## 1. Econometric Methodology Underlying Fiscal Sustainability Analysis

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### Overview
- Objective: Examine sustainability of fiscal policy under uncertainty in three emerging market economies: Brazil, Mexico, and Turkey.
- Complementary assessments:
  - Retrospective: “If historical policies were to be continued into the future, would fiscal policy be sustainable—or will a modification of policies be required?”
  - Prospective: “What policies should be undertaken today in order to prevent the need for further adjustments in the future?”
- Methodological emphasis:
  - Simple (near) vector autoregression (VAR) for historical decomposition.
  - Multivariate stochastic simulations for prospective analysis.
  - Normative innovation: links “fan chart” forecasts to an objective function to compute required fiscal adjustments probabilistically.

### Key definitions and accounting identities
- Period budget constraint:
  - bt-1(1+r) + γt – τt = bt
  - where b is real government debt, γ is noninterest expenditures, τ are tax revenues.
- Intertemporal constraint:
  - b-1/(1+r) − E{Σ ps t/(1+r) t} = E{lim (bt/(1+r) t-1} t=0 t→∞
  - ps t = τt − γt is the expected primary surplus.
- No-Ponzi game condition:
  - E{lim bt/(1+r) t-1}= 0 t→∞
- Decompositions:
  - θt = θP + z(θ)t
  - pst ≡ τt − γt = θP − κ + z(ps)t
  - bt − bt-1 ≡ γt + θt − τt ≡ κ + z(θ)t − z(ps)t ≡ κ + zt

### Retrospective sustainability: approaches and conceptual points
- Approaches summarized:
  - Fiscal gap (noneconometric): ps* = {(r − λ)/(1+λ)}b where λ = GDP growth.
  - Stationarity tests of the deficit ∆bt = κ + zt.
  - Cointegration tests of revenues, expenditures, and debt.
  - Link ps t = κ + αbt-1: solvency if α > 0.
  - Historical decomposition (this paper): near-VAR to attribute debt evolution to baseline policy vs accumulated shocks; classify nonpolicy shocks as “lucky” or “unlucky,” and policy shocks as departures from implicit fiscal rule.
- Conceptual notes:
  - Intertemporal solvency is the least restrictive notion of sustainability (conditions (2) and (3)).
  - Government can run a constant deficit and remain solvent if debt growth is less than the interest rate r (McCallum (1984)).
  - Debt stabilization corresponds to κ = 0; tax-smoothing implies τP = γP + θP.

### Retrospective methodology highlights
- Near-VAR historical decomposition:
  - Vector X includes real debt (b), real primary deficit (pd), and nonpolicy variables (interest rates, exchange rates, industrial output, oil prices).
  - Historical decomposition expresses each element of X as baseline projection plus orthogonal impacts of shocks accumulated from the base period.
  - Change in debt ∆b at M+j:
    - ∆b_M+j = ∆b(base)_M+j + z*_b1j + z*_b2j + ..... z*_bIj
  - Policy sustainable over M+1 through M+j if:
    - b(base)_M+j / GDP_M+j ≤ b_M / GDP_M
- Definitions for counterfactuals and luck/unlucky:
  - ∆b(omit i)_M+j = ∆b_M+j - z*_bij
  - Lucky if b(omit i)_M+j > b_M+j; Unlucky if b(omit i)_M+j < b_M+j.

### Prospective sustainability: simulations and normative objective
- Simulation framework:
  - Simulated debt for t > J:
    - b(sim)_t = b(sim)_t-1*(1 + r(sim)_t) + pd(sim)_t
  - Simulated r and pd:
    - r(sim)_t = ζ_r0 + ζ*_r1t + ζ*_r2t + ..... ζ*_rIt
    - pd(sim)_t = ζ_p0 + ζ*_p1t + ζ*_p2t + ..... ζ*_pIt
  - Reports means, standard deviations, and fractiles (median, 75th, 90th percentiles) of simulated debt/GDP ratios.
  - Menu of policy options by modifying ζ_p0 (mean primary surplus).
- Normative objective (prudence / avoidance of undesirable outcomes):
  - Example CARA objective: Φ(τ_t) = -1/φ exp(-φ τ_t), φ ≤ 0.
  - Minimization yields:
    - τ_t* = κ_t* + γ_t + r b_t-1
    - κ_t* ≡ -φ σ_t^2 /2 ≥ 0
  - Interpretation:
    - For φ < 0, precautionary motive implies primary surplus positively related to variance of tax burden; debt ratio should fall over time.
    - φ = 0 reduces to Blanchard et al. debt stabilization benchmark.
  - Policy menu from simulations:
    - Identify average primary surplus required to keep debt ratio constant for all but the worst w-percent of cases (w = 50 percent, 75 percent, 90 percent) over horizons of one to five years.
    - Longer horizons imply lower required short-run adjustment (lower required primary surplus) because debt reduction benefits are cumulative.
- Practical caveat:
  - Lucas critique: policy changes may alter market behavior not captured by the econometric model; ad-hoc adjustments may be required.

### Comparison with extant methods
- Accounting-based fiscal gap assumes full knowledge of long-run GDP growth and interest rates.
- Econometric approach models joint interactions and uncertainty, providing richer information than accounting frameworks.
- Other stochastic simulation studies present mean forecasts and confidence bands; this paper converts tail probabilities into policy-relevant average primary surplus targets.

### Policy interpretations
- Sustainability is probabilistic under shocks to interest rates, exchange rates, output, and other variables.
- Authorities may target higher primary surpluses to reduce probability of future adjustments.
- A primary surplus that reduces probability of future adjustments to less than 50 percent will, on average, reduce the debt.
- The framework provides concrete targets: average primary surplus required to stabilize debt with specified confidence levels (90 percent and 75 percent) over one- to five-year horizons.
- Policymakers should consider model limitations and possible feedbacks from policy changes to market behavior.

### Brazil — retrospective decomposition (2000:5–2005:6) — key quantified results
- Initial Debt (b_M): 50.5 (percent of GDP)
- End Period Debt (b_M+J): 50.8 (percent of GDP)
  - Baseline Projection (b(base)_M+J): 50.7 (percent of GDP)
  - Shock Component (b_M+J - (b(base)_M+J)): 0.2 (percent of GDP)
- Shocks: variance and historical decomposition (percent of total variation in debt; b(omit)_M+J Percent of GDP) — preserved exactly as presented:
  - Oil Price (poil): 0.7 551.2
  - Exchange rate + int rat (ε+r): 97.2 50.2
  - Industrial Production (ip): 1.9 51.0
  - Primary Deficit (pd): 0.1 350.9
- Primary surplus indicators:
  - Initial primary surplus (ps(base)): 3.5 (percent of GDP)
  - Debt stabilizing constant primary surplus: 4.0 (percent of GDP)
- Findings:
  - Movements in exchange rates and interest rates jointly explained over 97 percent of variation in the debt ratio over 2000:5–2005:6.
  - When debt peaked in September 2002, the cumulative adverse impact of ε and r shocks (b_t – b(omit ε+r)_t) was about 13 percent of GDP.
  - By mid-2005 the gap (b_t – b(omit ε+r)_t) fell to about 0.6 percent of GDP.
  - Innovations in industrial production affected debt accumulation to a much smaller extent (under 2 percent of total variation); in 2003 output shocks helped reduce debt, with b(omit ip)_t – b_t about 1.3 percent of GDP in August 2003.
  - Primary surplus ratio rose from about 3.5 percent of GDP at end-2000 to over 6 percent by mid-2005 (4.8 percent end-year).
  - Counterfactual: if primary surplus had initially been adjusted to about 4 percent of GDP (rather than 3.5 percent), the debt ratio would have been stabilized without further increases in primary surplus.

### Brazil — prospective sustainability (higher interest rate scenario; Table 4b(i))
- Baseline first year primary surplus/GDP ps = 4.5 %
- Debt/GDP statistics (Mean, Standard Deviation, Median, 75th Percent, 90th Percent) by horizon:
  - Mean: 1 Year 52.19; 2 Years 52.51; 3 Years 53.05; 4 Years 53.65; 5 Years 54.72
  - Standard Deviation: 1 Year 6.64; 2 Years 9.95; 3 Years 13.39; 4 Years 16.08; 5 Years 19.35
  - Median: 1 Year 51.82; 2 Years 51.93; 3 Years 51.41; 4 Years 51.28; 5 Years 51.73
  - 75th Percent: 1 Year 56.63; 2 Years 58.55; 3 Years 61.29; 4 Years 62.30; 5 Years 64.18
  - 90th Percent: 1 Year 60.79; 2 Years 65.98; 3 Years 70.38; 4 Years 74.87; 5 Years 79.31
- Policy menu: primary surplus required to stabilize debt with given probabilities (initial ps):
  - 50 % probability requires initial ps of: 1 Year 5.44; 2 Years 5.17; 3 Years 5.14; 4 Years 5.14; 5 Years 5.20
    - average debt ratio, end of horizon: 51.40 for 1–5 Years
  - 75 % probability requires initial ps of: 1 Year 9.31; 2 Years 7.78; 3 Years 7.41; 4 Years 6.85; 5 Years 6.66
    - average debt ratio, end of horizon: 1 Year 47.30; 2 Years 45.75; 3 Years 43.85; 4 Years 43.57; 5 Years 42.79
  - 90 % probability requires initial ps of: 1 Year 12.92; 2 Years 10.55; 3 Years 8.75; 4 Years 8.92; 5 Years 8.60
    - average debt ratio, end of horizon: 1 Year 43.52; 2 Years 39.79; 3 Years 39.41; 4 Years 34.13; 5 Years 31.38
- Interpretation:
  - To stabilize debt on average over any horizon requires a primary surplus of at least 5 percent of GDP.
  - Required primary surplus to keep debt from rising with probability 75 percent falls as horizon increases: 9.3 percent for 1-year horizon, 6.7 percent for 5-year horizon.
  - For 90 percent probability over 5-year horizon required initial ps is 8.6 percent of GDP.

### Brazil — prospective sustainability (lower interest rate scenario; Table 4b(ii))
- First year primary surplus/GDP ps = 4.5 %
- Scenario assumptions: interest rates about 8½ percent (average); GDP growth about 3 ½ percent.
- Selected statistics preserved exactly:
  - Mean: 1 Year 48.5; 2 Years 46.3; 3 Years 44.1; 4 Years 41.7; 5 Years 39.5
  - Standard Deviation: 1 Year 3.8; 2 Years 5.3; 3 Years 6.7; 4 Years 7.5; 5 Years 8.4
  - Median: 1 Year 48.4; 2 Years 45.9; 3 Years 43.6; 4 Years 41.3; 5 Years 38.9
  - 75th Percent: 1 Year 51.0; 2 Years 49.6; 3 Years 48.6; 4 Years 46.1; 5 Years 44.5
  - 90th Percent: 1 Year 53.5; 2 Years 53.7; 3 Years 52.3; 4 Years 51.7; 5 Years 50.2
- Policy menu (90 % stabilizing probability requires initial primary surplus of):
  - 1 Year 6.6; 2 Years 5.5; 3 Years 5.0; 4 Years 4.6; 5 Years (table shows a 3-year horizon required initial primary surplus is 5 percent of GDP).
- Key outcome:
  - Under these assumptions, by 2010 average debt falls to 39½ percent; by end-of-horizon the probability that debt does not rise exceeds 90 percent.

### Brazil — counterfactual prospective (2000–05; Table 4c)
- First year primary surplus/GDP ps = 3.5
- Debt/GDP statistics by horizon:
  - Mean: 1 Year 50.43; 2 Years 51.23; 3 Years 52.27; 4 Years 53.54; 5 Years 55.26
  - Standard Deviation: 1 Year 4.37; 2 Years 6.41; 3 Years 8.48; 4 Years 10.03; 5 Years 12.12
  - Median: 1 Year 50.22; 2 Years 51.15; 3 Years 52.15; 4 Years 53.11; 5 Years 54.33
  - 75th Percent: 1 Year 53.47; 2 Years 55.23; 3 Years 57.73; 4 Years 59.44; 5 Years 62.08
  - 90th Percent: 1 Year 56.29; 2 Years 59.66; 3 Years 63.44; 4 Years 66.76; 5 Years 70.82
- Counterfactual findings:
  - Over the 5-year horizon mean debt/GDP ratio rises from 50.4 percent to 55.3 percent.
  - Simulated debt exceeds 64.2 percent and 79.3 percent with probabilities of 25 percent and 10 percent, respectively.
- Policy menu (stabilizing debt with given probabilities):
  - 50 % requires primary surplus of: 1 Year 3.21; 2 Years 3.81; 3 Years 4.01; 4 Years 4.10; 5 Years 4.18
    - average debt ratio, end of horizon: 1 Year 50.76; 2 Years 50.13; 3 Years 50.66; 4 Years 50.93; 5 Years 51.42
  - 75 % requires primary surplus of: 1 Year 6.21; 2 Years 5.62; 3 Years 5.54; 4 Years 5.38; 5 Years 5.36
    - average debt ratio, end of horizon: 1 Year 47.62; 2 Years 46.74; 3 Years 45.60; 4 Years 45.12; 5 Years 44.49
  - 90 % requires primary surplus of: 1 Year 8.65; 2 Years 7.43; 3 Years 7.00; 4 Years 6.62; 5 Years 6.50
    - average debt ratio, end of horizon: 1 Year 45.08; 2 Years 42.84; 3 Years 40.76; 4 Years 39.47; 5 Years 37.77
- Caveats:
  - Recent debt management reduced fraction of debt denominated or indexed to the U.S. dollar; this may reduce exchange rate risk only if exchange rate shocks are not transmitted to interest rates.
  - Some simulations omitting exchange rate shocks yielded results very close to Table 4.

### Mexico — retrospective and prospective highlights
- Retrospective (1999:5–2005:4):
  - Initial Debt (bM): 19.70 (percent of GDP)
  - End Period Debt (bM+J): 18.10
    - Baseline Projection (b(base)M+J): 17.69
    - Shock Component: 0.41
  - Variance decomposition (percent of total variation; percent of GDP contribution):
    - Exchange rate + interest rate (ε+r): 15.5; 18.23
    - Deficit (∆b, includes pd): 79.6; 17.40
    - Industrial Production (ip): 2.2; 18.29
    - Oil Price (poil): 2.8; 18.08
  - Findings:
    - Base-period debt/GDP ~19 percent; baseline forecast 17.7 percent — fiscal policy sustainable by traditional measure.
    - Discretionary shocks had a slightly positive impact on debt; omitting these shocks would have reduced debt by about one-half percent of GDP.
    - Oil price shocks had a small but positive impact on debt, suggesting oil windfalls were spent rather than saved.
- Prospective (from 2005; Table 5b):
  - Initial period primary surplus/GDP ps = 2.1%
  - Debt/GDP statistics (Mean, Std Dev, Median, 75th Percent, 90th Percent) by horizon:
    - Mean: 1 Year 45.0; 2 Years 43.5; 3 Years 41.9; 4 Years 40.2; 5 Years 38.7
    - Standard Deviation: 1 Year 2.1; 2 Years 3.4; 3 Years 4.2; 4 Years 4.9; 5 Years 5.6
    - Median: 1 Year 44.9; 2 Years 43.3; 3 Years 41.5; 4 Years 40.0; 5 Years 38.1
    - 75th Percent: 1 Year 46.5; 2 Years 45.7; 3 Years 44.6; 4 Years 43.1; 5 Years 42.0
    - 90th Percent: 1 Year 47.7; 2 Years 47.9; 3 Years 47.6; 4 Years 46.6; 5 Years 46.0
  - Key outcomes:
    - Mean projection reduces debt from 45.0 percent in 2005 to 38.7 percent in 2010.
    - By 2010, a 10 percent chance debt will exceed 46 percent.
  - Policy menu:
    - 75 % requires primary surplus of: 1 Year 3.2; 2 Years 2.3; 3 Years 1.9; 4 Years 1.6; 5 Years 1.5
      - average debt ratio, end of horizon: 1 Year 42.7; 2 Years 43.1; 3 Years 42.6; 4 Years 42.3; 5 Years 41.9
    - 90 % requires primary surplus of: 1 Year 4.4; 2 Years 3.2; 3 Years 2.8; 4 Years 2.4; 5 Years 2.3
      - average debt ratio, end of horizon: 1 Year 42.7; 2 Years 41.2; 3 Years 39.9; 4 Years 39.1; 5 Years 38.0
  - Resource-revenue caveat:
    - Spending from oil windfalls appears to have been used to boost spending rather than the surplus; if oil revenues fall, preserving the same primary surplus implies symmetric cuts to spending or raising non-oil revenues.

### Turkey — retrospective and prospective highlights
- Historical context:
  - Currency crises in 1994 and 2000–01 increased debt via banking sector losses and defensive interest rate hikes.
  - Under recent IMF program, Turkey achieved a primary surplus exceeding 6 ½ percent of GDP; debt ratio fell from over 90 percent in 2000 to about 55 ½ percent in 2005–06.
- Retrospective quantifications (Table 6a context):
  - Initial Debt (bM): 43.2 (percent of GDP)
  - End Period Debt (bM+J): 48.8 (percent of GDP)
  - Baseline Projection (b(base)M+J): 49.1 (percent of GDP)
  - Shock Component (bM+J - (b(base)M+J)): -0.2 (percent of GDP)
  - Percent of total variation in debt (two-number entries preserved exactly):
    - Oil Price (poil): 8.3 and 48.1
    - Exchange rate + interest rate (ε + r): 20.4 and 49.3
    - Deficit (∆b, includes pd): 60.0 and 50.9
    - Industrial Production (ip): 11.3 and 47.1
  - Specific effects:
    - Omitting industrial production shocks reduces debt by about 1.9 percent of GDP.
    - Omitting exchange rate and interest rate shocks leaves debt lower than baseline by about 1 percent of GDP.
- Prospective assumptions and outcomes (Table 6b):
  - Scenario assumptions:
    - Mean primary surplus assumed 6.5 percent of GDP in 2006 and afterwards.
    - Average economic growth just under 5 percent.
    - Average real interest rate about 8 percent per annum.
    - Below-the-line shocks (public assumption of financial sector obligations) prospectively assumed zero.
  - Debt-path statistics (preserved exactly):
    - No Shock Scenario: 49.6 45.5 40.8 36.2 31.7
    - Mean: 51.3 49.2 46.0 42.8 39.4
    - Standard Deviation: 6.3 9.7 11.7 13.5 15.1
    - Median: 50.9 48.0 44.8 40.4 37.3
    - 75th Percent: 55.3 55.0 52.9 50.9 47.2
    - 90th Percent: 59.9 61.9 61.3 60.8 58.9
  - Risk and stabilization requirements:
    - Over the five year horizon, there is a 10 percent probability that debt/GDP will rise to at least 59 percent.
    - Stabilizing debt with probability 90% requires first year primary surplus of: 10.8 9.5 8.5 8.1 7.5 (horizons 1–5 years).
    - Corresponding average primary surplus/GDP, years 1–5: 10.3 9.1 8.0 7.6 7.1
    - Average debt ratio, end of horizon: 47.4 43.8 41.2 38.2 36.5
  - Illustrative scenarios:
    - No-shock scenario reduces debt/GDP from 55.5 percent to about 32 percent by 2010.
    - When random shocks included, mean debt ratio falls to about 39 percent; tail risks substantial.
    - One-year horizon stabilization with 90 percent probability requires first-year primary surplus just under 11 percent of GDP; five-year horizon average required about 7 percent of GDP.

### Comparative conclusions, policy implications, and suggested next steps
- Comparative scope:
  - Paper examined sustainability under uncertainty for Brazil, Mexico, and Turkey, both retrospectively and prospectively.
- Methodological advantages:
  - VAR-based framework uses data to inform the policy menu more richly than accounting frameworks and converts tail probabilities into explicit primary surplus targets.
- Policy implications:
  - Shocks materially affect debt outcomes; authorities may need higher primary surpluses to achieve high-probability stabilization.
  - Longer horizons reduce required average primary surplus for achieving given stabilization probabilities.
- Suggested next steps from the text:
  - Place analysis into a general equilibrium model to permit welfare analysis of costs and benefits of further fiscal adjustment.
  - Determine optimal primary surplus and debt reduction path conditional on specific technology and preferences for a country.

*Italic source: _wp06295 - 1. Econometric Methodology Underlying Fiscal Sustainability Analysis.......................16*

### 1. Econometric Methodology Underlying Fiscal Sustainability Analysis.......................16

### 1. Econometric Methodology Underlying Fiscal Sustainability Analysis.......................16

### Overview
- Objective: Examine sustainability of fiscal policy under uncertainty in three emerging market economies: Brazil, Mexico, and Turkey.
- Two complementary assessments:
  - Retrospective: “If historical policies were to be continued into the future, would fiscal policy be sustainable—or will a modification of policies be required?”
  - Prospective: “What policies should be undertaken today in order to prevent the need for further adjustments in the future?”
- Methodological emphasis: use of a simple (near) vector autoregression (VAR) for historical decomposition and multivariate stochastic simulations for prospective analysis.
- Distinction from prior work: links “fan chart” forecasts to an objective function to compute required fiscal adjustments probabilistically (normative approach).

### Key Definitions and Identities
- Period budget constraint (notation preserved from source):
  - bt-1(1+r) + γt – τt = bt
  - where b is real government debt, γ is noninterest expenditures, τ are tax revenues.
- Intertemporal constraint (forward substitution):
  - b-1/(1+r) − E{Σ ps t/(1+r) t} = E{lim (bt/(1+r) t-1} t=0 t→∞
  - ps t = τt − γt is the expected primary surplus.
- No-Ponzi game condition:
  - E{lim bt/(1+r) t-1}= 0 t→∞
- Interest expenditures decomposition:
  - θt = θP + z(θ)t
- Primary surplus decomposition:
  - pst ≡ τt − γt = θP − κ + z(ps)t
- Deficit representation:
  - bt − bt-1 ≡ γt + θt − τt ≡ κ + z(θ)t − z(ps)t ≡ κ + zt

### Retrospective Sustainability
- Question answered: whether historical policies, if continued, would be sustainable.
- Approaches summarized include:
  - Fiscal gap (noneconometric): evaluates historical primary surplus against debt-stabilizing benchmark ps* = {(r − λ)/(1+λ)}b, where λ = GDP growth.
  - Stationarity tests of the deficit ∆bt = κ + zt (time-series econometric): solvency guaranteed by stationarity of real deficit but debt may still rise if deficit fluctuates around a non-zero mean.
  - Cointegration tests of revenues and expenditures: solvency guaranteed by cointegration of primary expenditures, revenues, and debt, but debt may still rise unless vector of coefficients is [1,-1,r] with no constant or trend.
  - Link between primary surplus and debt (ps t = κ + αbt-1): solvency assured if α > 0, but κ need not be zero.
  - Historical decomposition (this paper): uses a simple (near) VAR to attribute evolution of debt from a base period to either baseline policy or accumulated shocks; classifies contributions of nonpolicy variable shocks as “luck” or “unlucky,” and shocks to fiscal policy (primary deficit) as departures from an implicit fiscal rule.
- Conceptual points:
  - Intertemporal solvency is the least restrictive notion of sustainability (conditions (2) and (3)); government can run a constant deficit and remain solvent if debt growth is less than the interest rate r (McCallum (1984)).
  - Debt stabilization corresponds to κ = 0; tax-smoothing rationale implies long-run taxes τP = γP + θP, equivalent to debt stabilization.

### Prospective Sustainability
- Question answered: what policies today prevent future adjustments.
- Standard (noneconometric) benchmark: target primary surplus that stabilizes debt conditional on forecasts for GDP growth and interest rates (Blanchard and others (1990); Talvi and Végh (2000)).
- Stress-test approaches (IMF (2003)): evaluate outcomes under adverse shocks in isolation (e.g., two standard deviations).
- Stochastic simulation approaches: multivariate stochastic simulations of debt accumulation produce “fan charts” since forecast variance increases with horizon (Hoffmaister and others (2001); Garcia and Rigobon (2004); Celasun, Debrun, and Ostry (2006); Penalver and Thwaites (2006)).
- This paper’s normative innovation:
  - Links fan-chart forecasts to an objective function (similar to Tanner and Carey (2005)) that reflects avoidance of undesirable outcomes (prudence).
  - Calculates the average primary surplus required to stabilize debt with probability 90 percent (and, where applicable, 75 percent) for one- to five- year horizons.
- Practical caveat: Lucas critique — policy changes may alter behavior of market participants in ways not captured by the econometric model; ad-hoc adjustments may be required and this limitation is shared with other debt sustainability frameworks.

### Methodology Highlights
- Retrospective analysis:
  - Use near-VAR historical decomposition to separate baseline policy path from shocks to interest rates, exchange rates, output, and fiscal policy.
  - Baseline forecast corresponds to the debt stabilization notion used in fiscal gap approaches.
- Prospective analysis:
  - Simulate the estimated multivariate stochastic model to generate distributions (fan charts) of future debt paths.
  - Map the upper tail probabilities of debt outcomes into required average primary surplus adjustments via an objective function emphasizing avoidance of high-debt outcomes (value-at-risk style).
- Comparison with extant methods:
  - Accounting-based fiscal gap calculations assume full knowledge of long-run GDP growth and interest rates; econometric approach models joint interactions and uncertainty.
  - Other stochastic simulation studies typically present mean forecasts and confidence bands; this paper explicitly converts tail probabilities into policy-relevant average primary surplus targets.

### Policy Implications and Interpretations
- Sustainability is inherently probabilistic in the presence of shocks to interest rates, exchange rates, output, and other variables; authorities may target higher primary surpluses to reduce the probability of future adjustments.
- A primary surplus that reduces the probability of future adjustments to less than 50 percent will, on average, reduce the debt.
- The normative framework provides concrete targets: the average primary surplus required to stabilize debt with specified confidence levels (90 percent and 75 percent) over horizons of one to five years.
- Policymakers should recognize limitations of econometric models (Lucas critique) and consider possible feedbacks from policy changes to market behavior when implementing recommended fiscal adjustments.

*Italic source: _wp06295 - 1. Econometric Methodology Underlying Fiscal Sustainability Analysis.......................16*

### 1. Fiscal gap

### 1. Fiscal gap

### Methods and Taxonomy
- Listed non-econometric and econometric approaches:
  - Fiscal gap (noneconometric). Blanchard and others (1990); Talvi-Végh (2000). Primary surplus should be equal to debt stabilizing benchmark ps* = {(r-λ)/(1+λ)}b, λ = GDP growth.
  - 1a. Fiscal gap (noneconometric). Croce and Juan-Ramon (2003). Like approach (1) but permits gradual adjustment.
  - 2. Stress test (noneconometric). IMF (2003a) and subsequent country reports. Targeted primary surplus typically aims at debt reduction. Alternative scenarios for two standard deviation shocks to interest rates, growth, etc.
  - 3. Value-at-Risk (noneconometric). Kopits and Barnhill (2003, applied to Ecuador). Examines main sources of shocks to net worth.
  - 4. Value-at-Risk (econometric). Adrogué (2004, applied to Central American countries). Forecasts deficit, debt.
  - 5. Simulated debt projections, baseline policies (econometric or other stochastic model). Celasun, Debrun, and Ostry (2006), and Garcia and Rigobon (2004); see also Hostland and Karam (2005). Projects debt accumulation under uncertainty (means and confidence intervals, including “fan charts”).
  - 6. Simulations debt projections, baseline and adjustment policies (econometric). This paper; see also Hoffmaister and others (2001), Guerson (2004), Koeva (2005), Penalver and Thwaites (2006). Uses projections similar to (5), includes alternative policies, consistent with objective to avoid further adjustment for all but the worst w-percent of cases.

### Overview of Methodology
- Model framework:
  - Uses a near-vector autoregression (VAR) model of fiscal policy.
  - Vector X includes real debt (b), real primary deficit (pd), and nonpolicy variables such as interest rates, exchange rates, industrial output, oil prices.
  - Time series model development steps: unit root tests, determination of optimal lag length, analysis of model structure and identification, diagnostic procedures.
  - Regime isolation primarily via prior country knowledge; discrete intercept shifts (dummy variables) used in some cases.
- Historical decomposition and variance decomposition:
  - Historical decomposition expresses each element of X as sum of (i) baseline projection conditional on information available in base period M and (ii) orthogonal impacts of shocks accumulated from M+1 forward.
  - Change in debt ∆b at M+j:
    - ∆b_M+j = ∆b(base)_M+j + z*_b1j + z*_b2j + ..... z*_bIj
  - Debt level at end of M+j:
    - b_M+j = b_M+j-1 + ∆b(base)_M+j + z*_b1j + z*_b2j + ..... z*_bIj
  - Policy sustainable over M+1 through M+j if:
    - b(base)_M+j / GDP_M+j ≤ b_M / GDP_M
  - Counterfactual (omit i) deficit and debt:
    - ∆b(omit i)_M+j = ∆b_M+j - z*_bij
    - b(omit i)_M+j = b(omit i)_M+j-1 + ∆b_M+j - z*_bij
  - Definition of “lucky” and “unlucky” with respect to non-policy shock i:
    - Lucky if b(omit i)_M+j > b_M+j
    - Unlucky if b(omit i)_M+j < b_M+j
- Taxonomy summary (Table 3):
  - Categories hinge on baseline sustainability and whether shocks are beneficial (“Lucky”) or adverse (“Unlucky”):
    - Sustainable and lucky: debt does not rise.
    - Sustainable but unlucky: policy.
    - Unsustainable but lucky.
    - Unsustainable and unlucky: debt rises.

### Retrospective Sustainability: interpretation and issues
- Baseline definitions:
  - pd(base) often estimated as a fixed mean, but may include time trends or dummy variables if mean primary surplus changed during sample.
  - “Fiscal dominant” or “non-Ricardian” regimes: primary surplus invariant to shocks from other variables; literature notes implications for monetary policy, but intertemporal budget can be balanced if average primary surplus is high enough.
- Role of shocks:
  - Interest rate shocks can have cumulative impacts on debt that do not cancel out even if r_t fluctuates about r(base).
  - Sequence matters: adverse shocks early can boost debt and not be fully neutralized by later good shocks.
- Shocks to policy variables:
  - Policy shocks reflect departures from estimated policy reaction functions, capturing discretionary policy and random shocks to primary surplus processes.
  - Counterfactual: if expansionary shock omitted, debt would have been lower; if contractionary shock omitted, debt would have been higher.

### Prospective Sustainability / Objective Function
- Simulation framework:
  - Simulated debt b(sim)_t for t > J:
    - b(sim)_t = b(sim)_t-1*(1 + r(sim)_t) + pd(sim)_t
  - Simulated interest rate and primary deficit:
    - r(sim)_t = ζ_r0 + ζ*_r1t + ζ*_r2t + ..... ζ*_rIt
    - pd(sim)_t = ζ_p0 + ζ*_p1t + ζ*_p2t + ..... ζ*_pIt
  - ζ_r0 and ζ_p0 are assumed mean levels; ζ* terms are simulated impacts of shocks.
  - Simulations report means, standard deviations, and fractiles (median, 75th, and 90th percentiles) of simulated debt/GDP ratios.
  - Can modify mean primary surplus ζ_p0 to generate menu of policy options.
- Normative objective and risk aversion:
  - Authority objective example: CARA / exponential objective Φ(τ_t) = -1/φ exp(-φ τ_t), where φ ≤ 0 is “prudence.”
  - Minimizing such cost function yields long-run (expected) relationship between tax rates, expenditures, and debt:
    - τ_t* = κ_t* + γ_t + r b_t-1
    - where κ_t* ≡ -φ σ_t^2 /2 ≥ 0
  - For φ < 0 (precautionary motive): primary surplus positively related to variance of tax burden (γ+rb); debt ratio should fall over time.
  - If φ = 0, this collapses to debt stabilization benchmark proposed by Blanchard and others.
  - Prudence parameter -φ interpreted as willingness to pay for precautionary cushion; if -φ ≥ -φ(z) for some critical value, government willing to levy taxes today to “cover itself” with probability (1–z).
- Policy menu from simulations:
  - Simulations identify primary surplus required to keep debt ratio constant for all but the worst w-percent of cases (w = 50 percent, 75 percent, 90 percent) over a given horizon.
  - Longer horizons imply less stringent short-run adjustment (lower required primary surplus) because debt reduction benefits are cumulative.
  - Counterfactual prospective analyses can use data ending at prior date M+J* (J* < J) to assess what conclusions would have been reached using only information available then.

### Brazil, 2000–05: empirical application
- Background:
  - Public debt rose from about 30 percent of GDP during the 1990s to about 51 percent in 2005.
  - 2000–05 period: primary surplus rose from about zero to just over 3 percent of GDP in 2000; debt/GDP was about 49 percent then. Staff projections had envisaged gradual reduction to about 46 ½ percent of GDP by 2005.
  - Instead, debt ratio rose between 2000 and 2004, peaking at about 60 percent of GDP in 2002; by 2004 it fell but did not meet initial projections.
- VAR specification for Brazil:
  - X(Brazil)_t = [ip_t, pd_t, ε_t, r_t]
    - ip: industrial production index
    - pd: primary deficit
    - ε: real depreciation (bilaterally, against the U.S. dollar)
    - r: implicit average real interest factor r_t = ([b_t + pd_t]/b_t-1) - 1
  - Exogenous variables: change in oil prices and discrete intercept dummy variables.
  - Principal estimates use mid-1995 to mid-2005 sample with two dummy intercepts:
    - Crisis dummy: D = 1 for t = 1999:1–1999:4, D = 0 otherwise
    - Floating period dummy: D = 0 for t = 1995:5–1999:4, D = 1 thereafter
  - Time trend included to capture increases in primary surplus during 2000–05.
  - Aikaike and Schwarz tests suggest 4 lags.
- Retrospective analysis (baseline mid-2000 (M = 2000:5) to mid-2005):
  - Initial Debt (b_M): 50.5 (percent of GDP)
  - End Period Debt (b_M+J): 50.8 (percent of GDP)
    - Baseline Projection (b(base)_M+J): 50.7 (percent of GDP)
    - Shock Component (b_M+J - (b(base)_M+J)): 0.2 (percent of GDP)
  - Shocks: variance and historical decomposition (percent of total variation in debt; b(omit)_M+J Percent of GDP)
    - Oil Price (poil): 0.7 551.2 (Note: values appear together in source formatting)
    - Exchange rate + int rat (ε+r): 97.2 50.2
    - Industrial Production (ip): 1.9 51.0
    - Primary Deficit (pd): 0.1 350.9
  - Initial primary surplus (ps(base)): 3.5 (percent of GDP)
  - Debt stabilizing constant primary surplus: 4.0 (percent of GDP)
  - Key findings:
    - Movements in exchange rates and interest rates jointly explained over 97 percent of variation in the debt ratio over 2000:5–2005:6.
    - When debt peaked in September 2002, the cumulative adverse impact of ε and r shocks (b_t – b(omit ε+r)_t) was about 13 percent of GDP.
    - By mid-2005 the gap (b_t – b(omit ε+r)_t) fell to about 0.6 percent of GDP.
    - Innovations in industrial production affected debt accumulation to a much smaller extent (under 2 percent of total variation); in 2003 output shocks helped reduce debt, with b(omit ip)_t – b_t about 1.3 percent of GDP in August 2003.
    - Primary surplus ratio rose from about 3.5 percent of GDP at end-2000 to over 6 percent by mid-2005 (4.8 percent end-year).
    - Illustrative counterfactual: if primary surplus had initially been adjusted to about 4 percent of GDP (rather than 3.5 percent), the debt ratio would have been stabilized without further increases in primary surplus.
- Notes on data and robustness:
  - All Brazilian debt data corrected for contingent liabilities.
  - Alternative estimates using post-1999 data confirm that upswing in debt from 2001–03 was largely due to innovations to exchange rates and interest rates rather than baseline policy.
  - End-period values for b_t and b(base)_t are very close; omission of the crisis dummy alters this result.

### Prospective Analysis for Brazil (from 2005 onward)
- Simulation setup:
  - Baseline primary surplus for initial simulation year (2005:6) set to roughly actual policy: about 4 ½ percent of GDP.
  - Table 4b(i) scenario assumes real interest factor = 12.8 and mean GDP growth just under 4 percent.
  - Simulations conducted with 1000 draws reveal a modest increase in the mean debt/GDP ratio (detailed simulated values and percentiles are in the source tables not reproduced here).

*Source: _wp06295 - 1. Fiscal gap (IMF working paper content provided).*

### 51.4 percent in 2005 to 54.7 percent in 2010. They also show the probability of less desirable

### _wp06295 - 51.4 percent in 2005 to 54.7 percent in 2010. They also show the probability of less desirable

### Brazil — Prospective sustainability (higher interest rate scenario; Table 4b(i))
- Baseline first year primary surplus/GDP ps = 4.5 %
- Statistics (Mean, Standard Deviation, Median, 75th Percent, 90th Percent) by Time Horizon:
  - Mean: 1 Year 52.19; 2 Years 52.51; 3 Years 53.05; 4 Years 53.65; 5 Years 54.72
  - Standard Deviation: 1 Year 6.64; 2 Years 9.95; 3 Years 13.39; 4 Years 16.08; 5 Years 19.35
  - Median: 1 Year 51.82; 2 Years 51.93; 3 Years 51.41; 4 Years 51.28; 5 Years 51.73
  - 75th Percent: 1 Year 56.63; 2 Years 58.55; 3 Years 61.29; 4 Years 62.30; 5 Years 64.18
  - 90th Percent: 1 Year 60.79; 2 Years 65.98; 3 Years 70.38; 4 Years 74.87; 5 Years 79.31
- Policy menu: primary surplus required to stabilize debt (b) with given probabilities:
  - 50 % probability; Requires initial ps of: 1 Year 5.44; 2 Years 5.17; 3 Years 5.14; 4 Years 5.14; 5 Years 5.20
    - average debt ratio, end of horizon: 51.40 for 1–5 Years
  - 75 % probability; Requires initial ps of: 1 Year 9.31; 2 Years 7.78; 3 Years 7.41; 4 Years 6.85; 5 Years 6.66
    - average debt ratio, end of horizon: 1 Year 47.30; 2 Years 45.75; 3 Years 43.85; 4 Years 43.57; 5 Years 42.79
  - 90 % probability; Requires initial ps of: 1 Year 12.92; 2 Years 10.55; 3 Years 8.75; 4 Years 8.92; 5 Years 8.60
    - average debt ratio, end of horizon: 1 Year 43.52; 2 Years 39.79; 3 Years 39.41; 4 Years 34.13; 5 Years 31.38
- Key interpretation:
  - To stabilize debt on average over any horizon requires a primary surplus of at least 5 percent of GDP.
  - Required primary surplus to keep debt from rising with probability 75 percent falls as horizon increases: 9.3 percent for 1-year horizon (mean debt falls to 47.3 percent of GDP), 6.7 percent for 5-year horizon (mean debt falls to 42.8 percent in 2010).
  - For 90 percent probability over 5-year horizon, required primary surplus is 8.6 percent of GDP (mean debt falls to 31.4 percent in 2010).
- Risk quantiles illustrate substantial tail risk: by 2010 the debt ratio may exceed 64.2 percent with probability 25 percent and 79.3 percent with probability 10 percent (reported elsewhere in the text).

### Brazil — Prospective sustainability (lower interest rate scenario; Table 4b(ii))
- First year primary surplus/GDP ps = 4.5 %
- Scenario assumptions: interest rates about 8½ percent (average) over the period; GDP growth about 3 ½ percent.
- Statistics (selected exact entries):
  - Mean: 1 Year 48.5; 2 Years 46.3; 3 Years 44.1; 4 Years 41.7; 5 Years 39.5
  - Standard Deviation: 1 Year 3.8; 2 Years 5.3; 3 Years 6.7; 4 Years 7.5; 5 Years 8.4
  - Median: 1 Year 48.4; 2 Years 45.9; 3 Years 43.6; 4 Years 41.3; 5 Years 38.9
  - 75th Percent: 1 Year 51.0; 2 Years 49.6; 3 Years 48.6; 4 Years 46.1; 5 Years 44.5
  - 90th Percent: 1 Year 53.5; 2 Years 53.7; 3 Years 52.3; 4 Years 51.7; 5 Years 50.2
- Policy menu (90 % stabilizing probability requires initial primary surplus of):
  - 1 Year 6.6; 2 Years 5.5; 3 Years 5.0; 4 Years 4.6; 5 Years (ellipsis in table) — table shows a 3-year horizon required initial primary surplus is 5 percent of GDP.
- Key outcome:
  - Under these assumptions, by 2010 average debt falls to 39½ percent; by end-of-horizon the probability that debt does not rise exceeds 90 percent.

### Brazil — Counterfactual prospective (2000–05; Table 4c)
- First year primary surplus/GDP ps = 3.5
- Statistics (Mean, Std Dev, Median, 75th Percent, 90th Percent) by Time Horizon:
  - Mean: 1 Year 50.43; 2 Years 51.23; 3 Years 52.27; 4 Years 53.54; 5 Years 55.26
  - Standard Deviation: 1 Year 4.37; 2 Years 6.41; 3 Years 8.48; 4 Years 10.03; 5 Years 12.12
  - Median: 1 Year 50.22; 2 Years 51.15; 3 Years 52.15; 4 Years 53.11; 5 Years 54.33
  - 75th Percent: 1 Year 53.47; 2 Years 55.23; 3 Years 57.73; 4 Years 59.44; 5 Years 62.08
  - 90th Percent: 1 Year 56.29; 2 Years 59.66; 3 Years 63.44; 4 Years 66.76; 5 Years 70.82
- Counterfactual findings:
  - Over the 5-year horizon (2000 through 2005) mean debt/GDP ratio rises from 50.4 percent to 55.3 percent.
  - Simulated debt exceeds 64.2 percent and 79.3 percent with probabilities of 25 percent and 10 percent, respectively.
- Policy menu (stabilizing debt b with probability):
  - 50 %: Requires primary surplus of: 1 Year 3.21; 2 Years 3.81; 3 Years 4.01; 4 Years 4.10; 5 Years 4.18
    - average debt ratio, end of horizon: 1 Year 50.76; 2 Years 50.13; 3 Years 50.66; 4 Years 50.93; 5 Years 51.42
  - 75 %: Requires primary surplus of: 1 Year 6.21; 2 Years 5.62; 3 Years 5.54; 4 Years 5.38; 5 Years 5.36
    - average debt ratio, end of horizon: 1 Year 47.62; 2 Years 46.74; 3 Years 45.60; 4 Years 45.12; 5 Years 44.49
  - 90 %: Requires primary surplus of: 1 Year 8.65; 2 Years 7.43; 3 Years 7.00; 4 Years 6.62; 5 Years 6.50
    - average debt ratio, end of horizon: 1 Year 45.08; 2 Years 42.84; 3 Years 40.76; 4 Years 39.47; 5 Years 37.77
- Caveats:
  - Recent debt management reduced fraction of debt denominated or indexed to the U.S. dollar; this may reduce exchange rate risk only if exchange rate shocks are not transmitted to interest rates.
  - Some simulations omitting exchange rate shocks yielded results very close to those in Table 4.

### Mexico — Retrospective analysis, 1999:5–2005:4 (Table 5a)
- Initial Debt (bM): 19.70 (percent of GDP; table header "Percent of GDP")
- End Period Debt (bM+J): 18.10
  - Baseline Projection (b(base)M+J): 17.69
  - Shock Component (bM+J - (b(base)M+J)): 0.41
- Variance decomposition: Percent of total variation in debt and percent of GDP contribution
  - Exchange rate + interest rate (ε+r): 15.5 percent of total variation; 18.23 (Percent of GDP)
  - Deficit (∆b, includes pd): 79.6 percent of total variation; 17.40 (Percent of GDP)
  - Industrial Production (ip): 2.2 percent of total variation; 18.29 (Percent of GDP)
  - Oil Price (poil): 2.8 percent of total variation; 18.08 (Percent of GDP)
- Findings:
  - In the base period (M = 1999:5), debt/GDP ratio ~19 percent; baseline forecast debt ratio at end-of-sample 17.7 percent — fiscal policy sustainable for the traditional measure.
  - Discretionary shocks had a slightly positive impact on the debt; omitting these shocks would have reduced debt by about one-half percent of GDP.
  - Oil price shocks had a small but positive impact on debt, suggesting oil windfalls were spent rather than saved.

### Mexico — Prospective analysis from 2005 onward (Table 5b)
- Initial period primary surplus/GDP ps = 2.1%
- Statistics (Mean, Std Dev, Median, 75th Percent, 90th Percent) by Time Horizon:
  - Mean: 1 Year 45.0; 2 Years 43.5; 3 Years 41.9; 4 Years 40.2; 5 Years 38.7
  - Standard Deviation: 1 Year 2.1; 2 Years 3.4; 3 Years 4.2; 4 Years 4.9; 5 Years 5.6
  - Median: 1 Year 44.9; 2 Years 43.3; 3 Years 41.5; 4 Years 40.0; 5 Years 38.1
  - 75th Percent: 1 Year 46.5; 2 Years 45.7; 3 Years 44.6; 4 Years 43.1; 5 Years 42.0
  - 90th Percent: 1 Year 47.7; 2 Years 47.9; 3 Years 47.6; 4 Years 46.6; 5 Years 46.0
- Key outcome and risk:
  - A modest primary surplus around 2.1 percent of GDP will reduce debt from 45.0 percent of GDP in 2005 to 38.7 percent in 2010 on the mean projection.
  - By 2010, there is a 10 percent chance that debt will exceed 46 percent.
- Policy menu (stabilizing debt with given probabilities over horizons):
  - 75 % requires primary surplus of: 1 Year 3.2; 2 Years 2.3; 3 Years 1.9; 4 Years 1.6; 5 Years 1.5
    - average debt ratio, end of horizon: 1 Year 42.7; 2 Years 43.1; 3 Years 42.6; 4 Years 42.3; 5 Years 41.9
  - 90 % requires primary surplus of: 1 Year 4.4; 2 Years 3.2; 3 Years 2.8; 4 Years 2.4; 5 Years 2.3
    - average debt ratio, end of horizon: 1 Year 42.7; 2 Years 41.2; 3 Years 39.9; 4 Years 39.1; 5 Years 38.0
- Caveats specific to resource revenues:
  - Spending from oil windfalls appears to have been used to boost spending rather than the surplus.
  - If oil revenues fall, preserving the same primary surplus implies symmetric cuts to spending; retaining both current expenditures and the primary surplus would require raising additional non-oil revenues.

### Turkey — Retrospective summary and context
- Historical context:
  - Turkey experienced chronic high inflation and fiscal imbalances; currency crises in 1994 and 2000–01 increased debt via banking sector losses and defensive interest rate hikes.
  - Under a recent IMF program, Turkey achieved a primary surplus exceeding 6 ½ percent of GDP; together with higher GDP growth and real appreciation, debt ratio fell from over 90 percent of GDP in 2000 to about 55 ½ percent in 2005–06.
- Econometric notes:
  - Estimations use monthly data from mid-1994 to mid-2005; vector X t defined as for Mexico (equation (13)); 8 lags included.
  - A crisis dummy equals unity for 2001:2–2001:6 to account for the extraordinary currency crisis.
- Retrospective finding:
  - Prior to the 2001 currency crisis, fiscal policy was unsustainable.
  - In mid-1996, initial debt/GDP ratio about 43.2 percent.
  - Shocks to fiscal policy account for 60 percent of total variation in debt; about three-fourths of this variability is due to shocks from below the line, including financial sector obligations.

*Italic: Source — content extracted from the provided IMF PDF chapter.*

### 1.9 percent of GDP. However, this effect was largely offset by shocks to industrial

### _wp06295 - 1.9 percent of GDP. However, this effect was largely offset by shocks to industrial

### Retrospective decomposition and key quantitative findings
- Initial Debt (bM): 43.2 (percent of GDP context in Table 6a).
- End Period Debt (bM+J): 48.8 (percent of GDP context in Table 6a).
- Baseline Projection (b(base)M+J): 49.1 (percent of GDP context in Table 6a).
- Shock Component (bM+J - (b(base)M+J)): -0.2 (percent of GDP context in Table 6a).
- Percent of total variation in debt (b(omit)M+J) — Percent of GDP contributions by shock type (Table 6a):
  - Oil Price (poil): 8.3 and 48.1 (two numbers appear in the source under this line; preserved exactly as presented).
  - Exchange rate + interest rate (ε + r): 20.4 and 49.3.
  - Deficit (∆b, includes pd): 60.0 and 50.9.
  - Industrial Production (ip): 11.3 and 47.1.
- Specific shock effects discussed in text:
  - Omitting industrial production shocks reduces the debt by about 1.9 percent of GDP.
  - After the 2001 crisis, volatility in exchange rates and interest rates increased debt levels; omitting such shocks leaves debt lower than baseline by about 1 percent of GDP.

### Prospective analysis from 2005 onward (Table 6b assumptions and outcomes)
- Scenario assumptions (upper portion of Table 6b):
  - Mean primary surplus over is assumed to be 6.5 percent of GDP in 2006 and afterwards.
  - Average economic growth is just under 5 percent.
  - Average real interest rate is about 8 percent per annum.
  - Prospective scenario includes shocks to the primary balance (pd) and the real interest payments.
  - Prospectively assumed "below the line" shocks—such as public assumption of financial sector obligations—are zero.
- Debt-path statistics (Table 6b; all numeric entries preserved exactly):
  - Time Horizon columns: 1 Year, 2 Years, 3 Years, 4 Years, 5 Years.
  - No Shock Scenario: 49.6 45.5 40.8 36.2 31.7
  - Mean: 51.3 49.2 46.0 42.8 39.4
  - Standard Deviation: 6.3 9.7 11.7 13.5 15.1
  - Median: 50.9 48.0 44.8 40.4 37.3
  - 75th Percent: 55.3 55.0 52.9 50.9 47.2
  - 90th Percent: 59.9 61.9 61.3 60.8 58.9
- Risk assessment and stabilization requirements (lower portion of Table 6b):
  - Over the five year horizon, there is a 10 percent probability that the debt/GDP ratio will rise to at least 59 percent of GDP.
  - Stabilizing debt with probability 90% requires first year primary surplus of: 10.8 9.5 8.5 8.1 7.5 (by horizon 1 through 5 years respectively).
  - Corresponding average primary surplus/GDP, years 1–5: 10.3 9.1 8.0 7.6 7.1
  - Average debt ratio, end of horizon: 47.4 43.8 41.2 38.2 36.5
- Illustrative scenario statements from text:
  - In the absence of any shocks (“No shock scenario,” first line of Table 6b), the debt/GDP ratio falls from 55.5 percent of GDP to about 32 percent of GDP by 2010.
  - When random shocks are included, the mean debt ratio falls to about 39 percent of GDP.
  - For a one-year horizon, stabilizing with 90 percent probability would require a primary surplus of just under 11 percent of GDP in the first year (declining thereafter, about 10 percent over the entire horizon).
  - For a five-year horizon, the required primary surplus must average about 7 percent of GDP over the five-year horizon.

### Figures and purged-series interpretations
- Figure 6: Turkey: Real Public Debt Purged of Exchange Rate and Interest Rate Shocks (b(omit ε,r); Units are millions of 2001 Turkish Lira).
  - Text interpretation: volatility in exchange rates and interest rates after the 2001 crisis contributed to higher debt levels; omitting those shocks lowers debt relative to baseline by about 1 percent of GDP.
- Figure 7: Turkey: Real Public Debt Purged of Deficit Shocks (b(omit ps, ∆b); Units are millions of 2001 Turkish Lira).
  - Text interpretation: omitting industrial production shocks reduces debt by about 1.9 percent of GDP (industrial production shocks had a substantial offsetting effect in retrospective decomposition).

### Summary and policy-relevant conclusions
- Comparative scope:
  - Paper examined sustainability of fiscal policy under uncertainty in Brazil, Mexico, and Turkey, both retrospectively and prospectively.
- Methodological advantages claimed:
  - The econometric VAR-based framework uses data to inform the policy process more richly than accounting frameworks.
  - The framework communicates a clearer menu of options for policymakers than other currently used frameworks.
- Policy-relevant implications for Turkey (from prospective results):
  - Cautious optimism is warranted under assumptions stated (ps ≈ 6.5 percent; growth just under 5 percent; real interest ≈ 8 percent).
  - Nevertheless, shocks materially affect outcomes: random shocks raise mean debt outcomes relative to no-shock scenarios and imply nontrivial probabilities of debt increases (10 percent chance of reaching at least 59 percent of GDP over five years).
  - Stabilizing debt with high probability requires considerably higher primary surpluses in the short run; longer horizons lower the required average primary surplus.
- Suggested next steps (from text conclusions):
  - Place the analysis into a general equilibrium model to permit a true welfare analysis of costs and benefits to further fiscal adjustment.
  - Determine the optimal primary surplus and debt reduction path conditional on specific technology and preferences for a country.

### Appendix — econometric methodology and diagnostics (selected)
- VAR system specification (A1):
  - Endogenous vector yt includes: change in industrial production index (ip), real primary surplus (ps), percent change of the real bilateral exchange rate (ε), and the real interest rate (r): (r, pd, ip, ε)' preserved ordering as in source.
  - For Mexico and Turkey, real operational deficit (change in real debt ∆b) is also included.
- Unit root and stationarity testing:
  - Augmented Dickey-Fuller and Phillips-Perron tests performed; results summarized in Table A.1 indicate stationarity for all elements of yt and oil price growth (element of Zt).
  - ADF and PP numeric entries preserved exactly where shown (e.g., ip ADF for Brazil: -5.61**; pd ADF for Mexico: -6.71**; ε ADF for Turkey: -5.55**; etc.).
- Identification approach:
  - Initial model uses Choleski decomposition with ordering: ip, ps, ε, r.
  - Structural approach with additional zero-restrictions also tried; yielded results similar to Choleski ordering.
- Historical decomposition methodology:
  - Equations (A4)–(A8) outline decomposition that separates baseline forecast from accumulated impact of shocks, permitting purging variables of selected shocks’ effects.
- Estimation summaries:
  - Brazil VAR (Table A.2): Degrees of Freedom = 99; Lags = 4; various R(bar)2 and F-statistics reported in source tables.
  - Mexico VAR (Table A.3): Degrees of Freedom = 59; Lags = 6.
  - Turkey VAR (Table A.4): Degrees of Freedom = 81; Lags = 8; R(bar)2 entries and t-statistics for Crisis Dummy reported in source.
- Brazil alternative specifications (Table A.5 and Figures A.1–A.2):
  - Versions (i)–(v) differ by sample and inclusion of crisis dummy, flex regime dummy, and time trend; main version (i) is 95:5–05:6 with Crisis Dummy, Flex Regime Dummy, and Time Trend.
  - Text notes version (iii) materially differs from other versions, yielding substantially higher baseline end-2005 debt when the 1999 crisis dummy is omitted.
  - Figures illustrate observed and purged debt series across alternative specifications.

*Source: Central Bank of Turkey and author’s estimates; content unit as provided.*

### REFERENCES

### _wp06295 - REFERENCES

### Foundational theoretical works
- Barro, Robert J., 1979, “On the Determination of the Public Debt,” Journal of Political Economy, Vol. 87, No. 5 (Part 1, October), pp. 940–71.
- Sargent, Thomas J., 1987, Macroeconomic Theory, 2nd Edition (Orlando, Florida: Academic Press).
- McCallum, Bennett T., 1984, “Are Bond-Financed Deficits Inflationary? A Ricardian Analysis,” Journal of Political Economy, Vol. 92, No. 1 (February), pp. 123–35.
- 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.
- Aiyagari, S. Rao, Albert Marcet, Thomas J. Sargent, and Juha Seppälä, 2002, “Optimal Taxation without State-Contingent Debt,” Journal of Political Economy, Vol. 110, No. 6 (December), pp. 1220–54.
- Trehan, Bharat, and Carl E. Walsh, 1990, “Seigniorage and Tax Smoothing in the United States, 1914–86,” Journal of Monetary Economics, Vol. 25, No. 1 (January), pp. 97–112.

### Empirical studies on fiscal sustainability and deficits
- Ahmed, S., and Rogers, J.H., 1995, “Government Budget Deficits and Trade Deficits: Are Present Value Constraints Satisfied in Long-Term Data?” Journal of Monetary Economics Vol. 36, No. 2 (November), pp. 351–74.
- Blanchard, O.J., and others., 1990, “The Sustainability of Fiscal Policy: New Answers to an Old Question,” OECD Economic Studies, Vol. 15 (Autumn), pp. 7–34.
- Bohn, H., 1991, “Budget Balance Through Revenue or Spending Adjustments—Some Historical Evidence for the United States,” Journal of Monetary Economics Vol. 27, No. 3 (June), pp. 333–59.
- Bohn, H., 1998, “The Behavior of U.S. Public Debt and Deficits,” Quarterly Journal of Economics, Vol. 113, No. 3 (August), pp. 949–63.
- Bohn, H., 2005, “The Sustainability of Fiscal Policy in the United States,” Working Paper, UCSB (California: Santa Barbara). Available via the Internet: http://www.econ.ucsb.edu/%7Ebohn/papers/DebtUS.pdf
- Hakkio, Craig S., and Mark Rush, 1991, “Is the Budget Deficit Too Large?" Economic Inquiry, Vol. 29, No. 3 (July), pp. 429–45.
- Hamilton, James D., and Marjorie A. Flavin, 1986, “On the Limitations of Government Borrowing: A Framework for Empirical Testing,” American Economic Review, Vol. 76, No. 4 (September), pp. 808–19.
- Haug, A.A., 1991, “Cointegration and Government Borrowing Constraints—Evidence for the United States,” Journal of Business & Economic Statistics, Vol. 9, No. 1 (January), pp. 97–101.
- Wilcox, David W., 1989, “The Sustainability of Government Deficits: Implications of the Present-Value Borrowing Constraint,” Journal of Money, Credit, and Banking, Vol. 21, No. 3 (August), pp. 291–306.
- Trehan, Bharat, and Carl E. Walsh, 1991, “Testing Intertemporal Budget Constraints: Theory and Applications to U.S. Federal Budget and Current Account Deficits,” Journal of Money, Credit, and Banking, Vol. 23, No. 2 (May), pp. 206–23.
- Quintos, C.E., 1995, “Sustainability of the Deficit Process with Structural Shifts,” Journal of Business and Economic Statistics, Vol. 13, No. 4 (October), pp. 409–17.
- Martin, G.M., 2000, “U.S. Deficit Sustainability: A New Approach Based on Multiple Endogenous Breaks,” Journal of Applied Econometrics, Vol. 15, No. 1 (January–February), pp. 83–105.
- Burbidge, John and Alan Harrison, 1985, “A Historical Decomposition of the Great Depression to Determine the Role of Money,” Journal of Monetary Economics, Vol. 16, No. 1 (July), pp. 45–54.
- Haug, A.A., 1991, “Cointegration and Government Borrowing Constraints—Evidence for the United States,” Journal of Business & Economic Statistics, Vol. 9, No. 1 (January), pp. 97–101.
- Leachman, L., Bester, A., Rosas, G. and Lange, P., 2005, “Multicointegration and Sustainability of Fiscal Practices,” Economic Inquiry, Vol. 43, No. 2 (April), pp. 454–466.

### Methodological and econometric sources
- Dickey, D., and W.A. Fuller, 1979, "Distribution of the Estimators for Time Series Regressions with a Unit Root," Journal of the American Statistical Association, Vol. 74, pp. 427–31.
- MacKinnon, James, 1991, "Critical Values for Cointegration Tests," in R.F. Engle and C.W.J. Granger, eds, Long-Run Economic Relationships, pp. 267–76 (London: Oxford).
- Burnside, C., 2005, “Some Tools for Fiscal Sustainability Analysis,” in Craig Burnside, ed. Fiscal Sustainability in Theory & Practice (forthcoming; Washington: World Bank).
- Kopits, George, and Theodore F. Barnhill, 2003, “Assessing Fiscal Sustainability Under Uncertainty,” IMF Working Paper 03/79 (Washington: International Monetary Fund).
- Uctum, M., and Wickens, M., 2000, “Debt and Deficit Ceilings, and Sustainability of Fiscal Policies: An Intertemporal Analysis,” Oxford Bulletin of Economics and Statistics Vol. 62, No. 2 (May), p. 197.
- Hostland, Douglas, and Philippe Karam, 2005, “Assessing Debt Sustainability in Emerging Markets using Stochastic Simulation Methods,” IMF Working Paper Forthcoming (Washington: International Monetary Fund).
- Celasun, Oya, Xavier Debrun, and Jonathan Ostry, 2006, “Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A "Fan-Chart" Approach,” IMF Working Paper 06/67 (Washington: International Monetary Fund).
- Kopits, George, and Theodore F. Barnhill, 2003, “Assessing Fiscal Sustainability Under Uncertainty,” IMF Working Paper 03/79 (Washington: International Monetary Fund).

### Country and regional studies
- Adrogué, Ricardo, 2005, Central America: Global Integration and Regional Cooperation, IMF Occasional Paper No. 243, Chapter 4, pp. 59–68 (Washington: International Monetary Fund).
- Bauer, Andreas, 2002, “The Financial Soundness of Mexico’s Pension System,” Chapter IV in Mexico Selected Issues. (Washington: International Monetary Fund). Available via the Internet, http://www.imf.org/external/pubs/ft/scr/2002/cr02238.pdf
- Garcia, Márcio, and Roberto Rigobon, 2004, “A Risk Management Approach to Emerging Market's Sovereign Debt Sustainability with an Application to Brazilian Data,” NBER Working Paper No. 10336 (Cambridge, MA: National Bureau of Economic Research).
- Mendoza, Enrique G., and P. Marcelo Oviedo, 2004, “Public Debt, Fiscal Solvency, and Macroeconomic Uncertainty in Latin America: The Cases of Brazil, Colombia, Costa Rica, and Mexico,” NBER Working Paper No. W10637 (Washington: National Bureau of Economic Research).
- Hoffmaister, A. W., M. Rojas, M. Saenz, M. Segura, and E. Tenorio, 2001, “Solvency of the Overall Public Sector: A preliminary Empirical Study for Costa Rica,” Central Bank of Costa Rica, Economics Division, Research Note 04–01 (San José, Costa Rica: Central Bank).
- Guerson, Alejandro, 2004, “Fiscal Policy for Good: Reducing Macroeconomic Volatility in Uruguay.” (Washington: World Bank). Available via the Internet: http:// www.ecomod.org/files/papers/1183.pdf
- Tanner, Evan, 1995, “Intertemporal Solvency and Indexed Debt: Evidence from Brazil, 1976–91,” Journal of International Money and Finance (August) Vol. 14, Issue 4, pp. 549–73.
- Tanner, Evan, and Peter Liu, 1994, “Is the Budget Deficit 'Too Large'?: Some Further Evidence,” Economic Inquiry, July, Vol. 32, Issue. 3, pp. 511–18.
- Tanner, Evan, and Alberto Ramos, 2003, “Fiscal Sustainability and Monetary versus Fiscal Dominance: Evidence from Brazil, 1991–2000,” Applied Economics (May), Vol. 35, Issue. 7, pp. 859–73.
- Koeva, Petya, 2005, “The Implementation of the Golden Rule over the Cycle,” Chapter III in United Kingdom: Selected Issues. (Washington: International Monetary Fund). Available via the Internet: http://www.imf.org/external/pubs/ft/scr/2005/cr0581.pdf
- Deutsche Bank, 2006, “Brazil: O pais do futuro? Economic Scenarios for the next 15 years,” (Frankfurt: Deutsche Bank Research). Available via the Internet: http://www.dbresearch.com
- Penalver, Adrian, and Gregory Thwaites, 2006, “Fiscal Rules for Debt Sustainability in Emerging Markets: The Impact of Volatility and Default Risk” mimeo (London: Bank of England).
- Telatar, E., N. Bolatoglu, and F. Telatar, 2004, “A New Approach on Testing the Behaviour of the Governments Towards Sustainability of Fiscal Policy in a Small-Open and Politically Instable Economy,” Applied Economics Letters, Vol. 11, No. 5 (April), pp. 333–36.

### IMF, World Bank, and related policy publications
- International Monetary Fund, 2003a, “Sustainability Assessments—Review of Application and Methodological Refinements.” Available via the Internet: http://www.imf.org/external/np/pdr/sustain/2003/061003.pdf
- International Monetary Fund, 2003b, World Economic Outlook (September 2003), “Public Debt in Emerging Markets: Is It Too High?” Chapter III, pp 113–52 (Washington: International Monetary Fund). Available via the Internet: http://www.imf.org/external/pubs/ft/weo/2003/02/pdf/chapter3.pdf
- Kopits, George, and Theodore F. Barnhill, 2003, “Assessing Fiscal Sustainability Under Uncertainty,” IMF Working Paper 03/79 (Washington: International Monetary Fund).
- Celasun, Oya, Xavier Debrun, and Jonathan Ostry, 2006, “Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A "Fan-Chart" Approach,” IMF Working Paper 06/67 (Washington: International Monetary Fund).
- Hostland, Douglas, and Philippe Karam, 2005, “Assessing Debt Sustainability in Emerging Markets using Stochastic Simulation Methods,” IMF Working Paper Forthcoming (Washington: International Monetary Fund).

*Reference list as provided in _wp06295 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06295.pdf_