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 you’re supposed to do for free.
Problems
I First one — obvious, ex-post 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 you’re supposed to do for free.
Problems
I First one — obvious,
ex-post 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 you’re supposed to do for free.
Problems
I First one — obvious, ex-post 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 you’re supposed to do for free.
Problems
I First one — obvious, ex-post 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 you’re supposed to do for free.
Problems
I First one — obvious, ex-post 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 you’re supposed to do for free.
Problems
I First one — obvious, ex-post 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 Rent-seeking 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 Rent-seeking 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 inspector’s problem is:
maxssP (RK > s).
I When K is trivialmax
ss P (R >
s
K)︸ ︷︷ ︸
1−FR(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 inspector’s problem is:
maxssP (RK > s).
I When K is trivialmax
ss P (R >
s
K)︸ ︷︷ ︸
1−FR(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 inspector’s problem is:
maxssP (RK > s).
I When K is trivialmax
ss P (R >
s
K)︸ ︷︷ ︸
1−FR(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 inspector’s problem is:
maxssP (RK > s).
I When K is trivialmax
ss P (R >
s
K)︸ ︷︷ ︸
1−FR(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(α), 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(α), 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(α), 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(α), 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(α), 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
( s
K2
)dFR
).
I Tobin’s 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
( s
K2
)dFR
).
I Tobin’s 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
( s
K2
)dFR
).
I Tobin’s 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
KHα
Inspector’schoice
KLα
s s∗1
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
Inspector’schoice
KLα
s s∗1
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
Inspector’schoice
KLα
s
s∗1
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
Inspector’schoice
KLα
s s∗1
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
Inspector’schoice
KLα
s s∗1
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
KLα
Inspector’schoice
ss∗2
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
KLα
Inspector’schoice
s
s∗2
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
KLα
Inspector’schoice
ss∗2
Eqm bribe
Predictions
The SquanderingI Consider a situation where both restricted and abundance equilibria exist.
s
s 45◦ line
KHα
KLα
Inspector’schoice
ss∗2
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
KHα
KLα
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
KHα
KLα
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
KHα
KLα
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 welfare-neutral.
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: bribe-takers 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 rent-seeking.I No strategic complementarities.
Discussion and Conclusion
ConclusionI Transfer bribery is not welfare-neutral.
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: bribe-takers 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 rent-seeking.I No strategic complementarities.
Discussion and Conclusion
ConclusionI Transfer bribery is not welfare-neutral.
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: bribe-takers 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 rent-seeking.I No strategic complementarities.
Discussion and Conclusion
ConclusionI Transfer bribery is not welfare-neutral.
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: bribe-takers 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 rent-seeking.I No strategic complementarities.
Discussion and Conclusion
ConclusionI Transfer bribery is not welfare-neutral.
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: bribe-takers 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 rent-seeking.
I No strategic complementarities.
Discussion and Conclusion
ConclusionI Transfer bribery is not welfare-neutral.
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: bribe-takers 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 rent-seeking.I No strategic complementarities.
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