## 1. The Balance Sheet Framework

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---

### Overview and purpose
- Public Sector Balance Sheets (PSBS) present all accumulated assets and liabilities under the control of government, including central, state and local governments, extrabudgetary units, public corporations, natural resources and pension liabilities to public sector employees.
- The intertemporal PSBS (IPSBS) combines the static balance sheet with the net present value of future expenditure and revenue to present a complete picture of long-term fiscal health against the intertemporal budget constraint.
- Coverage and database history:
  - October 2018 Fiscal Monitor compiled PSBS for a sample of 31 countries.
  - The accompanying database has been enlarged to cover 38 countries comprising some two-thirds of global GDP.
- Application in this paper:
  - Applies IPSBS to the G7 countries, covering the period before the COVID-19 pandemic.
  - Assesses public sector strength as of the end 2018 on currently implemented and legislated policies.
  - Presents INFW and a hypothetical one-time fiscal adjustment that would balance countries’ books.
  - Provides comprehensive sensitivity analysis and documents INFW evolution for three G7 countries where data are available.

### Key definitions and solvency condition
- Net Financial Worth (NFW)t = FAt – Lt (FA: financial assets; L: total liabilities).
- Intertemporal Net Financial Worth (INFW)t = NFWt + sum over j=1..T of (Rt+j − Gt+j)/(1+ r)^j.
  - INFW captures public sector nondebt liabilities and financial assets in addition to debt; nonfinancial public assets are not taken into account when calculating INFW.
  - Solvency condition: INFW ≥ 0 under normal conditions for growth and interests.
- Intertemporal budget constraint (debt as NPV of future primary balances):
  - Bt/Yt = sum over j=1..∞ of dj (Rt+j − Gt+j)/Yt+j with discount factors dj = Π (1+gt+k)/(1+rt+k).
  - Assumes limT→∞ Π dj Bt/ YT = 0 to avoid infinite debt holdings.

### Framework and modeling assumptions
- Static NFW computed following IMF PSBS database methodologies; updates for G7 countries up to 2018.
- Future costs computed via long-term fiscal projections for 50 years under an unchanged policy assumption.
  - Medium-term: Year 1 to 6 use October 2018 IMF WEO projections.
  - Long-term: Year 7 to 50 use a production-function approach for output growth:
    - gY = β(gL + gHW) + (1−β) gK + gTFP
    - Population projections from UN World Population Prospects (2017).
    - gL computed using future population projections multiplied by employment rate by age cohort, with employment rates held constant at Year 0 levels.
    - β held constant at the 5-year historical average.
    - gHW set to difference between WEO employment growth and gL for Year 6 and then held constant.
    - gK set to WEO's real gross fixed capital formation growth for Year 6 and then held constant.
    - gTFP held constant at the Year 6 residual rate from WEO projections.
  - Fiscal projections hold primary revenue and primary expenditure other than health and pension constant as share of GDP at the Year 6 WEO level; projections of primary balances are driven by health and pension expenditure.

### Projections of pension and health expenditure
- Pension expenditure:
  - Focuses on old-age pension expenditure (does not include other pensions such as disability pensions or public service pensions already in static NFW).
  - PE_t driven by Pop65+, coverage ratio (CR_t), and replacement rate (RR_t); CR_t captures retirement age; RR_t shows generosity of benefits relative to per-worker GDP.
  - Assumptions on CR_t and RR_t incorporate announced and codified policy, including policy to be implemented in the future.
- Health expenditure:
  - Driven by growth of per capita health spending, which has outpaced per capita GDP in all seven countries for the last two decades.
  - Projection separates spending for population 65+ and 0–64, applying acceleration factors α65+ and α0–64 to capture growth of health spending relative to GDP per capita growth.
  - Baseline α values derived from historic averages and applied throughout projection horizon.

### Discount rates, interest-growth differentials, and sensitivity
- Baseline applies the same discount rates to all seven countries to isolate effects of non-rate differences on INFW.
  - Medium-term discount rates use the average interest projections for seven countries from October 2018 WEO.
  - Long-term interest rates assumed to increase gradually until 2049 to reach 4½ percent — the average of long-run interest projections made by other institutions.
  - Result: interest-growth differentials vary across countries.
- Baseline country-specific long-run interest-growth differential assumptions cited:
  - Canada - 4.0 percent between 2023-2091
  - Germany, France, Italy, and UK – 5.0 percent between 2026-2070
  - Japan – 3.0 percent in 2044
  - US – 4.6 percent in 2049
  - Weighted average of these figures by GDPs is 4.5 percent.
  - The same weighted-average changes little (4.4 percent) if using projections made after the COVID-19 pandemic.
- Sensitivity analysis extensively examines alternative scenarios for interest-growth differentials and interest paths.

### Static PSBS and net worth (2016–2018): key statistics
- Average consolidated assets and liabilities across seven countries in 2016:
  - Assets average 190 percent of GDP
  - Liabilities average 225 percent of GDP
- Of total average assets:
  - 94 percent of GDP comprise nonfinancial assets
  - 96 percent of GDP are financial assets
- Comparison with 31-country average (IMF 2018):
  - 31-country average: 86 percent of GDP of financial assets and 152 percent of GDP of liabilities
- Range of consolidated public sector liabilities (2016):
  - 140 percent of GDP in Canada to 317 percent of GDP in Japan
  - Public service pension obligations example: 87 percent of GDP in UK
- Range of consolidated public sector assets (2016):
  - 135 percent of GDP in UK to 311 percent of GDP in Japan
- Static net worth in 2016:
  - Four out of seven countries have net worth in or close to positive territory
  - Canada: +36 percent of GDP in 2016
  - Japan, US, and Germany: static net worth only slightly negative
  - UK and Italy: large static negative net worth
- Static Net Financial Worth (NFW) in 2018:
  - All seven countries have large negative static NFW in 2018
  - Range from -47 percent of GDP in Canada to -190 percent of GDP in UK
- Changes 2016–2018:
  - Static NFW improved in all seven countries
  - Canada and Germany experienced improvements of more than 10 percent of GDP each

### Baseline INFW projections and drivers
- INFW in 2018 (baseline) for G7 countries:
  - Range from -170 percent of GDP in Canada to -392 percent of GDP in US
  - All seven countries feature large negative INFW in 2018
- Projected primary balances:
  - Large projected future primary deficits contribute to negative INFW in all countries
  - In all countries except Italy, primary deficits follow a downward trajectory throughout the projection horizon (driven mainly by rising health spending)
  - UK projected to see the largest drop of primary balances by over 9 percentage points of GDP between 2018 and 2068
  - Germany projected drop just over 8 percentage points of GDP between 2018 and 2068
  - Italy’s primary balances projected to gradually improve toward the end of the projection horizon
- Health and pension spending projections (2018–2068):
  - Health spending drives projected primary deficits; pension spending projected broadly to remain at current level
  - Projected increase in health spending between 2018 and 2068:
    - Japan: almost 9 percentage points of GDP
    - UK: 8 percentage points of GDP
    - Canada: 3 percentage points of GDP
  - Excluding aging effects shows Canada and Germany increases driven by population aging; other countries driven mainly by per-person health spending
  - Pension spending: existing policy (increasing retirement age and reducing replacement rate) counteracts aging pressure; Italy’s pension spending projected to drop sharply after the 2040s

### Adjustment needs to meet intertemporal budget constraint
- One-time permanent fiscal adjustment needed to bring INFW to 0 (growth and discount rates unchanged from baseline):
  - Range from 3.6 percent of GDP in Canada to over 10 percent of GDP in Japan
- Adjustment needed to make only the intertemporal part (present values of primary balances) equal zero:
  - US: 6.5 percent of GDP
  - Japan: 4.4 percent of GDP
- Making adjustments gradually over a decade would increase total adjustment need modestly by 0.4-2.0 percentage points of GDP
- Drivers of adjustment size:
  - Higher interest rates and lower growth increase adjustment needs
  - For countries with primary deficits throughout the horizon (France, Japan, US), a larger interest-growth differential reduces the (negative) value of cost of future policies and hence improves INFW
  - For countries with primary surpluses throughout the horizon the opposite effect occurs

### Long-run growth outlooks and demographics (selected)
- Long-run real growth rates:
  - Canada, Germany, France, UK, and US: around 1½ percent in the long run
  - Japan and Italy: around ½ percent in the long run
- Old Age Dependency Ratios (OADRs) at end of projection horizon:
  - Canada, France, UK and US: between 42 and 48 percent
  - Germany, Italy and Japan: 58, 60 and 70 percent respectively

### Sensitivity analysis: interest-growth differentials and health spending acceleration
- INFW sensitivity to discount rate:
  - INFW generally sensitive to changes in interest-growth differentials; relation is non-linear and convex
  - A decrease in the discount rate lowers INFW more than a similar increase improves INFW
- Alternative interest-rate scenario:
  - Same long-run interest-growth differential applied to all seven countries, evolving to increase differentials to 1 percent by 2049
  - Modest changes in INFW for all countries except Japan
    - Japan’s INFW becomes -389 percent of GDP under alternative scenario
    - Italy’s INFW does not change much due to u-shaped path of primary balances and lower duration
- Sensitivity to acceleration factors in per-person health spending:
  - Shifting acceleration factors for persons aged 65 years and over by ± 0.5 point can change INFW by as much as 200 percent of GDP
  - Japan and Italy’s INFW are less sensitive to acceleration factors than other countries due to lower GDP per capita growth

### Intertemporal Net Worth (INW) incorporating nonfinancial assets
- INW computed by replacing NFW with Net Worth (NW) and adding discounted net investment in nonfinancial (produced) assets (gross fixed capital formation minus consumption of fixed assets), modeling depreciation via asset lives and sufficiency of capital maintenance expenditure.
- Baseline INW in 2018:
  - All seven countries have negative INW in 2018
  - Range from -36 percent of GDP in Canada to 249 percent of GDP in UK
  - Implication: none of seven countries meets their intertemporal budget constraint under INW concept
- Scenarios on capital expenditure:
  - Monetization scenario (no capital expenditure throughout horizon; halting maintenance):
    - INW worsens in all countries except Canada and UK
    - Canada and UK have relatively low general government fixed assets (30 percent of GDP in Canada; 41 percent of GDP in UK) so stopping capital expenditure can improve INW under accounting assumptions
  - Increased capital expenditure scenario (capital expenditure 1 percentage point of GDP higher at every point in time):
    - INW remains broadly unchanged from baseline in all countries; decreases in primary balances offset increases in net investments
- Adjustment needs to make INW zero:
  - Adjustment needs average 3.6 percent of GDP across countries
  - For countries with static NW close to zero (Germany, France, Japan, and US), adjustment needs to make INW zero are similar to those to make present values of primary balances zero

### Historical INFW methodology and decomposition (Canada, Japan, UK)
- Historical INFW estimated by reproducing vintage macro-fiscal projections over a 50-year horizon using vintage WEO projections and vintage UN population projections.
- Annual changes decomposed into five factors:
  - (i) medium-term levels of primary balances,
  - (ii) pension policy parameters (coverage and replacement ratios),
  - (iii) health projection acceleration factors,
  - (iv) population projections,
  - (v) residual mainly associated with growth.
- Empirical finding on short-term drivers:
  - Short-term changes in INFW are driven primarily by fiscal policies rather than changes in growth or demographic outlooks.
  - Largest annual observed swings in INFW between 1989 and 2018 included:
    - +110 percent of GDP in Canada (1994)
    - -173 percent of GDP in UK (2001)
    - -194 percent of GDP in Japan (2008)
- Country case highlights:
  - Canada: INFW improved to around -90 percent of GDP in late 1990s due to deficit reduction; early 2000s reinvestment in health worsened INFW; post-global financial crisis improvement returned INFW to 1989 level.
  - Japan: INFW close to breakeven (-33 percent of GDP) in 1990; worsened by more than 300 percent of GDP since then; fiscal expansions and rising per-capita health spending contributed.
  - UK: INFW moved from -289 percent of GDP (1992) to -82 percent (1999) due to expenditure reductions; 2000 NHS Plan accelerated health spending and pushed INFW below -355 percent of GDP in 2002; fiscal consolidation post-crisis improved INFW, but 2018 NHS expansion announcement drove INFW to -352 percent of GDP at end 2018.

### INFW and government borrowing costs — empirical estimates
- Objective: estimate relationship between INFW and slopes of future 1–10-year government bond yield curves using Canada, Japan, and UK time series (1989–2018).
- Regression specification:
  - (r_{i,t+10}^{(10)} – r_{i,t+10}^{(1)}) = β0 + β1 INFW_{i,t} + β2 X_{i,t} + β3 YEAR_{t} + ε_{i,t}
  - Controls X_{i,t}: growth rate of per capita real GDP, CPI change, general government net lending (share of GDP), and debt (share of GDP).
  - Ten-year-ahead forward spreads derived from implied forward rates.
- Estimation and inference:
  - Pesaran Cross-section Dependence tests indicate cross-sectional dependence for several variables.
  - Feasible generalized least squares (FGLS) used to address cross-sectional correlation with heteroskedastic errors; panel has T = 30 and N = 3 (T/N = 10).
  - Robustness checks include fixed effects and OLS-PCSE.

Key coefficient estimates (Table 1)
- INFW: -0.0028 (Without lag) and -0.0026 (With lag(1)); standard errors [0.0011] and [0.0011]
- Real GDP per capita growth: 0.1020 and 0.0895; standard errors [0.0664] and [0.0661]
- CPI change: 0.0283 and -0.0452; standard errors [0.0779] and [0.0777]
- General gov't net lending: 0.0571 and 0.0652; standard errors [0.0336] and [0.0339]
- General gov't debt: 0.0033 and 0.0034; standard errors [0.0022] and [0.0022]
- Observations: 90 (Without lag), 87 (With lag)
- Number of countries: 33
- Year dummies included

Robustness and interpretation
- Baseline estimation: a 10-percentage increase in INFW (in terms of GDP) reduces spreads between ten-year-ahead ten-year and one-year government bond yields by 2.8 basis points.
- INFW can swing by 200 percent of GDP, implying interest rate changes of over 0.5 percent points.
- Fixed-effect estimation yields INFW coefficient with appropriate sign but not statistically significant; OLS-PCSE yields similar results to baseline.
- Country-specific estimates:
  - Canada: INFW -0.0063*** [0.0016]
  - Japan: INFW -0.0011 [0.0011]
  - UK: INFW -0.0006 [0.0006]
- Panel unit root tests: Fisher and Im-Pesaran-Shin tests reject non-stationarity for most variables except general government debt.
- Limitation: small sample size; expanding sample recommended.

### Policy-relevant conclusions and implications
- Intertemporal balance sheets for the G7 show all G7 countries fall well short of their intertemporal budget constraints on current policies.
- The average INFW across the G7 is minus 267 percent of GDP.
- Among the G7:
  - US INFW: minus 392 percent of GDP
  - Canada INFW: minus 170 percent of GDP
- Closing these gaps would require adjustments to the primary balance of an average of almost 7 percent of GDP.
- Swings of order 200 percent of GDP in INFW are not uncommon; short-term fluctuations chiefly driven by fiscal policy, long-run deterioration driven by demographic developments and future health obligations.
- Market implications:
  - A 10-percentage point of GDP increase in INFW associated with a 2.8 basis point reduction in future 1–10 year yield spreads, controlling for deficits and debt, suggesting INFW contains information beyond traditional fiscal metrics.
  - Results are suggestive given sample limitations; expanding country coverage would strengthen inference.

### Infrastructure depreciation, maintenance, and capital expenditure rules (selected)
- Without sufficient capital repairs:
  - Life of asphalt pavement can shorten from around 60 years to 30 years with only recurrent maintenance and no capital repair.
  - Some bridge decks can shorten from 53 years to 35 years without capital repairs.
  - To prevent reduction of the life of road sections, maintenance amount around 67 percent of initial investments in real terms has to be made during the life-time.
- Depreciation model links asset life shortening (up to 50 percent) proportionally to cumulative shortage in required capital maintenance; minimum required investment operationalized as 50 percent of initial investments in real time, spread across asset life.
- Allocation rule prioritizes minimum required investments for older assets before newer ones; if GFCF exceeds minimum requirements, remainder used to produce new assets.
- Implication: insufficient capital maintenance can materially shorten asset lifetimes and affect INW via changes in net investment needs and depreciation.

_Authors’ estimates and IMF PSBS database as presented in wpiea2021128-print-pdf._

### 1. The Balance Sheet Framework  ___________________________________________ 6

### 1. The Balance Sheet Framework

### Overview and purpose
- Public Sector Balance Sheets (PSBS) present all accumulated assets and liabilities under the control of government, including central, state and local governments, extrabudgetary units, public corporations, natural resources and pension liabilities to public sector employees.
- The intertemporal PSBS (IPSBS) combines the static balance sheet with the net present value of future expenditure and revenue to present a complete picture of long-term fiscal health against the intertemporal budget constraint.
- Coverage and database history:
  - October 2018 Fiscal Monitor compiled PSBS for a sample of 31 countries.
  - The accompanying database has been enlarged to cover 38 countries comprising some two-thirds of global GDP.
- Application in this paper:
  - Applies IPSBS to the G7 countries, covering the period before the COVID-19 pandemic.
  - Assesses public sector strength as of the end 2018 on currently implemented and legislated policies.
  - Presents INFW and a hypothetical one-time fiscal adjustment that would balance countries’ books.
  - Provides comprehensive sensitivity analysis and documents INFW evolution for three G7 countries where data are available.

### Key definitions and concepts
- Net Financial Worth (NFW)t = FAt – Lt (FA: financial assets; L: total liabilities).
- Intertemporal Net Financial Worth (INFW)t = NFWt + sum over j=1..T of (Rt+j − Gt+j)/(1+ r)^j.
  - INFW captures public sector nondebt liabilities and financial assets in addition to debt; nonfinancial public assets are not taken into account when calculating INFW.
  - Solvency condition: INFW ≥ 0 under normal conditions for growth and interests.
- Intertemporal budget constraint (debt as NPV of future primary balances):
  - Bt/Yt = sum over j=1..∞ of dj (Rt+j − Gt+j)/Yt+j with discount factors dj = Π (1+gt+k)/(1+rt+k).
  - Assumes limT→∞ Π dj Bt/ YT = 0 to avoid infinite debt holdings.

### Framework and modeling assumptions
- Static NFW is computed following IMF PSBS database methodologies; the paper updates NFW for G7 countries up to 2018.
- Future costs of fiscal policy computed via long-term fiscal projections for 50 years under an unchanged policy assumption.
  - Medium-term: Year 1 to 6 use October 2018 IMF WEO projections.
  - Long-term: Year 7 to 50 use a production-function approach for output growth:
    - gY = β(gL + gHW) + (1−β) gK + gTFP
    - Population projections from UN World Population Prospects (2017).
    - gL computed using future population projections multiplied by employment rate by age cohort, with employment rates held constant at Year 0 levels.
    - β held constant at the 5-year historical average.
    - gHW set to difference between WEO employment growth and gL for Year 6 and then held constant.
    - gK set to WEO's real gross fixed capital formation growth for Year 6 and then held constant.
    - gTFP held constant at the Year 6 residual rate from WEO projections.
  - Fiscal projections hold primary revenue and primary expenditure other than health and pension constant as share of GDP at the Year 6 WEO level; projections of primary balances are driven by health and pension expenditure.

### Projections of pension and health expenditure
- Pension expenditure:
  - Focuses on old-age pension expenditure (does not include other pensions such as disability pensions or public service pensions already in static NFW).
  - Projection formula components:
    - PE_t driven by Pop65+, coverage ratio (CR_t), and replacement rate (RR_t).
    - CR_t captures retirement age; RR_t shows generosity of benefits relative to per-worker GDP.
  - Assumptions on CR_t and RR_t incorporate announced and codified policy, including policy to be implemented in the future.
- Health expenditure:
  - Driven by growth of per capita health spending, which has outpaced per capita GDP in all seven countries for the last two decades.
  - Projection formula separates spending for population 65+ and 0–64, applying acceleration factors α65+ and α0–64 to capture growth of health spending relative to GDP per capita growth.
  - Baseline α values are derived from historic averages and applied throughout projection horizon.

### Discount rates, interest-growth differentials, and sensitivity
- Baseline applies the same discount rates to all seven countries to isolate effects of non-rate differences on INFW.
  - Medium-term discount rates use the average interest projections for seven countries from October 2018 WEO.
  - Long-term interest rates assumed to increase gradually until 2049 to reach 4½ percent — the average of long-run interest projections made by other institutions.
  - As a result, interest-growth differentials vary across countries.
- Sensitivity:
  - INFW is sensitive to discount rates; extensive sensitivity analysis is performed (appendices referenced for methods and sensitivity).
  - The paper examines alternative scenarios for interest-growth differentials and interest paths.

### Empirical findings on INFW and interest rates
- Regression results for Canada, the UK and Japan:
  - A modest but statistically significant relationship is found between INFW and the slope of future yield curves.
  - On average, a 10-percentage point of GDP increase in INFW reduces spreads between the ten-year ahead one- and ten-year interest rates on government bonds by 2.8 basis points.
  - Interpretation: improvements in INFW are associated with yield curve flattening, suggesting market reassessment of sovereign credit and interest rate risks.
  - Caveat: robustness challenges remain given limited sample size.

### Organization of the paper
- Section II: detailed framework for intertemporal balance sheet analysis.
- Section III: baseline projections of INFW for G7 countries and sensitivity analysis.
- Section IV: evolution of G7’s INFW over time.
- Section V: relationship between INFW and long-term sovereign interest rates.
- Section VI: conclusion.

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021128-print-pdf.pdf*

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### Baseline discount rate and interest-growth assumptions
- Country-specific long-run interest-growth differential assumptions cited:
  - Canada - 4.0 percent between 2023-2091 (the Fiscal Sustainability Report 2018 by the Parliamentary Budget Officer)
  - Germany, France, Italy, and UK – 5.0 percent between 2026-2070 (the 2018 Aging Report by the European Commission)
  - Japan – 3.0 percent in 2044 (the 2014 Actuarial Estimate by the Ministry of Health, Labor and Welfare)
  - US – 4.6 percent in 2049 (the 2019 Long-Term Budget Outlook by the Congressional Budget Office)
- The weighted average of these figures by GDPs is 4.5 percent.
- The same weighted-average changes little (4.4 percent) if using projections made after the COVID-19 pandemic.
- Baseline discount rate assumptions are held constant at that level afterwards (reference to Figure 3 in source).

### Static public sector balance sheets (PSBS) and net worth (2016–2018)
- Average consolidated assets and liabilities across seven countries in 2016:
  - Assets average 190 percent of GDP
  - Liabilities average 225 percent of GDP
- Of total average assets:
  - 94 percent of GDP comprise nonfinancial assets
  - 96 percent of GDP are financial assets
- Comparison with the average of 31 countries (IMF 2018):
  - 31-country average: 86 percent of GDP of financial assets and 152 percent of GDP of liabilities
  - G7: assets similar in size but much higher liabilities
- Range of consolidated public sector liabilities (2016):
  - 140 percent of GDP in Canada to 317 percent of GDP in Japan
  - General government debt is the biggest contributor
  - Public service pension obligations example: 87 percent of GDP in UK
- Range of consolidated public sector assets (2016):
  - 135 percent of GDP in UK to 311 percent of GDP in Japan
- Around half of public sector assets comprise nonfinancial assets on average across the seven countries (mainly infrastructure owned by general government)
- Static net worth in 2016:
  - Four out of seven countries have net worth in or close to positive territory
  - Canada: +36 percent of GDP in 2016 (driven by large nonfinancial assets including natural resources)
  - Japan, US, and Germany: static net worth only slightly negative
  - UK and Italy: large static negative net worth
- Static Net Financial Worth (NFW) in 2018:
  - All seven countries have large negative static NFW in 2018
  - Range from -47 percent of GDP in Canada to -190 percent of GDP in UK
- Changes in static NFW between 2016 and 2018:
  - Static NFW improved in all seven countries
  - Canada and Germany experienced improvements of more than 10 percent of GDP each
  - Canada improvement mainly from increase in value of general government assets
  - Germany improvement mainly from reduction in general government debt

### Baseline projections and drivers of INFW (Intertemporal Net Financial Worth)
- INFW in 2018 (baseline) for G7 countries:
  - Range from -170 percent of GDP in Canada to -392 percent of GDP in US
  - All seven countries feature large negative INFW in 2018
- Projected primary balances:
  - Large projected future primary deficits contribute to negative INFW in all countries
  - Projections use consistent methods across the seven countries
  - In all countries except Italy, primary deficits follow a downward trajectory throughout the projection horizon (driven mainly by rising health spending)
  - UK projected to see the largest drop of primary balances by over 9 percentage points of GDP between 2018 and 2068
  - Germany projected drop just over 8 percentage points of GDP between 2018 and 2068
  - Italy’s primary balances projected to gradually improve toward the end of the projection horizon (pension spending decrease, demographic factors)
- Health and pension spending projections (2018–2068):
  - Health spending drives the projected primary deficits; pension spending projected broadly to remain at current level
  - Increase in health spending driven by fast growth of per person health spending
  - Projected increase in health spending between 2018 and 2068:
    - Japan: almost 9 percentage points of GDP
    - UK: 8 percentage points of GDP
    - Canada: 3 percentage points of GDP (lowest increase among peers)
  - Comparison excluding aging effects (holding OADR constant at 2018 levels) shows:
    - In Canada and Germany the increase in health expenditure is driven by population aging
    - In other countries the increase is driven mainly by per-person health spending through price and volume increases
  - Pension spending:
    - Projected to remain at current level or increase only modestly in most countries
    - Existing pension policy (increasing retirement age and reducing replacement rate) counteracts aging pressure
    - Italy: pension spending projected to drop sharply after the 2040s when population aging reverses

### Adjustment needs to meet intertemporal budget constraint
- One-time permanent fiscal adjustment needed to bring INFW to 0 (growth and discount rates unchanged from baseline):
  - Range from 3.6 percent of GDP in Canada to over 10 percent of GDP in Japan
- Adjustment needed to make only the intertemporal part (present values of primary balances) equal zero:
  - US: 6.5 percent of GDP
  - Japan: 4.4 percent of GDP
- Making adjustments gradually over a decade would increase total adjustment need modestly by 0.4-2.0 percentage points of GDP
- Drivers of adjustment size:
  - Countries with higher interest rates and lower growth face larger adjustment needs
  - For countries with primary deficits throughout the horizon (e.g., France, Japan, US), a larger interest-growth differential reduces the (negative) value of cost of future policies and hence improves INFW
  - For countries with primary surpluses throughout the horizon the opposite effect occurs

### Long-run growth outlooks and demographics
- Long-run real growth rates:
  - Canada, Germany, France, UK, and US: around 1½ percent in the long run
  - Japan and Italy: around ½ percent in the long run
- After the WEO projection period, changes in real growth rates driven only by demographic changes
- Old Age Dependency Ratios (OADRs) at end of projection horizon:
  - Canada, France, UK and US: between 42 and 48 percent
  - Germany, Italy and Japan: 58, 60 and 70 percent respectively
- Low growth in Japan implies larger interest-growth differentials than peers, increasing size of future primary surpluses needed to offset negative static NFW

### Sensitivity analysis: interest-growth differentials and health spending acceleration
- INFW sensitivity to discount rate:
  - INFW is generally sensitive to changes in interest-growth differentials
  - Relation between INFW and interest rates is non-linear
  - A decrease in the discount rate lowers INFW more than a similar increase in the discount rate improves INFW (convex response)
- Alternative interest-rate scenario:
  - Applies same long-run interest-growth differential to all seven countries, evolving to increase differentials to 1 percent by 2049 in each country
  - Results: modest changes in INFW for all countries except Japan
    - For Japan the difference in Year 50 discount rate between scenarios is more than 2 percent (for Canada, Germany, France, UK, and US less than 0.5 percent)
    - Japan’s INFW becomes -389 percent of GDP under alternative scenario
    - Italy’s INFW does not change much despite large change in differential due to u-shaped path of primary balances and lower duration
- Sensitivity to acceleration factors in per-person health spending:
  - Per-person health spending is assumed to increase at growth rates of GDP per capita multiplied by acceleration factors (α65+ and α0-64)
  - Historical acceleration factors can fluctuate by 0.5 point or greater in a year
  - Shifting acceleration factors for persons aged 65 years and over by ± 0.5 point can change INFW by as much as 200 percent of GDP
  - Japan and Italy’s INFW are less sensitive to acceleration factors than other countries due to lower GDP per capita growth

### Intertemporal Net Worth (INW) incorporating nonfinancial assets
- INW computed by replacing NFW with Net Worth (NW) and adding discounted net investment in nonfinancial (produced) assets (gross fixed capital formation minus consumption of fixed assets), modeling depreciation via asset lives and sufficiency of capital maintenance expenditure
- Baseline INW in 2018:
  - All seven countries have negative INW in 2018
  - Range from -36 percent of GDP in Canada to 249 percent of GDP in UK
  - Implication: none of seven countries meets their intertemporal budget constraint under INW concept
- Scenarios on capital expenditure:
  - Monetization scenario (no capital expenditure throughout horizon; halting maintenance):
    - INW worsens in all countries except Canada and UK despite lower capital outlays
    - In Canada and UK stopping capital expenditure improves INW because general government fixed assets are relatively low (30 percent of GDP in Canada; 41 percent of GDP in UK)
    - Monetization could have further negative impacts if economic losses from deteriorated infrastructure are considered
  - Increased capital expenditure scenario (capital expenditure 1 percentage point of GDP higher at every point in time):
    - INW remains broadly unchanged from baseline in all countries
    - Decrease in primary balances and increases in net investments associated with higher capital expenditure virtually cancel each other out
- Adjustment needs to make INW zero:
  - Adjustment needs average 3.6 percent of GDP across countries
  - For countries with static NW close to zero (Germany, France, Japan, and US), adjustment needs to make INW zero are similar to those to make present values of primary balances zero

### Evolution of INFW and historical decomposition (overview)
- Analysis of historical INFW time series developed for Canada, Japan, and UK (choice driven by data availability and long time-series of static PSBS and vintage general government fiscal projections)
- Historical analysis intended to shed light on effects of unanticipated shocks (e.g., 2008-09 global financial crisis) and subsequent adjustments, and on how demographic shifts and policy reforms affected IPSBS
- Note: long time-series data of nonfinancial assets needed to compute evolution of INW are not available for all three countries in the historical analysis

*Source: Authors’ estimates and IMF PSBS database, as presented in the provided content unit.*

### 36.      Historical INFW is estimated by incorporating and reproducing vintage macro-

### wpiea2021128-print-pdf - 36. Historical INFW methodology, drivers, and link to borrowing costs

### Methodology for estimating historical INFW
- Historical INFW is estimated by incorporating and reproducing vintage macro-fiscal projections over a 50-year horizon following the methodology described in Section II.
- Population projections use vintage UN World Population Prospects latest available for past years.
- Time horizons and projection rules:
  - Medium-term: Year 1 to 6 based on vintage macro-fiscal projections of historical WEO vintages.
  - Long-term: Year 7 to 50 output projections follow equation (3).
  - Primary revenue and expenditure other than health and pension expenditure held constant at its Year 6 level (as share of GDP).
  - Health and pension expenditure projections follow equations (4) and (5).
  - Pension projections incorporate assumptions on coverage and replacement rates reflecting pension reform measures implemented or on the books in past years.
  - Health projection acceleration factors are derived from moving averages for three to eight years.
    - Moving average for eight years used for per-person health spending acceleration for population below 64 years old.
    - Moving average for three years used for per-person health spending acceleration for population above 65 years old.
    - When moving average is below 1, acceleration factors are assumed to be 1.
    - A ceiling on acceleration factors is set for each country; where health policy guarantees a minimum growth rate of per-person health spending (e.g., Japan), acceleration factors combine the minimum growth rate and expected long-run nominal growth rates.
- Interest rate assumptions in historical INFW:
  - Interest rates are assumed to converge to the level that makes the interest-growth differential equal to one percent in the long run (same as the alternative interest rate scenario in Section III).
  - Paths of interest rates incorporate projections of historical WEO vintages for the medium-term and beyond Year 6 gradually converge to a one percent interest-growth differential in Year 31, held constant afterward.

### Decomposition of annual changes and main drivers
- Annual changes in INFW are decomposed into five factors:
  - (i) medium-term levels of primary balances,
  - (ii) policy parameters of pension projections (coverage and replacement ratios),
  - (iii) acceleration factors of health projections,
  - (iv) population projections,
  - (v) a residual mainly associated with growth.
- Decomposition approach: compute alternative INFWs changing only one specific factor while keeping other assumptions constant.
- Empirical finding on short-term drivers:
  - Short-term changes in INFW are driven primarily by fiscal policies rather than changes in growth or demographic outlooks.
  - Largest annual observed swings in INFW between 1989 and 2018 included:
    - +110 percent of GDP in Canada (1994),
    - -173 percent of GDP in UK (2001),
    - -194 percent of GDP in Japan (2008).
  - The decomposition shows medium-term changes in primary balances are the largest contributors to annual INFW changes; changes in health policy (acceleration factors) are also important; changes in growth, interest rates, or demographic outlooks had less influence on short-term fluctuations.

### Country case studies and key quantitative developments
- Canada
  - INFW improved to around -90 percent of GDP in the late 1990s.
  - Improvement mainly due to deficit reduction measures by federal and provincial governments.
  - Early 2000s: INFW worsened to below -300 percent of GDP, mostly due to changes in health policy (reinvestment in health sector, 2004 health accord increased health and social transfers, accelerating per capita health spending).
  - After the global financial crisis, INFW improved, returning to its 1989 level; tightening of health policy contributed importantly to deficit reduction.
  - Pension policy had little impact on Canada’s INFW in the absence of major reforms.
- Japan
  - INFW was close to breakeven (-33 percent of GDP) in 1990; since then worsened by more than 300 percent of GDP.
  - Between 1991 and 1994, INFW was reduced by around 50 to 100 percent of GDP every year due to fiscal expansion after asset price bubbles burst.
  - Early 2000s: pension reforms had positive impact on INFW, but increases in medium-term primary deficits in 2002 and 2008 reversed those gains.
  - Health spending negative impacts: introduction of long-term care insurance and steady per capita nominal health spending growth on people older than 65 years of 1.5 percent per year on average between 2000 and 2018, while GDP per capita grew by 0.2 percent per year on average.
  - Long-term growth potential declined from around 1.8 percent to ½ percent after 2010.
- United Kingdom
  - INFW moved from -289 percent of GDP at the 1992 crisis to -82 percent of GDP in 1999 due to expenditure reductions and Spending Review process.
  - Announcement of the National Health System 2000 Plan accelerated growth of per capita nominal health spending on people over 65 from 5 percent per year (1993–1999) to 8 percent per year (2000–2009), driving INFW down to below -355 percent of GDP in 2002.
  - Post-global financial crisis: fiscal consolidation improved medium-term primary surplus and INFW to above -200 percent of GDP in 2013.
  - 2018 announcement expanding National Health System spending drove INFW down to -352 percent of GDP at end 2018.
  - State pension reforms had mixed impacts: some increases in pension ages had positive effects; the introduction of the “triple lock” had negative effects.

### Drivers of cumulative long-term changes in INFW
- Long-term drivers differ from short-term:
  - Factors with smaller roles in annual changes, such as growth outlooks (residual) and demographic projections, have very visible long-run impacts on INFW.
- Country-specific cumulative impacts:
  - UK: expansive health policy had persistent negative impact; medium-term primary balance changes did not have long-lasting impact due to alternating consolidation and expansion periods.
  - Japan: pension reforms had significant positive cumulative effects but were offset by persistent fiscal expansion and expansion of health policy for aging population.
  - Canada: fiscal consolidation had a consistent positive long-run effect; pension and health policy had little cumulative influence.

### INFW and government borrowing costs — empirical approach and specification
- Objective: estimate long-run relationship between INFW and government borrowing costs using INFW time series for Canada, Japan, and UK; examine relationship between INFW and slopes of future 1–10-year government bond yield curves.
- Rationale and literature:
  - Prior work suggests relationships between intertemporal budget balances/fiscal policy and interest rates paid by governments; estimating these relationships faces endogeneity challenges because interest rates and fiscal variables are cyclical.
  - Static NFW evidence: a 10 percentage point of GDP increase in static NFW lowers long-term government bond yields by around 9 basis points in advanced economies (controlling for debt levels).
  - Modeling based on INFW expands analysis to intertemporal assets and liabilities.
- Dependent variable and approach:
  - Regress spreads between future short and long-term interest rates on INFW using market-implied future interest rates to separate short-term cyclical effects.
  - Use ten-year-ahead spreads between one and ten year interest rates.
  - Under rational expectations, the ten-year-ahead spread equals the difference between one and ten year rates in year 10; in practice, yield curves also reflect market views on credit and interest rate risks.
- Model specification (equation (6)):
  - (r_{i,t+10}^{(10)} – r_{i,t+10}^{(1)}) = β0 + β1 INFW_{i,t} + β2 X_{i,t} + β3 YEAR_{t} + ε_{i,t}
    - r_{i,t+10}^{(10)} and r_{i,t+10}^{(1)} are projected ten-year-ahead ten-year and one-year interest rates for country i at time t.
    - Ten-year-ahead ten-year and one-year rates computed as implied forward rates between 20-year and ten-year spot rates and 11-year and ten-year spot rates respectively.
    - INFW_{i,t} is INFW of country i at time t.
    - X_{i,t} includes controls: growth rate of per capita real GDP, changes in CPI, general government net lending (as share of GDP), and debt (as share of GDP).
    - YEAR_{t} is a year dummy to control time effects.
  - Sample period: 1989 to 2018.
  - Sample countries: Canada, Japan, and UK.
- Data sources and variable choices:
  - Spot rate data derived from websites of the Bank of Canada, Japan’s Ministry of Finance, and the Bank of England.
  - Control variables obtained from the IMF WEO database.
  - Choice rationale: use per capita real GDP and net lending instead of variables included in INFW computation to avoid endogeneity; implied forward rates eliminate short-term rate fluctuations.
- Regression technique and inference considerations:
  - Pesaran Cross-section Dependence tests reject cross-sectional independence at 1 percent for four out of six variables.
  - Feasible generalized least squares (FGLS) used to address cross-sectional correlation, with heteroskedastic error structure and cross-sectional correlation.
  - Caveat: FGLS can generate optimistic standard errors when T is not sufficiently larger than N; this panel has T = 30 years and N = 3 countries (T to N ratio = 10).
  - FGLS does not include individual fixed effects; reported that FGLS and fixed-effect estimation generate similar coefficients for this panel.
  - Robustness checks employ other regression techniques.

*Source: Authors’ estimates and analysis in wpiea2021128-print-pdf - 36.*

### 51.      The baseline estimation results suggest the existence of a relationship between

### wpiea2021128-print-pdf - 51.      The baseline estimation results suggest the existence of a relationship between

### Baseline estimation results: INFW and interest rate spreads
- The baseline estimation suggests a relationship between INFW and spreads between future long- and short-term interest rates.
- Coefficients on INFW are statistically significant and economically meaningful (Table 1).
- A 10-percentage increase in INFW (in terms of GDP) reduces spreads between ten-year-ahead ten-year and one-year government bond yields by 2.8 basis points.
- INFW can swing by 200 percent of GDP, which would imply interest rate changes of over 0.5 percent points.
- Coefficients of control variables are generally not statistically significant.
- Similar results are obtained when lagged explanatory variables are used.

Key coefficient estimates (from Table 1)
- INFW: -0.0028 (Without lag) and -0.0026 (With lag(1)); both marked **
  - Standard errors: [0.0011] and [0.0011]
- Real GDP per capita growth: 0.1020 (Without lag) and 0.0895 (With lag)
  - Standard errors: [0.0664] and [0.0661]
- CPI change: 0.0283 (Without lag) and -0.0452 (With lag)
  - Standard errors: [0.0779] and [0.0777]
- General gov't net lending: 0.0571 (Without lag) and 0.0652 (With lag); second marked *
  - Standard errors: [0.0336] and [0.0339]
- General gov't debt: 0.0033 (Without lag) and 0.0034 (With lag)
  - Standard errors: [0.0022] and [0.0022]
- Constant: -1.239*** (Without lag) and -0.699 (With lag)
  - Standard errors: [0.4685] and [0.4720]
- Observations: 90 (Without lag), 87 (With lag)
- Number of countries: 33
- Year dummies: Yes

### Robustness checks
- Fixed effect estimation with country and year fixed effects: coefficients of INFW retain appropriate signs but are not statistically significant (Table 2).
- Ordinary Least Square estimation with panel-correlated standard errors (alternative for heteroskedasticity and correlation across panels) generates similar results.
- Country-specific estimation shows mixed results.
- Using data on estimated term premium from Bauer (2014) as explanatory variable (sample 1990-2008) yields coefficients of similar level and statistical significance as the baseline, confirming a relationship between INFW and interest rate spreads.
- Panel unit root tests reject the null that all panels are non-stationary for all variables at 1 to 10 percent significance levels, except for general government debt (Table 3).
- Including the first difference of general government debt instead of its level in the model leaves INFW coefficient of similar level and statistical significance.
- Limitations: results affected by limited number of countries in the panel; expanding the sample could improve robustness.

Selected robustness table highlights (Panel and country-specific)
- Panel (fixed effects): INFW -0.0004 [0.0008]
- Panel (OLS-PCSE): INFW -0.0011 [0.0008]
- Canada: INFW -0.0063*** [0.0016]
- Japan: INFW -0.0011 [0.0011]
- UK: INFW -0.0006 [0.0006]
- Observations: Panel (fixed effects) 90; Panel (OLS-PCSE) 90; Canada 30; Japan 30; UK 30
- Number of countries: Panel 33; Canada 1; Japan 1; UK 1
- R-squared: Panel (fixed effects) 0.5850; Panel (OLS-PCSE) 0.6144; Canada 0.5569; Japan 0.2337; UK 0.6649

Unit root test p-values (Table 3)
- Fisher test p-values: ri,t+10(10) - ri,t+10(1): 0.0000; INFW: 0.0385; Real GDP per capita growth: 0.0000; CPI change: 0.0000; General gov’t net lending: 0.0017; General gov’t debt: 0.5874
- Im-Pesaran-Shin p-values: ri,t+10(10) - ri,t+10(1): 0.0001; INFW: 0.0560; Real GDP per capita growth: 0.0002; CPI change: 0.0063; General gov’t net lending: 0.2791; General gov’t debt: 0.9607

### Conclusions and policy-relevant findings
- Intertemporal balance sheets derived for the G7 show all G7 countries fall well short of their intertemporal budget constraints on current policies.
- The average INFW across the G7 is minus 267 percent of GDP.
- Among the G7:
  - US INFW: minus 392 percent of GDP (largest shortfall)
  - Canada INFW: minus 170 percent of GDP (smallest shortfall)
- Closing these gaps would require adjustments to the primary balance of an average of almost 7 percent of GDP.
- Size of required adjustments varies across countries; not necessarily proportional to INFW shortfall or current debt levels due to interest and growth differentials.
- For three countries with data over time (Japan, UK, Canada):
  - Japan and UK have recorded INFW deteriorations in excess of 300 percent of GDP over the past 40 years.
  - Canada’s INFW ended largely where it began.
  - Swings of the order of 200 percent of GDP in both directions are not uncommon.
  - Short-term fluctuations mostly driven by fiscal policy changes; long-run deterioration driven by demographic developments and future health obligations.
- Relationship between long-term government borrowing rates and INFW:
  - On average, a 10-percentage point of GDP increase in INFW reduces spreads between future 1 and 10 year yields of government bonds by 2.8 basis points.
  - Effects control for government deficits and level of debt, suggesting INFW adds information beyond standard fiscal metrics.
- Implications:
  - Financial markets may provide signals on sustainability of long-term government policy obligations related to future health and pension spending, over and above current government assets and liabilities.
  - Limited sample size challenges robustness; expanding analysis to more countries is recommended.

### Appendix highlights: Methods and baseline assumptions
- Methods for updating net financial worth:
  - Canada, Japan, UK: NFW figures updated following methods and data sources specified in the metadata documents of the IMF PSBS database.
  - France, Germany: NFW figures updated following PSBS metadata; general government financial assets and liabilities (except civil service pension liabilities) derived from Eurostat database.
  - Italy: figures derived from De Angelis et. al. (forthcoming).
- Selected baseline assumptions for Canada (2018 to 2068 snapshots)
  - Old-age dependency ratio (65+/15-64): 0.26 (2018), 0.32 (2024), 0.38 (2030), 0.42 (2040), 0.44 (2050), 0.47 (2060), 0.48 (2068)
  - Real GDP growth rate: 1.88 (2018), 1.70 (2024), 1.73 (2030), 1.77 (2040), 1.67 (2050), 1.67 (2060), 1.72 (2068)
  - Nominal GDP growth rate: 3.62 (2018), 3.81 (2024), 3.85 (2030), 3.88 (2040), 3.79 (2050), 3.78 (2060), 3.83 (2068)
  - Deflator change rate: 1.71 (2018), 2.08 (2024 onward)
  - Primary balances: -0.08 (2018), 0.07 (2024), -1.81 (2030), -2.89 (2040), -3.54 (2050), -4.42 (2060), -4.70 (2068)
  - Primary revenue: 37.67 (2018) and 37.91 (from 2024 onward)
  - Old age pension spending (authors): 3.90 (2018), 4.73 (2024), 5.58 (2030), 6.09 (2040), 6.42 (2050), 6.86 (2060), 7.02 (2068)
  - Health spending (authors): 7.88 (2018), 8.90 (2024), 9.93 (2030), 10.50 (2040), 10.81 (2050), 11.24 (2060), 11.37 (2068)
  - Coverage ratios and replacement ratios for pensions are specified (e.g., Coverage ratio (CPP & QPP): 1.09 across years listed)
  - Acceleration factors for health expenditure by age group specified (e.g., Acceleration factor for HE 65+ : -0.58 (2018 note), 1.00 (2024 onward) with explanatory footnotes)
  - Pension and health reforms incorporated (Canada: Health 2011 announcement on Canada Health Transfer growth rules)
- Selected baseline assumptions for Germany (2018 to 2068 snapshots)
  - Old-age dependency ratio (65+/15-64): 0.33 (2018), 0.37 (2024), 0.45 (2030), 0.53 (2040), 0.54 (2050), 0.58 (2060), 0.58 (2068)
  - Real GDP growth rate: 1.52 (2018), 1.17 (2024), 1.10 (2030), 1.39 (2040), 1.30 (2050), 1.33 (2060), 1.46 (2068)
  - Nominal GDP growth rate: 3.06 (2018), 3.33 (2024), 3.27 (2030), 3.56 (2040), 3.47 (2050), 3.50 (2060), 3.64 (2068)
  - Deflator change rate: 1.52 (2018), 2.14 (2024 onward)
  - Primary balances: 2.57 (2018), 1.16 (2024), -0.72 (2030), -3.33 (2040), -4.14 (2050), -5.28 (2060), -5.62 (2068)
  - Primary revenue: 46.19 (2018) and 45.75 (from 2024 onward)
  - Old age pension spending (authors): 7.62 (2018), 8.03 (2024), 8.95 (2030), 10.40 (2040), 10.68 (2050), 11.16 (2060), 11.15 (2068)
  - Health spending (authors): 9.14 (2018), 9.77 (2024), 10.74 (2030), 11.89 (2040), 12.43 (2050), 13.09 (2060), 13.44 (2068)
  - Pension and health reforms incorporated (e.g., 2004 and 2007 pension reforms; 2007 Health Insurance Competition Enhancing Act; 2010 GVK Finance Act; 2011 Pharmaceutical Market Reform Act)

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021128-print-pdf.pdf*

### Introduction of assessment of “added therapeutic benefit” of new medicines when

### Introduction of assessment of “added therapeutic benefit” of new medicines when determining prices to be paid by the health insurance funds

### Key demographic and macroeconomic projections (selected countries)
- France
  - Old-age dependency ratio (65+/15-64): 0.32 (2018); 0.36 (2024); 0.40 (2030); 0.46 (2040); 0.47 (2050); 0.47 (2060); 0.48 (2068)
  - Real GDP growth rate: 1.72 (2018); 1.43 (2024); 1.44 (2030); 1.49 (2040); 1.51 (2050); 1.51 (2060); 1.48 (2068)
  - Labor share (Av. 2014-18): 0.52
  - Nominal GDP growth rate: 2.53 (2018); 3.15 (2024); 3.16 (2030); 3.20 (2040); 3.23 (2050); 3.22 (2060); 3.19 (2068)
  - Deflator change rate: 0.79 (2018); 1.69 (2024 onward)
  - Primary balances: -0.91 (2018); -1.39 (2024); -2.70 (2030); -3.84 (2040); -3.77 (2050); -3.37 (2060); -3.35 (2068)
  - Primary revenue: 53.42 (2018); 51.31 (2024 onward)
  - Primary exp other than PE & HE: 32.76 (2018); 29.92 (2024 onward)
  - Old-age pension spending (authors): 12.11 (2018); 12.64 (2024); 13.22 (2030); 13.32 (2040); 12.57 (2050); 11.48 (2060); 10.81 (2068)
  - Health spending (authors): 9.46 (2018); 10.15 (2024); 10.88 (2030); 11.92 (2040); 12.60 (2050); 13.28 (2060); 13.94 (2068)

- Italy
  - Old-age dependency ratio (65+/15-64): 0.37 (2018); 0.41 (2024); 0.48 (2030); 0.63 (2040); 0.66 (2050); 0.63 (2060); 0.60 (2068)
  - Real GDP growth rate: 0.86 (2018); 0.65 (2024); 0.57 (2030); 0.62 (2040); 0.80 (2050); 0.85 (2060); 0.86 (2068)
  - Labor share (Av. 2014-18): 0.39
  - Nominal GDP growth rate: 1.71 (2018); 2.15 (2024); 2.08 (2030); 2.13 (2040); 2.31 (2050); 2.37 (2060); 2.37 (2068)
  - Deflator change rate: 0.85 (2018); 1.50 (2024 onward)
  - Primary balances: 1.39 (2018); 0.19 (2024); -1.76 (2030); -4.98 (2040); -4.72 (2050); -2.85 (2060); -2.15 (2068)
  - Primary revenue: 46.28 (2018); 46.42 (2024 onward)
  - Primary exp other than PE & HE: 25.21 (2018); 25.28 (2024 onward)
  - Old-age pension spending (authors): 13.14 (2018); 13.92 (2024); 15.14 (2030); 17.14 (2040); 16.14 (2050); 13.74 (2060); 12.58 (2068)
  - Health spending (authors): 6.53 (2018); 7.03 (2024); 7.75 (2030); 8.98 (2040); 9.72 (2050); 10.24 (2060); 10.71 (2068)

- Japan
  - Old-age dependency ratio (65+/15-64): 0.46 (2018); 0.50 (2024); 0.53 (2030); 0.64 (2040); 0.71 (2050); 0.72 (2060); 0.70 (2068)
  - Real GDP growth rate: 0.81 (2018); 0.50 (2024); 0.44 (2030); 0.26 (2040); 0.38 (2050); 0.49 (2060); 0.53 (2068)
  - Labor share (Av. 2014-18): 0.51
  - Nominal GDP growth rate: 0.71 (2018); 1.37 (2024); 1.31 (2030); 1.13 (2040); 1.25 (2050); 1.36 (2060); 1.40 (2068)
  - Deflator change rate: -0.10 (2018); 0.87 (2024 onward)
  - Primary balances: -2.92 (2018); -2.00 (2024); -2.19 (2030); -4.88 (2040); -7.55 (2050); -9.52 (2060); -10.76 (2068)
  - Primary revenue: 32.45 (2018); 33.32 (2024 onward)
  - Primary exp other than PE & HE: 17.49 (2018); 17.08 (2024 onward)
  - Old-age pension spending (authors): 9.69 (2018); 9.27 (2024); 8.61 (2030); 9.27 (2040); 9.97 (2050); 10.12 (2060); 9.90 (2068)
  - Health spending (authors): 8.19 (2018); 8.97 (2024); 9.82 (2030); 11.86 (2040); 13.81 (2050); 15.63 (2060); 17.10 (2068)

- UK
  - Old-age dependency ratio (65+/15-64): 0.29 (2018); 0.32 (2024); 0.36 (2030); 0.41 (2040); 0.44 (2050); 0.47 (2060); 0.47 (2068)
  - Real GDP growth rate: 1.40 (2018); 1.53 (2024); 1.55 (2030); 1.58 (2040); 1.50 (2050); 1.54 (2060); 1.57 (2068)
  - Labor share (Av. 2014-18): 0.49
  - Nominal GDP growth rate: 3.32 (2018); 3.55 (2024); 3.57 (2030); 3.60 (2040); 3.52 (2050); 3.56 (2060); 3.59 (2068)
  - Deflator change rate: 1.90 (2018); 1.99 (2024 onward)
  - Primary balances: 0.15 (2018); 0.05 (2024); -1.43 (2030); -3.58 (2040); -5.59 (2050); -7.86 (2060); -9.28 (2068)
  - Primary revenue: 36.00 (2018); 36.22 (2024 onward)
  - Primary exp other than PE & HE: 23.80 (2018); 22.97 (2024 onward)
  - Old-age pension spending (authors): 4.43 (2018); 4.65 (2024); 5.00 (2030); 5.45 (2040); 5.95 (2050); 6.46 (2060); 6.60 (2068)
  - Health spending (authors): 7.62 (2018); 8.55 (2024); 9.67 (2030); 11.38 (2040); 12.89 (2050); 14.65 (2060); 15.93 (2068)

- US
  - Old-age dependency ratio (65+/15-64): 0.24 (2018); 0.29 (2024); 0.33 (2030); 0.36 (2040); 0.36 (2050); 0.40 (2060); 0.42 (2068)
  - Real GDP growth rate: 2.93 (2018); 1.62 (2024); 1.59 (2030); 1.64 (2040); 1.59 (2050); 1.51 (2060); 1.51 (2068)
  - Labor share (Av. 2014-18): 0.53
  - Nominal GDP growth rate: 5.43 (2018); 3.67 (2024); 3.64 (2030); 3.68 (2040); 3.64 (2050); 3.55 (2060); 3.55 (2068)
  - Deflator change rate: 2.44 (2018); 2.01 (2024 onward)
  - Primary balances: -3.54 (2018); -2.91 (2024); -4.91 (2030); -6.44 (2040); -7.68 (2050); -9.65 (2060); -11.30 (2068)
  - Primary revenue: 28.95 (2018); 31.15 (2024 onward)
  - Primary exp other than PE & HE: 20.83 (2018); 20.03 (2024 onward)
  - Old-age pension spending (authors): 4.11 (2018); 5.11 (2024); 5.79 (2030); 6.24 (2040); 6.39 (2050); 6.92 (2060); 7.34 (2068)
  - Health spending (authors): 7.55 (2018); 8.94 (2024); 10.25 (2030); 11.33 (2040); 12.42 (2050); 13.86 (2060); 15.09 (2068)

### Assumptions and projection parameters (selected)
- Pension projection assumptions (examples)
  - France: Coverage ratio 1.27 (2018); 1.24 (2024); 1.22 (2030); 1.17 (2040 onward). Replacement ratio 0.19 (2018); 0.19 (2024); 0.18 (2030); 0.16 (2040); 0.15 (2050); 0.14 (2060); 0.13 (2068).
  - Italy: Coverage ratio 0.90 (2018); 0.86 (2024); 0.81 (2030); 0.77 (2040); 0.76 (2050); 0.75 (2060); 0.73 (2068). Replacement ratio 0.25 (2018); 0.24 (2024); 0.24 (2030); 0.22 (2040); 0.20 (2050); 0.18 (2060); 0.18 (2068).
  - Japan: Coverage ratio 1.42 (2018); 1.31 (2024); 1.21 (2030 onward). Replacement ratio 0.13 (2018); 0.12 (2024); 0.12 (2030); 0.11 (2040 onward).

- Health projection acceleration factors (examples)
  - France: Acceleration factor for HE 65+ = 0.21 (2018)²; 1.00 (2024 onward)4/. Acceleration factor for HE 0-64 = 2.88 (2018)³; 1.42 (2024 onward)5/.
  - Italy: Acceleration factor for HE 65+ = 1.14 (2010)2/; 1.14 (2024 onward)4/. Acceleration factor for HE 0-64 = 1.61 (2010)3/; 1.50 (2024 onward)4/.
  - Japan: Acceleration factor for HE 65+ = 0.22 (2018)1/; 1.73 (2024 onward)3/. Acceleration factor for HE 0-64 = 1.20 (2018)2/; 1.20 (2024 onward).
  - UK: Acceleration factor for HE 65+ = 0.66 (2018)1/; 1.20 (2024 onward)3/. Acceleration factor for HE 0-64 = 0.84 (2018)2/; 1.62 (2024 onward)3/.
  - US: Acceleration factor for HE 65+ = 0.43 (2018)2/; 1.78 (2024 onward)4/; thereafter assumed 1.00 (2030 onward). Acceleration factor for HE 0-64 = 1.56 (2018)3/; 1.56 (2024 onward).

- Notes on calculation methods for acceleration factors (preserved phrasing from source)
  - 1/ Calculated as average annual growth rate of per-person health spending between 2016-18 divided by average annual growth rate of GDP per capita between 2010-18
  - 2/ Calculated as average annual growth rate of per-person health spending between 2010-18 divided by average annual growth rate of GDP per capita between 2010-18
  - 3/ Calculated as average (or average of acceleration factors) across specified prior periods as described country-by-country
  - 4/ In the absence of the long-term cost containment measures, per-person health spending for population above 65 years old is assumed to grow at the same rate as GDP per capita
  - 5/ The acceleration factor for per-person health spending for population below 64 years old is assumed to be around half of the historical average in 2018, to avoid explosive projections

### Pension and health reforms taken into account (selected country measures)
- France (selected health reforms)
  - 1997 reform: Introduction of ONDAM ceilings
  - 2004 reform: Unification of pricing systems by public and private hospitals
  - 2010 reform: Introduction of cost contamination measures including limits to drug procurement and adherence to ONDAM ceilings
- Italy (selected pension & health reforms)
  - 1995 reform: Gradual shift from the Defined Benefit scheme to the National Defined Contribution scheme
  - 2010 reform: Indexation of the eligibility age to changes in life expectancy
  - 2007 Finance Law and onward: Requirements of regions’ “Deficit Reduction plans”
- Japan (selected reforms)
  - 2000 reform: Gradual rise of retirement age from 60 to 65 until 2025 for men and 2030 for women
  - 2000 reform (health): Introduction of the long-term care insurance
  - 2008 reform (health): Introduction of the late-elderly care scheme and a gradual increase in co-payment by late-elderly persons
- UK (selected pension & health reforms)
  - 2011 reform: Introduction of “Triple Lock” to increase the new State Pension by the highest of average earnings, CPI, or 2.5 percent
  - 2014 Pension Act: Increase of retirement age to 67 years old between 2026 and 28 and to 68 years old between 2044 and 46
  - June 2018 Announcement (health): PM announced to rise NHS England resource spending by 3.4 percent per year in real terms from 2018-19 to 2023-24
- US (selected health reforms)
  - 2010 Affordable Care Act: Introduction of a health insurance coverage option and Introduction of cost-reduction provisions for Medicare
  - 2015 Medicare Access and CHIP Reauthorization Act: Introduction of additional cost-reduction provisions for Medicare

### Sensitivity of INFW to interest rate changes
- Definitions and formulas (preserved notation and expressions)
  - Effective Duration = [L_{δ−Δδ} − L_{δ+Δδ}] / [2 L_{δ} r Δδ]
  - Effective Convexity = [L_{δ−Δδ} + L_{δ+Δδ} − 2 L_{δ}] / [2 L_{δ} (Δδ)^2]
  - L_{δ} is INFW with discount rates δ; Δδ is the change in discount rate.
- Key qualitative findings
  - All seven countries have negative future costs of fiscal policy, implying increase in interest rates will reduce liabilities in the intertemporal PSBS.
  - Sensitivity of INFW to interest rate changes depends on INFW composition and the timing of future primary deficits.
  - Japan, Italy, and France have shorter durations because static NFW comprises more than half of their INFW.
  - Longer durations occur where large primary deficits shift further into the future (example: UK).
  - Convexity of INFW broadly follows the same pattern as duration.
- Comparative remarks preserved from source
  - Average durations of INFW for ±1 percent changes in interest rates are 16, similar to durations of pension liabilities measured by Chandler (2017), ranging from 14 to 20.
  - Average convexity of INFW for ±1 percent changes in interest rates are 268, larger than convexity of certain bonds reported by Shiller et. al. (2014), ranging from 0.7 to 218.

### Methods for estimating Intertemporal Net Worth (INW)
- Incorporation of capital investments into stock of nonfinancial produced assets
  - Accounting identity for change in stock of fixed assets:
    - A_t − A_{t−1} = GFCF_t − C_t + δ_t A_{t−1}
  - When scaled by nominal GDP and solved similarly to prior equation, obtain:
    - A_t / Y_t = Σ_{j=1}^{∞} d'_j (GFCF_{t+j} − G_{t+j} / Y_{t+j})
  - Discount factor:
    - d'_j = ∏_{k=1}^{j} (1+g_{t+k}) / (1+δ_{t+k})
  - Assuming stock of nonfinancial produced assets is fully depreciated at infinite horizon (lim_{T→∞} ∏ d'_T A_T / Y_T = 0), adding to prior equations yields INW formula:
    - INW_t = II_t + Σ_{j=1}^{T} (R_{t+j} − G_{t+j}) / (1+r)^j + Σ_{j=1}^{∞} d'_j (GFCF_{t+j} − G_{t+j} / Y_{t+j})
- Assumptions on revaluation gains
  - Revaluation gains assumed to follow price changes; δ_t follow GDP deflators.
  - Revaluation gains/losses of non-produced assets are volatile; mean of revaluation rates of non-produced assets assumed to be zero in the long run.

*Source: IMF staff estimates and text from the provided IMF PDF content.*

### 61.      The life of infrastructure assets will be shortened without sufficient capital

### The life of infrastructure assets will be shortened without sufficient capital repairs

### Key findings
- The life of asphalt pavement can shorten from around 60 years to 30 years when only recurrent maintenance is undertaken and no capital repair is made after the initial investment.
- The life of some bridge decks can be shortened from 53 years to 35 years without capital repairs.
- To prevent reduction of the life of road sections, maintenance with the amount of around 67 percent of initial investments in real terms has to be made during the life-time.

### Depreciation model and assumptions
- The consumption of fixed capital is calculated as the average stock of nonfinancial produced assets during a year times depreciation rates.
- The model estimates a depreciation rate of produced nonfinancial assets depending on sufficiency of capital maintenance during the lifetime.
- Assumed parameters and relationships:
  - The life of produced nonfinancial assets will be shortened by up to 50 percent, in proportion to a cumulative shortage in required capital maintenance.
  - The amount of capital maintenance required for keeping the life of assets is assumed to be 50 percent of initial investments in real time, spread across the life-time.
  - The stock of produced assets in Year 0 (2018) are assumed to be all produced in Year 0 with V0 = the amount of the stock in Year 0.

### Depreciation and required-investment equations (as presented)
- Depreciation rate for assets produced at time t, observed at time T:
  - d_{t,T} = 1 / N_{t,T}
- N_{t,T} is life of assets produced at time t as of time T in terms of number of years; c is a constant showing a historical average of depreciation rates, derived from national account statistics of respective countries.
- The model links d_{t,T} to required and actual investments via:
  - I_{t,T} = mmin(50% × 1/c, 1/c × (1 − (θ_{t,t+k} − I_{t,t+k}) / θ_{t,t+k} × 1/c_{j_k}))
  - (equations presented in the source text with symbols θ_{t,T}, I_{t,T}, c, and σ)
- Amount of minimum required investment is based on:
  - θ_{t,T} = V_t × 50% × c × Σ_{k=1}^{j} (1 + σ_{t+k})
  - where V_t is amount of initial investment made for assets produced at time t, and σ_T is GDP deflator at time T.

### Allocation rule for capital expenditure
- Allocation of capital expenditure prioritizes minimum required investment of assets built in an earlier year over that of assets built in a later year.
- Actual investment follows:
  - I_{t,T} = mmin(0, GFCF_T − Σ_{k=0}^{t'} θ_{k,T})  with t' < t
  - GFCF_T is total gross fixed capital formation at time T.
- If remainder in capital expenditure exists after meeting all minimum required investments of assets built in previous years, the remaining amount is assumed to be used to produce new assets.

### Implications
- Insufficient capital maintenance can materially shorten asset lifetimes—empirical examples indicate reductions up to about 50 percent for some assets.
- Maintaining asset life requires substantial recurring investment: the paper operationalizes this as 50 percent of initial investment spread over the asset life, and cites a specific road maintenance benchmark of around 67 percent of initial investment in real terms over the life-time.

*Source: wpiea2021128-print-pdf - 61.      The life of infrastructure assets will be shortened without sufficient capital repairs*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021128-print-pdf.pdf_