Decentralized Bribery

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Decentralized Bribery
Sergey V. Popov
Moscow, December 14, 2012
Centre for Institutional StudiesHigher School of Economics

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious, expost verifiable.I Second one a transfer.I This paper: there are welfare implications for the second type of bribe.

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious,
expost verifiable.I Second one a transfer.I This paper: there are welfare implications for the second type of bribe.

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious, expost verifiable.
I Second one a transfer.I This paper: there are welfare implications for the second type of bribe.

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious, expost verifiable.I Second one
a transfer.I This paper: there are welfare implications for the second type of bribe.

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious, expost verifiable.I Second one a transfer.
I This paper: there are welfare implications for the second type of bribe.

Introduction
Bribery
Bribes
I Likhoimstvo = taking bribes for doing bad stuff.I Mzdoimstvo = taking bribes for doing stuff youre supposed to do for free.
Problems
I First one obvious, expost verifiable.I Second one a transfer.I This paper: there are welfare implications for the second type of bribe.

Introduction
Literature
Empirical Literature
I Exposure to corruption less investment, slower growth.I Corrupt economies are heavily regulated.I Putin is blamed for economic development, but not for corruption.
Theoretical Literature
I Stealing from governmental coffers is bad for development.I Rentseeking is vacuous.I Bribes can improve the allocation.

Introduction
Literature
Empirical Literature
I Exposure to corruption less investment, slower growth.I Corrupt economies are heavily regulated.I Putin is blamed for economic development, but not for corruption.
Theoretical Literature
I Stealing from governmental coffers is bad for development.I Rentseeking is vacuous.I Bribes can improve the allocation.

Introduction
This Paper
Questions
I How does the transfer bribe affect the capital market?I Can it be beneficial?I Can it harm?
Answers
I It can make the society worse off by scaring small businesses away.I It might not be a good idea to decentralize potential bribery.

Introduction
This Paper
Questions
I How does the transfer bribe affect the capital market?I Can it be beneficial?I Can it harm?
Answers
I It can make the society worse off by scaring small businesses away.
I It might not be a good idea to decentralize potential bribery.

Introduction
This Paper
Questions
I How does the transfer bribe affect the capital market?I Can it be beneficial?I Can it harm?
Answers
I It can make the society worse off by scaring small businesses away.I It might not be a good idea to decentralize potential bribery.

Model
Fundamentals
Agents
I Agents consume a single good.I Agents have roles: investor or inspector.
Roles
I investor gets a random project, need to invest K, after investmentobserves return R, needs to pass an inspection.
I inspector asks for a bribe, if not paid does not pass the project.

Model
Fundamentals
Agents
I Agents consume a single good.I Agents have roles: investor or inspector.
Roles
I investor gets a random project, need to invest K, after investmentobserves return R, needs to pass an inspection.
I inspector asks for a bribe, if not paid does not pass the project.

Model
Fundamentals
Agents
I Agents consume a single good.I Agents have roles: investor or inspector.
Roles
I investor gets a random project, need to invest K, after investmentobserves return R, needs to pass an inspection.
I inspector asks for a bribe, if not paid does not pass the project.

Model
InvestorsI Investor observes K project size.I Expects to pay a bribe s.I Investor chooses whether to start up a project:
I After investment, project return R is observed.I If s > RK, investor can decide to not pay the bribe and walk away.I Expected return is E[RK s]+ K.
I Will start up the project if E[R s/K]+ > 1.
ResultWhen K > K(s), investor participates.

Model
InvestorsI Investor observes K project size.I Expects to pay a bribe s.I Investor chooses whether to start up a project:
I After investment, project return R is observed.I If s > RK, investor can decide to not pay the bribe and walk away.I Expected return is E[RK s]+ K.
I Will start up the project if E[R s/K]+ > 1.
ResultWhen K > K(s), investor participates.

Model
InvestorsI Investor observes K project size.I Expects to pay a bribe s.I Investor chooses whether to start up a project:
I After investment, project return R is observed.I If s > RK, investor can decide to not pay the bribe and walk away.I Expected return is E[RK s]+ K.
I Will start up the project if E[R s/K]+ > 1.
ResultWhen K > K(s), investor participates.

Model
InspectorsI Inspector know neither K nor R of the project.I Inspector decides on the bribe size s, believing in K.I The inspectors problem is:
maxssP (RK > s).
I When K is trivialmaxss P (R >
s
K)
1FR(s/K)
.
I The solution iss/K =
1 FR(s/K)fR(s/K)
.

Model
InspectorsI Inspector know neither K nor R of the project.I Inspector decides on the bribe size s, believing in K.I The inspectors problem is:
maxssP (RK > s).
I When K is trivialmaxss P (R >
s
K)
1FR(s/K)
.
I The solution iss/K =
1 FR(s/K)fR(s/K)
.

Model
InspectorsI Inspector know neither K nor R of the project.I Inspector decides on the bribe size s, believing in K.I The inspectors problem is:
maxssP (RK > s).
I When K is trivialmaxss P (R >
s
K)
1FR(s/K)
.
I The solution iss/K =
1 FR(s/K)fR(s/K)
.

Model
InspectorsI Inspector know neither K nor R of the project.I Inspector decides on the bribe size s, believing in K.I The inspectors problem is:
maxssP (RK > s).
I When K is trivialmaxss P (R >
s
K)
1FR(s/K)
.
I The solution iss/K =
1 FR(s/K)fR(s/K)
.

Model
InspectorsI In general, the solution is
s = +0 (1 FR(s/K)) fK(K)dK +0
1/KfR(s/K)fK(K)dK
=EK [P (R > s
/K)]
EK [1/KfR(s/K)]
.
I R Exp(), and two levels of investment size (KH and KL) produce
s
Only H types
Both H andL types

Model
InspectorsI In general, the solution is
s = +0 (1 FR(s/K)) fK(K)dK +0
1/KfR(s/K)fK(K)dK
=EK [P (R > s
/K)]
EK [1/KfR(s/K)]
.
I R Exp(), and two levels of investment size (KH and KL) produce
s
Only H types
Both H andL types

Model
InspectorsI In general, the solution is
s = +0 (1 FR(s/K)) fK(K)dK +0
1/KfR(s/K)fK(K)dK
=EK [P (R > s
/K)]
EK [1/KfR(s/K)]
.
I R Exp(), and two levels of investment size (KH and KL) produce
s
Only H types
Both H andL types

Model
InspectorsI In general, the solution is
s = +0 (1 FR(s/K)) fK(K)dK +0
1/KfR(s/K)fK(K)dK
=EK [P (R > s
/K)]
EK [1/KfR(s/K)]
.
I R Exp(), and two levels of investment size (KH and KL) produce
s
Only H types
Both H andL types

Model
InspectorsI In general, the solution is
s = +0 (1 FR(s/K)) fK(K)dK +0
1/KfR(s/K)fK(K)dK
=EK [P (R > s
/K)]
EK [1/KfR(s/K)]
.
I R Exp(), and two levels of investment size (KH and KL) produce
s
Only H types
Both H andL types

Model
EquilibriumI The equilibrium is (K, s) such that:
I all projects bigger than K are implemented;I the bribe size is s;I both are optimal decisions subject to rational beliefs.
I Equilibrium existsI autarky: no projects are implementedI restricted: a subset of projects is implementedI abundance: all projects are implemented

Model
EquilibriumI The equilibrium is (K, s) such that:
I all projects bigger than K are implemented;I the bribe size is s;I both are optimal decisions subject to rational beliefs.
I Equilibrium existsI autarky: no projects are implementedI restricted: a subset of projects is implementedI abundance: all projects are implemented

Predictions
Capital MarketI The expected return of a project of size K is [R s/K]+ 1.I The total profit is [RK s]+ K.I The derivative of that with respect to K is
Average return ( +sK
(R s
K
)dFR 1
)+K
Extra chance of no cancelling ( +sK
( sK2
)dFR
).
I Tobins marginal Q is bigger than 1.I Data in a corrupt economy would suggest increasing the scale of
investment...I but increase in scale will only increase the bribe size.

Predictions
Capital MarketI The expected return of a project of size K is [R s/K]+ 1.I The total profit is [RK s]+ K.I The derivative of that with respect to K is
Average return ( +sK
(R s
K
)dFR 1
)+K
Extra chance of no cancelling ( +sK
( sK2
)dFR
).
I Tobins marginal Q is bigger than 1.I Data in a corrupt economy would suggest increasing the scale of
investment...
I but increase in scale will only increase the bribe size.

Predictions
Capital MarketI The expected return of a project of size K is [R s/K]+ 1.I The total profit is [RK s]+ K.I The derivative of that with respect to K is
Average return ( +sK
(R s
K
)dFR 1
)+K
Extra chance of no cancelling ( +sK
( sK2
)dFR
).
I Tobins marginal Q is bigger than 1.I Data in a corrupt economy would suggest increasing the scale of
investment...I but increase in scale will only increase the bribe size.

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
Inspectorschoice
KL
s s1
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
Inspectorschoice
KL
s s1
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
Inspectorschoice
KL
s
s1
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
Inspectorschoice
KL
s s1
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
Inspectorschoice
KL
s s1
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
KL
Inspectorschoice
ss2
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
KL
Inspectorschoice
s
s2
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
KL
Inspectorschoice
ss2
Eqm bribe

Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45 line
KH
KL
Inspectorschoice
ss2
Eqm bribe

Predictions
The SquanderingI What if there is a signal about the investment size?..
I Say, with probability q the signal is correct (H when investor is of type Hand I if investor is of type I).
I Then inspectors will believe their signals if both types of firms start up...

Predictions
The SquanderingI What if there is a signal about the investment size?..I Say, with probability q the signal is correct (H when investor is of type H
and I if investor is of type I).
I Then inspectors will believe their signals if both types of firms start up...

Predictions
The SquanderingI What if there is a signal about the investment size?..I Say, with probability q the signal is correct (H when investor is of type H
and I if investor is of type I).I Then inspectors will believe their signals if both types of firms start up...

Predictions
Imperfect ObservationI What if there is a signal about the investment size?..
s
s 45 line
KH
KL
s
H signal
L signal
Bad eqm bribe

Predictions
Imperfect ObservationI What if there is a signal about the investment size?..
s
s 45 line
KH
KL
s
H signal
L signal
Bad eqm bribe

Predictions
Imperfect ObservationI What if there is a signal about the investment size?..
s
s 45 line
KH
KL
s
H signal
L signal
Bad eqm bribe

Discussion and Conclusion
ExtensionsI Private information about returns
I If investors have a signal about R before investment, almost the same story.I If inspectors have a signal about each project, need to be able to convince
the investor that he needs to pay higher bribe.
I Honest inspectorsI Improve the participation constraint, might invite small businesses.I Will let go the big fish
I Complaining to superiorsI Lowers the participation constraint.I Does not have to lower the bribe.I Total welfare should increase...
I ...

Discussion and Conclusion
ExtensionsI Private information about returns
I If investors have a signal about R before investment, almost the same story.I If inspectors have a signal about each project, need to be able to convince
the investor that he needs to pay higher bribe.I Honest inspectors
I Improve the participation constraint, might invite small businesses.I Will let go the big fish
I Complaining to superiorsI Lowers the participation constraint.I Does not have to lower the bribe.I Total welfare should increase...
I ...

Discussion and Conclusion
ExtensionsI Private information about returns
I If investors have a signal about R before investment, almost the same story.I If inspectors have a signal about each project, need to be able to convince
the investor that he needs to pay higher bribe.I Honest inspectors
I Improve the participation constraint, might invite small businesses.I Will let go the big fish
I Complaining to superiorsI Lowers the participation constraint.I Does not have to lower the bribe.I Total welfare should increase...
I ...

Discussion and Conclusion
ExtensionsI Private information about returns
I If investors have a signal about R before investment, almost the same story.I If inspectors have a signal about each project, need to be able to convince
the investor that he needs to pay higher bribe.I Honest inspectors
I Improve the participation constraint, might invite small businesses.I Will let go the big fish
I Complaining to superiorsI Lowers the participation constraint.I Does not have to lower the bribe.I Total welfare should increase...
I ...

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)I There are some nontrivial implications for the size and efficiency of
government.I Not rentseeking.I No strategic complementarities.

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)I There are some nontrivial implications for the size and efficiency of
government.I Not rentseeking.I No strategic complementarities.

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)
I There are some nontrivial implications for the size and efficiency ofgovernment.
I Not rentseeking.I No strategic complementarities.

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)I There are some nontrivial implications for the size and efficiency of
government.
I Not rentseeking.I No strategic complementarities.

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)I There are some nontrivial implications for the size and efficiency of
government.I Not rentseeking.
I No strategic complementarities.

Discussion and Conclusion
ConclusionI Transfer bribery is not welfareneutral.
I It might improve welfare when outside wage is low.I It might put the economy in a bad equilibrium, where not all projects start
up.
I Decentralization creates an inefficiency: bribetakers cannot coordinate toswitch to a better equilibrium.
I Recovery rate higher bribe can go down (does not have to!)I There are some nontrivial implications for the size and efficiency of
government.I Not rentseeking.I No strategic complementarities.