Decentralized Bribery

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

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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, 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 youre 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 youre 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 youre 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 youre 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 youre 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 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 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.