1. Macroeconomic Diagnostics (MDSx)8
Fiscal Sustainability

2. MDSx 8 1 1
About Module 8
Standard

3. MDSx 8 2 1
Fiscal Sustainability
Standard

4. Fiscal Sustainability
A definition…
A situation in which a government is expected to be able to continue servicing its debt without an unrealistically large adjustment to its balance of revenues and expenditure, without debt restructuring or default

5. Key Concepts for Assessment:
Fiscal Sustainability
Key Concepts for Assessment:
Solvency Ability to repay debt
Liquidity Ability to rollover debt
Realistic adjustment Plausible primary balance path

6. Government able to service debt without renegotiating or defaulting
Solvency
Key Points:
Current debt stock is fully covered by expected future primary balances
Government able to service debt without renegotiating or defaulting
Debt ratio stabilizes or declines

7. Financing is sufficient to meet maturing obligations
Liquidity
Key Points:
Financing is sufficient to meet maturing obligations
Continued market access and low risk of rollover
Well balanced debt profile and debt level is “not too high”

8. Realistic macroeconomic assumptions and projections
Realistic Adjustment
Key Points:
Realistic macroeconomic assumptions and projections
Adjustment is economically and politically feasible
Potential growth is preserved at a satisfactory level

9. The International Monetary Fund (IMF) Framework:
Debt Sustainability Analysis
The International Monetary Fund (IMF) Framework:
Market Access Countries (MAC) DSA For high income countries
Low Income Countries (LIC) DSF For low income countries

10. MDSx 8 2 2
Public Debt Burden Indicators
Standard

11. Gross Debt
A definition…
All liabilities that require future payment of interest and/or principal by the debtor to the creditor, or all liabilities held in debt instruments.

12. Gross Financing Needs
A definition…
Overall new borrowing requirement (budget deficit) plus debt maturing during the year.
Gross Financing Needs
Primary Deficit
Debt
Service = +

13. Debt Stock Gross Financing Needs
Debt Burden Indicators
Used by IMF DSA Frameworks:
Debt Stock
Gross Financing Needs
GDP
Export Proceeds
Fiscal Revenue

14. MDSx 8 3 1
Closed Economy Public Debt Dynamics
Standard

15. 𝑮 𝒕 + 𝒊 𝒕 𝑫 𝒕−𝟏 = 𝑻 𝒕 +( 𝑫 𝒕 − 𝑫 𝒕−𝟏 )
Government Budget Constraint
Government Expenditure
non-interest (Gt)
interest (it Dt)
Government Revenues
tax and non-tax (Tt)
New debt (Dt - Dt-1) =
𝑮 𝒕 + 𝒊 𝒕 𝑫 𝒕−𝟏 = 𝑻 𝒕 +( 𝑫 𝒕 − 𝑫 𝒕−𝟏 )
i = nominal interest rate

16. Government Primary Balance
The primary balance, PB is the difference between revenue (T) and non-interest expenditure (G):
𝑷𝑩𝒕= 𝑻 𝒕 − 𝑮 𝒕

17. Public Debt Dynamics
In a Closed Economy:
𝑫 𝒕 = 𝟏+ 𝒊 𝒕 𝑫 𝒕−𝟏 − 𝑷𝑩 𝒕

18. 𝑫 𝒕 𝒀 𝒕 = 𝟏+ 𝒊 𝒕 𝑫 𝒕−𝟏 𝒀 𝒕 − 𝑷𝑩 𝒕 𝒀 𝒕 𝑌 𝑡 = 𝑌 𝑡−1 1+ 𝑔 𝑡 (1+ 𝜋 𝑡 )
Public Debt Dynamics
In a Closed Economy:
𝑫 𝒕 𝒀 𝒕 = 𝟏+ 𝒊 𝒕 𝑫 𝒕−𝟏 𝒀 𝒕 − 𝑷𝑩 𝒕 𝒀 𝒕
𝐷𝑡−1 is divided by 𝑌𝑡
We can express:
We can also write:
𝑌 𝑡 = 𝑌 𝑡−1 1+ 𝑔 𝑡 (1+ 𝜋 𝑡 )
(1+ 𝑖 𝑡 )= 1+ 𝑟 𝑡 (1+ 𝜋 𝑡 )
r = real interest rate
π = inflation rate based on GDP deflator
g = real growth rate

19. 𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Public Debt Dynamics
In a Closed Economy:
𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡

20. MDSx 8 3 2
Closed Economy Public Debt Dynamics in Excel
Excel

21. EXCEL

22. MDSx 8 3 3
Interest Rate - Growth Differential
Standard

23. 𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Interest Rate - Growth Differential
The differential between the average interest rate paid on government debt and the growth rate of the economy.
𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
𝑑 𝑡 − 𝑑 𝑡−1 = 𝑟 𝑡 − 𝑔 𝑡 𝑔 𝑡 𝑑 𝑡−1 − 𝑝𝑏 𝑡
The interest rate – growth differential is the differential between the average interest rate paid on government debt and the growth rate of the economy.
To calculate the interest rate – growth differential, we need to remember the equation for the low of motion of the public debt.
Let’s subtract the debt to GDP ratio of the previous period small d(t-1) from both sides of this equation.
We get the following. The change in the debt ratio depends on the difference between the real interest rate paid on debt (r) and the real GDP growth rate (g), divided by (1+g) and minus the primary balance. Let’s define this equation as equation 6.
This term defines the so called automatic debt dynamics, or impact of real interest rate and GDP growth rate on debt ratio dynamics.
The difference between interest rate and growth rate adjusted to growth rate defines the interest rate – growth differential.
Conceptually it is the rate at which the debt-to-GDP ratio would grow if the primary balance were zero and debt service (principal and interest) were financed by issuing more debt.

24. Key to assess government debt sustainability.
Interest Rate - Growth Differential
Key to assess government debt sustainability.
Positive: unfavorable debt dynamics
Negative: favorable debt dynamics
The higher the Interest Rate - Growth Differential (i > g), the larger the fiscal effort necessary to put the debt ratio on a downward path.
The interest rate-growth differential plays a critical role in Debt Sustainability Analysis.
A positive value of the differential – interest rate greater than economic growth rate -- clearly would lead to unfavorable debt dynamics. This means the government’s service of the debt exceeds the additional income produced by the economy.
Negative value * of the differential would lead to a favorable debt dynamic, as the interest rate paid on the debt by the government is lower than the real rate at which the economy growth.
Recall from law of motion of the debt that debt accumulation is also driven by the primary balance The better the primarybalance is the less need there is for more borrowing.
Taking into consideration what we have just discussed about the interest rate-growth differential, we are also able to conclude that a higher interest rate-growth differential would require a larger fiscal effort, or larger primary surplus, to put the debt ratio on a stable path. In fact, we will find that if the differential is positive, we must run a primary surplus in order to stabilize the debt. We’ll be showing you how to calculate that debt stabilizing primary balance in an upcoming module.

25. An Example: Interest Rate - Growth Differential Projections
Remember from our example in Excel that the debt to GDP ratio was increasing.
Since we assumed for simplicity that primary balance is zero, then the values of the interest rate and growth rate determined the path of the debt ratio in the case of country X.
We assumed that the nominal effective interest rate was around 11%, while inflation was 8% and growth was 2%.
In this case the real effective interest rate was approximately 3%.
So, real interest rate is higher than the growth rate The debt ratio was increasing.

26. An Example: Interest Rate - Growth Differential Projections
Now, let’s assume that the nominal effective interest rate is around 9% instead of 11% . This would imply that the real effective interest rate is approximately 0.9%
Yes, now the economy is growing at a faster rate than the interest rate paid by the government on its debt.
This means that the debt ratio dynamics is favorable. You see that debt ratio will go down and continue doing so if assumptions don’t change.

27. MDSx 8 3 4
Open Economy Public Debt Dynamics
Standard

28. In an Open Economy: Public Debt Dynamics Debt stock at time t
Exchange rate at time t
Let’s start from the composition of debt in the open economy.
Dt is overall stock of public debt expressed in local currency. It consists of debt denominated in local currency D with a superscript d, and debt denominated in foreign currency D with superscript f.
We express foreign currency debt in local currency, and therefore, we multiply D (f) by e(t) which is a nominal exchange rate. We define nominal exchange rate as units of domestic currency per unit of foreign currency, let’s say per one United States dollar.

29. Dynamics of total debt in an Open Economy:
Public Debt Dynamics
Dynamics of total debt in an Open Economy:
𝐷 𝑡 = 1− 𝛼 𝑡− 𝑖 𝑡 𝐷 𝑡−1 + 𝛼 𝑡−1 1+ 𝑖 𝑡 𝑓 1+ 𝜀 𝑡 𝐷 𝑡−1 − 𝑃𝐵 𝑡
α - share of foreign currency debt in total debt
if- nominal interest rate on debt in foreign currency
ε – change in the exchange rate (+ depreciation)
Now, consider what percentage or share of the debt is denominated in foreign currency. We will call that parameter the greek letter “alpha.”
Here you see what the debt dynamics will be in an open economy case – when some of our debt is denominated in a foreign currency.
Total debt stock at time (t) equals the sum of local and foreign currency debt stock from the previous period (t-1) plus interest payments on both.
Note, here is a new term (1+ epsilon), that captures change in the exchange rate, or depreciation or appreciation of the local currency vis a vis a foreign currency.
That means that the dynamics of foreign currency debt expressed in local currency will depend not only on the interest rate paid on foreign currency debt but also on the developments of the exchange rate.
And the last element in this equation is the primary balance.
Let’s denote this equation as equation 7.

30. In an Open Economy: Public Debt Dynamics
𝑑 𝑡 = 1− 𝛼 𝑡− 𝑖 𝑡 𝑔 𝑡 1+ 𝜋 𝑡 𝑑 𝑡−1 + 𝛼 𝑡−1 1+ 𝑖 𝑡 𝑓 1+ 𝜀 𝑡 𝑔 𝑡 1+ 𝜋 𝑡 𝑑 𝑡−1 − 𝑝𝑏 𝑡
𝑖𝑓 nominal interest rates on foreign currency debt
𝑖 nominal interest rates on domestic currency debt
g rate of real GDP growth
π rate of inflation
α share of foreign currency debt in total debt
ε change in nominal exchange rate of local currency
We can further re-write equation 7 in terms of ratios to GDP and we get equation 8.
We will omit the details of derivation in this video, but we encourage you to look at the additional material below this video to the slides to this unit where you can find how the following equations are derived.
You see that the first term is a familiar term from the closed economy case. We multiply it by (1-alpha) as this is the part of the debt denominated in local currency.
The second term is the part of the debt denominated in foreign currency. The difference between the two terms is the interest rate i(f) and the term (1+ epsilon).
Let’s denote this equation 8.
We can further simplify this equation.

31. 𝑑 𝑡 = 1− 𝛼 𝑡−1 1+ 𝑟 𝑡 + 𝛼 𝑡−1 1+ 𝑟 𝑡 𝑓 (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Public Debt Dynamics
In an Open Economy:
𝑑 𝑡 = 1− 𝛼 𝑡− 𝑟 𝑡 + 𝛼 𝑡−1 1+ 𝑟 𝑡 𝑓 (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
𝑟= 1+𝑖 1+𝜋 −1
𝑟 𝑓 = 1+ 𝑖 𝑓 1+𝜀 1+𝜋 −1
The term in the big brackets represent a weighted average of the real effective interest rates on local currency and foreign currency debt: r and r(f) respectively.
r is a familiar real effective interest rate from the closed economy case.
r(f) is a real effective interest rate on public debt denominated in foreign currency. The real effective interest rate on foreign currency is calculated taking into consideration the exchange rate depreciation or appreciation. *
Let’s denote this equation 9.
𝑟 is real effective interest rate on domestic currency debt
𝑟 𝑓 is real effective interest rate on foreign currency debt

32. 𝑑 𝑡 = 1+ 𝑟 𝑡 𝑤 1+ 𝑔 𝑡 𝑑 𝑡−1 − 𝑝𝑏 𝑡 𝑟 𝑡 𝑤 = 𝛼 𝑡−1 𝑟 𝑡 𝑓 + 1− 𝛼 𝑡−1 𝑟 𝑡
Public Debt Dynamics
In an Open Economy:
𝑑 𝑡 = 1+ 𝑟 𝑡 𝑤 𝑔 𝑡 𝑑 𝑡−1 − 𝑝𝑏 𝑡
𝑟𝑤 weighted average of domestic and foreign real effective interest rates:
𝑟 𝑡 𝑤 = 𝛼 𝑡−1 𝑟 𝑡 𝑓 + 1− 𝛼 𝑡−1 𝑟 𝑡
We can further shorten equation 9
Now, this looks very similar to the debt dynamics in closed economy. The small r(w) is a weighted average of the real effective interest rates on domestic currency debt and foreign currency debt.
This is the law of motion of the public debt in the open economy.
As in the case of a closed economy, the key parameters that affect debt dynamics in an open economy case are interest rates paid on public debt, GDP growth rate, inflation rate, and primary balance.
An additional factor that will drive debt dynamics in an open economy is the change in the exchange rate.
Let’s denote this equation 10.

33. MDSx 8 3 5
Open Economy Public Debt Dynamics in Excel
Excel

34. EXCEL

35. MDSx 8 4 1
Debt-Stabilizing Primary Balance
Standard

36. Debt-Stabilizing Primary Fiscal Balance
Is used…
To assess whether current fiscal policy is consistent with a stable debt-to-GDP ratio.
To indicate how much effort is required to achieve a stable debt ratio.
The primary balance that can keep the debt ratio stable given assumptions of interest rate, growth and other, is called debt stabilizing primary balance.
It is used to assess whether the current fiscal policy is consistent with a stable debt-to-GDP ratio and to indicate how much effort (or how much adjustment) is required to achieve a stable debt ratio.

37. 𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Debt-Stabilizing Primary Fiscal Balance
Derivation:
𝑑 𝑡 = (1+ 𝑟 𝑡 ) (1+ 𝑔 𝑡 ) 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Closed economy:
𝑑 𝑡 = 1+ 𝑟 𝑡 𝑤 𝑔 𝑡 𝑑 𝑡−1 − 𝑝𝑏 𝑡
Open economy:
Let’s derive an equation to calculate the debt stabilizing primary balance.
For this purpose, we need to start from the law of motion of the debt.
These are equations for closed and open economy cases respectively, that we have derived earlier in this module.
Let’s denote the term (1+r) over (1+g) with a Greek letter phi for the closed economy* and phi star for the open economy to keep the equation brief*.

38. 𝑑𝑡= 𝜙 𝑡 𝑑 𝑡 −1 − 𝑝𝑏 𝑡 𝑝𝑏 ∗ = 𝑑 𝑡−1 ( 𝜙 𝑡 −1) Derivation:
Debt-Stabilizing Primary Fiscal Balance
Derivation:
𝑑𝑡= 𝜙 𝑡 𝑑 𝑡 −1 − 𝑝𝑏 𝑡
𝑝𝑏 ∗ = 𝑑 𝑡−1 ( 𝜙 𝑡 −1)
We then rewrite the debt path equation using letter phi.
What we want to do is to find what primary balance should be to keep dt the same as d(t-1).
And next we express primary balance (pb) in terms of d(t-1) and phi.
Now we can use this equation to calculate what the primary balance should be to keep the debt ratio constant, given other assumptions of economic growth, interest rates, inflation and exchange rates.

39. MDSx 8 4 2
Debt-Stabilizing Primary Balance in Excel
Excel

40. EXCEL

41. MDSx 8 4 3
Baseline Scenario
Standard

42. Built around the Macroeconomic Framework:
Baseline Scenario
Built around the Macroeconomic Framework:
The most likely scenario for countries based on current and projected government policies.
The programmed macroeconomic adjustment for program (or near-program) countries.

43. Assumptions in the Baseline Scenario:
Medium-Term Projections
Assumptions in the Baseline Scenario:
Macroeconomic assumptions –
Growth projections
Cost of financing
Inflation
Exchange rate
Fiscal projections –
Primary balance

44. GDP growth: Cost of financing: Primary balance path:
Medium-Term Projections
GDP growth:
Cyclical position of the economy
Other medium-term factors
Cost of financing:
Inflation forecast and monetary policy stance
Developments in the global financial markets
Primary balance path:
Projected government policies

45. MDSx 8 4 4
Baseline Scenario in Excel
Excel

46. EXCEL

47. MDSx 8 5 1
Debt Level
Standard

48. Related Risks: High Debt Large primary fiscal surpluses to service it
Exacerbates vulnerability to shocks
Exposure to a higher risk of a rollover crisis
May be detrimental to economic growth

49. Benchmarks: Debt Burden Indicators
Country specific definition of “low” and “high” levels of debt.
Some countries run into difficulties at relatively low levels of debt.

50. IMF MAC Benchmarks for Classification
Public debt level (ratio to GDP):
50% for emerging markets
60% for advanced economies
Public growth financing needs (ratio to GDP):
10% for emerging markets
15% for advanced economies

51. MDSx 8 5 2
Macro-Fiscal Stress Testing
Standard

52. Identifying Fiscal Risks:
Macro-Fiscal Stress Tests
Identifying Fiscal Risks:
Potential impact of adverse shocks on the debt path
Macroeconomic risks comprise shocks to:
Economic growth
Interest rates
Exchange rate
Primary balance

53. Contingent Liabilities
A definition…
Obligations of the government, whose timing and magnitude depend on the occurrence of some uncertain future event outside the government’s control.

54. Arise from explicit or implicit guarantees to:
Contingent Liabilities
Arise from explicit or implicit guarantees to:
Public entities
Public-private partnerships
Depositors
Support to private companies deemed too big to fail

55. MDSx 8 5 3
Macro-Fiscal Stress Testing in Excel
Excel

56. EXCEL

57. MDSx 8 6 1
Summarizing What We Have Learned
Standard

58. MDSx 8 7 1
Assessing Diagnostica
Standard