ECO 2173 Analyzing Public Debt under Uncertainty: Project

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Analyzing Public Debt under Uncertainty: Project

The federal government of Canada has recently outlined its fiscal policy for the next 5 years in Budget 2024.  You are the lead analyst working for the King’s Institute of Public Finance, a renowned Fiscal Policy Thinktank based in London. You are being tasked with assessing the sustainability of the government’s fiscal plan under the assumption that its medium term (2023-2028) policies will remain in place until the end of 2055.  

Budget 2024 outlines detailed economic and fiscal projections for the medium term. You will use these projections as your foundation. To extend these projections into the long-term (from 2029 to 2055), please refer to the following assumptions provided below.

Long-term economic assumptions

The King’s Institute of Public Finance is a member of the Canadian Council of Private Sector Economists (CPSE), which produces long-term economic projections based on a consensus among its members. Leverage the following long-term economic assumptions in your analysis.

Ø Inflation is expected to remain constant at a 2 per cent annual rate over the 2029-20255 period.

Ø Real GDP (i.e., g) is projected to grow by an average of 1.6 per cent per year from 2029 to 2055.

Ø From 2029 to 2038, the CPSE expects the real effective interest rate (r) on federal debt to go up by 0.05 percentage points each year. After 2038, the real interest rate is expected to stay the same as it was in 2038.

Long-term fiscal assumptions

Given the current policies of the government, the King’s Institute of Public Finance assumes that beyond 2028:  

Ø Revenues and program spending will grow in line with nominal GDP.

Ø Net actuarial losses will be constant at their 2015-2022 historical average.

Tasks

1. Baseline long-term projection of debt to GDP ratio

Create a fiscal model that extends the Budget 2024 medium-term forecast of the federal debt-to-GDP ratio to the long-term (up to 2055) using the provided long-term assumptions. Illustrate your baseline projection with a chart. Additionally, provide commentaries on your baseline projection, discussing key trends and any notable observations.

2. Incorporate uncertainty

Now that you have produced a baseline long-term projection of debt, extend your model by incorporating the uncertainty surrounding the long-term trajectory of the federal debt. For this analysis, you can rely on the following assumptions for the Monte-Carlo simulation:

Ø Model uncertainty surrounding debt by generating systematically 300 independent shocks to r, g, and pb in each year (i.e., 300 scenarios for each of the three variables from 2029 to 2055).

§ Shocks to r, g, and pb are assumed to follow a normal distribution, with a mean of 0, and a standard deviation calculated by using historical data from 1982 to 2022.

Once all the 300 alternative scenarios for r, g, and pb have been created, for each scenario of r, g and pb in a given year, derive the corresponding value of the debt to GDP ratio for each year (2029 to 2055) by using the debt equation (i.e., d(t)=(1+rt)/(1+gt)*d(t-1)-pbt)).

3. Build a fan chart

Illustrate the uncertainty that surrounds the baseline projection of the debt ratio by presenting a fan chart with the following specifications. See chart 1 below as a visual reference only:

§ One outer band covering outcomes in the 5^th to 95^th percentiles of the distribution.

§ One inner band covering outcomes in the 20^th to 80^th percentiles of the distribution.

§ Baseline long-term projection

§ A line representing the 2028 debt level

Chart 1. Long-term federal debt to GDP ratio

Note: For illustrative purposes only

Note: You will likely notice that the values in cells containing your shocks will tend to update every time that you run an operation somewhere in Excel. This will result in your scenarios and fan chart constantly changing, which may cause differences between what you based your analysis on and what I will see when reviewing your Excel file. To overcome this issue, once you have produced your scenarios, create a replica of your Excel file by saving it under a different file name (Firstname_Lastname_Debt Model_Frozen). In the replica, copy and paste values of your r, g, and pb shocks (not debt). This should freeze the cell values containing the shocks. You will submit both the original and the replica files. Then proceed with the next task.

4. Debt Sustainability Analysis

a. Baseline scenario

Conduct a debt sustainability of your baseline projection under both analytical frameworks covered in the course:

v Framework 1: Sustainability = Declining debt to GDP

o Currently used by the Parliamentary Budget Officer. We covered it in Section 2.

o When analyzing sustainability, use the 2028 debt level as the reference for comparing long-term 2055 debt level. (This is why you were asked to add a line representing the 2028 debt level in the chart)

v Framework 2: Sustainability = High probability of declining debt to GDP

o Currently used by IMF. Covered it in Section 3.

o More precisely, sustainability = more than 80% probability that 2055 debt is below 2028 debt level.

o Use the upper limit of the 20^th to 80^th percentile band as a guide.

To help you structure your analysis, think of the following questions:

§ What is your assessment of debt sustainability of the baseline scenario under both frameworks?

o Is debt sustainable under one framework but not under the other?

§ Whether debt is sustainable or not, what is the required permanent change in the primary balance starting in 2029 (so not immediate) that would ensure that 2055 long-term debt is stable at 2028 level?

o This is a version of the fiscal gap where changes are made starting in 2029 to keep long-term debt at 2028 level

o Tips: You can estimate this quickly by using Excel’s “Goal Seek” technique taught in Section 2. Essentially, start with an alternative scenario that matches the baseline scenario (remember we went over creating alternative scenarios). Then tell Excel to set 2055 debt of your alternative scenario to the value of your 2028 debt level by changing the cell in your “command center” that is associated with permanent changes in your long-term assumption of pb.

b. Alternative scenarios

Analyze the impact of the following changes in the baseline long-term (i.e., starting in 2029) assumptions of r and g. How would the 2055 debt change relative to its baseline level if:

§ Long-term g was lower than in the baseline by 1.5 percentage point over the 2029-2055 period? What is your assessment of debt sustainability under both frameworks?

§ Long-term g was higher than in the baseline by 1.5 percentage point over the 2029-2055 period? What is your assessment of debt sustainability under both frameworks?

§ Long-term r was lower than in the baseline by 1.5 percentage point over the 2029-2055 period? What is your assessment of debt sustainability under both frameworks?

§ Long-term r was higher than in the baseline by 1.5 percentage point over the 2029-2055 period? What is your assessment of debt sustainability under both frameworks?

Project Deliverables

§ Write your analysis in a short report (2-5 pages), including charts.

§ Submit the report as a PDF file.

§ Original Excel file housing a well-organized model containing:

o a sheet for the baseline scenario,

o a sheet for the alternative scenario;

o a functionality for conducting simulations of long-term r, g, and pb (i.e., the simulation’s “command center” connected to the alternative scenario;

o separate sheets for Monte-Carlo shocks of r, g, and pb.

o Separate sheets for scenarios of r, g, and pb related to their corresponding Monte-Carlo shocks sheet.

o A fan chart

o Tips: It’s probably best to build the fan chart bands around the alternative scenario. This would allow you to see your fan chart move when you try to look at alternative scenarios of r, g, and pb. If there are no changes to these 3 variables, then your alternative scenario should give you the same result as your baseline scenario.

o a sheet for the Econ data

o a sheet for the fiscal data

§ Replica Excel file with frozen values of shocks.

Historical Data Sources:

You’ll need historical data going back to 1981 in order to compute:

§ Standard deviation based on 1982-2022;

§ 2015-2022 average for Net Actuarial Losses).

Here are the different places where you can find them:

Ø Historical fiscal data (check out the summary statement of transactions sheet): https://www.canada.ca/en/department-finance/services/publications/fiscal-reference-tables/2023.html

Ø Historical GDP data:  https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610022201

Ø Medium term forecast (Budget 2024): https://budget.canada.ca/2024/report-rapport/anx1-en.html#a1

o Medium term economic outlook: Table A1.1 (refer to Budget 2024 data)

o Medium term fiscal outlook: Table A1.5