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.