## wp17195

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---

### Introduction and motivation
- Over the past decade, the number of countries with independent fiscal councils (IFCs) has more than tripled, to almost 40 (end-2015).
- IFCs act as public finance watchdogs that improve the quality of public debate but do not control fiscal policy instruments.
- Two primary deficit-bias sources in the model:
  - Partisan/myopic bias (Alesina and Tabellini (1990)): incumbents spend more now because they may be voted out of office.
  - Opportunistic signaling bias (Rogoff and Sibert (1988)): incumbents overspend to appear more competent to voters.
- IFCs are modeled as increasing precision of a noisy public signal s1 about incumbent competence (increase in hμ, reduction in σμ^2), thereby potentially reducing the opportunistic debt bias.

### Model structure and first-best benchmark
- Two-period political-economy framework with incumbent P in period 1 and an election at the start of period 2 between P and challenger Q.
- Voter heterogeneity and primitives:
  - Competence η: stochastic, not directly observed; prior ηPQ ~ N(η̄, ση0^2) with η̄ > 0 and ση0^2 > 0.
  - Congruence Δ: orthogonal to competence; voters prefer P if ηP − ηQ ≥ +Δ (decision rule uses Δ).
- Resource constraint and shocks:
  - Period-t public consumption gt (t=1,2) determined by resource allocation including debt d with d ≤ D; independent shock ε ~ N(0, σε0^2).
- Information:
  - Voters observe g1 and noisy signal s1 = η1 + μ with μ ~ N(0, σμ^2). A fiscal council raises hμ (precision).
- Social planner (first-best):
  - Planner reappoints incumbent if η1 ≥ η̄ + Δ.
  - First-best debt dFB satisfies first-order condition (4); selection effects do not alter dFB due to quasi-linearity of felicity u.

### Political equilibrium and equilibrium debt de
- Voters form posterior beliefs about incumbent competence using g1 and s1; posterior mean given by equation (5).
- Posterior variance σh^2 (equation (6)) increases with hε and hμ and decreases with hη.
- Incumbent re-election probability p(d) = 1 − Φ(Γ(d,d;h)) with Γ defined in (9); higher d raises observed g1 and can raise p(d).
- Incumbent chooses d to maximize electoral prospects and private utility; equilibrium de characterized by first-order condition (13).
- Equilibrium debt de is always above first-best dFB because of:
  - Partisan/myopic bias (probability of re-election < 1).
  - Opportunistic signaling motive (increasing d to improve perceived competence).

### Effect of increased transparency (IFC role) — comparative statics and propositions
- IFC introduction modeled as marginal increase in hμ.
- Comparative statics (equation (15)): sign of de/dhμ is opposite to sign of H(Δ) defined in (15); H(Δ) aggregates partisan and opportunistic channels.
- Clear limiting cases (Proposition 1):
  - If hε → 0 (g1 very noisy so qh → 0, opportunistic motive suppressed):
    - Increased hμ raises equilibrium debt if Δ < 0 (incumbent electoral advantage).
    - Increased hμ lowers equilibrium debt if Δ > 0 (incumbent electoral disadvantage).
    - If Δ = 0, equilibrium debt is unaffected.
- Ambiguity in general case:
  - Two opposing forces when hμ increases:
    - Erosion of debt’s signaling effectiveness (qh falls) → weakens opportunistic motive.
    - Greater informativeness (σh^2 rises) → increases marginal impact of perception changes on re-election chances (φ/σ terms), potentially strengthening opportunistic motive.
  - Condition under which greater transparency mitigates opportunistic motive (equation (16)):
    - (2/h)(hε + hμ)/hh + Δ ≤ Δ̄ (threshold Δ̄ defined in text); if Δ is sufficiently limited, increased transparency lowers opportunistic incentive; otherwise it can strengthen it.

- Marginal-impact result (Proposition 2):
  - Abstracting from partisan motive, a marginal increase in hμ lowers equilibrium debt if Δ < Δ̄, increases equilibrium debt if Δ > Δ̄.

- Joint behavior of partisan and opportunistic motives (Proposition 3):
  - There exist two thresholds (L_{K,hε}, H_{K,hε}) such that:
    - (I.a) if Δ < L_{K,hε} equilibrium debt increases with hμ,
    - (I.b) if L_{K,hε} < Δ < H_{K,hε} equilibrium debt decreases with hμ,
    - (I.c) if Δ > H_{K,hε} equilibrium debt increases with hμ.
  - Threshold properties:
    - L_{K,hε} is decreasing in both K and hε with lim_{K→∞} L_{K,hε} = −Δ and lim_{hε→0} L_{K,hε} = 0.
    - H_{K,hε} is decreasing in K and decreasing in hε for hε sufficiently small with lim_{K→∞} H_{K,hε} = Δ and lim_{hε→0} H_{K,hε} = ∞.
  - Intuition: IFCs can increase equilibrium debt only when congruence Δ gives a large electoral advantage; when competence matters sufficiently (including Δ = 0), IFCs mitigate debt bias by weakening opportunistic incentives.

### Incumbent’s and voters’ preferences over IFCs
- Incumbent utility U (equation (17)); marginal utility ∂U/∂hμ (equation (18)) is ambiguous due to three effects:
  - Effect on equilibrium public consumption: positive if equilibrium debt falls.
  - Effect on re-election chances: negative if transparency reduces incumbent’s electoral advantage.
  - Selection effect: conditional on re-election, greater transparency raises average competence and is unambiguously positive.
- Incumbent willingness (Proposition 4):
  - (a) If 0 ≤ Δ ≤ H_{K,hε} incumbent is better off with an IFC.
  - (b) If Δ ≤ L_{K,hε} and K sufficiently large, incumbent is worse off with an IFC.
  - (c) Remaining parameter regions: effect ambiguous (characterized by equation (19)).
  - Special case (no opportunistic motive): with K large, introducing an IFC makes incumbent worse off if Δ < 0 and better off if Δ > 0.
- Voters’ (social) welfare SU (equation (20)):
  - Voters value selection effects and impact on equilibrium debt; re-election motives absent.
  - Marginal social welfare ∂SU/∂hμ (equation (21)): voters prefer an IFC if increased transparency lowers equilibrium debt; ambiguous otherwise.
- Voter vs incumbent (Proposition 5):
  - (a) If L_{K,hε} ≤ Δ ≤ H_{K,hε}, voters are better off with an IFC.
  - (b) If Δ < L_{K,hε} or Δ > H_{K,hε}, voters are worse off with an IFC for K sufficiently large.
  - Potential mismatches:
    - Voters may favor an IFC while incumbent opposes it when K large and Δ near L_{K,hε}.
    - Incumbent may favor an IFC while voters oppose it when K large and Δ slightly above H_{K,hε}.

### Additional information channels (ρ, γ, hτ) and robustness
- Alternative channels modeled:
  - A signal s2 on debt: s2 = d + τ with τ ~ N(0, στ^2), precision hτ = 1/στ^2.
  - Probability ρ of observing true debt d.
  - Probability γ of observing true competence η1.
- Comparative statics results:
  - hτ: "An increase in hτ has no impact on equilibrium debt ed, PU and SU." Rationale: in pure-strategy equilibrium s2 is ignored.
  - ρ (Proposition 7): An increase in ρ necessarily lowers equilibrium debt ed and raises both incumbent utility PU and social welfare SU. If ρ → 1 opportunistic debt bias disappears.
  - γ (Proposition 8): If Δ > 0 an increase in γ necessarily lowers ed and raises PU and SU. If Δ < 0 the effect of γ on ed, PU and SU is ambiguous; for ρ sufficiently close to one (opportunistic motive weak) ed increases with γ, PU decreases with γ for K sufficiently large, and SU decreases with γ if first-period felicity concavity is sufficiently weak.
- Signaling interpretation and literature links:
  - Relaxing assumption that government lacks private information on competence converts setting into signaling game; literature yields mixed implications on debt behavior depending on informational structure and refinements.

### Empirical patterns and stylized facts
- End-2015: close to 40 IFCs fitting IMF definition.
- IFC remits and behaviors (summary of figures):
  - All IFCs mandated to produce positive analyses of fiscal policy.
  - Large majority assess long-term sustainability and prepare/assess macro and budgetary forecasts.
  - More than three-quarters of councils established after 2005 monitor compliance with fiscal rules.
  - More than half provide recommendations; some councils explicitly banned from recommending.
  - Relatively few perform costing of policy measures.
- Channels of influence:
  - Overwhelmingly indirect via public reports and media.
  - Slightly less than half hold formal consultations/hearings with policymakers.
  - Forecasts by IFCs rarely binding; in ~20 percent of cases, government must publicly justify not using IFC forecasts/recommendations (“comply-or-explain”).
- Guarantees of independence:
  - Most councils have formal safeguards: prohibition of political interference; appointment/dismissal rules; funding safeguards (separate budget chapter, multiyear appropriations, extra-budgetary transfers).
- Empirical regression (panel, EU countries, 1999–2016):
  - Dependent variable: ABS(PB_{i,t-1,t} − PB_{i,t+1,t}) (absolute primary balance forecast error).
  - Regressor: D_IFC lagged one year.
  - Fixed-effect coefficient β1 = −0.68 with robust standard error 0.17.
    - Interpretation: presence of an IFC reduces the absolute forecast error in the primary balance by 0.7 percentage points of GDP.
  - Controls: fiscal rules index FR_{i,t-1}, lagged output gap Y_{i,t-1}, lagged debt-to-GDP D_{i,t-1}, country and year fixed effects.
- Stylized facts consistent with theory:
  - Stylized fact 1: Most IFCs were introduced in countries where one or more fiscal rules already existed (complementarity).
  - Stylized fact 2: IFCs tend to emerge in systems with weaker executive dominance and stronger checks and balances.
- Empirical proxies (panel averages; country samples and differences preserved exactly):
  - Sample of 23 OECD countries
    - No IFC: Polariz = 1.07; Maj = 0.57; Checks = 4.04
    - IFC: Polariz = 1.71; Maj = 0.54; Checks = 4.77
    - Difference: Polariz = 0.64***; Maj = -0.033**; Checks = 0.74***
  - Sample of 58 OECD and non-OECD countries
    - No IFC: Polariz = 0.71; Maj = 0.63; Checks = 3.49
    - IFC: Polariz = 1.51; Maj = 0.54; Checks = 4.57
    - Difference: Polariz = 0.80***; Maj = -0.088***; Checks = 1.08***

### Policy implications, normative insights and design recommendations
- IFCs can increase social welfare by improving voter information and reducing opportunistic spending, but effects are context-dependent:
  - If increased transparency lowers equilibrium debt, voters unambiguously prefer an IFC.
  - If increased transparency raises equilibrium debt (possible when Δ confers large electoral advantage), IFCs can harm voters and incumbents.
- Recommended institutional design lessons:
  - Pair IFC introduction with formal fiscal rules/restraints to contain potential adverse effects of transparency on debt.
  - Give IFCs broad remit: analyse long-term public debt sustainability and monitor fiscal performance against numerical fiscal rules to reduce collateral damage.
  - Ensure strict guarantees of independence, including budgetary safeguards, to enhance IFC resilience.
  - Tailor IFC institutional models to country-specific political characteristics to build political consensus; externally imposed IFCs are vulnerable.
- Research priorities:
  - Extend model to allow government superior private information about its competence (signaling via debt).
  - Formally study complementarities between IFCs and fiscal rules.

### Appendix: proof highlights and technical properties
- Second-order condition: condition (14) suffices for s.o.c. of incumbent maximization given f.o.c. (11); relies on u'' < 0 and hazard-rate properties of standard normal φ/ (1−Φ).
- Roots and thresholds (A.2 proof of Proposition 3):
  - H(Δ) = (φ/σ_h)·G(Δ) with G(Δ) a cubic c1·Δ^3 + c2·Δ^2 − c3·Δ + c4 with 0 < ci; G has three real roots LΔ < 0, HΔ > 0, and a large negative root.
  - Dependence of roots on K and hε characterized: increasing K decreases roots; limits given (e.g., lim_{K→∞} L_{K,hε} = −Δ).
- Characterization of disagreement regions (A.3):
  - Parameter regions exist where society favors an IFC while incumbent opposes, and vice versa; analytic inequalities identify these regions.
- Extended model (ρ, γ) proofs (A.4):
  - First-order condition (22) derived from weighted-information cases (probabilities γ, (1−γ)ρ, (1−γ)(1−ρ)).
  - Proposition 7: ∂ed/∂ρ < 0 and ∂PU/∂ρ > 0 and ∂SU/∂ρ > 0.
  - Proposition 8: If Δ > 0, ∂ed/∂γ < 0 and ∂PU/∂γ, ∂SU/∂γ > 0; if Δ < 0 effects are ambiguous and depend on ρ and K.

*Source: Appendix A and related sections of wp17195 (IMF Working Paper).*

### Box 15867, 1001 NJ Amsterdam, The Netherlands; phone: +31.20.5255241; r.sloof@uva.nl.

### wp17195 - Box 15867, 1001 NJ Amsterdam, The Netherlands; phone: +31.20.5255241; r.sloof@uva.nl.

### Prefatory notice
- "This Working Paper should not be reported as representing the views of the IMF."
- "The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy."
- "Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate."

### Table of contents (major themes and sections)
- I. Introduction ............................................................................................................................3
- II. Independent Fiscal Councils on the Rise ..............................................................................7
- III. The Model ..........................................................................................................................11
- IV. First-Best Benchmark: The Social Planner Solution .........................................................14
- V. Debt Choice in the Political Game ......................................................................................15
  - A. Belief Formation and Updating...............................................................................15
  - B. Election Outcome ....................................................................................................17
  - C. Equilibrium Public Debt..........................................................................................18
- VI. More Transparency? The Effect of a Fiscal Council on Equilibrium Debt .......................20
- VII. Who Wants a Fiscal Council? The Incumbent’s Case .....................................................24
- VIII. Who Wants a Fiscal Council? The Voters’ Case ............................................................26
- IX. Other Manifestations of Fiscal Transparency ....................................................................29
- X. Politics and the Emergence of IFCs: Are Stylized Facts Consistent with Theory? ............33
- XI. Conclusion .........................................................................................................................35

### Analytical focus areas (inferred from section headings)
- The emergence, remit, and influence channels of Independent Fiscal Councils (IFCs).
- A formal model characterizing political debt choice, belief formation, election outcomes, and equilibrium public debt.
- Comparison to a first-best social planner benchmark.
- Analysis of how increased fiscal transparency and introduction of an IFC affect equilibrium debt, incumbents’ incentives, and voter welfare.
- Examination of other manifestations of fiscal transparency and empirical consistency with theory.

### Figures and tables listed in the unit
- Table 1: Panel Averages of Variables Capturing Polarization Elements...........................................34
- Figure 1. Number of Independent Fiscal Councils in the World ..........................................................8
- Figure 2. The Remit of Fiscal Councils ................................................................................................9
- Figure 3. Channels of Influence on the Budget Process........................................................................9
- Figure 4. Guarantees of Independence ................................................................................................10
- Figure 5: Debt, Transparency and Electoral Advantage .....................................................................23
- Figure 6. Introducing an IFC: Effect on Incumbent’s Utility..............................................................26
- Figure 7. Introducing an IFC: Effects on Social Welfare vs. Incumbent’s Utility..............................28

### Supplementary material
- Appendix

*Source: wp17195 - Box 15867, 1001 NJ Amsterdam, The Netherlands; phone: +31.20.5255241; r.sloof@uva.nl.*

### Appendix A: Additional proofs ..........................................................................................

### wp17195 - Appendix A: Additional proofs

### Introduction and motivation
- Over the past decade, the number of countries with independent fiscal councils (IFCs) has more than tripled, to almost 40.
- IFCs do not control fiscal policy instruments but act as public finance watchdogs expected to improve the quality of the public debate on fiscal policy.
- Two primary sources of deficit bias in the model:
  - Partisan/myopic bias (Alesina and Tabellini (1990)): incumbents spend more now because they may be voted out of office.
  - Opportunistic signaling bias (Rogoff and Sibert (1988)): incumbents overspend to appear more competent to voters.
- IFCs improve fiscal transparency by reducing noise in voters’ signals about incumbent competence, thereby potentially alleviating the opportunistic debt bias.

### Model setup (two-period political-economy framework)
- Two political parties: incumbent P and challenger Q. P holds office in period 1; election at start of period 2.
- Voters evaluate parties on:
  - Competence (η): stochastic, not directly observed; transforms resources into public goods.
  - Congruence (Δ): orthogonal to competence; captures ideology/taste alignment. If PQ ηη ≥ +Δ, voters prefer P.
  - Prior distribution: ηPQ ~ N(η̄, ση0^2) with η̄ > 0 and ση0^2 > 0.
- Resource constraint and shocks:
  - Period-t public consumption gt (t=1,2) given by equation (1) (resource allocation includes debt d).
  - Independent shock ε ~ N(0, σε0^2).
  - Net public debt in period 1 is d, with d ≤ D.
- Information and signals:
  - Voters observe g1 and a noisy public signal s1 about competence: s1 = η1 + μ with μ ~ N(0, σμ^2).
  - A fiscal council is modeled as an increase in the precision of s1 (increase in hμ), i.e., a reduction in σμ^2.
- Utility:
  - Time-separable, quasi-linear felicity u(g): u' > 0, u'' < 0 (concave in period 1, linear in period 2).
  - Parties value being in office (K). If not elected, party receives utility K− with KDη > −.

### Key analytical benchmarks and equilibrium characterization
- Social planner (first-best):
  - Planner reappoints incumbent if η1 ≥ η̄ + Δ.
  - First-best debt dFB characterized by first-order condition (4): E'1 u'(η, ε) + ... = 1 (selection effects do not affect dFB due to quasi-linearity).
- Political equilibrium:
  - Voters form posterior beliefs about incumbent competence using g1 and s1; posterior mean given by equation (5).
  - Voter’s posterior variance measure σh^2 (equation (6)) increases with hε and hμ and decreases with hη.
  - Incumbent’s re-election probability p(d) = 1 − Φ(Γ(d,d;h)) with Γ defined in (9); higher d raises re-election probability by increasing observed g1.
  - Incumbent chooses debt taking voters’ beliefs as given; first-order condition for equilibrium debt de (equation (13)):
    - Left-hand side: E'1 u'(η, ε) + ... scaled by σh
    - Right-hand side: −Φ(Δ) − qh⋅Δ⋅(...) + Ke + ... (captures partisan and opportunistic motives).
  - Equilibrium debt de is always above first-best dFB due to:
    - Partisan/myopic bias (probability of re-election < 1).
    - Opportunistic signaling motive (raising d to improve perceived competence).

### Effect of increased transparency (role of an IFC)
- Introduction of a fiscal council modeled as an increase in hμ (higher precision of s1).
- Comparative statics (equation (15)):
  - de/dhμ has opposite sign to H(Δ) defined in (15).
  - H(Δ) captures:
    - Effect of increased precision on re-election odds (partisan effect via Δ).
    - Effect on opportunistic incentives (via qh and how debt changes voters’ perception).
- Clear cases and Proposition 1:
  - If hε → 0 (g1 very noisy; suppresses opportunistic motive so qh → 0):
    - An increase in hμ raises equilibrium debt if Δ < 0 (incumbent has electoral advantage).
    - An increase in hμ lowers equilibrium debt if Δ > 0 (incumbent has electoral disadvantage).
    - If Δ = 0, equilibrium debt is unaffected.
  - Intuition: when opportunistic motive is absent, increased precision simply weakens incumbent’s ability to exploit congruence advantage (if any), changing myopia incentives accordingly.
- Ambiguous general case:
  - Two opposing forces when increasing hμ:
    - Erosion of debt’s effectiveness as a signal (qh falls) → weakens opportunistic motive.
    - Greater informativeness (σh^2 rises) → increases marginal impact of perception changes on re-election chances (φ/σ terms), potentially strengthening opportunistic motive.
  - Condition under which greater transparency mitigates opportunistic motive (equation (16)):
    - (2/h)(hε + hμ)/hh + Δ ≤ Δ̄, where Δ̄ defined in text (preserves exact formulation as in source).
    - If Δ is sufficiently limited (congruence advantage small), increased transparency lowers opportunistic incentive; otherwise it can strengthen it.

### Empirical patterns and evidence reported
- At end-2015, close to 40 IFCs fitting the IMF definition were in activity (three-fold increase in less than 10 years).
- IFC remits (selected summary from Figures discussed):
  - All IFCs mandated to produce positive analyses of fiscal policy.
  - Large majority assess long-term sustainability and prepare/assess macro and budgetary forecasts.
  - More than three-quarters of councils established after 2005 monitor compliance with fiscal policy rules.
  - More than half provide recommendations; some are explicitly banned from doing so.
  - Relatively few perform costing of policy measures.
- Channels of influence:
  - Overwhelmingly indirect via public reports and media impact.
  - Slightly less than half hold formal consultations/hearings with policymakers.
  - Forecasts by IFCs are rarely binding; in ~20 percent of cases, government must publicly justify not using IFC forecasts/recommendations (“comply-or-explain”).
- Guarantees of independence:
  - Most councils benefit from formal guarantees: prohibition of political interference, appointment/dismissal rules, funding safeguards (separate budget chapter, multiyear appropriations, extra-budgetary transfers).
- Empirical regression (panel of EU countries, 1999–2016):
  - Dependent variable: ABS(PB_{i,t-1,t} − PB_{i,t+1,t}) (absolute primary balance forecast error).
  - Regressor D_IFC (dummy for presence of IFC lagged one year).
  - Fixed-effect regression yields coefficient β1 = −0.68 with robust standard error 0.17.
    - Interpretation in text: presence of an IFC reduces the absolute forecast error in the primary balance by 0.7 percentage points of GDP.
  - Controls included: fiscal rules index FR_{i,t-1}, lagged output gap Y_{i,t-1}, lagged debt-to-GDP D_{i,t-1}, country and year fixed effects.

### Policy implications and normative insights
- An IFC can increase social welfare by improving the precision of voters’ information about competence, thereby reducing futile opportunistic spending.
- However, when voters care about both competence and congruence, an IFC can have ambiguous effects:
  - For some ranges of Δ (electoral advantage), introducing an IFC lowers equilibrium debt; for other ranges it can raise debt.
  - Voters’ support for an IFC depends on its effect on debt and on average competence of re-elected incumbents.
  - Incumbents’ preferences may diverge from society’s; a moderately popular incumbent may prefer not to install an IFC despite social gains.
- Complementarity with formal fiscal restraints:
  - The introduction of an IFC should often be paired with formal fiscal rules/restraints to prevent potential adverse effects of greater transparency on public debt in certain political environments.
- Positive interpretation:
  - The model helps explain cross-country heterogeneity in IFC adoption, weak institutional design, and episodes of government–IFC tension as political conditions change (e.g., when congruence eclipses competence).
- Normative caution:
  - Greater transparency is not a universal panacea; its net effect depends on political context (role of congruence Δ, informativeness parameters hε, hμ, hη).

*Italicized attribution: Source content from "Appendix A: Additional proofs" of wp17195 (IMF working paper).

### introduction of an IFC mitigates the opportunistic deficit bias thus widens as

### introduction of an IFC mitigates the opportunistic deficit bias thus widens as

### Marginal impact of fiscal transparency on opportunistic debt motive (Proposition 2)
- Proposition 2: All else equal, and abstracting from the partisan motive to raise debt above the first best level 푑퐹퐵, a marginal increase in fiscal transparency h lowers equilibrium debt if   , while it increases equilibrium debt if   .
- Interpretation:
  - Greater h can either mitigate or exacerbate the opportunistic motive to increase debt depending on the relation between  and the threshold .
  - Note: The proposition considers small (i.e. marginal) increases in h. As  increases without bounds with h, large increases in h effectively result in cases where    always applies.

### Joint behavior of partisan and opportunistic motives (Proposition 3)
- Key observations:
  - The strength of partisan and opportunistic motives move in the same direction with greater transparency when    (large electoral advantage for the incumbent) or 0    (moderate electoral disadvantage for the incumbent).
  - If   , the opportunistic motive grows without bounds as K increases, while the partisan motive is independent of K. Therefore, for sufficiently large K the opportunistic motive dominates.
  - When opportunistic motive disappears in the limit as 0 h , the partisan motive alone determines the debt bias.
- Proposition 3 (formal statement):
  - (I) The overall effect on equilibrium debt of introducing an IFC depends on the incumbent’s electoral disadvantage . In particular, there exist two thresholds (,LKh and (,HKh), with ((,0,LH K h K h         ), such that:
    - (I.a) if (,LKh   equilibrium debt increases with h,
    - (I.b) if ((,,LH K h K h       equilibrium debt decreases with h,
    - (I.c) if (,HKh   equilibrium debt increases with h.
  - (II) Threshold properties:
    - (,LKh is decreasing in both K and h, with (lim, L K Kh      and (0 lim,0 L h Kh      0.
    - (,HKh is decreasing in K and decreasing in h for h sufficiently small, with (lim, H K Kh      and (0 lim, H h Kh      .
- Intuition:
  - Establishing an IFC can increase equilibrium debt only if congruence (political alignment) confers a large electoral advantage to one candidate.
  - When competence matters sufficiently (including the case where only competence matters, 0 ), an IFC mitigates the debt bias by weakening opportunistic incentives while leaving partisan motive unaffected.

### Incumbent’s willingness to establish an IFC (Proposition 4)
- Incumbent’s equilibrium utility (equation (17)):
  - ( ) ( ) ( ) ( ) 1 E 1 / / P e e h h h U u d K d K                        
- Marginal utility with respect to h (equation (18)):
  - The sign of U/h is ambiguous; three effects operate:
    - Effect of h on equilibrium public consumption (first term): greater transparency improves intertemporal allocation only if equilibrium debt falls.
    - Effect of h on re-election chances (second term): if transparency lowers re-election odds (e.g., incumbent with electoral advantage 0 that transparency erodes), this reduces the incentive to establish an IFC.
    - Selection effect (final term): conditional on re-election, greater transparency produces an unambiguously positive selection effect by yielding, on average, a more competent incumbent.
- Rearranged expression (equation (19)):
  - The sign depends crucially on the term in curly brackets; this term is unambiguously signed when  and H() have the same sign.
- Proposition 4 (summary):
  - (a) If (0, H Kh     , the incumbent is better off with an IFC than without.
  - (b) If (, L Kh     and K is sufficiently large, the incumbent is worse off with an IFC than without.
  - (c) In remaining cases, the effect is ambiguous and characterized by (19).
  - Note: Absent an opportunistic motive (0 h  and 0 h q ), and with K sufficiently large, introducing an IFC makes the incumbent worse off if 0  and better off if 0 .
- Implications and examples:
  - If incumbent has a moderate electoral disadvantage, he welcomes an IFC because transparency lowers equilibrium debt and raises re-election odds; includes special case 0 (voters assess only competence).
  - If incumbent has a large political advantage and K is large, introducing an IFC may reduce incumbent utility because transparency can raise debt and reduce re-election chances, offsetting selection gains.

### Voters’ perspective on an IFC and social welfare (Proposition 5)
- Social welfare in equilibrium (equation (20)):
  - ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 11,1, 1 ˆˆ E1/E| / E// S eee h V V h ee hhh U u d d d                                                 
- Comparison with planner’s objective:
  - For given equilibrium debt, expressions (20) and (3) are identical except h features in (20) instead of  in (3).
  - Since h   (from (6)), the sum of last two terms in (20) is smaller than corresponding sum in (3).
  - Intuition: social planner benefits from a larger positive selection effect because 1 is observed perfectly after period 1, while voters rely on noisy estimates.
- Marginal social welfare with respect to h (equation (21)):
  - Voters’ views shaped only by selection effect and impact of transparency on equilibrium debt; re-election concerns absent.
  - An IFC is always preferred by voters if greater transparency lowers debt; ambiguous otherwise.
- Proposition 5 (summary):
  - (a) If ((,, LH K h K h       ), voters are better off with an IFC than without.
  - (b) If (, L Kh     or if (, H Kh    ), voters are worse off with an IFC than without for K sufficiently large.
  - In absence of opportunistic motive (0 h q ) and assuming concavity of first-period felicity is sufficiently weak, voters are worse off with an IFC than without if 0  and better off if 0 .
- Comparison between incumbent and voters (Figure 7 discussion):
  - Agreement occurs when (0, H Kh      or when (, L Kh     and K is sufficiently large).
  - Potential disagreements:
    - Voters may favor an IFC when incumbent opposes it: occurs when K is large and (,0 L Kh      , especially when  close to (, L Kh  .
    - Incumbent may favor an IFC when voters oppose it: occurs for K sufficiently large when  is above but close to (, H Kh  ; an incumbent with large but not crippling electoral disadvantage may set up an IFC to boost re-election chances despite higher opportunistic debt.

### Other manifestations of fiscal transparency (robustness)
- Alternative information channels considered (in addition to 1g and 1s):
  1. A signal on the level of public debt 2 sd    , with ( )2 ~ 0, N    and 2 1/ h     ;
  2. A positive probability  of observing the true debt d (and 1−휌 of not observing it);
- Interpretation:
  - IFCs can operate not only by reducing noise in competence signals but also by clarifying the true state of public finances (e.g., signal on debt level, or probability of observing true debt).
  - Most fiscal councils play a role in clarifying public-sector balance sheets and assessing realism of plans; in the model this corresponds to increasing probability of observing true values or providing direct signals on debt.

*Source: wp17195 - introduction of an IFC mitigates the opportunistic deficit bias thus widens as (PDF chapter/section).*

### 3. A  positive  probability

### 3. A  positive  probability

### Comparative statics: additional information channels (ρ, γ, hτ)
- Introducing an IFC can increase hμ and may also raise hτ, ρ, or γ. The paper notes:
  - hτ (additional noisy signal s2 on public debt) plays no role in pure-strategy equilibrium: s2 is ignored because voters rely on their equilibrium belief ˆV d = d and s2 is always consistent with any belief ˆV d and thus cannot prove such beliefs wrong. Off the equilibrium path s2 is also uninformative because voters do not know whether they are on or off the equilibrium path. Conclusion: variations in hτ have no impact.
- Proposition 6:
  - "An increase in hτ has no impact on equilibrium debt ed, PU and SU."

### First-order condition with observable competence and debt (equation (22))
- Adding the three information channels (certainty about η1 or d, and observable competence with probability γ) leads to a modified first-order condition for equilibrium debt shown in expression (22). Key structural differences relative to the baseline (equation (13)):
  - The second term is scaled by (1−γ)·(1−ρ), the probability that debt remains unobservable and can be used opportunistically to affect the incumbent’s electoral advantage.
  - A new final term on the r.h.s. captures the impact of possible debt observability on the partisan motive: with probability γ the incumbent’s equilibrium probability of re-election equals (1/ησ − ΦΔ) rather than (1/hσ − ΦΔ).

### Equilibrium utilities and welfare with partial observability (equations (23) and (24))
- Equilibrium utility of the incumbent PU (equation (23)) and equilibrium social welfare SU (equation (24)) incorporate new terms reflecting:
  - The direct effect of γ on the incumbent’s re-election probability: the first new term in PU is positive when 0Δ> and negative when 0Δ<, reflecting that an increase in γ affects the incumbent’s re-election probability positively when 0Δ> and negatively when 0Δ<.
  - Improved selection (with probability γ) from observable competence, which is necessarily positive and raises expected competence alignment between elected policymakers and voters.
  - For SU, a single added term (relative to baseline) reflects the overall positive impact of additional information on selection between competence and congruence; the net effect is necessarily positive (otherwise the voter’s election rule would be suboptimal).

### Propositions on ρ and γ (from expressions (22)–(24))
- Proposition 7:
  - "An increase in ρ necessarily lowers equilibrium debt ed and raises both PU and SU."
  - Intuition: increased observability of debt (higher ρ) mitigates the opportunistic motive to raise debt, benefiting both incumbent and voters; if ρ→1 the opportunistic debt bias disappears.
- Proposition 8:
  - If 0Δ> then an increase in γ necessarily lowers equilibrium debt ed and raises both PU and SU.
  - If 0Δ< then an increase in γ has an ambiguous effect on ed, PU and SU. In that case, for ρ sufficiently close to one (i.e. when the opportunism motive vanishes):
    - equilibrium debt is increasing in γ,
    - PU decreases with γ for K sufficiently large,
    - SU decreases with γ if the concavity of first-period utility is sufficiently weak.
  - Intuition: improved information about incumbent competence (higher γ) has effects qualitatively similar to variations in hμ; the sign and welfare implications depend critically on the incumbent’s prior electoral advantage Δ (congruence).

### Alternative signaling interpretation and literature connections
- Relaxing the assumption that the government is not better informed about its own competence turns the setting into a signaling game (incumbent may use observable debt as a signal).
  - Beetsma and Debrun (2017) analyze a two-type pooling-signaling setup and find that less noise in the independent signal lowers pooling equilibrium debt, but equilibrium selection is not fully resolved.
  - Daley and Green (2014) derive stability-based refinements that can select pooling equilibria when the independent noisy signal is sufficiently informative relative to the good type’s cost advantage.
  - No trivial generalization to more than two types; noisy signaling literature yields mixed implications for overall information revelation.

### Stylized facts and empirical patterns linked to theory
- Stylized fact 1: Most IFCs were introduced in countries where one or more fiscal rules were already in place. Interpretation: fiscal rules can contain collateral damage (stronger debt bias) from introducing an IFC, making countries with fiscal rules more likely to adopt an IFC.
- Stylized fact 2: Fiscal councils have tended to emerge in more mature, liberal-democratic systems where democratic accountability leads to changes in governing teams. Interpretation per theory:
  - Stronger executive grips and large private benefits from office make creation of an IFC less likely; constrained executives and coalition systems (e.g., the Netherlands) provide fertile ground for effective IFCs where competence matters more than congruence.
- Empirical proxies for executive strength (World Bank DPI indicators):
  - Variables: "Polariz" (maximum polarization), "Maj" (margin of majority = government seats / total seats), "Checks" (prevalence of checks and balances).
  - Panel averages for country-years with and without an IFC:

    Sample of 23 OECD countries
    - No IFC: Polariz = 1.07; Maj = 0.57; Checks = 4.04
    - IFC: Polariz = 1.71; Maj = 0.54; Checks = 4.77
    - Difference: Polariz = 0.64***; Maj = -0.033**; Checks = 0.74***

    Sample of 58 OECD and non-OECD countries
    - No IFC: Polariz = 0.71; Maj = 0.63; Checks = 3.49
    - IFC: Polariz = 1.51; Maj = 0.54; Checks = 4.57
    - Difference: Polariz = 0.80***; Maj = -0.088***; Checks = 1.08***

  - Interpretation: For all three proxies, statistically significant differences align with theory: countries with IFCs tend to exhibit higher measured polarization (Polariz), lower government majority margins (Maj), and greater checks and balances (Checks), consistent with IFCs emerging where executives are less dominant.

- Additional stylized fact: IFCs remained rare and are sometimes subject to executive pressures. Incumbency advantages make it difficult for governments to establish or preserve IFCs without strong legal protections.

### Policy-relevant findings and design lessons
- IFCs are not guaranteed to improve fiscal outcomes; they can exacerbate bias toward excessive public debt in some contexts.
- Whether an IFC benefits voters and/or incumbents depends on:
  - the relative strength of partisan (congruence) versus opportunistic motives,
  - the incumbent’s prior electoral advantage Δ,
  - the degree to which debt or competence is observable (ρ, γ).
- Design recommendations:
  - Give IFCs a broad remit including analysing long-term public debt sustainability and monitoring fiscal performance against numerical fiscal rules to reduce potential collateral damage (stronger debt bias).
  - Ensure strict guarantees of independence, including safeguards on financial resources, to enhance IFC sustainability.
  - Adapt the IFC’s institutional model to country-specific political characteristics to increase political consensus; externally imposed IFCs are likely to be vulnerable or ignored.
- Suggested avenues for further research:
  - Relax the assumption that the government lacks superior information about its own competence (introducing signaling via debt choices).
  - Study the complementarities between IFCs and fiscal rules formally, motivated by the empirical pattern that IFCs are often established when fiscal rules already exist.

*Italic: Source — wp17195, "3. A  positive  probability" (chapter/section) from the provided IMF PDF.*

### References

### wp17195 - References

### References
- Bibliographic list of cited works, including:
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  - Alt, J.E., Lassen, D.D. and S. Rose (2006), IMF Staff Papers 53, Special Issue, 30–57.
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  - Alt, J.E., Lassen, D.D. and J. Wehner (2014), British Journal of Political Science 44, 04, 707–716.
  - Beck, T., Clarke, G., Groff, A., Keefer, P. and P. Walsh (2001), World Bank Economic Review 15, 1, 165–176.
  - Beetsma, R., and X. Debrun (2007), European Economic Review 51, 2, 453–478.
  - Beetsma, R., and X. Debrun (2017), in Ódor, L. (ed.), Rethinking Fiscal Policy after the Crisis, Cambridge University Press, Chapter 5, 138–166.
  - Beetsma, R., and H. Uhlig (1999), Economic Journal 109, 458, 546–571.
  - Beetsma, R., Debrun X., Fang X., Kim Y., Lledó V., Mbaye S., Yoon S., and Zhang X. (2017), IMF Working Paper, forthcoming.
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  - Daley, B., and B. Green (2014), Journal of Economic Theory 151, 114–145.
  - Debrun, X., Hauner, D. and M.S. Kumar (2013), Journal of Economic Surveys 23, 44–81. http://www.imf.org/external/np/fad/council/
  - Debrun, X., and T. Kinda (2017), Fiscal Studies, forthcoming. http://www.imf.org/external/np/fad/council/
  - Debrun, X., Kinda, T., Curristine, T., Eyraud, L. Harris, J. and J. Seiwald (2013), IMF Policy Paper, July 16.
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  - Debrun, X., Zhang, X. and V. Lledo (2017), The Fiscal Council Dataset: A Primer to the 2016 Vintage, URL: http://www.imf.org/external/np/fad/council/.
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  - Truyts, T., undated, Working Paper.

### Appendix A: Additional proofs
- A.1. Second-order condition
  - Shows condition (14) is sufficient for the second order condition (s.o.c.) of the incumbent’s maximization problem, given the first-order condition (f.o.c.) in (11).
  - Uses that u'' < 0 and properties of the hazard rate of the standard normal: φ(x)/[1−Φ(x)] > x.
  - Derives that if V̂,dd(·) > 0 then s.o.c. always satisfied; if V̂,dd(·) < 0 a sufficient condition reduces to an inequality that at V̂,dd = 0 yields 0 K d η + ... leading to (14).

- A.2. Proof of Proposition 3
  - Defines H(Δ) from (15) as H(Δ) = (φ/σ_h) · G(Δ) with G(Δ) a cubic: c1·Δ^3 + c2·Δ^2 − c3·Δ + c4, with 0 < ci.
  - Observes G(0) > 0, G(−Δ) < 0, G(Δ) > 0, so by intermediate value theorem G has three real roots: LΔ < 0, HΔ > 0, and LLΔ ≪ −Δ.
  - Notes (14) cannot hold for LLΔ and analyzes dependence of LΔ and HΔ on parameters K and h_ε:
    - Increasing K decreases both LΔ and HΔ; limits: lim_{K→∞} L_{K,h_ε}(Δ) = −Δ and lim_{K→∞} H_{K,h_ε}(Δ) = Δ (iff Δ ≠ Δ).
    - As h_ε → 0: max Δ → ∞ and min Δ → −∞; thus H_{K,h_ε}(Δ) → ∞ and LL_{K,h_ε}(Δ) → −∞. For h_ε = 0, G(Δ) linear with single root 0 so lim_{h_ε→0} L_{K,h_ε}(Δ) = 0.
  - Provides implicit differentiation for roots rΔ of G; shows sign(G_{h_ε}) at roots determines monotonicity:
    - For r = L_{K,h_ε}(Δ) with LΔ < 0, G_{h_ε} > 0 so L_{K,h_ε}(Δ) is decreasing in h_ε.
    - For r = H_{K,h_ε}(Δ) with HΔ large, G_{h_ε} < 0 so H_{K,h_ε}(Δ) is decreasing in h_ε for small h_ε, but not necessarily monotonic overall.

- A.3. Characterization of cases where the incumbent and society disagree about attractiveness of IFC
  - Shows existence of parameter regions where society favors installing an IFC while the incumbent opposes:
    - If L_{K,h_ε}(Δ) ≤ Δ < 0 and Δ in [L_{K,h_ε}(Δ), M_{K,h_ε}(Δ)) with K sufficiently large, then ∂P U / ∂h_μ < 0 while ∂S U / ∂h_μ > 0 (signs as given).
  - Shows existence of cases where society opposes but incumbent favors an IFC:
    - If Δ in (H_{K,h_ε}(Δ), HH_{K,h_ε}(Δ)] and K sufficiently large, then ∂P U / ∂h_μ > 0 while ∂S U / ∂h_μ < 0.

- A.4. Proofs of Propositions 7 and 8 (extended model)
  - Presents incumbent objective (A.2) for extended model with probabilities γ and ρ and discriminatory powers η, h, σ:
    - Explains three information cases with probabilities γ, (1−γ)ρ, and (1−γ)(1−ρ) and corresponding challenger standardized handicaps η/σ, h/σ, and Γ̂_{V,dd}.
    - First-order condition (22) follows from differentiating (A.2) w.r.t. d.
  - Equilibrium utilities:
    - Incumbent expected utility expressions use weighted averages leading to (23).
    - Society expected utility follows analogously leading to (24).
  - Proposition 7 (comparative statics in ρ):
    - Differentiating (22) w.r.t. ρ yields that ∂e d / ∂ρ < 0 independent of Δ.
    - Shows ∂P U / ∂ρ > 0 and ∂S U / ∂ρ > 0 given the sign of terms implied by (22).
  - Proposition 8 (comparative statics in γ):
    - Differentiating (22) w.r.t. γ yields expression (A.3); sign(∂e d / ∂γ) is opposite to sign of r.h.s.
    - If 0 < Δ then ∂e d / ∂γ < 0 necessarily; otherwise sign can be ambiguous.
    - For incumbent and society utilities, provides conditions under which ∂P U / ∂γ and ∂S U / ∂γ are positive or ambiguous, depending on Δ and other parameters (including ρ close to 1 and behavior of E''_e u d η ε).
  - Concludes with expressions for society’s equilibrium utility derivatives and sign conditions tied to Δ and first-order condition (22).

*Source: wp17195 - References (IMF Working Paper PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17195.pdf_