## tnmea2021005

## Source details

**Canonical URL:** [tnmea2021005](https://www.imf.org/-/media/files/publications/tnm/2021/english/tnmea2021005.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/tnm/2021/english/tnmea2021005.pdf.md)
- [Structured JSON version](/-/media/files/publications/tnm/2021/english/tnmea2021005.pdf.json)

---

### Overview and purpose of the Public Debt Dynamics Tool (DDT)
- The DDT is an Excel-based tool that:
  - Projects public debt as a percent of GDP.
  - Computes fiscal adjustment paths to achieve a user-defined debt target.
  - Computes associated interest expense.
  - Performs predefined and customized stress tests.
  - Produces fan charts.
  - Presents results in standardized output tables.
- Designed for capacity development by the IMF Institute for Capacity Development.
- Only 10 macrofiscal variables are required to run the DDT, enabling use in low-capacity environments and multi-country analyses.
- The DDT can be integrated into a country’s macroeconomic framework.

### How the DDT relates to LIC DSF and MAC DSA
- The DDT reproduces baseline public debt projections obtained using:
  - the government’s borrowing requirements (DDT approach), and
  - the government’s net debt issuances (LIC DSF and MAC DSA approaches).
- Differences vs. LIC DSF and MAC DSA:
  - Explicitly accounts for intra-year exchange rate fluctuations in debt projections and interest expense.
  - Computes fiscal adjustment paths that incorporate all exchange rate valuation effects.
  - Includes fan charts with a longer projection horizon than the MAC DSA (fan charts are not available in the LIC DSF).
  - Allows flexible adjustment of the projection period length.
- Limitations relative to LIC DSF and MAC DSA:
  - Focuses only on the public-debt-to-GDP ratio.
  - Does not present other solvency indicators (e.g., external-public-debt to exports), liquidity indicators (e.g., public gross financing needs), or comprehensive debt-profile indicators (besides the share of foreign-currency debt).
  - Lacks debt-burden thresholds and comprehensive realism-evaluation tools included in MAC DSA and LIC DSF.

### Core debt-dynamics framework
- Uses a debt dynamics equation derived from the government’s borrowing requirements: overall balance (primary balance minus interest expense) plus other net debt-creating flows; expressed in nominal terms and as a ratio to GDP.
- Key conceptual elements preserved:
  - Distinction between primary balance and overall balance.
  - Other net debt-creating flows (stand-alone items) such as recognition of contingent liabilities, debt relief, and drawdown of assets.
  - A stock-flow adjustment due to intra-period exchange rate fluctuations, endogenized so borrowing-requirements projections coincide with net-debt-issuance projections.
- The debt-to-GDP dynamics equation explicitly includes:
  - previous-period debt ratio;
  - the (gross) real cost of debt including exchange rate valuation effects;
  - real GDP growth;
  - domestic inflation (GDP deflator);
  - share of foreign-currency debt and rate of change of the end-of-period exchange rate (depreciation rate);
  - a stock-flow adjustment term capturing intra-period exchange rate valuation effects as a percent of GDP.

### Decomposition of contributors to changes in the debt-to-GDP ratio
- Identified contributors:
  - contribution of the real effective interest rate;
  - contribution of the exchange rate;
  - contribution of real GDP growth;
  - the primary balance and other net debt-creating flows;
  - the stock-flow adjustment due to intra-period exchange rate fluctuations.
- Caveats when applying the decomposition to historical data:
  - Unidentified flows from cross-exchange rate valuation effects (multiple foreign currencies).
  - Intra-period exchange rate fluctuations not captured by annual differences between average and end-of-period exchange rates.
  - Differences between accrual and cash accounting.
  - Use of market or face value measures for public debt.
  - In such cases, a residual term will appear reflecting differences between observed debt-ratio changes and identified contributors.

### Stock-flow adjustment for intra-period exchange rate fluctuations
- Rationale:
  - Valuation of year-end foreign-currency debt depends on the exchange rate at which transactions occur during the year versus the end-of-period rate.
- Practical assumption:
  - Transactions that affect the debt stock are assumed to occur at the average exchange rate; this enables equivalence with LIC DSF and MAC DSA projections.
- Formal treatment:
  - Stock-flow adjustment is endogenized and differs from zero only if end-of-period and average exchange rates differ and the stock of foreign-currency debt changes.
  - As a percent of GDP, the adjustment depends on the level of debt and is included in a closed-form debt dynamics equation where:
    - a valuation-adjusted (gross) cost of debt fully incorporates intra-period exchange rate effects;
    - a stock-flow coefficient distributes the stock-flow adjustment among relevant flow variables.
- Interpretation of the stock-flow coefficient:
  - No intra-period exchange rate fluctuations → coefficient = one.
  - Currency depreciates during the year and there is foreign-currency debt → coefficient > one.
  - Currency appreciates during the year and there is foreign-currency debt → coefficient < one.

### Role of real interest rates, real exchange rates, and fan charts
- Debt dynamics can be rearranged to highlight local- and foreign-currency real effective costs of debt and the role of the real exchange rate.
- The DDT uses the formulation with real costs and real exchange rates to build fan charts for scenario and stress-test analysis.

### Treatment of uncalled guarantees and contingent liabilities
- DDT by default focuses on public debt that comprises financial claims requiring payment of principal, interest, or both; contingent liabilities are excluded by default.
- If reported public debt includes uncalled guarantees, users can:
  - subtract uncalled guarantees to project debt using the main debt-dynamics equation, and
  - add back the stock of uncalled guarantees in the next period, including any exogenously-driven variation.
- DDT allows users to include the exogenous evolution of uncalled guarantees, reported as a stand-alone debt-creating flow.

### DDT inputs and user interface (including example country inputs)
- Data entry conventions:
  - User inputs must be entered in yellow-shaded cells within worksheets that have yellow tabs.
  - Light yellow-shaded cells indicate selectable inputs via drop-down menus.
  - White cells contain formulas and should not be overridden.
- Example Basic Inputs:
  - Country name: Macondo
  - First year of projections: 2021
  - Year for medium-term indicators: 2027
  - Definition of the public sector: central government
  - Includes public guarantees?: Ye s
  - Specify or define the guarantees: outstanding amount of loans guaranteed by the central government
- Input – Data (required annual data for 10 years of historical data and projections; projection period pre-specified to be 12 years):
  - Debt-related data required:
    - stock of total gross public debt (up to the year before the projection period starts)
    - uncalled guarantees as percent of GDP in local and foreign currency (if included)
    - share of public debt in foreign currency as percent of total debt (excluding uncalled guarantees)
  - Macrofiscal indicators required:
    - average and end-of-period nominal exchange rates (local currency per unit of foreign currency)
    - effective nominal interest rates on local- and foreign-currency debt
    - GDP deflator inflation
    - real GDP growth
    - primary balance
    - other net debt-creating flows
    - foreign GDP deflator inflation (for fan charts)
- Readme worksheet contains pull-down menus under “Basic Inputs” for initial selections.

### Adjustment paths inputs and fiscal-path modules to achieve a public debt target
- Required “Adjustment Paths Data Inputs” (example values):
  - Public debt-to-GDP target: 60.0
  - Adjustment path starts: 2022
  - Adjustment path ends: 2030
- Users may choose constant or time-varying values for key variables; pre-defined constant options include historical/projection averages and latest year before projections start.
- Example reported baseline values:
  - 10-year projection average for g (real GDP growth): 3.81
  - 10-year projection average for of (other net debt-creating flows): 0.90
- Fiscal-path modules:
  - Debt-stabilizing balances: compute primary and overall balance required to stabilize debt at previous-year level.
  - Constant primary/overall balance to reach a debt target: compute levels that, if implemented every adjustment year, achieve the debt target.
  - Constant yearly adjustment in primary/overall balance: compute constant fiscal yearly adjustment that would achieve the debt target.
  - Constant yearly debt reductions: present primary and overall balance paths achieving constant annual debt-ratio reductions (applies to debt excluding uncalled guarantees; debt target includes uncalled guarantees if applicable).
  - Customized adjustment scenario: combine a first period with a constant yearly adjustment and a second period with a constant primary balance; user specifies periods and second-period constant primary balance.

### Stress tests: design, inputs, and example specifications
- In the DDT only one variable is shocked at a time (all else remains baseline) to ensure transparency.
- Historical standard deviations: 10 years of data, except exchange rate depreciation (9 years).
- Historical averages: 10 years, except exchange rate depreciation and residual (9 years).
- For exchange rates, the shock is to the depreciation rate.
- Example stress-test input scalars (multiply historical standard deviation):
  - Primary balance shock: -1
  - GDP growth shock: -1
  - Interest rate shock: 1
  - Exchange rate depreciation shock: 1
- Example shock durations:
  - Primary balance shock starts: 2022; ends: 2023
  - GDP growth shock starts: 2022; ends: 2023
  - Interest rate shock starts: 2022; ends: 2023
  - Exchange rate depreciation shock starts: 2022; ends: 2023
- Worksheets for shocks:
  - Sh-pb, Sh-g, Sh-int, Sh-er present shock scenarios for the primary balance, GDP growth, interest rates, and exchange rates, respectively.
  - Between start and end years the shocked variable = baseline + multiple × historical standard deviation; other variables remain at baseline.

### Fan charts and stochastic simulations
- Fan charts follow the 2013 MAC DSA template and summarize possible evolution of the debt-to-GDP ratio by incorporating shocks and ordering resulting debt paths through confidence intervals.
- For simplicity, shocks consider only contemporaneous correlations; intertemporal correlations and autocorrelations are ignored.
- Fan charts rely on historical annual data of four key variables; the four variables shocked are:
  - the augmented primary balance (includes the residual in period t), and
  - the augmented real foreign effective interest rate (as described in the template).
- Using 1,000 shocks for the key variables, the DDT adds those shocks to baseline assumptions to compute 1,000 debt paths using equation (10); these 1,000 debt paths build the fan charts.
- Fan charts are built in worksheet Fan chart. Nine years of historical data and projections for the four variables are automatically populated; additional historical years can be included.
- Stochastic simulations produce fan charts for a 12-year projection horizon.
- Users must activate an embedded Excel macro (blue button) to generate fan charts; users can deactivate shocks to any of the four variables. Symmetric shocks produce symmetric fan charts; asymmetric fan charts can be built by restricting shock values.

### Standardized outputs and reporting
- Once yellow worksheet inputs are populated, the DDT automatically produces baseline and alternative scenarios, output tables, and charts.
- Standardized outputs present: country name, coverage of public sector debt, first year of projections, and whether uncalled guarantees are included.
- Main results appear in Output - Baseline and Output - Shocks worksheets.
- Output - Baseline:
  - Reports evolution of public debt using the public debt dynamics equation (8).
  - Presents a standard decomposition of contributions to debt changes and reports the stock-flow adjustment as a stand-alone item.
  - Includes a “Realism and Fiscal Adjustments” box with indicators:
    - i. debt levels over the medium term (“Year for medium-term indicators” in Readme) under the historical and primary balance scenarios;
    - ii. the debt-stabilizing primary balance in the first year of projections and over the medium term;
    - iii. the level and yearly change in the primary balance needed to reach a debt target after the adjustment period;
    - iv. probability assessment of the debt level being below that of the last historical year and below the user-defined debt target in the year in which the adjustment path ends.
  - If uncalled guarantees are inputted, outputs include those guarantees when reporting public debt dynamics.
- Output - Shocks:
  - Presents debt dynamics for alternative scenarios, the underlying assumptions, and fan charts.

### Appendix I — Equivalence between borrowing-requirements and net-debt-issuances approaches
- Equivalence result:
  - Public debt evolution can be computed using the government’s borrowing requirements (equation (1)) or government net debt issuances (equation (11)), provided a stock-flow adjustment term revalues foreign-currency flows from the average to the end-of-period exchange rate.
  - Consistency is established by defining gross financing needs (GFN) as the sum of resources needed to finance the period overall deficit (primary deficit plus interest expense) and period debt amortizations, and using the identity that all GFN not financed by other net debt-creating flows must be covered by gross debt issuances (equation (12)).
  - Rearranging (12) shows the overall deficit plus other net debt-creating flows equals net debt issuances; starting from (11) and using (12) one can recover (1).
- Practical implications:
  - Choice between (1) and (11) depends on availability of information and the questions being addressed (e.g., financing needs vs. drivers of debt changes).
  - MAC DSA and LIC DSF emphasize assessing liquidity risks and therefore project debt levels using equation (11).
  - To project GFN from (12) one needs projections for amortizations.

*tnmea2021005 — References and Appendices (content as provided).*

### References                                                                                                              

### tnmea2021005 - References

### Overview and purpose of the Public Debt Dynamics Tool (DDT)
- The DDT is an Excel-based tool that:
  - Projects public debt as a percent of GDP.
  - Computes fiscal adjustment paths to achieve a user-defined debt target.
  - Computes associated interest expense.
  - Performs predefined and customized stress tests.
  - Produces fan charts.
  - Presents results in standardized output tables.
- The tool was developed as part of capacity development work on macroeconomic frameworks for forecasting and policy analysis of the IMF Institute for Capacity Development.
- Only 10 macrofiscal variables are required to run the DDT, making it accessible for users without detailed financing data.
- The DDT can be integrated into a country’s macroeconomic framework and used in low-capacity environments and multi-country analyses.

### How the DDT relates to LIC DSF and MAC DSA
- The DDT reproduces baseline public debt projections obtained using:
  - The government’s borrowing requirements (DDT approach), and
  - The government’s net debt issuances (LIC DSF and MAC DSA approaches).
- The DDT differs from LIC DSF and MAC DSA in that:
  - It explicitly accounts for intra-year exchange rate fluctuations in debt projections and interest expense.
  - It computes fiscal adjustment paths that incorporate all exchange rate valuation effects.
  - It includes fan charts with a longer projection horizon than the MAC DSA (fan charts are not available in the LIC DSF).
  - It allows flexible adjustment of the projection period length.
- Limitations relative to LIC DSF and MAC DSA:
  - The DDT focuses only on the public-debt-to-GDP ratio.
  - It does not present other solvency indicators (e.g., external-public-debt to exports), liquidity indicators (e.g., public gross financing needs), or comprehensive debt-profile indicators (besides the share of foreign-currency debt).
  - The MAC DSA and LIC DSF present debt-burden thresholds and a comprehensive set of realism-evaluation tools not included in the DDT.

### Core debt-dynamics framework used by the DDT
- The DDT uses a debt dynamics equation derived from the government’s borrowing requirements: overall balance (primary balance minus interest expense) plus other net debt-creating flows; the equation is expressed both in nominal terms and as a ratio to GDP.
- Key conceptual elements preserved in the DDT:
  - The distinction between primary balance and overall balance.
  - Other net debt-creating flows (stand-alone items) such as recognition of contingent liabilities, debt relief, and drawdown of assets.
  - The stock-flow adjustment due to intra-period exchange rate fluctuations, endogenized so projections with the borrowing-requirements approach coincide with net-debt-issuance projections.
- The debt-to-GDP dynamics equation (as a share of GDP) explicitly includes:
  - The previous-period debt ratio.
  - The (gross) real cost of debt including exchange rate valuation effects.
  - Real GDP growth.
  - Domestic inflation (GDP deflator).
  - The share of foreign-currency debt and the rate of change of the end-of-period exchange rate (depreciation rate).
  - A stock-flow adjustment term capturing intra-period exchange rate valuation effects as a percent of GDP.

### Decomposition of contributors to changes in the debt-to-GDP ratio
- Identified contributors to changes in the debt ratio include:
  - The contribution of the real effective interest rate.
  - The contribution of the exchange rate.
  - The contribution of real GDP growth.
  - The primary balance and other net debt-creating flows.
  - The stock-flow adjustment due to intra-period exchange rate fluctuations.
- Caveats when applying the decomposition to historical data:
  - Unidentified flows from cross-exchange rate valuation effects (multiple foreign currencies).
  - Intra-period exchange rate fluctuations not captured by annual differences between average and end-of-period exchange rates.
  - Differences between accrual and cash accounting.
  - Use of market or face value measures for public debt.
  - In such cases, a residual term will appear reflecting differences between observed debt-ratio changes and identified contributors.

### Use of primary balance versus overall balance in projections
- The note presents formulas linking the primary balance and the overall balance as a percent of GDP, showing how total interest expense (which depends on intra-year exchange rate changes) maps between the two concepts.
- It is straightforward to switch the debt dynamics representation between:
  - Primary-balance-based equations, and
  - Overall-balance-based equations.
- The DDT produces debt projections both ways to assess implications of fiscal rules that constrain the overall balance.

### Stock-flow adjustment for intra-period exchange rate fluctuations
- Rationale:
  - When the government uses flow resources (e.g., the primary balance) to alter the stock of foreign-currency debt during the year, the exchange rate at which transactions occur matters for valuing year-end debt measured at the end-of-period exchange rate.
- Practical assumption in the DDT:
  - Transactions that affect the debt stock are assumed to occur at the average exchange rate; this simplification enables equivalence with LIC DSF and MAC DSA projections.
- Formal treatment:
  - The stock-flow adjustment is endogenized and differs from zero only if the end-of-period and average exchange rates differ and the stock of foreign-currency debt changes.
  - As a percent of GDP, the stock-flow adjustment depends on the level of debt and is included in a closed-form debt dynamics equation where:
    - A valuation-adjusted (gross) cost of debt fully incorporates intra-period exchange rate effects.
    - A stock-flow coefficient distributes the stock-flow adjustment among relevant flow variables.
- Interpretation of the stock-flow coefficient:
  - If there are no intra-period exchange rate fluctuations, the coefficient equals one.
  - If the currency depreciates during the year and there is foreign-currency debt, the coefficient is larger than one.
  - If the currency appreciates during the year and there is foreign-currency debt, the coefficient is smaller than one.
- The stock-flow adjustment explains, for example, why a primary balance used to repay foreign-currency debt at the average exchange rate may have a different effect on the end-of-period stock valued at the end-of-period exchange rate.

### Role of real interest rates, real exchange rates, and fan charts
- The debt dynamics equation can be rearranged to highlight:
  - Local- and foreign-currency real effective costs of debt.
  - The role of the real exchange rate.
- The DDT uses the formulation with real costs and real exchange rates to build fan charts as part of scenario and stress-test analysis.

### Treatment of uncalled guarantees and contingent liabilities
- The DDT focuses on public debt that comprises financial claims requiring payment of principal, interest, or both; contingent liabilities are excluded by default.
- If reported public debt includes uncalled guarantees, users can:
  - Subtract uncalled guarantees to project debt using the main debt-dynamics equation, and
  - Add back the stock of uncalled guarantees in the next period, including any exogenously-driven variation.
- The DDT allows users to include the exogenous evolution of uncalled guarantees, reported in output tables as a stand-alone debt-creating flow.

### DDT inputs and user interface
- Data entry conventions in the DDT:
  - User inputs must be entered in yellow-shaded cells within worksheets that have yellow tabs.
  - Light yellow-shaded cells indicate selectable inputs via drop-down menus.
  - White cells contain formulas and should not be overridden.
- The first step when using the DDT is populating country-specific and macrofiscal data.
- The Readme worksheet contains pull-down menus under the “Basic Inputs” header for initial selections.

*Technical Notes and Manuals 2021/005 — References and Appendices (content as provided).*

### 1.  country of interest;

### 1.  country of interest;

### Basic Inputs
- Required initial selections and definitions:
  - Country name: Macondo
  - First year of projections: 2021
  - Year for medium-term indicators: 2027
  - Definition of the public sector: central government
  - Includes public guarantees?: Ye s
  - Specify or define the guarantees: outstanding amount of loans guaranteed by the central government
- Note: The remainder inputs of the Readme worksheet concern fiscal adjustment paths and stress tests. It is recommended to fill out the Input - Data worksheet first.

### Input – Data (purpose and required annual data)
- Purpose: provide 10 years of historical annual data and projections for key macrofiscal inputs necessary to project debt-to-GDP ratios; projection period is pre-specified to be 12 years (can be manually extended).
- Required DDT inputs (necessary to project public debt using (8), plus uncalled guarantees if included, and foreign inflation for fan charts using (10)):
  - Debt-related data:
    - stock of total gross public debt, up to the year before the projection period starts (row 9, historical data only)
    - uncalled guarantees as percent of GDP in local and foreign currency (only needed if these are included in the definition of reported debt, rows 10-11)
    - share of public debt in foreign currency as percent of total debt (excluding uncalled guarantees, row 12). The template automatically computes the share of local-currency debt (excluding uncalled guarantees) as percent of total debt.
  - Macrofiscal indicators:
    - average and end-of-period nominal exchange rates (local currency per unit of foreign currency, rows 13-14)
    - effective nominal interest rates on local- and foreign-currency debt (rows 15-16)
    - GDP deflator inflation (row 17)
    - real GDP growth (row 18)
    - primary balance (row 19)
    - other net debt-creating flows (row 20)
    - foreign GDP deflator inflation (e.g., that of the US) to be used only for fan charts (row 21)

### Adjustment Paths Inputs
- Required user specifications under “Adjustment Paths Data Inputs”:
  - Public debt-to-GDP target: 60.0
  - Adjustment path starts: 2022
  - Adjustment path ends: 2030
- Functionality:
  - Users may choose different values for key macrofiscal inputs than baseline values (to reflect, e.g., fiscal multipliers and lower GDP growth during adjustment).
  - Users can input either constant values or “time-varying values” for key variables.
  - Pre-defined constant-value options: 10-year or 5-year historical averages; 5-year or 10-year projection averages; latest year before projections start; or “Set constant value manually” in yellow-shaded cells (column C, rows 31-37).
  - If choosing a historical or projected constant, column D, rows 31-37, automatically reproduces the relevant value.
  - Under “time-varying values,” the DDT uses baseline assumptions plus the “Additions to Baseline Assumptions for Fiscal Adjustment Paths” entered by the user (e.g., enter “–1” to make GDP growth 1 percentage point lower than baseline for specified years).
- Example reported values and structure (Baseline Assumptions From "Input - Data" Sheet, plus Additions to Baseline for Fiscal Adjustment Paths):
  - 10-year projection average for g (real GDP growth): 3.81
  - 10-year projection average for of (other net debt-creating flows): 0.90
- Additions to Baseline Assumptions for Fiscal Adjustment Paths (time-varying values) layout (variables shown for years 2020–2025):
  - αt (share excl. guarantees): share of foreign currency denominated debt in total debt, percent of total debt
  - et (LCU/FCU, avg): nominal average exchange rate, local currency per unit of foreign currency
  - et (LCU/FCU, eop): nominal end of period exchange rate, local currency per unit of foreign currency
  - itd: nominal effective interest rate on local currency denominated debt, percent
  - itf: nominal effective interest rate on foreign currency denominated debt, percent
  - πt: GDP deflator inflation, percent
  - gt: Real GDP growth, percent
  - oft: Other net debt-creating flows, percent of GDP
- Iteration note: The process can be iterative—computed fiscal adjustments may imply different growth outcomes, which can be updated until the user is satisfied.

### Stress Tests Inputs
- Stress tests inputs required under “Stress Tests Data Inputs”:
  - Size of the shock to each relevant variable (measured as a scalar factor that multiplies the historical standard deviation of each variable; column B, rows 43-46):
    - Primary balance shock: -1
    - GDP growth shock: -1
    - Interest rate shock: 1
    - Exchange rate depreciation shock: 1
  - Duration of shocks (example start and end years):
    - Primary balance shock starts: 2022
    - Primary balance shock ends: 2023
    - GDP growth shock starts: 2022
    - GDP growth shock ends: 2023
    - Interest rate shock starts: 2022
    - Interest rate shock ends: 2023
    - Exchange rate depreciation shock starts: 2022
    - Exchange rate depreciation shock ends: 2023

*tnmea2021005 - 1.  country of interest;*

### 2.  The years in which each shock starts and finishes.

### 2.  The years in which each shock starts and finishes.

### DDT shock design and data inputs
- In the DDT, only one variable is shocked at a time to allow transparency about sensitivity of debt projections to changes in each key variable (everything else remains as in the baseline).
- All selections and data inputted in the Readme and Input - Data worksheets are automatically transferred into the relevant worksheets of the template.
- Worksheets with green tabs present debt projections under the baseline and alternative scenarios; all calculations in green worksheets are automatic.
- Historical standard deviations consider 10 years of data, except for exchange rate depreciation, for which the nine years of data available are used.
- Historical averages consider 10 years of data, except for the exchange rate depreciation and the residual, for which the 9 years of available data are used.
- For exchange rates, the shock is to the depreciation rate.

### Fiscal-path modules to achieve a public debt target (V)
- Debt-stabilizing balances:
  - Worksheets DebtStabPrimBalance and DebtStabOverallBalance compute the primary and overall balance required to stabilize debt at the level of the previous year, either in the first projection year or the “Year for medium-term indicators” defined in Readme. Results reported in Output - Baseline.
- Constant primary/overall balance to reach a debt target:
  - Worksheets DebtTargetConstant_pb and DebtTargetConstant_ob compute the primary and overall balance levels that, if implemented every adjustment year, would achieve the debt target. Output reported in Output - Baseline.
- Constant yearly adjustment in primary/overall balance:
  - Worksheets DebtTargetConstantAdjustment_pb and DebtTargetConstantAdjustment_ob present the constant fiscal yearly adjustment (change in the primary and overall balances) that would achieve the debt target. This adjustment is reported in Output - Baseline.
- Constant yearly debt reductions:
  - Worksheets DebtTargetConstantDebtChange_pb and DebtTargetConstantDebtChange_ob present primary and overall balance paths that achieve constant annual debt-ratio reductions until the debt target is reached. No single summary statistic is presented in standardized output for this exercise.
  - Note: constant yearly debt reductions are for the stock of debt excluding uncalled guarantees. The debt target includes uncalled guarantees, if applicable.
- Customized adjustment scenario:
  - Worksheet CustomizedAdj allows combining a first period with a constant yearly adjustment and a second period with a constant primary balance such that the debt target is reached at end of the second period.
  - User inputs: first period start and end years in cells B51 and B52; year in which the debt target is reached in cell D52; constant primary balance for the second period in cell B54. Debt target and key variable values are as set in Readme.
  - This customized adjustment scenario is set for the primary balance; a similar exercise can be done for the overall balance.
- Example timing: Adjustment starts in 2022 and ends in 2030.

### Realism, stress tests, and scenario definitions (VI)
- Historical scenario:
  - Key macrofiscal inputs set at their historical averages throughout the projection period: nominal effective interest rates in local and foreign currency, growth, inflation, nominal exchange rate depreciation, primary balance, and other net debt-creating flows.
  - To fully capture historical contributions to debt changes, the average residual is added to other net-debt creating flows.
  - Assumptions of the historical scenario affect debt dynamics starting in the second projection year.
  - Historical scenario is automatically created in worksheet HistoricalSc. Debt level for the “Year for medium-term indicators” is reported in Output - Baseline (cell W23).
- Constant primary balance scenario:
  - All key macro fiscal inputs as in the baseline, except the primary balance, which starting in the second projection year is set at the level of the first projection year.
  - Created automatically in worksheet ConstanPBSc. Debt level for the “Year for medium-term indicators” reported in Output - Baseline (cell Y23).
- Shock scenarios:
  - Worksheets Sh-pb, Sh-g, Sh-int, and Sh-er present shock scenarios for the primary balance, GDP growth, effective nominal interest rates in local and foreign currencies, and the average and end-of-period nominal exchange rates, respectively.
  - For each shocked variable, between the starting and end years for the shock (defined in Readme), the shocked variable equals its baseline value plus a multiple (defined in Readme) of its historical standard deviations. All other macrofiscal variables take their baseline values.
  - For the exchange rates, the shock is to the depreciation rate.
- Customized scenario:
  - Worksheet CustomizedSc allows fully customized inputs (yellow-shaded cells) to define variables that determine debt evolution. Possible modeled events include natural disasters, PPP failures, bailouts of SOEs and subnational governments.

### Fan charts and stochastic simulations (VI.E)
- Fan charts follow the template of the 2013 MAC DSA and summarize possible evolution of the debt-to-GDP ratio by incorporating shocks to relevant macrofiscal variables and ordering resulting debt paths through confidence intervals.
- For simplicity, shocks are drawn considering only contemporaneous correlations among variables; intertemporal correlations and autocorrelations are ignored.
- Fan charts rely on historical annual data of four key variables to generate sample means and a variance-covariance matrix defining the joint normal distribution of shocks.
- The four variables shocked for the fan charts are: the augmented primary balance (where the augmented primary balance includes the residual in period t), and the augmented real foreign effective interest rate (as described in the template).
- Using 1,000 shocks for the key variables, the DDT adds those shocks to baseline assumptions to compute 1,000 debt paths using equation (10); these 1,000 debt paths are used to build the fan charts.
- Fan charts are built in worksheet Fan chart. Nine years of historical data and projections for the four variables are automatically populated using baseline assumptions (cells AS7:BA10). Additional years of historical data can be included (cells C7:AR10).
- Stochastic simulations produce fan charts for a 12-year projection horizon.
- Users must activate an embedded Excel macro by clicking the blue button to generate fan charts; users can deactivate shocks to any of the four variables (cells B42:45).
- Symmetric shocks produce symmetric fan charts; users can build asymmetric fan charts by restricting shock values (cells D42:45), e.g., restricting upside or downside shock values.

### Standardized outputs and reporting (VII)
- Once yellow worksheet inputs are populated, the DDT automatically produces baseline and alternative scenarios, output tables, and charts.
- Standardized outputs present: country name, coverage of public sector debt, first year of projections, and whether uncalled guarantees are included.
- Main results appear in Output - Baseline and Output - Shocks blue worksheets.
- Output - Baseline:
  - Reports evolution of public debt in the baseline using the public debt dynamics equation (8).
  - Presents a standard decomposition of contributions to debt changes and reports the stock-flow adjustment due to intra-period exchange rate fluctuations as a stand-alone item.
  - Includes a “Realism and Fiscal Adjustments” box with the following indicators:
    - i. debt levels over the medium term (“Year for medium-term indicators” in Readme) under the historical and primary balance scenarios;
    - ii. the debt-stabilizing primary balance in the first year of projections and over the medium term (“Year for medium-term indicators” in Readme);
    - iii. the level and yearly change in the primary balance needed to reach a debt target after the adjustment period (under parameters chosen in Readme);
    - iv. an assessment of the probability of the debt level being below that of the last historical year and below the user-defined debt target in the year in which the adjustment path ends (as defined in Readme).
  - If the user inputted uncalled guarantees, the output table will include those guarantees when reporting public debt dynamics.
- Output - Shocks:
  - Presents debt dynamics for alternative scenarios, the underlying assumptions for these scenarios, and fan charts.

*Technical Notes and Manuals 2021/005 — “2.  The years in which each shock starts and finishes.”*

### Appendix I: Equivalence between the Borrowing-Requirements Approach

### Appendix I: Equivalence between the Borrowing-Requirements Approach and Net-Debt-Issuances Approach for Projecting Public Debt

### Equivalence result
- The evolution of public debt can be computed using:
  - the government’s borrowing requirements determined by the fiscal balance and other net debt-creating flows (equation (1)), or
  - government net debt issuances (issuances minus amortizations) of foreign-currency debt (converted to local currency using the average exchange rate) and net debt issuances of local-currency debt (equation (11)), with the stock-flow adjustment term included to revalue foreign-currency flows from the average to the end-of-period exchange rate.
- Consistency between (1) and (11) is established by defining the government’s gross financing needs (GFN) as the sum of:
  - the resources needed to finance the period- overall deficit (primary deficit plus the interest expense) and
  - period- debt amortizations,
  and using the identity that all GFN not financed by other net debt-creating flows must be covered by gross debt issuances (equation (12)).
- Rearranging (12) shows that the government’s overall deficit plus other net debt-creating flows equals net debt issuances; thus, starting from (11) and using (12) one can recover (1).

### Practical implications for projections and risk assessment
- The choice between using (1) or (11) for projecting public debt depends on:
  - the availability of information to undertake projections, and
  - the type of questions to be addressed (for example, identifying government financing needs or the key drivers of public debt changes).
- Given the IMF’s emphasis on assessing liquidity risks in member countries, understanding the evolution of financing needs is a priority for both the MAC DSA and the LIC DSF, which therefore project debt levels using equation (11).
- Note: to project GFN from (12) one needs projections for amortizations.

*Source: tnmea2021005 - Appendix I: Equivalence between the Borrowing-Requirements Approach and Net-Debt-Issuances Approach for Projecting Public Debt*

---


_Source: https://www.imf.org/-/media/files/publications/tnm/2021/english/tnmea2021005.pdf_