## _wp1389

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---

### Summary and motivation
- Fiscal sustainability has become crucial after the global financial crisis as industrialized countries confront rising debt ratios, stagnant output growth, unfavorable demographic trends, and liabilities passed from financial sectors.
- Paper is a review with didactic flavor drawn from IMF Institute lectures and includes extensions to tools and indicators (e.g., stochastic DSAs, CCA).
- Figure referenced: Government Debt/GDP, Selected Countries, Weighted Average (Percent of GDP, 1991–2017).

### Definitions and core questions of sustainability
- Intertemporal solvency requirement: government must raise enough resources (in present value terms) to service obligations to preclude default or restructuring.
- Two complementary approaches:
  - Positive: "Is the fiscal policy of country X sustainable?"
  - Normative: "What policy should country X implement to assure a sustainable public debt trajectory?"
- Sustainable policy examples:
  - a chosen primary surplus maintained indefinitely, or
  - a rule/reaction function that, if continued, keeps the government solvent.
- Unsustainable: required primary adjustment to avoid default/restructuring is not feasible.

### Building blocks for Debt Sustainability Analysis (DSA)
- Core components:
  - accounting identities for public debt dynamics (one-period budget constraint),
  - econometric forecasts of prospective debt trajectories,
  - risk scenarios and stochastic simulations (Monte Carlo).
- Notation highlights:
  - t b = government debt as a ratio to GDP.
  - t r = the real rate of interest.
  - ˆ t y = the rate of growth of real GDP.
  - t  = expenditures on goods and services as a fraction of GDP.
  - t  = revenues as a fraction of GDP.
- Dynamic efficiency condition assumption: mean interest rate r exceeds mean growth rate ˆ y .

### Role and sizing of primary surpluses
- Primary surplus: ps =  −  (revenues minus non-interest expenditures).
- Target primary surplus: TAR ps = TAR  − TAR .
- To satisfy the intertemporal budget constraint without default, the present value of primary surpluses must cover debt.
- Maximum sustainable debt defined by inverting the stabilization expression:
  - max b = ˆˆ [(1) / ()] y r y ps     (expression style preserved in source).
- Limits on a government's ability to run primary surpluses determine maximum sustainable debt ratio; if current b > max b, restructuring may be desirable.

### Distribution of surpluses over time; objective functions and fiscal rules
- Tax-smoothing (Barro-Sargent) welfare objective: minimize present value of expected deadweight losses from taxation subject to budget constraint.
- Two loss-function cases:
  - Case (i): ''' 0   (no precautionary motive) → tax smoothing equates marginal costs across periods; policy invariant to volatilities.
  - Case (ii): ''' 0   (prudential/precautionary) → optimal rule responds to budgetary and financial risks; long-run debt tends to zero under certain forms.
- Representative numerical/illustrative figures:
  - 4.4 percent ps = appears in the source as structural/illustrative primary surplus.
  - Under a rule like (29), targeting a primary surplus of 4.9 percent ps reduces the probability that debt rises from 50 percent to 15 percent; this signals willingness to pay an extra 0.4 percent of GDP to lower risk.
- Key insight: distributing surpluses over time should equate marginal losses across periods and account for precautionary motives when stochastic risks exist.

### Uncertainty, stochastic indicators, and probabilistic target surpluses
- Stochastic DSA approach:
  - Introduce uncertainty in interest rates and GDP growth: r_t = r + e_t , y_t = y + e_t .
  - Baseline typically sets shocks to zero; adverse scenarios often set shocks two standard deviations from mean.
  - Monte Carlo simulations provide probabilities that debt will equal or exceed debt targets TAR t b > .
- Probabilistic target primary surplus:
  - ps* (debt-stabilizing primary surplus) is random because growth-adjusted interest factor (()/(1)ryy

) is random.
  - If growth-adjusted discount factor is normally distributed, ps* is normally distributed with:
    - Mean = [() / (1)]*mean   ryyb

    - Standard deviation = .[(   )/(1 )]*std dev   ryyb

  - TAR ps x defined so debt does not rise above forecast with x-percent probability.
- Illustrative Table/Figure exercise (six hypothetical countries):
  - Debt cases: b = 30 percent (Countries 1,2); b = 60 percent (Countries 3,4); b = 100 percent (Countries 5,6).
  - Growth-adjusted interest factor (r-y)/(1+y) = 2 percent in all cases.
  - "Low volatility" std dev = 0.3 percent; "High volatility" std dev = 2.0 percent.
  - Target primary surpluses computed for x = 0.5, 0.75, 0.85, 0.95.
  - Country 1 example:
    - primary surplus 0.6 percent of GDP → probability debt continues to rise = 50 percent (x=0.5).
    - raise to 0.66 percent → x=0.75.
    - raise to 0.69 percent → x=0.85.
    - raise to 0.75 percent → x=0.95.
- Key confirmations:
  - Higher debt or higher growth-adjusted discount factors require larger primary surpluses.
  - Higher volatility makes reducing probability of debt growth more difficult.
  - High debt combined with high volatility is most difficult to stabilize.

### Sustainability over the business cycle and uncertain potential output
- Primary surplus decomposition:
  - ps_t = ps_t^struc + ps_t^cyc.
  - Cyclical elasticities: ,1 cTAX   ; ,cSPEND  = 0 if expenditures smoothed.
- Tax-smoothing regime and uncertainty:
  - If potential output is uncertain, even with correct mean estimate, a pure tax-smoothing regime can cause upward drift in debt ratio.
- Table 3 example (tax smoothing with random-walk potential output):
  - Exp Ratio (g) = 20.00%
  - Tax Ratio (t) = 20.00%
  - "Pessimistic": P_y(realized)=105, surplus/yP = 0.95%
  - "Correct": P_y=100, surplus/yP = 0.00%
  - "Optimistic": P_y=95, surplus/yP = -1.05%
  - Mean surplus ratio-to-output = -0.033 percent (deficit) → debt ratio will grow under policy.

### Prospective liabilities and required adjustment examples
- Prospective liabilities (pensions, health, financial sector obligations) are discounted future flows; "true" debt = accumulated debt + prospective debt.
- Tax-smoothing that ignores prospective liabilities leads to delayed, larger future adjustments.
- BCG (Batini, Callegari, and Guerreiro (2010)) U.S. entitlement illustrative adjustments (percent of PV of GDP):
  - Adjustment needed to stabilize debt (end-2008 debt ratio = 44 percent of GDP; PV of GDP discounted at 3 percent):
    - 25-year horizon (2009-33): 4.4 / 4.6
    - 50-year horizon (2009-58): 6.1 / 6.7
    - 75-year horizon (2009-83): 7.7 / 8.4
    - Infinite Horizon (full repayment): 13.9 / 14.4
  - Interpretation: to offset first 25 years a fiscal adjustment of about 4.5 percent of GDP is required to stabilize debt at 44 percent of GDP; longer horizons imply larger required adjustments.

### Net worth approach and public-sector balance sheets
- Public net worth (as a fraction of GDP) nw = NF_a + F_a - GROSS_b - OLiab (notation preserved).
- Narrow net worth and evolution combine non-financial assets, financial assets, and gross debt dynamics.
- Policy insight:
  - Liquidating gross financial assets can service gross debt only if government changes its consumption decision; imputed consumption value of non-financial assets is not an automatic option for debt service without fiscal adjustment.

### Non-renewable resources: permanent income, narrow net worth, and bird-in-hand
- Oil example parameters and initial accounting:
  - r = 4.0%
  - real GDP growth = 3.5%
  - ow0 (2011) = 34.7 percent of GDP
  - of0 = 0
  - b0 = 25 percent of GDP
  - nnw0 = ow0 + of0 - b0 = 9.7 percent of GDP
  - Terminal value of oil fund in 2022: of2022 = 36.6 percent of GDP
- Policy experiments (Table 5 highlights):
  - Part B (Baseline):
    - psno = -1.00 (non-oil primary deficit 1 percent of GDP)
    - Debt b/GDP rises 25.0 → 37.6 by 2022
    - nnw falls 9.7 → -1.0 by 2022
    - Stabilizing net financial wealth at -1 percent in 2022 would require an adjustment of just over 1 percent of GDP in 2013 unless changed earlier
  - Part C (Net wealth preserving):
    - psno = -0.05
    - nnw remains 9.7 percent of GDP
    - Debt b/GDP rises 25.0 → 26.9 by 2022
    - Stabilizing ps in depletion year: -0.05; fiscal adjustment in depletion year: 0.00
  - Part D (Bird-in-hand):
    - Counts only returns r*of as available for spending; requires early surpluses when fund is small; allows larger deficits later relative to narrow net worth policy
- Policy takeaway: preserving narrow net worth smooths consumption and avoids abrupt near-term adjustments; BIH is more conservative early on but more permissive post-depletion.

### Contingent Claims Approach (CCA) and market indicators of default risk
- CCA treats present value of primary surpluses as a volatile asset; volatility reflects implementation risk about reaching fiscal targets.
- Market-implied default probabilities (Approximate Sovereign Cumulative Default Probabilities: 5-year bonds, Table 6):
  - AAA 0.0
  - AA 0.6
  - A 1.4
  - BBB 2.7
  - BB 9.0
  - B 22.0
  - CCC/CC 53.3
- CCA modeling elements:
  - PV of a perpetual constant primary surplus stream: PV = PS0 *(1)/(r - ŷ) (expression style preserved).
  - Stochastic evolution: dPV = (r * PV - PS) dt + σ_PS * PV dW (notation preserved).
  - σ_PS interpreted as market-assessed implementation risk.
- Contingent-claims diagnostics:
  - Distance-to-default (DTD) maps to probability of default via the cumulative normal distribution.
  - Credit spread SPR equals difference between rate on risky government debt and a riskless benchmark; spreads and probabilities tied to expected losses and recovery assumptions.
- Illustrative numerical example (Table 7 hypothetical economy):
  - Parameters:
    - ˆy = 2.8 percent
    - r = 3.8 percent
    - Y0 = 400
    - B/GDP = 150.0 (B = 600 currency units)
  - Scenario (i): PS PV = 600.0 (150.0% of GDP); Constant PS = 5.8 (1.4% of GDP); DTD = 0.63; Probability of default (5 years) = 26.6%; Spread = 6.2%
  - Scenario (ii): PS PV = 800.0 (200.0% of GDP); Constant PS = 7.7 (1.9% of GDP); DTD = 1.27; Probability of default = 10.2%; Spread = 2.2%
  - Scenario (iii): PS PV = 800.0; PS  rises from 0.2 → 0.23; DTD = 1.04; Probability = 14.9%; Spread = 3.2%
  - Implementation-risk quantiles (Horizon = 5 years, selected numbers preserved):
    - Scenario (i), primary surplus 10% level: 3.6 (0.9% of GDP)
    - Scenario (ii), primary surplus 10% level: 4.8 (1.2% of GDP)
    - Scenario (iii), primary surplus 10% level: 4.2 (1.1% of GDP)
- Analytical lessons:
  - Credibility and expectations management matter: higher σ_PS can offset benefits of fiscal adjustment by raising spreads.
  - Implementation risk acts as an implicit cost on fiscal adjustment.
  - Debt may be “too high” if required fiscal adjustment that reduces sovereign spread is infeasible.

### Evidence from the recent downturn and policy implications
- Countries with lower debt or net creditor public sectors were better positioned to increase non-interest public expenditures countercyclically.
  - Net creditor examples: Finland, Norway, Bulgaria, Chile (all but Bulgaria posted substantial increases in public spending ratios).
  - High-debt cases with less countercyclical policy: Switzerland, Italy, Greece, Japan, Israel.
- Empirical note: slope coefficient for industrialized countries is negative with t-statistic about 2.9 (informal due to few observations).
- Quality of fiscal policy matters: beyond size of adjustment, reform tax collection/administration, broaden tax base, eliminate wasteful expenditures, and provide efficient public goods to support growth and sustainability.
- General policy recommendations drawn from analyses:
  - Restrain debt if facing exogenous volatility.
  - Reduce domestic sources of volatility (erratic monetary policy, poorly functioning financial markets, unstable tax revenues/expenditures).
  - Adopt credible, well-communicated fiscal adjustments to lower implementation risk and sovereign spreads.
  - For resource-rich countries, use conservative long-run price estimates, link spending to long-run prices, and build buffer assets.

*Source: _wp1389 - 1. Summary, Recent Research on Public Debt Sustainability, Stochastic Approach*

### 1. Summary, Recent Research on Public Debt Sustainability, Stochastic Approach .............. 10

### 1. Summary, Recent Research on Public Debt Sustainability, Stochastic Approach

### Introduction: scope and motivation
- Fiscal sustainability has become crucial after the global financial crisis as industrialized countries confront:
  - rising debt ratios,
  - stagnant output growth,
  - unfavorable demographic trends,
  - liabilities passed from financial sectors.
- The paper is a review of recent work on debt sustainability with a didactic flavor drawn from IMF Institute lectures and includes some extensions of current tools and indicators.
- Figure 1: Government Debt/GDP, Selected Countries, Weighted Average (Percent of GDP, 1991–2017).

### Definitions and questions of sustainability
- Intertemporal solvency requirement: government must raise enough resources (in present value terms) to service obligations to preclude default or restructuring.
- Two complementary approaches:
  - Positive: "Is the fiscal policy of country X sustainable?"
  - Normative: "What policy should country X implement to assure a sustainable public debt trajectory?"
- A “sustainable policy” may be:
  - a chosen primary surplus maintained indefinitely, or
  - a rule/reaction function (explicit or implicit) that, if continued, keeps the government solvent.
- An “unsustainable” situation: the primary adjustment required to avoid default/restructuring is not feasible; sustainability implies feasibility of the required adjustment.

### Building blocks for Debt Sustainability Analysis (Section II)
- Core components:
  - accounting identities for public debt dynamics,
  - econometric forecasts of prospective debt trajectories,
  - these typically form the core of a Debt Sustainability Analysis (DSA).

### Role and sizing of primary surpluses (Sections III–IV)
- Primary surpluses (revenues minus non-interest expenditures) are critical to sustainability.
- To satisfy the intertemporal budget constraint without default, primary surpluses’ present value must be sufficient to cover debt.
- Limits on a government’s ability to run primary surpluses determine the maximum sustainable debt ratio for a country.

### Distribution of primary surpluses over time; objective functions and rules (Section V)
- Fiscal policy design requires an objective regarding intertemporal distribution of primary surpluses to avoid undue macroeconomic volatility.
- Minimizing overall losses from primary surpluses (including tax distortion costs) implies distributing surpluses over time to equate marginal losses across periods.
- Section V discusses alternative loss-function specifications and corresponding fiscal rules that determine the speed of debt reduction, if any.
- The discussion links to:
  - Woodford’s (2003) notion that a rule reflects an underlying optimization process,
  - Kydland and Prescott (1977) on credibility from simple, understandable rules.

### Uncertainty, precautionary motives, and stochastic indicators (Sections V–VII)
- Loss functions are suited for analyzing fiscal policy under uncertainty.
- If the government wishes to cushion the economy from exogenous shocks to interest rates and output, reducing debt can reflect a precautionary motive.
- Section VI introduces a fiscal indicator: the target primary surplus required to prevent debt from rising with a specified probability (a probabilistic/stochastic approach).
- Section VII examines counter-cyclical borrowing over the business cycle and shows:
  - If potential output is uncertain, even with a correctly estimated mean, a pure tax-smoothing regime can lead to an upward drift in debt levels.

### Prospective liabilities and alternative approaches (Sections VIII–IX)
- Section VIII extends analysis to include prospective liabilities such as pension and health benefits and financial sector obligations.
- Section IX discusses the recent net worth approach to public sector sustainability (reference to the 2001 IMF Government Financial Statistics manual).

### Non-renewable natural resources (Section X)
- Section X discusses non-renewable natural resources and their implications for fiscal sustainability.

### Didactic character and intended use
- The paper is intended as a comprehensive review and teaching resource covering many aspects of debt sustainability, while also presenting extensions to commonly used tools and indicators.
- The normative benchmark adopted assumes a well-intentioned government seeking sustainability without imposing excessive burdens on future taxpayers.

*Source: _wp1389 - 1. Summary, Recent Research on Public Debt Sustainability, Stochastic Approach*

### Section XI discusses how the Contingent Claims Approach (CCA) may be applied to public

### _wp1389 - Section XI discusses how the Contingent Claims Approach (CCA) may be applied to public

### Contingent Claims Approach (CCA) and implementation risk
- CCA treats the present value of primary surpluses as a volatile asset; this volatility may reflect uncertainty about the ability or the willingness of a fiscal authority to reach a stated primary surplus target.
- The CCA is particularly well-suited to examine implementation risk—the probability that an authority will not follow through with a fiscal plan.
- The discussion extends recent work by Gray, Bodie, and Merton (2007) and Gray, Lim, Loukoianova, and Malone (GLLM, 2008).
- Implementation risk and related concerns are discussed in IMF (2011, p. 58), Ostry, Ghosh, Kim, and Qureshi (OGKQ, 2010), and Ghosh, Kim, Mendoza, Ostry, and Querishi (GKMOQ, 2011).

### II. The building blocks of a Debt Sustainability Analysis (DSA)
- Three building blocks: the one-period budget constraint, forecasts, and risk scenarios.
- Base: debt dynamic equation—the one-period budget constraint expressed as a ratio to gross domestic product (GDP).

A. The public sector budget constraint
- Notation and meanings as given:
  - t b = government debt as a ratio to GDP.
  - t r = the real rate of interest.
  - ˆ t y = the rate of growth of real GDP.
  - t  = expenditures on goods and services as a fraction of GDP.
  - t  = revenues as a fraction of GDP.
- The equation says today’s debt ratio t b equals yesterday’s debt ratio t-1 b including both principal and interest t (1+ r ), adjusted for growth tt (1 + y )ˆ , plus expenditures  t, minus tax revenues  t.
- Assumption: the mean interest rate r exceeds the mean growth rate ˆ y ; this is the dynamic efficiency condition.
- Primary surplus: ps   =  .
- Target primary surplus: TAR ps = TAR   TAR  (TAR  is nominal marginal tax rate, TAR  is agreed-upon expenditure ratio).
- Error term st e reflects short-run randomness in either the effective tax rate, expenditures, or both.
- Substituting TAR ps into equation (1) yields a target value of debt: [|] TAR t t b E b ps = .

B. Ad-hoc targets for public debt and/or the primary surplus
- Goal to stabilize or reduce debt over an N period horizon: TAR t+N b =  b t , where 0 1   .
- If strict inequality ( < 1) implies debt ratio reduction, Croce and Juan-Ramón (2003) show the primary surplus must satisfy the derived expression (referenced in text).
- Special case of debt stabilization (1,1 N    ) → target primary surplus *(1,1) TAR t ps ps  .
- Intuition: to maintain a constant debt/GDP ratio, primary surplus must cover real interest payments minus an increment due to growth.
- Overall balance ob relates to primary surplus and nominal interest payments:
  - 1 t t t OB PS i B     (equation (6) as given).
- Even if primary surplus must be positive to stabilize debt, overall balance may be in deficit—so long as growth is positive (example: United States debt stabilizing overall balance is a deficit of about 3 percent of GDP).

C. Alternative scenarios in a Debt Sustainability Analysis
- Introduce uncertainty in interest rates and GDP growth:
  - tr t r e    (equation (8) style).
  - ty t y e    (equation (9) style).
- Substituting (2), (8), (9) into debt dynamics (1) highlights deterministic and random components (equation (10)).
- Practical DSAs simulate equation (10) forward, with baseline scenario typically setting all shock terms to zero and adverse scenarios imposing shocks (rt e > 0, yt e < 0) typically two standard deviations from their mean.
- Monte Carlo stochastic simulations provide probabilities that debt will equal or exceed some debt target TAR tt b > .
- Table 1 (summarized research) lists multiple authors, years, countries, and remarks (Hunt, Drew 1998 New Zealand; Hoffmaister, others 2001 Costa Rica; Garcia, Rigobon 2004 Brazil; Penalver, Thwaites 2006 Emerging Markets; Celasun, Debrun, Ostry 2007 Emerging Markets Fiscal Reaction Function; Tanner, Samake 2008 Brazil, Mexico, Turkey; Congressional Budget Office 2008 United States; Budina, Van Wijnbergen 2009 Turkey Includes seignorage forecasts; Frank, Ley 2009 Argentina, Brazil, S. Africa Regime changes (Markov switching model); Hadjenberg, Romeu 2010 Uruguay Includes parameter uncertainty; Kawakami, Romeu 2011 Brazil Fiscal Reaction Function).
- Empirical approaches: vector autoregressions and fiscal reaction functions (Hunt and Drew 1998; Hoffmaister et al. 2001; Garcia and Rigobón 2004; Penalver and Thwaites 2006; CDO 2007; Tanner and Samake 2008).
- Recent work examines regime changes, abnormal distributions, parameter uncertainty, fiscal transmission, and fiscal policy reaction functions.

### III. The government's present value constraint: restatement
- Two-period example: government begins period 1 with inherited debt 0 b and will service obligations in full at end of period 2.
- Targeted present value of primary surpluses: 12 [/] TAR ps ps    (notation preserved as in text).
- Under full credibility, market expectations equate to targeted present value and market value of government debt equals targeted present value (equations (11)-(14) progression in text).
- If not fully credible, initial value of debt adjusts to satisfy altered expectation condition (equations (15)-(16)).
- Governments may face restructuring/default/inflation as mechanisms for non-fulfillment; such outcomes are typically avoided where possible.
- Infinite horizon No Ponzi Game (NPG) condition expressed as lim/ (1)0 t t t b r      (equation (17) and related).
- Debt ratio may be expressed with nominal debt growth B  and nominal GDP growth Y  ; NPG satisfied so long as (1) / (1)(1)BY r       .
- Sustainability may require a fiscal rule where target primary surplus responds to debt: TAR t ps b  = >0 (equation (19) notation preserved); sustainability requires TAR  > 0 (Bohn 1998, 2008).
- Debt stabilization policy corresponds to BY =   .

### IV. Maximum sustainable debt
- Define maximum feasible primary surplus citizens can tolerate: max ps .
- Maximum debt ratio: max b obtained by inverting expression (5) and substituting max ps :
  - max ˆˆ [(1) / ()] b y r y ps     (equation (20) style preserved).
- Max debt is annuity value of max primary surplus adjusted for real GDP growth; if current b > max b a restructuring may be desirable; if * max ps ps > this implies adjustment not politically feasible.
- Cross-country comparison:
  - If country I and II have different growth and fiscal capacity, expression (22) shows a country that grows faster can sustain a higher debt ratio, and stronger fiscal institutions increase maximum sustainable debt.
- Policy implication: credible fiscal consolidations often must include reforms (tax collection, administration, base broadening, elimination of counterproductive regulations) to raise tolerable debt.

### V. Distributing surpluses over time: a fiscal objective function
- Governments must consider how primary surpluses are distributed over time (tax smoothing and volatility concerns).
- Objective: minimize present value of expected deadweight losses associated with tax collection subject to intertemporal budget constraint.
- Loss function specified with parameters ''' 0,0     and two cases for third moment: (i) ''' 0   and (ii) ''' 0   .
- Euler condition and implications:

Case (i): Barro-Sargent tax-smoothing (''' 0   or no volatility)
- Under certainty, optimal policy equates marginal costs of tax collection across periods (Barro 1979 result).
- Optimal tax rate *  t must be determined by substituting into budget constraint; yields restatement of equation (5).
- Rule implies debt stabilization is consistent with tax-smoothing objective.
- Limitations: policy invariant to volatilities of  , r and y  ; no precautionary saving; symmetry inconsistent with typical DSA focus on adverse but not favorable scenarios.

Case (ii): A prudent fiscal authority (''' 0   )
- Loss function with third moment captures precautionary concerns and interest in avoiding adverse scenarios.
- Fiscal burden in period: 1 t t fbr b      , where ˜ = ()/(1) r r y y      .
- Prospective variability of tax burden: 2 1 () t t E     .
- Variance of fiscal burden has components:
  - budgetary risks: 2 1 () t t     ,
  - financial risks linked to debt: 2 1 () t t r b r b     ,
  - covariance term assumed zero for exposition (equation (27) and discussion).
- Second-order Taylor approximation yields expression (28) linking stochastic simulation relevance to case (ii).
- Prudential element of taxes consists of budgetary risks and financial risks; if 2 1 () t t E      0 the second element exclusively reflects unexpected financing cost changes.
- Under special assumptions, fiscal rule takes form (29) (notation preserved); long-run debt tends to zero under that rule.
- Numerical illustrative example (text fragment preserved):
  - Assume an initial debt ratio 0 50 percentb = , average growth y  equal to 3 percent and the real interest rate r equal to 12 percent. Assume also that the standard deviation of ()/(1)ry y     is 1 percent and the distribution is standard normal. Under rule (25), the primary surplus chosen by the authority would be * (text truncates here in source).

- Equation references and derivations are presented in the source (equations (1)–(29) and related).

*Source: _wp1389 - Section XI discusses how the Contingent Claims Approach (CCA) may be applied to public*

### 4.4 percentps

### 4.4 percentps

### Structural Surpluses and Objective Functions
- Under a rule like (29), targeting a primary surplus of 4.9 percentps of GDP reduces the probability that debt rises from 50 percent to 15 percent; this signals willingness to pay an extra 0.4 percent of GDP to lower the risk of another adjustment.
- A modified rule with constant budgetary risks (2
1
()
tt
Econst


) implies a constant structural surplus and affects the term 2
1
()
tt
rbrb



even without interest rate shocks.
- The general rule includes a constant structural surplus:
  - 0ps is the structural primary surplus as a fixed percent of GDP and 0.
  - Since the structural surplus is positive, the country will be a net creditor in the long run.
- Substitution of (30) into budget constraint (1) yields:
  - 1
(1)
tt
bbps


- Over time, the government accumulates assets; its bounded net credit position converges to a finite bound (lim/
t
t
bps

).
- Rationale and caveats:
  - A positive structural surplus with zero  would imply boundless asset accumulation; budgetary risks and financial risks are inherently linked through the debt dynamic equation.
  - A structural surplus implements AMSS (2002) recommendation for a government “war chest” of assets to avoid distortionary tax financing and reduce macroeconomic volatility.

### Welfare-Based Objective Functions and Tax Timing
- Benevolent-planner approach: maximize consumer utility directly (Frank Ramsey 1927); an ad-hoc objective can reflect consumer welfare.
- Representative-consumer expected present value of utility assumed with ''''''
0,0,0UUU.
- For a ‘hand-to-mouth’ consumer (no assets) with income fixed and known (1,ttt
YY


) and  = (1)r, consumption equals disposable income: (1).
tttt    t
CYTY 
- The Euler equation ''
1
()(  )
tt
UC    UC


(for ) yields an expression similar to (28); since '''''
/0UU
, higher variability of the fiscal burden implies taxes need to be ‘front loaded’.
- Using CRRA utility, the optimal fiscal rule is similar to (30); exogenous natural resource revenues suggest expenditures should be optimally tilted upwards.
- Lump-sum taxes: only hand-to-mouth consumers care about the time path of taxes; Ricardian consumers smooth consumption.

### Evidence from the Recent Downturn: Debt and Expenditure Smoothing
- Countries with lower debt ratios or net creditor public sectors were better positioned to increase non-interest public expenditures countercyclically during the downturn.
- Examples with net credit positions:
  - Industrialized: Finland and Norway.
  - Emerging market: Bulgaria and Chile.
  - Of these, all but Bulgaria posted substantial increases in public spending ratios (more countercyclical policy).
- Cases with higher debt and less countercyclical policy include:
  - Industrialized: Switzerland, Italy, Greece, Japan.
  - Emerging market: Israel (relatively high debt and a fall in public spending ratio).
- Empirical note: slope coefficient for industrialized countries is negative with t-statistic about 2.9; analysis is intentionally informal due to few data points.

### Required Adjustment in an Uncertain Environment (Probabilistic Approach)
- When authorities permit debt ratio to grow until year T, from t+1 forward fiscal policy aims at debt stabilization/reduction.
- The debt-stabilizing primary surplus ps* is random because the growth-adjusted interest factor (()/(1)ryy

) is random.
- If the growth-adjusted discount factor is normally distributed, then ps* is normally distributed with:
  - Mean = [() / (1)]*mean   ryyb

  - Standard deviation = .[(   )/(1 )]*std dev   ryyb

- Target primary surplus ()
TAR
ps  x is defined to prevent debt rising above its year (t) forecast with x-percent probability; where *
[]
1
ry
y
psmean  b





.
- Table 2 and Figures 4a-4b calculations for six hypothetical countries:
  - Countries 1 and 2: “low” debt b = 30 percent of GDP.
  - Countries 3 and 4: “medium” debt b = 60 percent of GDP.
  - Countries 5 and 6: “high” debt b = 100 percent of GDP.
  - Growth-adjusted interest factor (r-y)/(1+y) = 2 percent in all cases.
  - “Low volatility” standard deviation = 0.3 percent.
  - “High volatility” standard deviation = 2.0 percent.
  - Target primary surplus calculated for x = 0.5, 0.75, 0.85, 0.95.
- Illustrative numeric example (Country 1):
  - If country 1 runs a primary surplus of 0.6 percent of GDP in year T+1, probability debt continues to rise = 50 percent (x=0.5).
  - To reduce probability to 25 percent (x=0.75) raise primary surplus to 0.66 percent of GDP.
  - For x=0.85 raise to 0.69 percent of GDP.
  - For x=0.95 raise to 0.75 percent of GDP.
- Key confirmations:
  - Higher primary surpluses are required with higher debt levels or higher growth-adjusted discount factors.
  - More prudent authorities (higher x) run higher primary surpluses.
  - Higher volatility makes reducing probability of debt growth more difficult (steeper lines in Figure 4b vs Figure 4a).
  - High debt combined with high volatility poses the greatest difficulty for debt stabilization (steepest line for b = 100 percent of GDP in Figure 4b).
- Policy implications:
  - Economic volatility is the enemy of fiscal sustainability.
  - Restrain debt for countries facing exogenous volatility.
  - Reduce domestic sources of volatility—erratic monetary policies, poorly functioning financial markets, undue variations in tax revenues and expenditures—to support fiscal sustainability.

### Sustainability Over the Business Cycle
- Primary surplus decomposed into structural and cyclical components:
  - () P
tPt
ps  strucy where P
t
y is trend (or potential) output.
  - Cyclical component: ,,
()()()()
PP
tcttc TAXc SPENDt t
pscycyyyy  with ,cTAX
 and ,cSPEND
 as cyclical elasticities for taxes and expenditures.
  - Total primary surplus: () ()
ttt
psps  strucps cyc
- Typical elasticities:
  - ,1
cTAX

 (net tax revenues fall in recessions, rise in expansions).
  - ,cSPEND
 = 0 if governments smooth expenditures.
- Debt stabilization requires:
  1. Structural surplus equals its debt-stabilizing value: *
()
t
ps  strucps (tax smoothing regime, equation (26)).
  2. Government knows potential output P
t
y with certainty.
- If potential output is uncertain, even implementing tax smoothing (26) with *
()
t
ps  strucps can lead to upward drift in the debt ratio despite correct estimation of mean P y.
- Example setup summarized in Table 3:
  - Initial potential output and actual output P
y0
(100).
  - Initial debt 0
b = 0.
  - Tax rate and ex-ante expenditure ratio set at 20 percent (==0.2).
  - With symmetric shocks ± 5 units:
    - Pessimistic case P
y1
= 105 → surplus ratio = 0.952 percent ([21–20]/105).
    - Optimistic case P
y1
= 95 → deficit ratio = - (text truncated in source).

*Source: _wp1389 - 4.4 percentps.*

### 1.053 percent of output ([19–20]/95).

### _wp1389 - 1.053 percent of output ([19–20]/95)

### Tax smoothing with uncertain potential output (Table 3 example)
- Scenario outcomes (yP(realized), yP(forecast), Primary Expenditures, Tax Revenue, Surplus, Surplus/yP(realized)):
  - "Pessimistic": 105, 100, 20, 21, 1, 0.95%
  - "Correct": 100, 100, 20, 20, 0, 0.00%
  - "Optimistic": 95, 100, 20, 19, -1, -1.05%
  - Mean: 100, 100, 20, 20, 0, -0.03%
- Parameter values reported:
  - Exp Ratio (g) 20.00%
  - Tax Ratio (t) 20.00%
- Key finding:
  - Potential output yp is assumed to follow a random walk.
  - Thus, the mean surplus ratio-to-output is -0.033 percent (deficit).
  - Dollar deficits average zero, but primary balance ratio is biased toward a deficit because a primary deficit is observed when potential output is lower.
  - Under this policy the debt ratio will grow (as shown formally by Tanner and Carey (2008)).

### Prospective liabilities
- Conceptual points:
  - Accumulated liabilities are the capitalized accumulation of past deficits; accumulated debt accB evolves as capitalized original debt plus capitalized deficit flows.
  - Distinction between discretionary primary surplus psd and non-discretionary element tw, with total primary surplus ps = psd - tw.
  - Prospective debt associated with non-discretionary deficits is the discounted sum of those prospective flows.
  - The ‘true’ debt equals accumulated debt plus prospective debt.
- Policy implication:
  - A tax smoothing policy implies a constant discretionary primary surplus psd whose level spreads payment for prospective liabilities evenly across all periods.
  - If the government disregards prospective liabilities, the delayed future adjustment will exceed the current required adjustment.
- Illustrative U.S. entitlement example (Batini, Callegari, and Guerreiro (BCG, 2010)):
  - Scenario 1 / Scenario 2 assumptions:
    - Real GDP Growth:
      - 2011-15 2.7 / 3.6
      - 2015-20 2.3 / 2.3
      - 2021-83 2.0 / 2.0
    - Real Interest Rate:
      - 2011-15 2.7 / 3.2
      - 2015-20 3.9 / 3.7
      - 2021-83 4.1 / 3.0
  - Adjustment needed to stabilize debt (in percent of PV of GDP):
    - 25-year horizon (2009-33): 4.4 / 4.6
    - 50-year horizon (2009-58): 6.1 / 6.7
    - 75-year horizon (2009-83): 7.7 / 8.4
    - Infinite Horizon (full repayment): 13.9 / 14.4
    - Effects of financial crisis excluded: 13.8 / 14.3
  - Notes:
    - Initial debt ratio (end-2008) is 44 percent of GDP; Present value of GDP obtained using discount rate of 3percent.
    - Scenario 2 reflects assumptions of US Congressional Budget Office.
  - Key interpretation:
    - To offset the first 25 years (2009–33) a fiscal adjustment of about 4.5 percent of GDP is required to stabilize the debt ratio at its end-2008 value, 44 percent of GDP.
    - Over 50 years the required adjustment rises to 6–6 ½ percent of GDP.
    - To offset 75 years requires about 8 percent of GDP.
    - For an infinite horizon the required adjustment is around 14 percent of GDP.
    - BCG estimates effect of the financial crisis on prospective debt is about 0.1 percent of GDP.

### The net worth approach
- Definitions and identities:
  - Public net worth (as a fraction of GDP) nw = NF a + F a - GROSS b - OLiab (using notation as in source).
  - NF a: recorded market value of non-financial assets; F a: financial assets; GROSS b: gross indebtedness; OLiab: other liabilities.
  - Prior sections used net debt; net debt definition implies accGROSS b - F a = acc b.
- Simplifying assumption for exposition: OLiab = 0.
- Evolution equations:
  - Financial assets and liabilities evolve according to expressions (41) and (42) (as in source).
  - Non-financial assets earn real rate of return net of depreciation equal to ρNF; gross return factor adjusted for real GDP growth is (1+ρNF)/(1+y).
  - Net worth relative to GDP evolves according to the equation displayed in the source combining NF, F, GROSS b, consumption and investment shares, and tax rates.
- Policy insight:
  - If government seeks to service gross debt without fiscal adjustment, gross financial assets may be liquidated; imputed consumption value of non-financial assets (e.g., occupied public building) does not provide an automatic option for debt service unless government changes its consumption decision (effectively a fiscal adjustment).

### Non-renewable resources: permanent income, narrow net worth, and bird-in-hand approaches (Table 5)
- Framework and variables:
  - Oil company generates period surplus zt (operational surplus).
  - Oil wealth ow0 is present value of net oil revenues from period 1 until depletion date N: ow0 = sum_{t=1..N} zt/θ^t (notation as in source).
  - Oil fund oft is hypothetical accounting financial asset evolving as oft = θ * of_{t-1} + zt (model interpretation).
  - Narrow public net worth nnw_t = ow_t + of_t - b_t (source notation).
- Numerical example assumptions:
  - r: real interest rate 4.0%
  - real GDP growth 3.5%
  - ow0 (2011) estimated to be 34.7 percent of GDP (prospective discounted revenues and costs).
  - Initial oil fund of0 = 0.
  - Initial debt b0 = 25 percent of GDP.
  - Thus initial narrow net worth nnw0 = ow0 + of0 - b0 = 34.7 + 0 - 25.0 = 9.7 percent of GDP.
  - Rate of return on oil fund equals debt interest rate = 4 percent.
  - Terminal value of oil fund in 2022: of2022 = 36.6 percent of GDP (present value equals ow0 = 34.7 percent of GDP).
- Table 5 highlights (Parts A–D):
  - Part B (Baseline policy):
    - psno (non-oil primary surplus / GDP) = -1.00 each period (non-oil primary deficit of 1 percent of GDP).
    - Debt b/GDP rises from 25.0 to 37.6 by 2022.
    - nnw (Net Worth / GDP) falls from 9.7 to -1.0 by 2022.
    - of - b (Net Financial Worth / GDP) evolves from -25.0 to -1.0 by 2022.
    - To stabilize net financial wealth at -1 percent in 2022 would require an adjustment of just over 1 percent of GDP in 2013 unless policy is changed earlier.
  - Part C (Net wealth preserving policy):
    - psno = -0.05 each period (non-oil primary surplus / GDP = -0.05).
    - nnw remains constant at 9.7 percent of GDP across periods.
    - Debt b/GDP rises modestly from 25.0 to 26.9 by 2022.
    - of - b (Net Financial Worth / GDP) rises to 9.7 by 2022.
    - Stabilizing ps in depletion year: -0.05; stabilizing fiscal adjustment in depletion year: 0.00.
  - Part D ("Bird-in-hand" policy):
    - of (bih) oil fund accumulates as in Part A; r*of gives flow of income from oil fund (e.g., 0.2, 0.4, ... up to 1.4 by 2022).
    - ps* (debt stabilizing primary surplus) reported as 0.12 each period.
    - 'Bird in hand' non-oil primary surplus declines over time from 0.12 down to -0.05 by later periods.
- Key policy comparisons and findings:
  - Focusing exclusively on financial wealth can distort the public sector position; preserving narrow net worth can allow smoother consumption paths and avoid abrupt near-term adjustments.
  - Computed net worth stabilizing non-oil primary surplus in example: (.04 + .035) / 1.035 * 9.70.05%psno = -0.05 (about 1/20th of GDP). (Expression as in source.)
  - Under the net worth stabilizing policy, a 1 percent adjustment in 2013 is avoided.
  - The Bird-In-Hand (BIH) approach counts only resources already placed into the natural resource fund (interest proceeds), and does not permit borrowing against unextracted resources; BIH tends to require early surpluses when fund is low but allows larger deficits after depletion relative to narrow net worth stabilizing policy.
  - Uncertainty in commodity prices argues for conservative long-run price estimates and precautionary structural surpluses; linking spending to long-run prices and building buffer assets reduces volatility.

### Contingent claims analysis and market indicators of default risk
- Market-implied default probabilities (Table 6: Approximate Sovereign Cumulative Default Probabilities: 5-year bonds):
  - AAA 0.0
  - AA 0.6
  - A 1.4
  - BBB 2.7
  - BB 9.0
  - B 22.0
  - CCC/CC 53.3
- CCA foundations and interpretation for sovereigns:
  - The Contingent Claims Approach (CCA) applies option-pricing theory (Black and Scholes (1973), Merton (1974)) to sovereigns by treating the present value of primary surpluses as sovereign "assets".
  - To keep primary surplus ratio to GDP constant, dollar primary surplus must grow at rate ŷ; the present value of a perpetual constant-primary-surplus stream is PV = PS0 *(1)/(r - ŷ) (expression as in source).
  - Sovereign "asset" dynamics are modeled as a stochastic process with capitalization of past primary surplus, a drift at rate r, and a volatility term capturing markets' view of implementation risk in achieving fiscal targets:
    - dPV = (r * PV - PS) dt + σ_PS * PV dW (expression and notation as in source: see equation (52)).
  - Interpretation of volatility σ_PS:
    - For sovereigns, σ_PS represents market-assessed implementation risk or uncertainty about authorities' ability/willingness to reach fiscal goals (IMF, 2011 referenced).
    - Example interpretation: If declared primary surplus target is 3 percent of GDP and PS σ = 0.3, then there are probabilities attached to lower realized primary surplus/GDP outcomes (as sketched in source).

*Source: _wp1389 - 1.053 percent of output ([19–20]/95).*

### 2.07 percent of GDP or lower, and so on.

### _wp1389 - 2.07 percent of GDP or lower, and so on.

### Contingent-claims framework for public-sector solvency
- The present value of primary surpluses evolves in continuous time with a stochastic shock term given by a Wiener process: /(0,1)dWtN.
- The term 2 0.5 * PS  reflects the uncertainty in the evolution of public sector (intangible) assets over time.
- Government net liabilities are measured as debt net of financial assets and may include prospective non-discretionary deficits PRO B 0 known with certainty.
- Over a horizon of t periods, government solvency condition: PV tt PSB.
- Distance-to-default (DTD) is the familiar expression from options literature, denoted as 2 d.
- The probability of default in period t is Pr(0) PV tt PSB; the risk-neutral measure equals the cumulative normal distribution evaluated at 2 d.

### Credit spreads and expected losses
- The credit spread t SPR is the difference between the rate on risky government debt and a riskless benchmark; it equals the logarithmic difference in prices of risky and riskless debt.
- Over a t-period horizon, expected losses t EL equal the value of riskless debt times the probability of non-repayment minus recovery value:
  - The first term: initial present value of the debt times the probability it will not be paid back.
  - The second term: recovery value of some stock of assets; defined as 00 PV APS. If loan not collateralized or guaranteed, 0.
- In the Merton-style interpretation, expected loss on a bond is like a short put with payoff max(, 0) PV BPS at maturity.

### Illustrative example (Table 7): hypothetical economy parameters
- Real rate of economic growth ˆy equals 2.8 percent.
- Risk-free interest rate r equals 3.8 percent.
- Initial GDP 0 400Y.
- Initial ratio of public debt to GDP: 150 percent (B = 600 currency units; % of GDP = 150.0).

Scenario summaries (Horizon = 5 years):
- Common assumptions:
  - Std. Dev. of PS  in Scenario (i) = 0.2.
  - Present value of primary surpluses PS PV and corresponding constant primary surplus ratio:
    - Scenario (i): PS PV = 600.0 (150.0% of GDP); Constant primary surplus = 5.8 (1.4% of GDP).
    - Scenario (ii): PS PV = 800.0 (200.0% of GDP); Constant primary surplus = 7.7 (1.9% of GDP).
    - Scenario (iii): PS PV = 800.0 (200.0% of GDP); Constant primary surplus = 7.7 (1.9% of GDP).
- Outcome metrics (Horizon = 5 years):
  - Distance to Default (DTD):
    - Scenario (i): 0.63
    - Scenario (ii): 1.27
    - Scenario (iii): 1.04
  - Probability of default N( - DTD):
    - Scenario (i): 26.6%
    - Scenario (ii): 10.2%
    - Scenario (iii): 14.9%
  - Spread SPR:
    - Scenario (i): 6.2%
    - Scenario (ii): 2.2%
    - Scenario (iii): 3.2%
- Implementation risk (primary surplus quantiles, Horizon = 5 years):
  - Primary surplus, 10% level:
    - Scenario (i): 3.6 (0.9% of GDP)
    - Scenario (ii): 4.8 (1.2% of GDP)
    - Scenario (iii): 4.2 (1.1% of GDP)
  - Primary surplus, 20% level:
    - Scenario (i): 4.3 (1.1% of GDP)
    - Scenario (ii): 5.8 (1.4% of GDP)
    - Scenario (iii): 5.3 (1.3% of GDP)
  - Primary surplus, 30% level:
    - Scenario (i): 5.0 (1.3% of GDP)
    - Scenario (ii): 6.7 (1.7% of GDP)
    - Scenario (iii): 6.2 (1.6% of GDP)

Scenario summaries (Horizon = 10 years):
- Distance to Default (DTD):
  - Scenario (i): 0.9
  - Scenario (ii): 0.9
  - Scenario (iii): 1.1
- Probability of default N( - DTD):
  - Scenario (i): 18.8%
  - Scenario (ii): 18.8%
  - Scenario (iii): 14.1%
- Spread SPR:
  - Scenario (i): 2.1%
  - Scenario (ii): 2.1%
  - Scenario (iii): 1.5%
- Implementation risk (primary surplus quantiles, Horizon = 10 years):
  - Primary surplus, 10% level:
    - Scenario (i): 3.1 (0.8% of GDP)
    - Scenario (ii): 4.1 (1.0% of GDP)
    - Scenario (iii): 3.4 (0.9% of GDP)
  - Primary surplus, 20% level:
    - Scenario (i): 4.1 (1.0% of GDP)
    - Scenario (ii): 5.4 (1.4% of GDP)
    - Scenario (iii): 4.7 (1.2% of GDP)
  - Primary surplus, 30% level:
    - Scenario (i): 5.0 (1.2% of GDP)
    - Scenario (ii): 6.6 (1.7% of GDP)
    - Scenario (iii): 5.9 (1.5% of GDP)

Illustrative scenario narrative and numeric outcomes:
- Scenario (i) Initial program:
  - Targets PS PV = 600 currency units; constant primary surplus 5.8 units (1.4% of GDP).
  - Five-year probability of default: 26.6 percent.
  - Five-year spread: 6.2 percent (market-observed).
  - Implementation shortfalls: worst 10% outcome primary surplus = 0.5 percent of GDP or lower; worst 20% = 1.1 percent or less; worst 30% = 1.3 percent.
- Scenario (ii) Adjustment—no increase in implementation risk:
  - Targets PS PV = 800 (200 percent of GDP); constant primary surplus 7.7 units (1.9% of GDP) — a permanent adjustment of ½ of one percent of GDP.
  - Default probability falls from 26.6 percent to 10.2 percent.
  - Spread falls by 400 basis points from 6.2 percent to 2.2 percent (noting table lists 2.2% for Scenario (ii) at 5 years).
- Scenario (iii) Adjustment—increase in implementation risk:
  - Same PS PV = 800 (200 percent of GDP) but PS  rises from 0.2 to 0.23.
  - Default probability falls to about 14.9 percent (rather than 10.2 percent).
  - Spread falls to 3.2 percent—about 100 basis points higher than in Scenario (ii).

### Key analytical lessons (from the exercise)
- Credibility and expectations management:
  - Fiscal adjustments must be credible; otherwise increased PS  can erode gains from lower financing costs.
  - Fiscal adjustments should be clearly explained to the public to reduce implementation risk.
- Implicit cost of adjustment:
  - An increase in the standard deviation PS  can be seen as an implicit “tax” on fiscal adjustment.
  - Alternative definition for maximum sustainable debt: debt may be “too high” if a fiscal adjustment that also reduces the sovereign spread is not possible.

### Policy implications and broader considerations
- Positive assessments:
  - Significant progress has been made in tools for positive debt-sustainability assessments (e.g., Fund’s DSA template and refinements).
- Normative assessments:
  - Analytical tools have improved to evaluate which policies should be implemented to achieve fiscal sustainability and benefit citizens.
  - Policy assessments aim to make a case for disciplined and credible fiscal policies using welfare calculations or less formal criteria.
- Quality of fiscal policy:
  - In addition to the size of adjustment, quality matters: reduce distortions and waste in tax systems and administration, broaden tax base, eliminate wasteful government expenditures, and provide efficient public goods and services.
  - Such quality improvements support higher and more stable economic growth.

*Source: Author’s Calculations*

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### _wp1389 - REFERENCES

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- Barro, Robert J., 1979, “On the Determination of the Public Debt,” Journal of Political Economy, Vol. 87, No. 5 (October), pp. 940–71.
- Chari, V., Lawrence J. Christiano and Patrick J. Kehoe, 1994, “Optimal Fiscal Policy in a Business Cycle Model,” Journal of Political Economy, Vol. 102, No. 4, pp. 617–52.
- Fisher, Lance and Geoffrey Kingston, 2005, “Joint Implications of Consumption and Tax Smoothing,” Journal of Money, Credit, and Banking, Vol.37, No. 6 (December) pp. 1101–19.
- Kydland, Finn E. and Edward C. Prescott, 1977, “Rules Rather Than Discretion: The Inconsistency of Optimal Plans,” Journal of Political Economy, University of Chicago Press, Vol. 85, No. 3, pp. 473–91.
- Kingston, Geoffrey, 1991, “Should Marginal Tax Rates Be Equalized Through Time?” Quarterly Journal of Economics, Vol. 106, No. 3 (August), pp. 911–24.
- Lloyd-Ellis, Huw, Shiqiang Zhan, and Xiaodong Zhu, 2005, “Tax Smoothing with Stochastic Interest Rates: A Reassessment of Clinton's Fiscal Legacy,” Journal of Money, Credit and Banking, Vol. 37, No. 4 (August), pp. 699–724.
- Ramsey F.P., 1927, “A Contribution to the Theory of Taxation,” Economic Journal, Vol. 37, No. 145, pp. 47–61.
- Kotlikoff, Laurence J., 2003, Generational Policy (Cambridge, MA: MIT Press).
- Kumhof, Michael and Irina Yakadina, 2007, “Politically Optimal Fiscal Policy,” IMF Working Paper 07/68 (Washington: International Monetary Fund). www.imf.org/external/pubs/ft/wp/2007/wp0768.pdf
- Kumhof, Michael and Evan Tanner, 2008, “Government Debt: A Key Role in Financial Intermediation,” in A Festschrift for Guillermo Calvo. ed. by Carmen Reinhart, Carlos Vegh, and Andres Velasco (Cambridge, Massachusetts: MIT Press).
- Tanner, Evan and Kevin Carey, 2008, “The Perils of Tax Smoothing: Sustainable Fiscal Policy with Random Shocks to Permanent Output,” Czech Journal of Economics and Finance, Vol. 58, Issue 11–12, pp. 502–24.

### Probabilistic, risk-based, and contingent-claims approaches to sovereign/default risk
- Gapen, Michael T., Dale F. Gray, Yingbin Xiao, and Cheng Hoon Lim, 2004, “The Contingent Claims Approach to Corporate Vulnerability Analysis: Estimating Default Risk and Economy-Wide Risk Transfer,” IMF Working Paper 04/121 (Washington: International Monetary Fund).
- Gray, Dale F., Zvi Bodie, and Robert C. Merton, 2007, “Contingent Claims Approach to Measuring and Managing Sovereign Risk,” Journal of Investment Management, Volume 5, No. 4.
- Garcia, Márcio and Roberto Rigobon, 2005, “A Risk Management Approach to Emerging Market's Sovereign Debt Sustainability with an Application to Brazilian Data,” in Inflation Targeting, Debt, and the Brazilian Experience: 1999 to 2003, eds. Francesco Giavazzi, Ilan Goldfajn, and Santiago Herrera (Cambridge, Massachusetts).
- Hostland, Douglas and Philippe Karam, 2005, “Assessing Debt Sustainability in Emerging Market Economies Using Stochastic Simulation Methods,” IMF Working Paper 05/226 (Washington: International Monetary Fund). www.imf.org/external/pubs/ft/wp/2005/wp05226.pdf
- Gray, Dale F., Elena Loukoianova, Samuel W. Malone, Samuel W., and Cheng-Hoon Lim, 2008, “A Risk-Based Debt Sustainability Framework: Incorporating Balance Sheets and Uncertainty,” IMF Working Paper 08/40 (Washington: International Monetary Fund).
- Garcia, Carlos, Jorge Restrepo, and Evan Tanner, 2011, “Fiscal Rules in a Volatile World: A Welfare-Based Approach,” Journal of Policy Modeling, Vol. 33 (July–August), pp. 649–76.

### Precautionary savings, consumption behavior, and related macro topics
- Carroll, Christopher D. and Miles S. Kimball, 1996, “On the Concavity of the Consumption Function,” Econometrica, Vol. 64, No. 4, (July), pp. 981–92.
- Caballero, Ricardo, 1990, “Consumption Puzzles and Precautionary Savings,” Journal of Monetary Economics, Vol. 25, pp. 113–16.
- Cochrane, John, 1998, “A Frictionless View of U.S. Inflation,” in NBER Macroeconomics Annual 1998, eds. Ben S. Bernanke and Julio Rotemberg, Vol.13 (Cambridge: Massachusetts, National Bureau of Economic Research).
- Friedman, Milton, 1960, A Program for Monetary Stability (New York: Fordham University Press).
- Gouri nchas, Pierre-Olivier and Jonathan A. Parker, 2001, “The Empirical Importance of Precautionary Saving,” American Economic Review, Vol. 91, No. 2 (May), pp. 406–12.
- Huggett, Mark and Sandra Ospina, 2001, “Aggregate Precautionary Savings: When is the Third Derivative Irrelevant?” Journal of Monetary Economics, Vol. 48, No. 2 (October), pp. 373–96.
- Kimball, Miles, 1990, “Precautionary Savings in the Small and in the Large,” Econometrica, Vol. 58, No. 1, pp. 53–74.
- Talmain, Gabriel, 1998, “An Analytical Approximate Solution to the Problem of Precautionary Savings,” Journal of Economic Dynamics and Control, Vol. 23, pp. 113–24.
- Carroll, Christopher D. and Miles S. Kimball, 1996, “On the Concavity of the Consumption Function,” Econometrica, Vol. 64, No. 4, (July), pp. 981–92.

### Sovereign risk, financial markets, and option-pricing foundations cited
- Black, Fischer and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, pp. 637–54.
- Merton, Robert C., 1973, “Theory of Rational Option Pricing,” The Bell Journal of Economics and Management Science, Vol. 4, No. 1 (Spring), pp. 141–83. http://jstor.org/stable/3003143
- Merton, Robert C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2 (May), pp. 449–70.
- Black, Fischer and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, pp. 637–54.

### Natural resources, commodity revenues, and oil-producing country issues
- Barnett, Steven and Rolando J. Ossowski, 2003, “Operational Aspects of Fiscal Policy in Oil-Producing Countries,” in Fiscal Policy Formulation and Implementation in Oil-Producing Countries, edited by Jeffrey M. Davis, Rolando J. Ossowski, and Annalisa Fedelino (Washington: International Monetary Fund).
- Davis, Jeffery, Ronald Ossowski, and Annalisa Fedelino, 2003, “Fiscal Policy Formulation and Implementation in Oil-Producing Countries” (Washington: International Monetary Fund).
- Boskin, Michael J., Marc S. Robinson, Terrence O'Reilly, and Praveen Kumar, 1985, “New Estimates of the Value of Federal Mineral Rights and Land,” American Economic Review, Vol. 75, No. 5 (December), pp. 923–36.
- Van der Ploeg. Frederick, 2011, “Natural Resources: Curse or Blessing?” Journal of Economic Literature, Vol. 49, No. 2 (June), pp. 366–420.
- Van der Ploeg, Frederick and Anthony J. Venables, 2011, “Harnessing Windfall Revenues: Optimal Policies for Resource‐Rich Developing Economies,” Economic Journal, Vol. 121, No. 551 (March), pp. 1–30.
- Ley, Eduardo, 2009, Fiscal (and External) Sustainability (Washington: World Bank). www.siteresources.worldbank.org/INTDEBTDEPT/.../FSPrimer.pdf

### Methodology, simulation, forecasting, and technical manuals
- Hunt, Ben and Aaron Drew, 1998, “The Forecasting and Policy System: Stochastic Simulations of the Core Model,” Reserve Bank of New Zealand Discussion Paper No. G98/6 (Wellington, New Zealand). www.ssrn.com/abstract=321393
- Fedelino, Annalisa, Anna Ivanova, and Mark Horton, 2009, “Computing Cyclically Adjusted Balances and Automatic Stabilizers,” IMF Technical Notes and Manuals 09/05 (Washington: International Monetary Fund). http://www.imf.org/external/pubs/ft/tnm/2009/tnm0905.pdf
- Girouard, Nathalie and Christophe André, 2005, “Measuring Cyclically-Adjusted Budget Balances for OECD Countries,” Organization for Economic Co-operation and Development Working Paper No. 434 (Paris: France).
- Gapen, Michael T., Dale F. Gray, Yingbin Xiao, and Cheng Hoon Lim, 2004, “The Contingent Claims Approach to Corporate Vulnerability Analysis: Estimating Default Risk and Economy-Wide Risk Transfer,” IMF Working Paper 04/121 (Washington: International Monetary Fund).
- Hadjenberg, Alejandro and Rafael Romeu, 2010, “Parameter Estimate Uncertainty in Probabilistic Debt Sustainability Analysis,” Staff Papers, International Monetary Fund, Vol. 57 (September), pp. 61–83.
- Kawakami, Kei and Rafael Romeu, 2011, “Identifying Fiscal Policy Transmission in Stochastic Debt Forecasts,” IMF Working Paper 11/107 (Washington: International Monetary Fund). www.imf.org/external/pubs/ft/wp/2011/wp11107.pdf
- Hostland, Douglas and Philippe Karam, 2005, “Assessing Debt Sustainability in Emerging Market Economies Using Stochastic Simulation Methods,” IMF Working Paper 05/226 (Washington: International Monetary Fund). www.imf.org/external/pubs/ft/wp/2005/wp05226.pdf

### IMF and institutional publications, evaluations, and manuals
- Independent Evaluation Office of the International Monetary Fund, 2003, Evaluation Report: Fiscal Adjustment in IMF-Supported Programs (Washington). http://www.ieo-imf.org/ieo/files/completedevaluations/09092003main.pdf
- International Monetary Fund, 2001, Government Finance Statistics Manual (Washington). http://www.imf.org/external/pubs/ft/gfs/manual/
- International Monetary Fund, 2011, Fiscal Monitor, April 2011: Shifting Gears: Tackling Challenges on the Road to Fiscal Adjustment, World Economic and Financial Surveys (Washington). http://www.imf.org/external/pubs/ft/fm/2011/01/fmindex.htm

*Source: _wp1389 - REFERENCES*

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