## _wp15110 - References

## Source details

**Canonical URL:** [_wp15110 - References](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15110.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15110.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15110.pdf.json)

---

### I. Key objectives and scope
- Assess fiscal risks in Bangladesh by:
  - Presenting a framework to identify and classify fiscal risks.
  - Assessing sensitivity of the fiscal balance and public debt to macroeconomic shocks and conducting stochastic analyses of public debt-to-GDP.
  - Evaluating specific risks from contingent liabilities and the pension system.
  - Assessing institutional capacity limitations (budget forecasting errors, external debt management, data discrepancies).
- Main findings:
  - Fiscal balance is particularly sensitive to shocks to commodity prices and exchange rates.
  - Calls on government guarantees or recapitalization of state-owned banks could materially impact fiscal aggregates.
  - Unfunded pension liabilities and limited institutional capacity present medium- to long-term fiscal risks.

### II. Framework for fiscal risk analysis
- Risk categories:
  - General economic risks: shocks to macroeconomic variables (commodity prices, GDP growth, exchange rates, interest rates).
  - Specific fiscal risks: contingent liabilities (explicit and implicit).
  - Structural/institutional risks: weak capacity, spending rigidity, coordination failures.
- Transmission channels:
  - Macroeconomic shocks affect revenues, expenditures, and public debt dynamics.
  - Contingent liabilities become fiscal liabilities when triggered; implicit liabilities (e.g., financial sector bailouts) are particularly insidious.
  - Institutional weaknesses (poor information, unclear responsibilities) worsen risk management.

### III. Macroeconomic shocks and budget sensitivity (quantitative results)
- Method:
  - One standard deviation permanent shocks introduced from start of FY14 (commodity prices, exchange rate, domestic interest rate, GDP growth).
  - Fan-chart stochastic analysis based on sample statistics 1996–2012 for GDP growth, effective real interest rate, primary balance, real exchange rate.
- Scenario results (deviations from baseline, in percent of GDP; FY14–FY18):
  - Scenario A (30 percent increase in commodity prices, or 1 SD)
    - Overall Balance: -0.9, -0.8, -0.6, -0.4, -0.4
    - Total Debt: 0.9, 1.8, 2.4, 2.8, 3.1
  - Scenario B (10 percent depreciation in exchange rate)
    - Overall Balance: -0.9, -0.9, -0.8, -0.6, -0.6
    - Total Debt: 3.6, 4.6, 5.4, 6.0, 6.6
  - Scenario C (130 basis points increase in domestic interest rate, or 1SD)
    - Overall Balance: -0.2, -0.2, -0.3, -0.3, -0.3
    - Total Debt: 0.2, 0.5, 0.7, 1.0, 1.3
  - Scenario D (0.7 percent decrease in real GDP growth, or 1SD)
    - Overall Balance: -0.1, -0.1, -0.1, -0.1, -0.1
    - Total Debt: 0.1, 0.2, 0.3, 0.4, 0.5
- Shock-specific summaries:
  - Commodity prices (oil and urea):
    - A one standard deviation increase (roughly a 30 percent price increase) would increase the deficit by around 0.6 percent of GDP on average each year and lead to a cumulative debt increase of around 3.1 percent of GDP over five years.
    - FY13 total subsidies ~3.1 percent of GDP; energy-related subsidies ~1.7 percent of GDP; fertilizer subsidies ~1 percent of GDP.
  - Exchange rate:
    - A permanent 10 percent depreciation in the Taka/US$ would raise the deficit by around 0.8 percent of GDP on average yearly and increase the stock of debt by around 6.6 percentage points of GDP over five years.
  - Domestic interest rate:
    - A one standard deviation rise (130 basis points) would raise the deficit by around 0.3 percent of GDP and raise debt by around 1.3 percentage points of GDP over five years.
  - GDP growth:
    - A one standard deviation decline (around 0.7 percentage points) would reduce the overall fiscal balance by around 0.1 percent of GDP and increase debt by around 0.5 percent of GDP over five years.
- Stochastic analysis (fan charts):
  - After a combined shock to key macroeconomic variables, there is a 50 percent probability that the debt-to-GDP ratio remains between 36 and 40 percent.
  - Even restricting draws to only negative shocks, projected debt levels remain below referenced low-income country averages (42 percent and 48 percent cited for different groupings in 2012).

### IV. Specific fiscal risks
- Government loan guarantees:
  - Stock of government guaranteed debt rose from around 3.5 percent of GDP in FY04 to 5.7 percent of GDP (Taka 592 billion) by end-June 2013.
  - Guarantees provided to SOCBs represented around 30 percent of the total guarantees.
  - If guarantees materialize in full, they could noticeably increase public debt.
- State-owned banks (SOBs):
  - There are eight SOBs (4 commercial, 4 specialized).
  - SOBs represent around 32 percent of banking system assets, or roughly 24 percent of GDP.
  - SOBs account for the majority of outstanding non-performing loans (NPLs).
  - As of end-2013, the capital shortfall at these banks compared to the regulatory minimum stood at about 2.5 percent of GDP.
  - Many loans to state-owned enterprises are guaranteed by the government, preventing recognition as NPLs despite losses.
- Pension system and General Provident Fund (GPF):
  - Civil Servant Retirement Scheme (CSRS):
    - Noncontributory, defined benefit scheme; retirement eligibility age 59.
    - In FY13 the government assigned Tk 60 billion to the pension bill (0.57 percent of GDP).
    - Bangladesh employs roughly 1.2 million civil servants; around 35,000–40,000 retire every year.
    - UN projections: share of elderly (aged 60 and above) will more than triple as share of total population by 2050 from current 6 percent; old-age dependency ratio will increase substantially.
    - Pension spending decomposition assumptions:
      - Benefit ratio assumed constant at about 1.32.
      - Eligibility ratio assumed constant at 0.04.
    - Projected pension spending (percent of GDP): average 2010–2012 = 0.5; 2013 = 0.5; 2020 = 0.5; 2030 = 0.9; 2040 = 1.2; 2050 = 1.8.
  - General Provident Fund (GPF):
    - Mandatory defined contribution; civil servants contribute minimum 10 percent of salaries.
    - As of end-FY13, GPF stock of contributions amounted to Tk 204 billion, plus Tk 24 billion in interest (roughly 2.2 percent of GDP).
    - GPF is unfunded in practice: cash flows are used to finance the deficit.
    - GPF currently generating surpluses of around Tk 30 billion, but net cashflows could become negative as retirements rise.
  - Universal pension illustrative costs (using poverty line benchmark converted to roughly Tk 1,500 per month by end-FY13):
    - Age 60+: beneficiaries 9.9 million; fiscal cost 1.9 percent of GDP (11.9 percent of total government expenditures).
    - Age 65+: beneficiaries 6.7 million; fiscal cost 1.3 percent of GDP (8.0 percent of total government expenditures).
    - Age 70+: beneficiaries 4.1 million; fiscal cost 0.8 percent of GDP (4.9 percent of total government expenditures).
    - Age 75+: beneficiaries 2.1 million; fiscal cost 0.4 percent of GDP (2.5 percent of total government expenditures).
    - Long-run illustrative trajectory:
      - If pensions grow with inflation (assumed 6 percent) and nominal GDP growth 12 percent, the most expensive case (60 and over) could approach almost 7 percent of GDP in the long run if the pension per capita grows in line with GDP per capita and qualifying population increases.

### V. Institutional capacity and data issues
- Budgeting practices and forecasting:
  - Systematic deviations observed: revenues and expenditures often fall short of budget targets.
  - Over last four years (average):
    - Total revenues below budget target by around 4 percent (0.5 percent of GDP).
    - Non-tax revenue average deviation 16 percent.
    - Total expenditures below budget by 8.5 percent (around 1.4 percent of GDP).
    - Capital spending underexecution around 19 percent below target on average.
  - For 11 of the last 12 years, both revenues and expenditures underperformed budget projections; expenditure authorizations are legally binding while revenues are projections.
- External borrowing and debt management:
  - Fast increase in non-concessional external borrowing: annual average external debt disbursement in FY12 and FY13 is around 180 percent higher than annual average for FY05–FY11.
  - Steps taken: creation of a Technical Committee on Nonconcessional Borrowing; continued strengthening needed for assessment, approval, and monitoring of external loans and guarantees.
- Data discrepancies:
  - Significant discrepancy between NBR and CGA revenue data.
  - Cumulative gap between NBR and CGA over FY12–FY13 roughly Tk 90 billion (almost one percent of GDP), with CGA typically showing lower figures.
  - These inconsistencies undermine transparency and complicate fiscal policymaking.

### VI. Conclusions and policy recommendations (selected)
- Key conclusions:
  - Fiscal balance sensitive to commodity price and exchange rate shocks; a one standard deviation shock to commodity prices or a 30 percent devaluation may increase the deficit by between 0.6 to almost 1 percent of GDP on average per year relative to baseline.
  - Calls on guarantees or additional recapitalization of SOBs could materially raise public debt if realized.
  - Unfunded pension obligations and GPF pose medium- to long-term fiscal pressures; unfunded pension cost could rise from 0.5 percent of GDP today to about 2 percent of GDP by 2050 absent reforms; a universal pension could cost up to about 6 percent of GDP per year (or higher) depending on design and indexing.
  - Institutional weaknesses (budget forecasting, debt management, data discrepancies) raise fiscal risks and weaken transparency.
- Policy recommendations:
  - Fully integrate fiscal risk analysis into government policy decision-making and into an integrated asset and liability management strategy in coordination with Bangladesh Bank.
  - Build government capacity to analyze and measure fiscal risks; implement a system of treasury cash flow forecasts.
  - Improve debt records and reporting; modernize the National Saving Directorates (link interest rates to market/benchmark securities; make issuance and record-keeping electronic).
  - Reduce currency risks in government liability structure (e.g., cap on foreign-denominated debt and on foreign-denominated government guarantees).
  - Publish a Debt Statistical Bulletin for total central government debt (external, domestic, and loan guarantees).
  - Establish a full set of policies and procedures for issuance of loan guarantees; prioritize and limit new guaranteed obligations.
  - Reform pensions:
    - Implement a contributory pension scheme for civil servants to replace the current non-contributory regime.
    - Reform GPF via creation of notional accounts and an investment fund to accumulate assets.
    - Consider institutionalizing a non-contributory pension for the poor and developing voluntary defined contribution retirement schemes for all adults to mobilize long-term domestic investment funds.

*Source: IMF Staff calculations and Bangladesh Authorities as presented in the content unit.*

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

### _wp15110 - References

### I. Key objectives and scope
- Assess fiscal risks in Bangladesh by:
  - Presenting a framework to identify and classify fiscal risks.
  - Assessing sensitivity of the fiscal balance and public debt to macroeconomic shocks and conducting stochastic analyses of public debt-to-GDP.
  - Evaluating specific risks from contingent liabilities and the pension system.
  - Assessing institutional capacity limitations (budget forecasting errors, external debt management, data discrepancies).
- Main finding summary:
  - Fiscal balance is particularly sensitive to shocks to commodity prices and exchange rates.
  - Calls on government guarantees or recapitalization of state-owned banks could materially impact fiscal aggregates.
  - Unfunded pension liabilities and limited institutional capacity present medium- to long-term fiscal risks.

### II. Framework for fiscal risk analysis
- Three organized risk categories used in the paper:
  - General economic risks: shocks to macroeconomic variables (commodity prices, GDP growth, exchange rates, interest rates).
  - Specific fiscal risks: contingent liabilities (explicit and implicit).
  - Structural/institutional risks: weak capacity, spending rigidity, coordination failures.
- Transmission channels:
  - Macroeconomic shocks affect revenues, expenditures, and public debt dynamics.
  - Contingent liabilities become fiscal liabilities when triggered; implicit liabilities (e.g., financial sector bailouts) are particularly insidious.
  - Institutional weaknesses (poor information, unclear responsibilities) worsen risk management.

### III. Macroeconomic shocks and budget sensitivity (quantitative results)
- Method:
  - One standard deviation permanent shocks introduced from start of FY14 (commodity prices, exchange rate, domestic interest rate, GDP growth).
  - Fan-chart stochastic analysis based on sample statistics 1996–2012 for GDP growth, effective real interest rate, primary balance, real exchange rate.

- Scenario results (Table 1: deviations from baseline, in percent of GDP; FY14–FY18):
  - Scenario A (30 percent increase in commodity prices, or 1 SD)
    - Overall Balance: -0.9, -0.8, -0.6, -0.4, -0.4
    - Total Debt: 0.9, 1.8, 2.4, 2.8, 3.1
  - Scenario B (10 percent depreciation in exchange rate)
    - Overall Balance: -0.9, -0.9, -0.8, -0.6, -0.6
    - Total Debt: 3.6, 4.6, 5.4, 6.0, 6.6
  - Scenario C (130 basis points increase in domestic interest rate, or 1SD)
    - Overall Balance: -0.2, -0.2, -0.3, -0.3, -0.3
    - Total Debt: 0.2, 0.5, 0.7, 1.0, 1.3
  - Scenario D (0.7 percent decrease in real GDP growth, or 1SD)
    - Overall Balance: -0.1, -0.1, -0.1, -0.1, -0.1
    - Total Debt: 0.1, 0.2, 0.3, 0.4, 0.5

- Key shock-specific summaries:
  - Commodity prices (oil and urea):
    - A one standard deviation increase (roughly a 30 percent price increase) would increase the deficit by around 0.6 percent of GDP on average each year and lead to a cumulative debt increase of around 3.1 percent of GDP over five years.
    - FY13 total subsidies ~3.1 percent of GDP; energy-related subsidies ~1.7 percent of GDP; fertilizer subsidies ~1 percent of GDP.
  - Exchange rate:
    - A permanent 10 percent depreciation in the Taka/US$ would raise the deficit by around 0.8 percent of GDP on average yearly and increase the stock of debt by around 6.6 percentage points of GDP over five years.
  - Domestic interest rate:
    - A one standard deviation rise (130 basis points) would raise the deficit by around 0.3 percent of GDP and raise debt by around 1.3 percentage points of GDP over five years.
  - GDP growth:
    - A one standard deviation decline (around 0.7 percentage points) would reduce the overall fiscal balance by around 0.1 percent of GDP and increase debt by around 0.5 percent of GDP over five years.

- Stochastic analysis (fan charts):
  - After a combined shock to key macroeconomic variables, there is a 50 percent probability that the debt-to-GDP ratio remains between 36 and 40 percent.
  - Even restricting draws to only negative shocks, projected debt levels remain below referenced low-income country averages (42 percent and 48 percent cited for different groupings in 2012).

### IV. Specific fiscal risks
- Government loan guarantees:
  - Stock of government guaranteed debt rose from around 3.5 percent of GDP in FY04 to 5.7 percent of GDP (Taka 592 billion) by end-June 2013.
  - Guarantees provided to SOCBs represented around 30 percent of the total guarantees.
  - If guarantees materialize in full, they could noticeably increase public debt.

- State-owned banks (SOBs):
  - There are eight SOBs (4 commercial, 4 specialized).
  - SOBs represent around 32 percent of banking system assets, or roughly 24 percent of GDP.
  - SOBs account for the majority of outstanding non-performing loans (NPLs).
  - As of end-2013, the capital shortfall at these banks compared to the regulatory minimum stood at about 2.5 percent of GDP.
  - Many loans to state-owned enterprises are guaranteed by the government, preventing recognition as NPLs despite losses.

- Pension system and General Provident Fund (GPF):
  - Civil Servant Retirement Scheme (CSRS):
    - Noncontributory, defined benefit scheme; retirement eligibility age 59.
    - In FY13 the government assigned Tk 60 billion to the pension bill (0.57 percent of GDP).
    - Bangladesh employs roughly 1.2 million civil servants; around 35,000–40,000 retire every year.
    - UN projections: share of elderly (aged 60 and above) will more than triple as share of total population by 2050 from current 6 percent; old-age dependency ratio will increase substantially.
    - Pension spending decomposition assumptions:
      - Benefit ratio assumed constant at about 1.32.
      - Eligibility ratio assumed constant at 0.04.
    - Projected pension spending (percent of GDP): average 2010–2012 = 0.5; 2013 = 0.5; 2020 = 0.5; 2030 = 0.9; 2040 = 1.2; 2050 = 1.8.
  - General Provident Fund (GPF):
    - Mandatory defined contribution; civil servants contribute minimum 10 percent of salaries.
    - As of end-FY13, GPF stock of contributions amounted to Tk 204 billion, plus Tk 24 billion in interest (roughly 2.2 percent of GDP).
    - GPF is unfunded in practice: cash flows are used to finance the deficit.
    - GPF currently generating surpluses of around Tk 30 billion, but net cashflows could become negative as retirements rise.
  - Universal pension illustrative costs:
    - Using poverty line benchmark converted to roughly Tk 1,500 per month by end-FY13.
    - Fiscal cost in 2012 depending on minimum retirement age:
      - Age 60+: beneficiaries 9.9 million; fiscal cost 1.9 percent of GDP (11.9 percent of total government expenditures).
      - Age 65+: beneficiaries 6.7 million; fiscal cost 1.3 percent of GDP (8.0 percent of total government expenditures).
      - Age 70+: beneficiaries 4.1 million; fiscal cost 0.8 percent of GDP (4.9 percent of total government expenditures).
      - Age 75+: beneficiaries 2.1 million; fiscal cost 0.4 percent of GDP (2.5 percent of total government expenditures).
    - Long-run illustrative trajectories:
      - If pensions grow with inflation (assumed 6 percent) and nominal GDP growth 12 percent, the most expensive case (60 and over) could approach almost 7 percent of GDP in the long run if the pension per capita grows in line with GDP per capita and qualifying population increases.

### V. Institutional capacity and data issues
- Budgeting practices and forecasting:
  - Systematic deviations observed: revenues and expenditures often fall short of budget targets.
  - Over last four years (average):
    - Total revenues below budget target by around 4 percent (0.5 percent of GDP).
    - Non-tax revenue average deviation 16 percent.
    - Total expenditures below budget by 8.5 percent (around 1.4 percent of GDP).
    - Capital spending underexecution around 19 percent below target on average.
  - For 11 of the last 12 years, both revenues and expenditures underperformed budget projections, creating risks because expenditure authorizations are legally binding while revenues are projections.

- External borrowing and debt management:
  - Fast increase in non-concessional external borrowing: annual average external debt disbursement in FY12 and FY13 is around 180 percent higher than annual average for FY05–FY11.
  - Steps taken: creation of a Technical Committee on Nonconcessional Borrowing; continued strengthening needed for assessment, approval, and monitoring of external loans and guarantees.

- Data discrepancies:
  - Significant discrepancy between NBR and CGA revenue data.
  - Cumulative gap between NBR and CGA over FY12–FY13 roughly Tk 90 billion (almost one percent of GDP), with CGA typically showing lower figures.
  - These inconsistencies undermine transparency and complicate fiscal policymaking.

### VI. Conclusions and policy recommendations (selected)
- Key conclusions:
  - Fiscal balance sensitive to commodity price and exchange rate shocks; a one standard deviation shock to commodity prices or a 30 percent devaluation may increase the deficit by between 0.6 to almost 1 percent of GDP on average per year relative to baseline.
  - Calls on guarantees or additional recapitalization of SOBs could materially raise public debt if realized.
  - Unfunded pension obligations and GPF pose medium- to long-term fiscal pressures; unfunded pension cost could rise from 0.5 percent of GDP today to about 2 percent of GDP by 2050 absent reforms; a universal pension could cost up to about 6 percent of GDP per year (or higher) depending on design and indexing.
  - Institutional weaknesses (budget forecasting, debt management, data discrepancies) raise fiscal risks and weaken transparency.

- Policy recommendations (bulleted):
  - Fully integrate fiscal risk analysis into government policy decision-making and into an integrated asset and liability management strategy in coordination with Bangladesh Bank.
  - Build government capacity to analyze and measure fiscal risks; implement a system of treasury cash flow forecasts.
  - Improve debt records and reporting; modernize the National Saving Directorates (link interest rates to market/benchmark securities; make issuance and record-keeping electronic).
  - Reduce currency risks in government liability structure (e.g., cap on foreign-denominated debt and on foreign-denominated government guarantees).
  - Publish a Debt Statistical Bulletin for total central government debt (external, domestic, and loan guarantees).
  - Establish a full set of policies and procedures for issuance of loan guarantees; prioritize and limit new guaranteed obligations.
  - Reform pensions:
    - Implement a contributory pension scheme for civil servants to replace the current non-contributory regime.
    - Reform GPF via creation of notional accounts and an investment fund to accumulate assets.
    - Consider institutionalizing a non-contributory pension for the poor and developing voluntary defined contribution retirement schemes for all adults to mobilize long-term domestic investment funds.

*Source: IMF Staff calculations and Bangladesh Authorities as presented in the content unit.*

### References

### References

### Cited works
- Ahmed, Shamim (2004). "The monetary transmission mechanism in Bangladesh". Bangladesh development studies(0304-095X), 30(3/4), p.31.
- Alam, Shamim, 2012, “Evolution of the Bangladeshi Provident Fund and its Investment: Towards and Independent Trustee.” PhD Dissertation in Legal Science, University of Canberra.
- Brixi, Hana Polackova, and Allen Schick, eds., 2002, Government at Risk: Contingent Liabilities and Fiscal Risk(s?) (New York: Oxford University Press).
- Budina, Nina and Murray Petrie, 2013, Managing and Controlling Fiscal Risks, in Public Financial Management and Its Emerging Architecture, International Monetary Fund (forthcoming).
- Chalk, Nigel, and Richard Hemming, 2000, “Assessing Fiscal Sustainability in Theory and Practice,” in Fiscal Sustainability, papers presented at a Banca d’Italia Research Department Workshop, Perugia, Italy, January.
- Cebotari, Aliona, Jeffrey Davis, Lusine Lusinyan, Amine Mati, Paolo Mauro, Murray Petrie, and Ricardo Velloso, 2009, “Fiscal Risks: Sources, Disclosure, and Management.” IMF.
- Celasun, O., X. Debrun and J.D. Ostry, 2006, “Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A ‘Fan-Chart’ Approach,” IMF Working Paper, WP/06/67.
- Cottarelli, Carlo, 2013, “Fiscal Risks and Fiscal Sustainability,” in Carlo Cottarelli, Phil Gerson, and Abdel Senhadji (eds.), Post-Crisis Fiscal Policy, Forthcoming (Cambridge, MA: MIT Press).
- Debrun, X., D. Hauner, and M. Kumar, 2009, “Independent Fiscal Agencies,” Journal of Economic Surveys, Vol. 23, 1, pp. 44-81.
- Fenochietto, Ricardo, and Carola Pessino, 2013, “Understanding Countries’ Tax Effort.” MF Working Paper WP/13/244.
- Gali, Jordi, and Roberto Perotti, 2003, “Fiscal Policy and Monetary Integration in Europe,” Economic Policy, Vol. 37 (October), pp. 533–72.
- Hemming, Richard, 2006, Public-Private Partnerships, Government Guarantees, and Fiscal Risk (Washington: International Monetary Fund).
- International Monetary Fund, 2012, “Bangladesh: First Review under the Three-Year Arrangement Under the Extended Credit Facility and Request for Waiver of Nonobservance of a Performance Criterion,” Staff Report, IMF Country Report No. 13/61.
- International Monetary Fund, 2013, “Bangladesh: Second Review Under the Three-Year Arrangement Under the Extended Credit Facility and Request for Modification of Performance Criteria—Staff Report, Staff Supplement and Statement; Press Release on the Executive Board Discussion; and Statement by the Executive Director for Bangladesh,” Staff Report, IMF Country Report No. 13/157.
- International Monetary Fund, 2009, “Computing Cyclically Adjusted Balances and Automatic Stabilizers,” Technical Notes and Manuals, Fiscal Affairs Department.
- Irwin, Timothy, 2003, “Public Money for Private Infrastructure—Deciding When to Offer Guarantees, Output-Based Subsidies, and Other Fiscal Support,” Working Paper No. 10 (Washington: World Bank).
- Kim, Cheolsu, and Guatam Bhardawaj, “South Asia Pension Forum: Fostering inclusive and sustainable pension systems in the region,” Mandaluyong City, Philippines: Asian Development Bank, 2011.
- Reinhart, Carmen, Kenneth S. Rogoff, and Miguel A. Savastano, 2003, “Debt Intolerance,” NBER Working Paper No. 9908, August 2003.
- Willmore, Larry, 2007, “Universal pensions for developing countries,” World Development 35:1 (January), pp. 24-51.
- Wyplosz, Charles, 2005, “Institutions for Debt Sustainability in Brazil,” in Inflation Targeting, Debt, and the Brazilian Experience, 1999 to 2003, ed. by Francesco Giavazzi, Ilan Goldfajn, and Santiago Herrera (Cambridge, Massachusetts: MIT Press).

### Annex 1. Methodology for the Production of the Fan Charts
- Sample and distributional assumption
  - Sample statistics are based on historical data over the period FY96-FY12.
  - A joint normal distribution is defined (normality assumed for simplicity).
- Modelling steps
  - Define a fiscal reaction function depending on the primary surplus, domestic real interest rate, real GDP growth rate, and real effective exchange rate.
  - Estimate an unrestricted auto-regression model (VAR) with these four variables (using Choleski decomposition factorization).
  - Generate projections for each of the four variables using:
    - (i) a deterministic projection from the VAR, and
    - (ii) a random shock drawn from a multivariate normal distribution with the same variance-covariance matrix as the one estimated for the in-sample errors of the VAR.
  - Add shocks to the baseline projected values of growth, interest rate, exchange rate, and primary balance in the debt evolution equation for periods t+1 to t+k (where k is length of projection period), to recursively generate debt-to-GDP ratio projections.
- Simulations and percentiles
  - Produce 1,000 simulated debt-to-GDP ratios in each year over the projection period.
  - Rank the ratios for each year from highest to lowest and assign the corresponding percentile of the 1,000 simulations to each ratio in each year.
  - Extract the 10th, 25th, 50th, 75th, and 90th percentiles to produce the fan chart.
  - The increasing spread of the distribution over the projection period reflects increased uncertainty over time since shocks can compound.
  - Note: Shocks are drawn taking into account only the contemporaneous correlations between variables, but a 90th percentile debt ratio path can be considered to reflect the impact of a sequence of bad shocks each year on the public debt ratio.
- Debt dynamics (as presented)
  - In its most basic form, the evolution of public debt can be characterized in the following way:
    - 1111 1 1 )1()1(     tt d t d t f t f t t t t OPBDiDi E E D      (1)
  - Definitions provided in the text:
    - Subscripts refer to time periods and superscript “f” and “d”, refer to foreign-currency and domestic-currency denominated debt, respectively.
    - f t D is the stock of foreign currency-denominated debt at the end of period t.
    - d t D is the stock of local currency-denominated debt at the end of period t.
    - t E is the nominal exchange rate (LC/USD) at the end of period t.
    - f t i 1 is the effective nominal interest rate on foreign currency-denominated debt at the end of period t+1.
    - d t i 1 is the effective nominal interest rate on domestic currency-denominated debt at the end of period t+1.
    - 1t PB is the government fiscal primary balance in period t+1.
    - 1t O are other factors, and the stock-flow residual that ensures that the identity holds.
  - Exchange rate process (as presented):
    - )1( 1 1    t t t E E           (2)
    - where t E is the nominal exchange rate Taka/US$ of period t.
  - Combined (as presented):
    -  111111 )1()1()1( 1 1             tt d t d t f t f ttt opbdidi g d    (3)
    - where lower letters represent the contemporaneous ratio to GDP.

*Content unit: _wp15110 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15110.pdf_