## 2.1 and 2.2

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---

### Measurement of real interest rates (Figure 2.1)
- Panel 1 (US maturities):
  - Real interest rates = US treasury rates for each maturity − Cleveland Fed measure of inflation expectations over the same period.
  - Data source: The Federal Reserve Economic Data (FRED). FRED mnemonics DSG[X] and EXPINF[X]YR where [X] stands for the respective maturity.
- Panel 2 (3-month horizon, cross-country):
  - Real interest rates = 3-month treasury rates − realized annual inflation over the same horizon in each country.
  - Japan: 3-month interbank rates are spliced with certificates of deposit from 1979 to 2002 to achieve a longer series.
  - Realized inflation rate = average of the annual inflation in the next three months.
  - Real rate formula (as presented) uses nominal interest rate i_t and monthly CPI index p_t with a 1/3 average of three forthcoming monthly annualized inflation terms multiplied by 100.
- Additional FRED mnemonics referenced:
  - IR3TIB01[XX]M156N; IR3TIB01JPM156N; IR3TCD01JPM156N; INDIR3TIB01STM; CPALTT01[XX]M659N.

### Real long-term bond yields and aggregation (Figure 2.2)
- Data:
  - Real long term bond yield data: WEO mnemonic FIGB_R from the WEO database.
- Sample composition:
  - 34 advanced economies: AUS, AUT, BEL, CAN, CHE, CYP, CZE, DEU, DNK, ESP, FIN, FRA, GBR, GRC, HKG, IRL, ISL, ISR, ITA, JPN, KOR, LUX, MAC, MLT, NLD, NOR, NZL, PRT, SGP, SVK, SVN, SWE, TWN, and USA.
  - 25 emerging market and developing economies: ARG, BIH, BLR, BRA, CHL, CHN, GHA, HRV, HUN, IDN, IND, MUS, MYS, NAM, PAN, PHL, POL, RUS, SLE, SYC, THA, TUR, TZA, UKR, and ZAF.
- Aggregation:
  - Aggregated using market-exchange-rate-based GDP weight (WEO mnemonics: GDPWGT and NGDPD) as:
    GGT_T_t = 1/3 (NGDPWGT_t−1 + NGDPWGT_t−2 + NGDPWGT_t−3)
- Bond maturity considered: greater than 1 year.

### Measuring the real natural rate — overview (Online Annex 2.2)
- Three empirical exercises based on a Kalman filter inspired by Laubach and Williams (2003):
  - (i) country-by-country estimate of the natural rate,
  - (ii) real-time estimate of natural rates over the pandemic contrasting filtered and smoothed estimates,
  - (iii) two-region simultaneous estimation for the US and the rest-of-the-world to quantify international dependencies.

### Country-by-country estimates — model structure and estimation (2.2.1)
- Model framework:
  - Kalman filter linked to a simple New Keynesian AD/IS and AS/PC model.
  - IS-curve relates percent deviation of real output from potential (output gap y_t^) to the real rate gap (r_t − r_t^⋆).
  - IS-curve specified (A.2.2.1) with autoregressive output gap terms, a squared sum of lagged real rate gaps, and an output-gap innovation ε_y^,t.
  - Phillips Curve (A.2.2.2) with lagged inflation polynomial B(L), lagged output gap, and inflation innovation ε_π,t.
  - Natural rate law of motion: 1 r_t^⋆ = g_t + z_t where z_t is a random walk: z_t = z_t−1 + ε_z,t.
  - Potential output dynamics: y_t^⋆ = y_t−1^⋆ + g_t−1 + ε_y^⋆,t and g_t = g_t−1 + ε_g,t.
- Estimation:
  - Unobserved states: potential output and real natural rate.
  - Observables: real output, inflation, lagged ex-ante real interest rate, and predetermined past output and inflation.
  - Estimated: output gap, real rate gap, natural rate, growth trend, stochastic growth drift, innovation variances.
  - Implementation reference: Wynne and Zhang (2018) appendix.
- Countries and samples:
  - Canada: 1962 Q4 — 2019 Q4
  - France: 1971 Q4 — 2019 Q4
  - Germany: 1971 Q4 — 2019 Q4
  - Japan: 1961 Q4 — 2019 Q4
  - UK: 1956 Q4 — 2019 Q4
  - USA: 1960 Q4 — 2019 Q4
- Ex ante real policy rate construction:
  - Expectation of average inflation over the four quarters ahead from a univariate AR(3) model of inflation estimated over the 40 quarters prior to the data point.
- Selected country data mnemonics provided for GDP, interest rates, and inflation (Canada, France, Germany, Japan, UK, USA).

### Two-region estimates — open-economy Kalman filter (2.2.2)
- Model extension:
  - Two-region Laubach and Williams (2003) setup with home and foreign AD relations and Phillips curves.
  - Home and foreign IS equations include real rate gaps relative to foreign natural rates and squared-sum real rate gap terms.
  - Phillips curves include import prices π_I,i and oil prices inflation π_O,i to capture open-economy inflation dynamics.
- Natural rate evolution:
  - Home and foreign natural rates depend on domestic and foreign stochastic growth with coefficients c_hh, c_fh, c_hf, c_ff and stochastic terms z_t^h, z_t^f.
  - Stochastic growth processes: g_t^h = g_t−1^h + ε_t^h and g_t^f = g_t−1^f + ε_t^f.
- Data and sample:
  - Home economy (US) observables: log real GDP, core inflation, oil price inflation, relative import price inflation, real rates (ex ante expectations as in single-country case).
  - Rest-of-the-world composed of 23 listed advanced and EMDE countries; BRICS = Brazil, Russia, India, China and South Africa represent EMDEs.
  - Sample start: 1960 Q1; representation: Overall, 90 percent of world GDP measured at PPP (IMF) is represented; at end of sample 2022 subset accounts for about 70 percent of IMF recorded world PPP GDP.
- Data sources:
  - Real GDP: OECD National Quarterly Accounts database mnemonics by ISO3 codes; China: China WEO quarterly data spliced and reindexed.
  - Core Inflation: CED MEI database mnemonics [XYZ].CPGRLE01.IXOB.Q.
  - Interest rates: Haver Analytics and IMF IFS series spliced to create longest possible unbalanced panel (example mnemonics listed).

### Structural model for drivers of the natural rate (Online Annex 2.3)
- Model used: adapted version of Platzer and Peruffo (PP, 2022).
- Coverage: United States, Japan, Germany, the UK, France, China, India, and Brazil (eight major economies covering some 70 percent of global GDP).
- Key model features:
  - Demographics: overlapping generations (74 cohorts), life-cycle savings for retirement, out-of-pocket health expenditure shocks, income inequality within generations affecting aggregate saving.
  - Productivity: exogenous deterministic aggregate productivity matched to data; monopolistic competition with exogenous mark-up.
  - Public sector: debt issuance, social security, transfers, financing via taxes; public debt and social security generosity affect desired savings and natural rate.
  - Open-economy: exogenous changes in NIIP affect domestic natural rate.
- Demographics and households:
  - 74 overlapping generations; entry at biological age 26; maximum age 99.
  - Newborns enter per fertility rate i_t; population growth N_t+1 = (1 + i_t) N_t.
  - Households face no-borrowing constraint; two assets: government bonds and capital; no-arbitrage ensures net return equality across assets (assumption noted to be amended in an extension).
  - Frictionless model implies output always at potential; return on government bonds coincides with natural rate.
- Labor productivity and preferences:
  - Labor productivity: permanent × transitory (AR(1)) × age-profile (hump-shaped).
  - Preferences: addilog form; elasticity of intertemporal substitution age-dependent and declines with age; richer households have higher saving rates.
- Production and government:
  - Cobb-Douglas with labor-augmenting technical progress and markup from monopolistic competition.
  - Government roles: public debt, social security, exogenous government consumption G, taxes/transfers (progressive income tax, consumption tax, capital income tax, profit tax); transfers include means-tested old-age floor.
- Capital flows and market clearing:
  - Exogenous foreign-owned net savings stock A* calibrated to NIIP.
  - Market clearing: K + B = Σ r_i + A* where K = domestic capital, B = government borrowing, r_i = savings supply by household i.
- Convenience yield (wedge between bond returns and net return on capital):
  - Adjusted no-arbitrage: 1 + r = 1 + r_k (1−ω) – δ
  - Wedge: (r_k − δ) − r = ω r_k ≡ wedge; ω acts like a tax on gross return on capital; δ is depreciation rate.
  - Wedge proceeds rebated to households as lump-sum transfers proportional to capital holdings; ω adjusted on transition path to hold wedge at desired level.
- Qualitative driver effects:
  - Higher TFP growth: net effect is higher natural rate (increases investment demand for savings; raises expected wages which can reduce saving, but model net is higher natural rate).
  - Demographics:
    - Increased life expectancy (constant retirement age) increases expected retirement duration, raising savings and increasing natural rate.
    - Population aging (shift mass to older ages): ambiguous effect due to non-monotonic lifecycle savings and labor supply.
    - Lower population growth rate reduces output growth, negatively affecting natural rate.
- Calibration targets and special parameter choices:
  - Two parameter types: Type I (calibrated from literature/data) and Type II (estimated via moment-matching).
  - Demographics from UN; mortality from UN World Population Prospects, 2022 Revision.
  - Target semi-elasticity of savings supply to interest rate change = 15 (Auclert et al (2021)).
  - Depreciation rate δ = 0.5; capital income tax τ_k = 0.3.
  - Elasticity of consumption out of permanent income φ_PPPP = 0.8.
  - No bequest motive; bequests accidental and distributed per SCF bequest distribution.
  - Use top 10 percent income share as proxy for top 10 percent labor income share where needed.
  - Country-specific calibration targets listed in Online Annex Table 2.3.2.

### Simulation experiments and scenarios
- Main experiments:
  1. Steady-state comparison:
     - Compare a 2015-2019 steady-state with a 1975-1979 steady-state.
     - Individual-driver contributions computed by changing each parameter to its 1975-1979 value while keeping others at 2015-2019 values; interaction effects imply individual contributions need not sum exactly to total change.
     - Special calibration deviations:
       - India: imposed minimum markup of zero to avoid negative markup in 1975-1979; resulting implied 1975-1979 labor share = 61.3% vs 73% in data; 2015-2019 steady-state labor share = 52%.
       - China: set markup to 5% and use inferred capital-to-output ratio 5.4 (data ratio 6.3 implies markup −1.5%).
     - For countries beyond the United States many parameters held constant at U.S. 2015-2019 values.
  2. Transition-path analysis:
     - Start date 1950, terminal date 2200 to ensure convergence.
     - Iterative calibration for Type II parameters; procedure stops after p = 2 in practice to align average natural rate in 2015-2019 on transition path with data.
     - Driver timing:
       - Baseline: demographic drivers change from 1950 to 2100 and are held constant at 2100 levels thereafter; other drivers start changing earliest in 2019.
       - Debt trajectory and forecast until 2028 from WEO (as of February 28, 2023) and held constant thereafter.
       - Advanced economies: TFP growth held constant at 2015-2019 average; EMs: linear convergence to advanced-economy average (2015-2019) by 2050.
- Higher government borrowing costs scenario:
  - Introduce wedge between return on physical capital and on government bonds calibrated to five-year average spread between a 10-year government bond and investment grade corporate bond yields in 2015-2019.
  - Scenario transition: linear to 2050 where wedge declines by 44 basis points relative to 2015-2019 average (difference between U.S. corporate bond spread in 2015-2019 and pre-2000 (1970-1999)).
  - Simultaneous change for US net savings stock A*: linear change by 79 percent of GDP by 2050 (difference of gross foreign portfolio investments in the U.S. between 2015-2019 average and pre-2000 average (1976-1999), Bureau of Economic Analysis).
  - Consequence: in this scenario the natural rate increases by around 100 basis points by 2050 in the United States.
  - Note: model does not capture endogenous response of capital flows to a change in the convenience yield.

### Fiscal policy framework and debt sustainability (Mian, Straub and Sufi (2021c) framework)
- Convenience yield: savers derive safety/liquidity benefits from holding government debt; convenience yield decreases with debt level and interest rate on government debt is endogenous r(b).
- Debt-dynamics equation (A.2.4.1):
  - ḃ = z + ( r(b) − g ) b
  - where ḃ is change in debt-to-GDP ratio, z denotes primary deficit, and g is growth rate.
- Implications:
  - If r > g, primary deficits are unsustainable; governments must run primary surpluses to stabilize debt-to-GDP.
  - If r < g and interest rates not endogenous to debt, any level of primary deficit can correspond to stable debt-to-GDP (Blanchard 2019).
  - Endogenous r(b) pins down a unique primary deficit z that stabilizes b when r(b) < g; setting ḃ = 0 yields z = −( r(b) − g ) b.
- Phase-diagram insights:
  - Points above stability arc: ḃ > 0 and debt rises forever; below arc: debt declines.
  - At low debt (b < b*) government can increase primary deficit and still converge (a “free lunch”); illustrative b* ≈ 90 percent of GDP in example.
  - Beyond b*, government must reduce deficit to stabilize b; beyond debt = 180 percent of GDP illustrative line, r(b) > g and primary surplus required.
  - Delaying deficit reduction raises debt and borrowing costs, necessitating larger subsequent reductions.
- Application:
  - Use r* projections and growth projections to construct debt-stabilizing arc, identify point implied by current policies (primary deficit in 2022), and compute necessary deficit reduction to place public debt on sustainable trajectory. Results for US and China displayed in Table 2.1 of the Chapter (not reproduced here).

### Data and source indicators (Online Annex Table 2.3.2)
- Mortality rates: UN World Population Prospects, 2022 Revision
- Population size by age: UN World Population Prospects, 2022 Revision
- TFP growth: Penn World Table PWT 10.0
- Government consumption: Penn World Table 10.0
- Public debt: IMF Global Debt Database (GDD), Mauro et al (2015)
- Asset-to-income ratio: wid.world
- Net International Investment Position: IMF
- Labor income profiles: LIS
- Labor share of income: PWT 10.0, WEO
- Top 10% income share: wid.world
- Natural rate of interest: Own calculations, Guofeng and Rees (2021), Pattanaik et al (2022), Ruch (2021)
- Corporate bond spreads used in wedge calibration: Moody’s Seasoned Baa Corporate Bond Yield (U.S.), S&P Investment Grade Corporate Bond Index (U.K., Japan), Eurozone S&P Investment Grade Corporate Bond Index (France, Germany)
- Out-of-pocket health spending and Social Security Spending: OECD and listed studies
- Retirement age: OECD

### Annex analysis for Brazil, France, Germany, India, Japan, and the UK — required fiscal adjustment (near-term and medium-term)
- Near-term adjustment (Baseline / Higher debt / 1970s labor share) — change in primary deficit, percentage points of GDP:
  - France: - 1.46 - 1.57 - 1.56
  - Germany: - 1.81 - 1.91 - 1.77
  - Japan: - 7.64 - 8.22 - 7.58
  - United Kingdom: - 1.99 - 2.12 - 2.03
  - Brazil: - 3.22 - 3.48 - 3.12
  - India: - 1.77 - 1.82 - 2.02
- Additional consolidation needed for medium-term adjustment (3 years) (Baseline / Higher debt / 1970s labor share), percentage points of GDP:
  - France: - 0.03 - 0.03 - 0.02
  - Germany: - 0.05 - 0.06 - 0.05
  - Japan: - 0.28 - 0.32 - 0.26
  - United Kingdom: - 0.05 - 0.06 - 0.04
  - Brazil: - 0.19 - 0.21 - 0.19
  - India: 0.00 0.00 0.00
- Additional consolidation needed for medium-term adjustment (5 years) (Baseline / Higher debt / 1970s labor share), percentage points of GDP:
  - France: - 0.04 - 0.05 - 0.04
  - Germany: - 0.10 - 0.12 - 0.09
  - Japan: - 0.49 - 0.54 - 0.46
  - United Kingdom: - 0.09 - 0.10 - 0.09
  - Brazil: - 0.31 - 0.33 - 0.34
  - India: - 0.01 - 0.01 - 0.01

### Drivers of cross-country differences and scenario mechanisms
- Japan’s large required reduction reflects:
  - Primary deficit in 2022 about 7.4 percent of GDP.
  - Targeted primary surplus at 0.2 percent of GDP.
  - Debt level at 261 percent of GDP.
- France, Germany, and the UK:
  - r − g trajectories for France and Germany are rather similar; UK slightly less favorable, explaining variation despite comparable 2022 primary deficits around 2.7 percent of GDP.
- Brazil and India:
  - Near-term needed adjustments: 3.2 pp for Brazil and 1.8 pp for India (baseline).
  - Worsening r − g dynamics raise cost of delayed adjustment for Brazil; India exhibits relatively more favorable medium-term r − g dynamics.
- Higher debt scenario:
  - Worsening r − g for all economies increases required adjustment.
  - Higher debt raises demand for savings and the natural rate; crowding out lowers growth along transition.
- 1970s labor share scenario:
  - Change in labor share modeled via markup change; ambiguous net effect on natural rate.
  - Results: France, UK, and India need more deficit reduction; Brazil, Germany, and Japan require less under this scenario.

### Sensitivity to the elasticity of interest rates with respect to debt (φ) and fiscal space
- Increasing φ (given increase in debt causes larger increase in government borrowing rates) erodes fiscal space substantially.
- Estimated threshold debt levels at baseline φ:
  - France: around 183 percent of GDP
  - Germany: 118 percent of GDP
  - India and the UK: roughly similar levels (exact figures not provided)
- Loss in fiscal space from an increase in φ:
  - Ranges from around 13 pp in Germany to 21 pp in France.
- Note: Brazil, China, Japan and the US excluded from this sensitivity because their current debt levels already exceed the threshold; for these economies a primary surplus is needed to stabilize debt-to-GDP in the long run.

### Geopolitical fragmentation — country blocs (Box 2.2)
- US Bloc:
  1. United States
  2. European Union Plus (EU+) = EU and Switzerland
  3. Other Advanced Economies = Australia, Canada, Iceland, Israel, Japan, Korea, New Zealand, Norway, and the United Kingdom
- China Bloc:
  1. China = China and Hong Kong SAR
  2. Southeast Asia = Brunei, Cambodia, Lao PDR, Malaysia, Myanmar, Philippines, Singapore, Thailand, and Vietnam
  3. Remaining Countries = Russia, South Africa, and Turkey plus the regions of Africa, the Caribbean, Central Asia, other Latin America, the Middle East, and Oceania, plus any other EMDEs not accounted for elsewhere
- Non-aligned regions:
  1. India and Indonesia = India, Indonesia
  2. Latin America = Argentina, Brazil, Chile, Colombia, Costa Rica, Mexico, and Peru

*Source: ch2annex - 2.1 and 2.2 — https://www.imf.org/-/media/files/publications/weo/2023/april/english/ch2annex.pdf*

### 2.1 and 2.2

### 2.1 and 2.2

### Figure 2.1 — Measurement of real short-term interest rates
- Panel 1:
  - Real interest rates = US treasury rates for each maturity − Cleveland Fed measure of inflation expectations over the same period.
  - Data source: The Federal Reserve Economic Data (FRED). FRED mnemonics DSG[X] and EXPINF[X]YR where [X] stands for the respective maturity.
- Panel 2:
  - Real interest rates = 3-month treasury rates − realized annual inflation over the same horizon in each country.
  - Japan: 3-month interbank rates are spliced with certificates of deposit from 1979 to 2002 to achieve a longer series.
  - Realized inflation rate = average of the annual inflation in the next three months.
  - Formula (as presented):
    푟푟푟푟푟푟푟푟 푖푖푖푖푖푖 푟푟푟푟푟푟푖푖푖푖 푟푟푟푟푖푖푟푟푖푖=푖푖
    푡푡
    −
    1
    3
    ��
    푝푝
    푡푡+1
    푝푝
    푡푡−11
    −1
    �
    +
    �
    푝푝
    푡푡+2
    푝푝
    푡푡−10
    −1
    �
    +
    �
    푝푝
    푡푡+3
    푝푝
    푡푡−9
    −1
    ��
    ×100
    where 푖푖
    푡푡 is the nominal interest rates and 푝푝
    푡푡 is the monthly CPI index.
- Additional FRED mnemonics used:
  - IR3TIB01[XX]M156N — 3-Month or 90-day Rates and Yields: Interbank Rates for [XX] where [XX] stands for the respective country’s alphabetic ISO2-code, Percent, Monthly, Not Seasonally Adjusted
  - IR3TIB01JPM156N — 3-Month or 90-day Rates and Yields: Interbank Rates for Japan, Percent, Monthly, Not Seasonally Adjusted
  - IR3TCD01JPM156N — 3-Month or 90-day Rates and Yields: Certificates of Deposit for Japan, Percent, Monthly, Not Seasonally Adjusted
  - INDIR3TIB01STM — Interest Rates: 3-month or 90-day rates and yields: Interbank rates: Total for India, Percent, Monthly, Not Seasonally Adjusted
  - CPALTT01[XX]M659N — Consumer Price Index: Total All Items for [XX] where [XX] stands for the respective country’s alphabetic ISO2-code, Growth rate same period previous year, Monthly, Not Seasonally Adjusted

### Figure 2.2 — Real long-term bond yields and aggregation
- Real long term bond yield data: WEO mnemonic FIGB_R from the WEO database.
- Sample composition:
  - 34 advanced economies: AUS, AUT, BEL, CAN, CHE, CYP, CZE, DEU, DNK, ESP, FIN, FRA, GBR, GRC, HKG, IRL, ISL, ISR, ITA, JPN, KOR, LUX, MAC, MLT, NLD, NOR, NZL, PRT, SGP, SVK, SVN, SWE, TWN, and USA.
  - 25 emerging market and developing economies: ARG, BIH, BLR, BRA, CHL, CHN, GHA, HRV, HUN, IDN, IND, MUS, MYS, NAM, PAN, PHL, POL, RUS, SLE, SYC, THA, TUR, TZA, UKR, and ZAF.
- Aggregation:
  - Aggregated using market-exchange-rate-based GDP weight (WEO mnemonics: GDPWGT and NGDPD) as:
    퐺퐺퐺퐺퐺퐺퐺퐺퐺퐺 푇푇
    푡푡
    =
    1
    3
    (
    푁푁퐺퐺퐺퐺퐺퐺 퐺퐺
    푡푡−1
    +푁푁퐺퐺퐺퐺퐺퐺 퐺퐺
    푡푡−2
    +푁푁퐺퐺퐺퐺퐺퐺 퐺퐺
    푡푡−3
    )
- Bond maturity considered: greater than 1 year.

### Online Annex 2.2 — Measuring the real natural rate (overview)
- Three empirical exercises based on a Kalman filter estimation inspired by Laubach and Williams (2003):
  - (i) country-by-country estimate of the natural rate,
  - (ii) real-time estimate of natural rates over the pandemic contrasting filtered and smoothed estimates to illustrate real-time uncertainty,
  - (iii) two-region simultaneous estimation for the US and the rest-of-the-world to quantify international dependencies.

### 2.2.1 Country-by-country estimates — model structure and estimation
- Model framework:
  - Kalman filter linked to a simple New Keynesian AD/IS and AS/PC model.
  - IS-curve relates the percent deviation of real output from potential (output gap 푦푦
    푡푡
    �) to the real rate gap (푟푟
    푡푡
    −푟푟
    푡푡
    ⋆).
  - IS-curve (A.2.2.1):
    푦푦
    푡푡
    �=α
    1
    푦푦
    푡푡−1
    �+α
    2
    푦푦
    푡푡−2
    �+
    푎푎
    푟푟
    2
    ∑(
    푟푟
    푡푡−푖푖
    −푟푟
    푡푡−푖푖
    ⋆
    )
    2
    푖푖=1
    +ε 
    푦푦
    �,푡푡
    where 푦푦
    푡푡
    �=100∗(y
    t
    −y
    t
    ⋆) and y
    t
    and y
    t
    ⋆ are the logarithms of real GDP and the unobserved potential output.
  - Phillips Curve (A.2.2.2):
    π
    t
     =  B
    (
    L
    )
    π
    t−1
    ++ b
    y
      푦푦
    푡푡−1
    �+  ε
    π,t
  - Natural rate law of motion:
    1
    푟푟
    푡푡
    ⋆
    =푔푔
    푡푡
    +푧푧
    푡푡
    where 푧푧
    푡푡
    follows a random walk:
    푧푧
    푡푡
    =푧푧
    푡푡−1
    +휀휀
    푧푧,푡푡
  - Potential output dynamics:
    푦푦
    푡푡
    ⋆
    =푦푦
    푡푡−1
    ⋆
    +푔푔
    푡푡−1
    +ε
    푦푦
    ⋆
    ,푡푡
    푔푔
    푡푡
    =푔푔
    푡푡−1
    +휀휀
    푔푔,푡푡
- Estimation:
  - System cast as a Kalman filter where unobserved states include potential output and the real natural rate.
  - Observables: real output, inflation, lagged ex-ante real interest rate, and predetermined past output and inflation.
  - The output gap, real rate gap, natural rate, growth trend, stochastic growth drift, and innovation variances are estimated.
  - Implementation reference: Wynne and Zhang (2018) appendix.
- Countries estimated: Canada, France, Germany, Japan, the United Kingdom, and the United States.
- Ex ante real policy rate construction: expectation of average inflation over the four quarters ahead from a univariate AR(3) model of inflation estimated over the 40 quarters prior to the data point.
- Country-by-Country Kalman Filter Data Sources (selected mnemonics as provided):
  - Canada: Real GDP NAEXKP01CAQ189S; Interest rates IRSTCB01CAM156N; Inflation CANCPICORMINMEI.
  - France: Real GDP Q.Y.FR.W2.S1.S1.B.B1GQ._Z._Z._Z.EUR.LR.N; Interest rates Q.U2.EUR.RT.MM.EURIBOR3MD_.HSTA and IRSTCI01FRM156N; Inflation FRACPICORMINMEI; ECB SDW mnemonic: M.FR.N.XEF000.4.INX.
  - Germany: Real GDP NAEXKP01DEQ661S; Interest rates IRSTCI01DEM156N; Inflation DEUCPICORMINMEI.
  - Japan: Real GDP Haver S158NGPC@G10 and RGDPNAJPA666NRUG; Interest rates IRSTCB01JPM156N; Inflation JPNCPICORMINMEI.
  - UK: Real GDP ABMI/UKEA; Interest rates BOERUKM; Inflation CPGRLE01.
  - USA: Real GDP GDPC1; Interest rates FEDFUNDS; Inflation PCEPILFE.
- Sample periods (Online Annex Table 2.2.2):
  - Canada: 1962 Q4 — 2019 Q4
  - France: 1971 Q4 — 2019 Q4
  - Germany: 1971 Q4 — 2019 Q4
  - Japan: 1961 Q4 — 2019 Q4
  - UK: 1956 Q4 — 2019 Q4
  - USA: 1960 Q4 — 2019 Q4

### 2.2.2 Two-region estimates — open-economy Kalman filter
- Model extension:
  - Two-region Laubach and Williams (2003) setup (Wynne and Zhang, 2018) with home and foreign AD relations and Phillips curves.
  - Home and foreign IS equations (A.2.2.3 and A.2.2.4):
    푦푦
    푡푡
    ℎ
    �=α
    1
    ℎ
    푦푦
    푡푡−1
    ℎ
    �+α
    2
    ℎ
    푦푦
    푡푡−2
    ℎ
    �+
    푎푎
    푟푟
    ℎ
    2
    ∑
    �푟푟
    푡푡−푖푖
    ℎ
    −푟푟
    푡푡−푖푖
    ℎ,∗
    �
    2
    푖푖=1
    +ε
    ℎ
    푦푦
    �,푡푡
    and similarly for the foreign economy.
  - Phillips curves include import prices π
    t
    I,i and oil prices inflation π
    t−1
    O,i to capture open-economy inflation dynamics (A.2.2.5 and A.2.2.6).
- Natural rate evolution now depends on domestic and foreign stochastic growth:
  - 푟푟
    푡푡
    ℎ,∗
    = 푐푐
    ℎ
    ℎ
    푔푔
    푡푡
    ℎ
    +푐푐
    푓푓
    ℎ
    푔푔
    푡푡
    푓푓
    +푧푧
    푡푡
    ℎ
  - 푟푟
    푡푡
    푓푓,∗
    =  푐푐
    ℎ
    푓푓
    푔푔
    푡푡
    ℎ
    +푐푐
    푓푓
    푓푓
    푔푔
    푡푡
    푓푓
    +푧푧
    푡푡
    푓푓
  - Stochastic growth processes:
    푔푔
    푡푡
    ℎ
    =푔푔
    푡푡−1
    ℎ
    +ε
    푡푡
    ℎ
    and
    푔푔
    푡푡
    푓푓
    =푔푔
    푡푡−1
    푓푓
    +ε
    푡푡
    푓푓
- Data and sample:
  - Home economy data: US log real GDP, core inflation, oil price inflation, relative import price inflation, and real rates with ex ante expectations computed as in single-country case.
  - Rest-of-the-world composed of: Australia, Austria, Belgium, Brazil, Canada, China, Finland, France, Germany, Greece, India, Ireland, Italy, Japan, Korea, Netherlands, Norway, Portugal, Russia, South Africa, Spain, Sweden, Switzerland, United Kingdom; BRICS = Brazil, Russia, India, China and South Africa represent EMDEs.
  - Sample start: 1960 Q1; coverage spottier early for BRICS.
  - Representation: Overall, 90 percent of world GDP measured at PPP (IMF) is represented. At the end of the sample 2022 the subset of countries considered account for about 70 percent of IMF recorded world PPP GDP.
- Two-region Kalman Filter data sources (selected):
  - Real GDP: OECD National Quarterly Accounts database mnemonic [XYZ].B1_GE.VPVOBARSA.Q where [XYZ] stands for ISO3-codes AUT, CAN, FRA, DEU, ITA, JPN, GBR, USA, AUS, BEL, FIN, GRC, IRL, NLD, NOR, PRT, KOR, ESP, SWE, CHE, BRA, IND, ZAF, RUS. China: China WEO quarterly data spliced and reindexed to purchasing power adjusted OECD NQA data.
  - Core Inflation: CED MEI database mnemonics [XYZ].CPGRLE01.IXOB.Q for ISO3-codes as above.
  - Interest rates: Haver Analytics with national sources and IMF IFS series spliced to create the longest possible unbalanced panel. Example Haver mnemonics: FFED@DAILY, N023RTAR@G10, N112RTAR@G10, N193RTAR@G10, C134IM@IFS, … OECD MEI mnemonics: 156IRSTCB01ST.Q (Canada), 132IRSTCI01ST.Q (France), 144IRSTCI01ST.Q (Sweden), 142IRSTCI01ST.Q (Norway), 138IR3TIB01ST.Q (Netherlands), 223IRSTFR01ST.Q (Brazil), 922IRSTCB01ST.Q (Russia).

### Online Annex 2.3 — Drivers of the natural rate in the structural model (model features and mechanisms)
- Model used: adapted version of Platzer and Peruffo (PP, 2022).
- Purpose: quantify contributions of various drivers to change in the natural rate and simulate its future path.
- Covered economies: United States, Japan, Germany, the UK, France, China, India, and Brazil (eight major economies covering some 70 percent of global GDP).
- Key model features:
  - Demographics: overlapping generations structure matching population-age pyramids; life-cycle savings for retirement; out-of-pocket health expenditure shocks; income inequality within generations affecting aggregate saving via differing marginal propensities to consume.
  - Productivity: aggregate productivity follows an exogenous, deterministic process matched to data; monopolistic competition introduces an exogenous mark-up.
  - Public sector: issues debt, runs social security, provides transfers, finances via various taxes; public debt and social security generosity affect desired savings and thus the natural rate.
  - Open-economy aspect: exogenous changes in net foreign asset position (NIIP) affect domestic natural rate (a drop in NIIP lowers domestic natural rates as additional supply of foreign savings raises total supply).
- Calibration targets per country: demographics, age-earnings profile, share of income to top ten percent, productivity trends, retirement age, pension system size, labor share, government debt, government consumption, and NIIP.
- Demographic dynamics:
  - 74 overlapping generations; households enter at biological age 26 and live at most until age 99.
  - Newborns enter each period according to fertility rate 푖푖�
    푡푡; total population growth 푁푁
    푡푡+1 = (1 +푖푖
    푡푡) 푁푁
    푡푡, determined by fertility and survival probabilities (can reflect migration).
- Households:
  - Agents move through work and retirement; exogenous retirement age; retired individuals receive savings returns and social security.
  - Two assets: government bonds and capital with return 푟푟. No-arbitrage ensures net return equality across assets (assumption noted to be amended in an extension).
  - No-borrowing constraint; dividend income possible.
  - Frictionless model implies output is always at potential; return on government bonds coincides with the natural rate in this economy.
- Labor productivity:
  - Product of permanent productivity, transitory productivity shock (AR(1)), and age-dependent productivity (hump-shaped).
  - Permanent productivity is high or low and constant across life; transitory shock introduces idiosyncratic income risk; age-profile matches hump-shaped real wage profiles.
- Preferences:
  - Addilog form (Houthakker, 1960; Straub, 2019).
  - Elasticity of intertemporal substitution is age-dependent and declines with age; richer households have higher saving rates, consistent with empirical evidence (Carroll, 2000; Straub, 2019).
- Production:
  - Cobb-Douglas with labor-augmenting technological progress and monopolistic competition generating a markup.
- Government roles:
  - Four roles: public debt issuance (affects savings demand), social security (generosity reduces private saving and raises natural rate), exogenous government consumption G (as resource cost increases natural rate), and taxes/transfers (progressive income tax, consumption tax, capital income tax, profit tax; more progressive taxes raise natural rate because burden falls disproportionately on high savers). Transfers include means-tested transfer to ensure consumption floor in old age.
- Capital flows and market clearing:
  - Introduce exogenous stock of net savings (foreign-owned) calibrated to matching NIIP.
  - Market clearing condition (A.2.3.1): K + B = ∑푟푟
    푖푖
    +퐴퐴
    ∗
    푖푖
    where K = domestic capital, B = government borrowing, 푟푟
    푖푖 = savings supply by household i, and 퐴퐴
    ∗ = net savings stock owned by foreigners (NIIP).
- Convenience yield (wedge between bond returns and net return on capital):
  - Adjusted no-arbitrage (A.2.3.2):
    1 + r = 1 + 푟푟
    푘푘
    (
    1−ω
    )
    – 훿훿
  - Wedge formulation (A.2.3.3):
    (푟푟
    푘푘
    −δ) − r = ω푟푟
    푘푘 ≡ wedge
  - Interpretation: ω acts like a tax on gross return on capital; 훿훿 is depreciation rate.
  - Proceeds from the wedge are rebated to households as lump-sum transfers in proportion to capital holdings; ω adjusted on transition path to hold wedge at desired level.
- Drivers table (described qualitatively):
  - Higher TFP growth: increases investment demand for savings and also raises expected wages which can reduce current saving; net effect in model is higher natural rate due to higher demand and lower supply.
  - Demographic change:
    - Increased life expectancy (constant retirement age) increases expected retirement duration, raising savings and increasing natural rate.
    - Population aging (shift mass to older ages): impact ambiguous since lifecycle savings and labor supply are non-monotonic.
    - Lower population growth rate reduces output growth, negatively affecting natural rate.

*Source: ch2annex - 2.1 and 2.2 — https://www.imf.org/-/media/files/publications/weo/2023/april/english/ch2annex.pdf*

### CHAPTER 2  THE NATURAL RATE OF INTEREST:

### CHAPTER 2  THE NATURAL RATE OF INTEREST: DRIVERS AND IMPLICATIONS FOR POLICY

### Drivers and economic mechanisms
- Demographic change affects the natural rate through multiple channels (labor supply, dependency ratios, savings demand, investment) and the net impact on the natural rate is ambiguous.
- An increase in inequality implies a larger share of output goes to high-saving households, increasing the supply of savings and depressing the natural rate.
- An expansion of public debt directly increases the demand for savings, raising natural rates.
- Government consumption financed ultimately by higher income taxes is assumed to depress the supply of savings and increase the natural rate.
- A rise in market power depresses production and demand for savings, while profits disproportionately go to the elderly population, reducing the supply of savings; the sign of the change in the natural rate is therefore ambiguous.
- Net international capital flows increase available savings in the domestic economy, lowering the natural rate.

### Calibration approach and parameter choices
- Two parameter types:
  - Type I: calibrated using literature estimates or empirical counterparts (population distribution, growth rate, mortality rates, government spending, public debt ratios).
  - Type II: estimated by minimizing distance between data moments and model counterparts.
- Population distribution matched using UN data; population growth rate refers to growth of 26-to-99-years old and implicitly includes net migration flows (migrants identical to domestic population, including asset holdings).
- Mortality rates taken from UN World Population Prospects, 2022 Revision.
- Additional calibration choices and targets:
  - Add semi-elasticity of savings supply to a change in the interest rate as a long run elasticity; target semi-elasticity = 15, following Auclert et al (2021).
  - Add the median coefficient of risk aversion to the calibration.
  - TFP growth: Solow residual (see section 2.3.4).
  - No bequest motive; bequests are accidental and distributed according to SCF bequest distribution.
  - Distribution of profits from Piketty et al (2018), updated relative to PP (2022).
  - Labor supply is inelastic; out-of-pocket health expenditures held constant over time.
  - Parameter differences from PP (2022): depreciation rate δ = 0.5; capital income tax τ_k = 0.3.
  - Elasticity of consumption out of permanent income φ_PPPP = 0.8 (conservative target, deviating from Straub (2019) baseline of 0.7).
  - When changing difference between permanent productivity terms, hold the average constant; for the inequality driver, only change permanent productivity and hold variance of innovation in transitory productivity constant.
  - Use top 10 percent income share as proxy for top 10 percent labor income share where direct data are not available.
- Country-specific parameters and sources are listed in Online Annex Table 2.3.2 (indicator list includes Mortality rates, Population size by age, TFP growth, Government consumption, Public debt, Asset-to-income ratio, NIIP, Labor income profiles, Labor share of income, Top 10% income share, Natural rate of interest, Out-of-pocket health spending, Social Security Spending, Retirement age).

### Simulation experiments and scenarios
- Two main experiments:
  1. Steady-state comparison: compare a 2015-2019 steady-state with a 1975-1979 steady-state (Figure 2.7). Type I and II parameters calibrated to 2015-2019; when simulating 1975-1979, only change parameters corresponding to candidate drivers of decline in the natural rate. Individual-driver contributions computed by changing each parameter to its 1975-1979 value while keeping others at 2015-2019 values; interaction effects mean individual contributions need not sum exactly to the total change.
     - Reference: 1970s chosen as common theoretical reference point and coincides with macro developments (baby boom joining labor force, slowdown in productivity growth, rise in income inequality).
     - Special calibration deviations:
       - India: Penn World Tables imply a sharp decline in labor share (~21 percentage points between mid-1970s and 2019). To avoid a negative markup in 1975-1979, impose minimum markup of zero and do not fully match change in labor share. Resulting 1975-1979 labor share implied = 61.3% vs 73% in data; 2015-2019 steady-state labor share = 52%.
       - China: data imply large capital-to-output ratio; set markup to 5% and use inferred capital-to-output ratio of 5.4 (data ratio is 6.3 implying a markup of -1.5%).
     - For countries beyond the United States, many parameters and calibration targets are held constant at the U.S. 2015-2019 values.
  2. Transition-path analysis: start date 1950, terminal date 2200 to ensure convergence (Figure 2.8, panel 1).
     - Iterative calibration procedure for Type II parameters across P iterations; algorithm begins with 2015-2019 steady-state calibration to targeted moments m_p^t and simulates full transition to derive model-implied moments m_p^m.
     - Define Δ(r)_p = m~(r)_t − m(r)_p^m (difference between targeted natural rate and model-implied natural rate in 2015-2019 for iteration p). If above tolerance, proceed to next iteration with adjusted steady-state target for the natural rate. In practice, procedure stops after p = 2; it ensures average natural rate in 2015-2019 on the transition path is close to data.
     - Drivers along transition:
       - Baseline: demographic drivers (population distribution, mortality rates, population growth rate) change from 1950 to 2100 and are held constant at 2100 levels thereafter. Demographic variables start in 1950 to avoid a jump in 2020; other drivers start to change earliest at 2019.
       - Debt trajectory and forecast until 2028 from WEO (as of February 28, 2023) and held constant thereafter.
       - Advanced economies: TFP growth held constant at 2015-2019 average. Emerging markets: linear convergence to advanced-economy average (2015-2019) by 2050.
- Higher government borrowing costs scenario:
  - Introduce a wedge between return on physical capital and on government bonds (Equation A.2.3.3). Calibrate steady-state wedge in 2015-2019 to five-year average spread between a 10-year government bond and investment grade corporate bond yields.
  - For the scenario change, assume a linear transition by 2050 to a new level: 2050 level is a decline in 2015-2019 average wedge by 44 basis points (difference between U.S. corporate bond spread in 2015-2019 and pre-2000 (1970-1999)).
  - Simultaneously change net savings stock owned by foreigners A* for the United States: feed in a linear change by 79 percent of GDP by 2050 (difference of gross foreign portfolio investments in the U.S. between 2015-2019 average and pre-2000 average (1976-1999), Bureau of Economic Analysis).
  - Consequence: in this scenario the natural rate increases by around 100 basis points by 2050 in the United States.
  - Note: model does not capture endogenous response of capital flows to a change in the convenience yield; this could be sizeable for safe asset providers like the United States.

### Fiscal policy framework and debt sustainability (Mian, Straub and Sufi (2021c) framework)
- The model assumes savers derive convenience benefits from holding government debt (safety and liquidity), captured by a “convenience yield” that reduces government borrowing cost (Krishnamurthy and Vissing-Jorgensen 2012; Caballero, Farhi and Gourinchas 2017b).
- Convenience benefits decrease with the debt level (convenience yield erodes as debt rises); interest rate on government debt is endogenous: r(b).
- Key debt-dynamics equation (A.2.4.1):
  - ḃ = z + ( r(b) − g ) b
  - where ḃ is change in debt-to-GDP ratio, z denotes primary deficit, and g is economy’s growth rate.
- Implications:
  - If r > g, primary deficits are unsustainable; governments must run primary surpluses to stabilize debt-to-GDP.
  - If r < g and interest rates are not endogenous to debt, any level of primary deficit can correspond to a stable debt-to-GDP (Blanchard 2019).
  - The Mian, Sufi and Straub framework introduces r endogenous to b, creating continuity: increasing debt raises rates, pinning down a unique primary deficit z that stabilizes b when r(b) < g.
  - Setting ḃ = 0 yields z = −( r(b) − g ) b, identifying the unique primary deficit needed to stabilize debt at each b.
- Phase-diagram interpretation (Online Annex Figure 2.4.1):
  - Points above the stability arc: ḃ > 0 and debt will rise forever; points below imply debt declines.
  - With r − g < 0, z can be positive; at low debt levels (b < b*), the government can increase primary deficit and still converge to the stable arc (a “free lunch”). In illustrative chart b* ≈ 90 percent of GDP.
  - Beyond b*, government must reduce its deficit to stabilize b. Beyond a debt of 180 percent of GDP (vertical dashed line in the illustration), r(b) becomes larger than g and government must run a primary surplus to ensure sustainability.
  - If current primary deficit is above the stability arc and debt exceeds b* (blue-dot scenario), deficit reduction is required; delaying reduction raises debt-to-GDP and borrowing costs, requiring larger subsequent deficit reductions.
- Application:
  - Because r − g is critical for debt sustainability, projections for r* and corresponding growth rates (from the “Outlook for the Natural Rate” section) are used to construct the debt-stabilizing arc for each economy, identify the point implied by current policies (primary deficit in 2022), and compute necessary deficit reduction to place public debt on a sustainable trajectory (long-run stabilizing arc). For the US and China, results are displayed in Table 2.1 of the Chapter.

### Data and source indicators (Online Annex Table 2.3.2)
- Mortality rates: UN World Population Prospects, 2022 Revision
- Population size by age: UN World Population Prospects, 2022 Revision
- TFP growth: Penn World Table PWT 10.0
- Government consumption: Penn World Table 10.0
- Public debt: IMF Global Debt Database (GDD), Mauro et al (2015)
- Asset-to-income ratio: wid.world
- Net International Investment Position: IMF
- Labor income profiles: LIS
- Labor share of income: PWT 10.0, WEO
- Top 10% income share: wid.world
- Natural rate of interest: Own calculations, Guofeng and Rees (2021), Pattanaik et al (2022), Ruch (2021)
- Corporate bond spreads used in wedge calibration: Moody’s Seasoned Baa Corporate Bond Yield (U.S.), S&P Investment Grade Corporate Bond Index (U.K., Japan), Eurozone S&P Investment Grade Corporate Bond Index (France, Germany)
- Out-of-pocket health spending: OECD
- Social Security Spending: OECD, Cuevas et al (2017), Fang and Feng (2018), Narayana (2015)
- Retirement age: OECD

*Source: CHAPTER 2 THE NATURAL RATE OF INTEREST: DRIVERS AND IMPLICATIONS FOR POLICY, International Monetary Fund | April 2023*

### Annex includes the analysis for Brazil, France, Germany, India, Japan, and the UK.

### Annex: Analysis for Brazil, France, Germany, India, Japan, and the UK

### Required fiscal adjustment: near-term and medium-term (by scenario)
- Online Annex Table 2.4.1 presents the deficit reduction required in each of the six economies (changes in primary deficit; percentage points of GDP).
- Near-term adjustment (Baseline / Higher debt / 1970s labor share):
  - France: - 1.46 - 1.57 - 1.56
  - Germany: - 1.81 - 1.91 - 1.77
  - Japan: - 7.64 - 8.22 - 7.58
  - United Kingdom: - 1.99 - 2.12 - 2.03
  - Brazil: - 3.22 - 3.48 - 3.12
  - India: - 1.77 - 1.82 - 2.02
- Additional consolidation needed for medium-term adjustment (3 years) (Baseline / Higher debt / 1970s labor share):
  - France: - 0.03 - 0.03 - 0.02
  - Germany: - 0.05 - 0.06 - 0.05
  - Japan: - 0.28 - 0.32 - 0.26
  - United Kingdom: - 0.05 - 0.06 - 0.04
  - Brazil: - 0.19 - 0.21 - 0.19
  - India: 0.00 0.00 0.00
- Additional consolidation needed for medium-term adjustment (5 years) (Baseline / Higher debt / 1970s labor share):
  - France: - 0.04 - 0.05 - 0.04
  - Germany: - 0.10 - 0.12 - 0.09
  - Japan: - 0.49 - 0.54 - 0.46
  - United Kingdom: - 0.09 - 0.10 - 0.09
  - Brazil: - 0.31 - 0.33 - 0.34
  - India: - 0.01 - 0.01 - 0.01

### Drivers of differences across countries
- The large required reduction for Japan reflects:
  - A sizable primary deficit in 2022, at about 7.4 percent of GDP.
  - A targeted primary surplus at 0.2 percent of GDP.
  - A sizable debt level at 261 percent of GDP.
- France, Germany, and the UK:
  - The 푟푟−푔푔 trajectories for France and Germany are rather similar, but a little less favorable for the UK.
  - This explains variation in required fiscal adjustment despite comparable 2022 primary deficits around 2.7 percent of GDP.
- Brazil and India:
  - Needed adjustments are 3.2 pp for Brazil and 1.8 pp for India (near-term, baseline).
  - Worsening 푟푟−푔푔 dynamics raise the cost of delayed adjustment for Brazil; India exhibits relatively more favorable medium-term dynamics for 푟푟−푔푔.

### Scenarios and mechanisms
- Higher debt scenario:
  - More adjustment is needed given a worsening 푟푟−푔푔 profile for all economies.
  - With higher debt, demand for savings is higher, which increases the path of the natural rate.
  - Along the transition, growth will be lower due to the crowding out effect on productive capital from the increase in the natural rate.
- 1970s labor share scenario:
  - Labor share changes are modeled as a change in the markup and have an ambiguous effect on the natural rate: a decline in markups implies more production, raising the demand for savings; but since profits disproportionately go to the elderly, savings supply increases with a lower markup.
  - Results indicate France, the UK, and India would need more deficit reduction, while Brazil, Germany, and Japan require less consolidation under this scenario.

### Sensitivity to the elasticity of interest rates with respect to debt (휑휑) and fiscal space
- Online Annex Figure 2.4.2 traces the impact of an increase in 휑휑 on the threshold debt level at which the sign of 푟푟−푔푔 reverses (from negative to positive).
  - Crossing this threshold requires shifting from a primary deficit to surplus to maintain a stable debt-to-GDP ratio; thus it can be interpreted as fiscal space.
  - An increase in 휑휑 (a given increase in debt now causes a larger increase in government borrowing rates) results in a relatively large erosion of fiscal space (dashed portions of bars).
- Estimated threshold debt levels at the baseline estimate of 휑휑:
  - France: around 183 percent of GDP
  - India and the UK: roughly similar levels (no exact figures provided in source)
  - Germany: 118 percent of GDP
- Loss in fiscal space from an increase in 휑휑:
  - Ranges from around 13 pp in Germany to 21 pp in France.
  - This erosion is non-negligible and more impactful for countries nearing their threshold levels, especially if currently running large primary deficits.
- Note on exclusions:
  - The sensitivity analysis uses the baseline projections for 푟푟∗. Brazil, China, Japan and the US are excluded from the analysis given that their current debt levels already exceed this threshold; for these economies, a primary surplus is needed to stabilize the debt-to-GDP ratio in the long run.

### Geopolitical fragmentation: country blocs used for analysis
- Box 2.2 defines three country blocs determined primarily by geopolitical alignment using the “ideal point distance” (IPD) from UNGA voting patterns.
- Blocs and constituent regions:
  - US Bloc:
    1. United States
    2. European Union Plus (EU+) = EU and Switzerland
    3. Other Advanced Economies = Australia, Canada, Iceland, Israel, Japan, Korea, New Zealand, Norway, and the United Kingdom
  - China Bloc:
    1. China = China and Hong Kong SAR
    2. Southeast Asia = Brunei, Cambodia, Lao PDR, Malaysia, Myanmar, Philippines, Singapore, Thailand, and Vietnam
    3. Remaining Countries = Russia, South Africa, and Turkey plus the regions of Africa, the Caribbean, Central Asia, other Latin America, the Middle East, and Oceania, plus any other EMDEs not accounted for elsewhere
  - Non-aligned regions:
    1. India and Indonesia = India, Indonesia
    2. Latin America = Argentina, Brazil, Chile, Colombia, Costa Rica, Mexico, and Peru

*Source: IMF staff calculations, Online Annex Table 2.4.1 and Online Annex Figure 2.4.2 (from the Annex analyzing Brazil, France, Germany, India, Japan, and the UK).*

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_Source: https://www.imf.org/-/media/files/publications/weo/2023/april/english/ch2annex.pdf_