPress, Cambridge.

[17] Leibenstein,H.(1996),\Allocative EÆciencyvs.`X-EÆciency'",AmericanEconomic

Re-view 56, 392-415.

[18] LeGallo, V.(1998), \Compulsory Competitive Tendering: The U.K. Experience," mimeo,

CIRANO (Montreal).

[19] Machlup,F(1967),\TheoriesoftheFirm: Marginalist,Behavioral,Managerial",American

Economic Review57, 1-33.

[20] Mirrlees,J.(1974),\NotesonWelfareEconomics,Information,andUncertainty",inBalch,

M., McFadden, D., and S.Wu (eds), Essays inEquilibriumBehavior, Amsterdam,

North-Holland.

[21] Nalebu , B. and Stiglitz, J. (1983), \Information, Competition, and Markets", American

Economic Review, Papers andProceedings73, 278-283.

[22] Riordan, M. and Sappington, D. (1988), \Optimal Contracts with Ex Post Information,"

Journal ofEconomic Theory 45, 189-199.

[23] Scharfstein,D.(1988),\ProductMarketCompetitionandManagerialSlack",RandJournal

of Economics19, 147-155.

[24] Shleifer,A (1985), \A Theory of Yardstick Competition", RandJournalof Economics16,

319-327.

[25] Schmidt,K. (1997), \ManagerialIncentives and ProductMarket Competition", Reviewof

(34)
(35)

Liste des publications au CIRANO *

Cahiers CIRANO / CIRANO Papers (ISSN 1198-8169)

99c-1

Les Expos, l'OSM, les universités, les hôpitaux : Le coût d'un déficit de 400 000 emplois

au Québec — Expos, Montréal Symphony Orchestra, Universities, Hospitals: The

Cost of a 400,000-Job Shortfall in Québec / Marcel Boyer

96c-1

Peut-on créer des emplois en réglementant le temps de travail? / Robert Lacroix

95c-2

Anomalies de marché et sélection des titres au Canada / Richard Guay, Jean-François

L'Her et Jean-Marc Suret

95c-1

La réglementation incitative / Marcel Boyer

94c-3

L'importance relative des gouvernements : causes, conséquences et organisations

alternative / Claude Montmarquette

94c-2

Commercial Bankruptcy and Financial Reorganization in Canada / Jocelyn Martel

94c-1

Faire ou faire faire : La perspective de l'économie des organisations / Michel Patry

Série Scientifique / Scientific Series (ISSN 1198-8177)

2000s-57

Law versus Regulation: A Political Economy Model of Instrument Choice in

Environmental Policy / Marcel Boyer et Donatella Porrini

2000s-56

Le retour à l’école / Marcel Dagenais, Claude Montmarquette, Nathalie

Viennot-Briot et Muriel Meunier

2000s-55

Le décrochage scolaire, la performance scolaire et le travail pendant les études :

un modèle avec groupe hétérogène / Marcel Dagenais, Claude Montmarquette,

Nathalie Viennot-Briot et Muriel Meunier

2000s-54

Vertical R&D Spillovers, Cooperation, Market Structure, and Innovation / Gamal

Atallah

2000s-53

Information Sharing and the Stability of Cooperation in Research Joint Ventures /

Gamal Atallah

2000s-52

A Theory of Routines as Mindsavers / Bernard Sinclair-Desgagné et Antoine

Soubeyran

2000s-51

Can Financial Intermediation Induce Economic Fluctuations? / Sanjay Banerji et

Ngo Van Long

2000s-50

Information Technology Sophistication in Hospitals: A Field Study in Quebec /

Guy Paré et Claude Sicotte

2000s-49

Does Comparable Worth Work in a Decentralized Labor Market? / Michael Baker

et Nicole M. Fortin

2000s-48

Occupational Gender Composition and Wages in Canada: 1987-1988 / Michael Baker

et Nicole M. Fortin

* Vous pouvez consulter la liste complète des publications du CIRANO et les publications elles-mêmes sur notre site

Internet à l'adresse suivante :

Figure

TABLE 1 Moral Hazard Adverse Selection Information structure Holmstr om (1982) Hermalin (1992)

Références

Documents relatifs

These preliminary results on the effect of density may reflect the individual strategies of colonization of banana fields by Cosmopolites sordidus that maximize

We reported on new additional evidences, from electron diffraction at 5 keV and Raman spectroscopy, supported by calculations, confirming the successful conversion of few-layer

(2007) Sign Language (SL) in Graphical Form: Methodology, modellisation and representations for gestural communication, Conference Proceedings of Interacting Bodies,2nd conference

Indicators were primarily drawn from the World Bank’s second Women’s Health and Safe Motherhood Project but also from the Department of Health’s national health reform programme

The proof is immediate by considering that the quadratic fidelity term and, under condition (3.10), the total functional J in (1.1), are both convex functions, hence locally

represents an irrational number.. Hence, large partial quotients yield good rational approximations by truncating the continued fraction expansion just before the given

Now that the importance of the financial sector’s development in explaining the volume of private investment in developing countries’ energy projects is established, let us

In mixed strategy equilibrium, the Perfect Bayesian Equilibrium (PBE) is given by (x*, y*, ρ), where x* and y* respectively define the probability to play Attack for terrorists