## _wp04220 - References

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---

### Introduction and research focus
- Examines the design of targeted expenditure programs financed by the central government but implemented by local governments, viewing donor-recipient relations as principal-agent problems.
- Two central issues identified:
  - Which services to decentralize (e.g., health care or education).
  - What mechanisms provide subnational governments incentives to meet central government objectives efficiently.
- Emphasis: the second issue—how to induce local governments not to divert transfers and to implement programs effectively.
- Time-consistency problem: central government cannot credibly make future transfers conditional on past performance because undistributed funds may lapse and central threats to cut transfers are often not credible.
- Policy option studied: introduce competition among local governments across districts and across time (regional competition and intertemporal competition) to restore incentives while allowing the central government to distribute all available transfers.

### Stylized three-period model — setup and primitives
- Two districts: A and B; three periods.
- Central government decides funds available for targeted expenditure program in district j in period t: m_jt, subject to budget constraints.
- Local government in district j may divert r_jt from m_jt; only the local government observes r_jt.
- Local governments restricted to r_jt ∈ {0, F m_jt}.
- Output of targeted expenditure program: g_jt = (m_jt − r_jt) h_jt.
- Local effectiveness h_jt is a random variable uniform on (0,1) and not observed directly; g_jt is observable and used to infer h_jt.
- Central government’s inference of local effectiveness: h_jtc = g_jt / (m_jt − r*_jt) where r*_jt is incumbent's equilibrium action.
- Central government utility per period: u(g_At,g_Bt) = g_At + g_Bt.
- Local government utility equals funds diverted r_jt only.
- Discount factor assumed equal to one.
- Pure strategy equilibrium defined by strategies m*_jt and r*_jt for j = A,B and t = 1,2,3.

### Case 1 — Benchmark without competition among local governments
- Central government budget per district and per period: T; m_jt ≤ T; funds cannot be reallocated across districts or periods; undistributed funds lapse.
- Equilibrium characterization:
  - m*_jt = T for all j and all t.
  - r*_jt = F T for all j and all t.
  - g*_jt = T (1 − F) h_jt for all j and all t.
- Expected output of the program: E[g*_jt] = T (1 − F)/2.
- Key implication: central government cannot effectively condition future transfers on current performance; local officials divert maximum feasible amount leading to low program success when F is large.

### Case 2 — Regional (horizontal) competition
- Central government budget per period equals 2T and can allocate between districts: m_At + m_Bt ≤ 2T.
- Timing and incumbency: local officials in periods two and three are last-period incumbents and thus have no incentive to support central interests; incentives to divert in later periods reduce to levels identified for period one.
- Period allocations:
  - If expected effectiveness equal in a period, each district receives T: m*_j1 = m*_j3 = T.
  - For period two: central government assigns 2T to the district it believes more effective: m*_A2 = 2T, T, or 0 depending on beliefs; m*_B2 = 2T − m*_A2.
  - r*_j2 = F m_j2 and r*_j3 = F T for all j.
- Propositions and equilibrium results:
  - Proposition 2: For any district j: m*_j1 = m*_j3 = T; r*_j2 = F m_j2; r*_j3 = F T; m*_A2 = 2T if A believed more effective, m*_A2 = T if equal, m*_A2 = 0 if B believed more effective; m*_B2 = 2T − m*_A2.
  - Proposition 3: r*_A1 = 0 and r*_B1 = 0 cannot be part of the equilibrium with regional competition.
  - Proposition 4: In the unique pure strategy equilibrium with regional competition r*_j1 = F T.
- Key implication: regional competition leads central government to concentrate period-two funds on the perceived better district, but regional competition alone does not eliminate diversion in period one; local governments still choose r*_j1 = F T.

### Case 3 — Intertemporal competition (reallocating funds across periods)
- In period two central government has budget 4T and can redistribute funds across periods two and three between districts (funds originally assigned to periods two and three can be reallocated across these periods and across districts).
- Introduces competition across time (incumbents in earlier periods compete with future local governments for future transfers).
- With intertemporal competition, it becomes possible to have equilibria with zero diversion in period one.
- Key propositions with numeric conditions:
  - Proposition 5: Let us assume that F > (1 − 1/3.5). Then, there is a pure-strategy equilibrium in which r*_A1 = r*_B1 = 0.
    - Proof sketch: If r_j1 = 0, expected utility of incumbent equals probability of receiving funds next period (3/8) times period-two utility (4 F T), yielding expected utility 3 F T/2. If r_j1 = F T, expected utility equals F T [1 + 3(1 − F)^2/2]. The no-diversion strategy is not a profitable deviation if F > (1 − 1/3.5).
  - Proposition 6: There is also a pure-strategy equilibrium in which r*_j1 = F T.
- Key implication: intertemporal competition can reduce diversion in period one (r*_j1 = 0) under the numeric condition F > (1 − 1/3.5), but multiple equilibrium outcomes exist (including r*_j1 = F T).

### Comparative insights and policy relevance
- Without any competition, central transfers are fully distributed but program outputs are low: E[g*_jt] = T (1 − F)/2.
- Regional competition improves allocation in period two (concentrating resources on better-performing districts) but does not eliminate first-period diversion (r*_j1 remains F T).
- Intertemporal competition (allowing reallocation of funds across periods) complements regional competition and can, under specific parameter conditions (F > (1 − 1/3.5)), induce incumbents to fully allocate transfers to the program in period one (r*_j1 = 0).
- Multiple equilibria exist under intertemporal competition: both low-diversion and high-diversion equilibria can occur; the mechanism can be crucial when the central government is not indifferent among helping different local governments.

### Equilibrium implications and multi-period extensions
- In the model, setting r_j1 = 0 can never be a profitable deviation and this is an equilibrium (the expected utility would be less than 4 F T with r_j1 = 0).
- Comparison of equilibria:
  - An equilibrium with r*_j1 = 0 can be sustained for a larger set of parameter values in a model with more periods.
  - An equilibrium with r*_j1 = F T is sustained for a smaller set of parameter values as the number of periods increases.
- Mechanism driving the change with more periods:
  - A local government’s benefits from being believed to be more effective are higher if it can participate in the program longer, and/or the central government can combine funds from more periods.
  - If local governments can choose r_j1 from a continuum, an equilibrium with r*_j1 < F T is likely to be the outcome.

### Policy extensions: the budgeting framework
- Core problem addressed:
  - Targeted expenditure programs financed by the central government and implemented by local governments may fail because local officials may not share center objectives — a time-consistency problem.
- Constraints in common settings:
  - Single-period budget frameworks, common in many developing countries, where undistributed funds are not available for future transfers, limit enforcement of conditional transfers.
  - Horizontal (regional) competition helps but is not sufficient to eliminate incentives to divert central funds.
- Proposed institutional responses:
  - Multi-year budget framework, including multi-year appropriations, would greatly facilitate achievement of central government objectives by allowing intertemporal competition across lower level jurisdictions.
  - Intertemporal budgeting and transfer frameworks are needed because local governments build reputations around program success while in charge; the central government need not transfer funds across distant periods—only that local officials prefer to receive funds in an earlier period.
  - Actionable contracts between the center and local governments would avoid manipulation of program funding for political advantage. Example contractual provision in the simple framework:
    - A local government would receive funds in the second period if and only if in the first period the program in this district produces better results than in the competing district and the local government performs better than an average local government.
  - Contracts should specify identifiable outputs where possible (even if outcomes are hard to specify or monitor). Illustrative monitoring approach:
    - If the transfer is designed to provide education to children until age 12, information systems could be established to monitor absenteeism, or children excluded from school.
    - Over time, improved information systems could permit more sophisticated monitoring of outcomes, including quality of education.

### Conclusions and avenues for further research
- Summary findings:
  - Regional competition helps but is insufficient to prevent diversion of central funds.
  - Intertemporal competition is important and can improve the performance of targeted expenditure programs, especially where regional competition is not possible.
- Institutional implications:
  - A multi-year budget framework appears desirable to operationalize the model’s mechanisms.
  - Simple and actionable contracts between the center and local governments would be helpful.
- Model limitations and extensions:
  - The paper uses a highly stylized three-period model to highlight incentives.
  - Extensions that would deepen understanding include:
    - Frameworks with more periods.
    - Models where reelection probabilities are different from zero and may be affected by program success.
    - Incorporating local government reputation to design optimal explicit contracts when local governments can commit.

*Source — _wp04220 - References*

### References..............................................................................................................

### _wp04220 - References

### Introduction and research focus
- Examines the design of targeted expenditure programs financed by the central government but implemented by local governments, viewing donor-recipient relations as principal-agent problems.
- Two central issues identified:
  - Which services to decentralize (e.g., health care or education).
  - What mechanisms provide subnational governments incentives to meet central government objectives efficiently.
- Emphasis of this paper: the second issue—how to induce local governments not to divert transfers and to implement programs effectively.
- Time-consistency problem: central government cannot credibly make future transfers conditional on past performance because undistributed funds may lapse and central threats to cut transfers are often not credible.
- Policy option studied: introduce competition among local governments across districts and across time (regional competition and intertemporal competition) to restore incentives while allowing the central government to distribute all available transfers.

### Stylized three-period model — setup and primitives
- Two districts: A and B; three periods.
- Central government decides funds available for targeted expenditure program in district j in period t: m_jt, subject to budget constraints.
- Local government in district j may divert r_jt from m_jt; only the local government observes r_jt.
- Local governments restricted to r_jt ∈ {0, F m_jt}, i.e., either use all funds or divert fraction F.
- Output of targeted expenditure program: g_jt = (m_jt − r_jt) h_jt.
- Local effectiveness h_jt is a random variable uniform on (0,1) and not observed directly; g_jt is observable and used to infer h_jt.
- Central government’s inference of local effectiveness: h_jtc = g_jt / (m_jt − r*_jt) where r*_jt is incumbent's equilibrium action.
- Central government utility per period: u(g_At,g_Bt) = g_At + g_Bt.
- Local government utility equals funds diverted r_jt only.
- Discount factor assumed equal to one.
- Pure strategy equilibrium defined by strategies m*_jt and r*_jt for j = A,B and t = 1,2,3.

### Case 1 — Benchmark without competition among local governments
- Budget constraint: for each district and each period central government has budget T; m_jt ≤ T; funds cannot be reallocated across districts or periods; undistributed funds lapse.
- Equilibrium characterization:
  - m*_jt = T for all j and all t.
  - r*_jt = F T for all j and all t.
  - g*_jt = T (1 − F) h_jt for all j and all t.
- Expected output of the program: E[g*_jt] = T (1 − F)/2.
- Key implication: central government cannot effectively condition future transfers on current performance; local officials divert maximum feasible amount leading to low program success when F is large.

### Case 2 — Regional (horizontal) competition
- Central government budget per period equals 2T and can allocate between districts: m_At + m_Bt ≤ 2T.
- Timing and incumbency: local officials in periods two and three are last-period incumbents and thus have no incentive to support central interests; incentives to divert in later periods reduce to levels identified for period one.
- Period allocations:
  - If expected effectiveness equal in a period, each district receives T: m*_j1 = m*_j3 = T.
  - For period two: central government assigns 2T to the district it believes more effective: m*_A2 = 2T, T, or 0 depending on beliefs; m*_B2 = 2T − m*_A2.
  - r*_j2 = F m_j2 and r*_j3 = F T for all j.
- Propositions and equilibrium results:
  - Proposition 2: For any district j: m*_j1 = m*_j3 = T; r*_j2 = F m_j2; r*_j3 = F T; m*_A2 = 2T if A believed more effective, m*_A2 = T if equal, m*_A2 = 0 if B believed more effective; m*_B2 = 2T − m*_A2.
  - Proposition 3: r*_A1 = 0 and r*_B1 = 0 cannot be part of the equilibrium with regional competition (i.e., neither district will choose zero diversion in period one).
  - Proposition 4: In the unique pure strategy equilibrium with regional competition r*_j1 = F T.
- Key implication: regional competition leads central government to concentrate period-two funds on the perceived better district, but regional competition alone does not eliminate diversion in period one; local governments still choose r*_j1 = F T.

### Case 3 — Intertemporal competition (reallocating funds across periods)
- In period two central government has budget 4T and can redistribute funds across periods two and three between districts (funds originally assigned to periods two and three can be reallocated across these periods and across districts).
- Introduces competition across time (incumbents in earlier periods compete with future local governments for future transfers).
- With intertemporal competition, it becomes possible to have equilibria with zero diversion in period one.
- Key propositions with numeric conditions:
  - Proposition 5: Let us assume that F > (1 − 1/3.5). Then, there is a pure-strategy equilibrium in which r*_A1 = r*_B1 = 0.
    - Proof sketch (as presented): If r_j1 = 0, expected utility of incumbent equals probability of receiving funds next period (3/8) times period-two utility (4 F T), yielding expected utility 3 F T/2. If r_j1 = F T, expected utility equals F T [1 + 3(1 − F)^2/2]. The no-diversion strategy is not a profitable deviation if F > (1 − 1/3.5).
  - Proposition 6: There is also a pure-strategy equilibrium in which r*_j1 = F T.
- Key implication: intertemporal competition can reduce diversion in period one (r*_j1 = 0) under the numeric condition F > (1 − 1/3.5), but multiple equilibrium outcomes exist (including r*_j1 = F T).

### Comparative insights and policy relevance
- Without any competition, central transfers are fully distributed but program outputs are low: E[g*_jt] = T (1 − F)/2.
- Regional competition improves allocation in period two (concentrating resources on better-performing districts) but does not eliminate first-period diversion (r*_j1 remains F T).
- Intertemporal competition (allowing reallocation of funds across periods) complements regional competition and can, under specific parameter conditions (F > (1 − 1/3.5)), induce incumbents to fully allocate transfers to the program in period one (r*_j1 = 0).
- Multiple equilibria exist under intertemporal competition: both low-diversion and high-diversion equilibria can occur; the mechanism can be crucial when the central government is not indifferent among helping different local governments.

*Italic: Source — _wp04220 - References*

### 4.5 FT. Therefore, r

### _wp04220 - 4.5 FT. Therefore, r

### Equilibrium implications and multi-period extensions
- In the model, setting r j1 = 0 can never be a profitable deviation and this is an equilibrium (the expected utility would be less than 4FT with r j1 = 0).
- Comparison of equilibria:
  - An equilibrium with r* j1 = 0 can be sustained for a larger set of parameter values in a model with more periods.
  - An equilibrium with r* j1 = FT is sustained for a smaller set of parameter values as the number of periods increases.
- Mechanism driving the change with more periods:
  - A local government’s benefits from being believed to be more effective are higher if it can participate in the program longer, and/or the central government can combine funds from more periods.
  - If local governments can choose r j1 from a continuum, an equilibrium with r* j1 < FT is likely to be the outcome.

### Policy extensions: the budgeting framework
- Core problem addressed:
  - Targeted expenditure programs financed by the central government and implemented by local governments may fail because local officials may not share center objectives — a time-consistency problem.
- Constraints in common settings:
  - Single-period budget frameworks, common in many developing countries, where undistributed funds are not available for future transfers, limit enforcement of conditional transfers.
  - Horizontal (regional) competition helps but is not sufficient to eliminate incentives to divert central funds.
- Proposed institutional responses:
  - Multi-year budget framework, including multi-year appropriations, would greatly facilitate achievement of central government objectives by allowing intertemporal competition across lower level jurisdictions.
  - Intertemporal budgeting and transfer frameworks are needed because local governments build reputations around program success while in charge; the central government need not transfer funds across distant periods—only that local officials prefer to receive funds in an earlier period.
  - Actionable contracts between the center and local governments would avoid manipulation of program funding for political advantage. Example contractual provision in the simple framework:
    - A local government would receive funds in the second period if and only if in the first period the program in this district produces better results than in the competing district and the local government performs better than an average local government.
  - Contracts should specify identifiable outputs where possible (even if outcomes are hard to specify or monitor). Illustrative monitoring approach:
    - If the transfer is designed to provide education to children until age 12, information systems could be established to monitor absenteeism, or children excluded from school.
    - Over time, improved information systems could permit more sophisticated monitoring of outcomes, including quality of education.

### Conclusions and avenues for further research
- Summary findings:
  - Regional competition helps but is insufficient to prevent diversion of central funds.
  - Intertemporal competition is important and can improve the performance of targeted expenditure programs, especially where regional competition is not possible.
- Institutional implications:
  - A multi-year budget framework appears desirable to operationalize the model’s mechanisms.
  - Simple and actionable contracts between the center and local governments would be helpful.
- Model limitations and extensions:
  - The paper uses a highly stylized three-period model to highlight incentives.
  - Extensions that would deepen understanding include:
    - Frameworks with more periods.
    - Models where reelection probabilities are different from zero and may be affected by program success.
    - Incorporating local government reputation to design optimal explicit contracts when local governments can commit.

*Source: _wp04220 - 4.5 FT. Therefore, r* j1 (extracted content).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04220.pdf_