## ch1onlineannex - Section 2

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---

### EBA CA Model refinements, data update, and sample
- Data updates and scope:
  - Extended all series to cover 1986–2023.
  - Incorporated historical data revisions for selected countries and updated periodically revised variables (demographics use UN World Population Prospects, 2024 Vintage).
  - Updated dataset covers 52 economies with annual data spanning 1986–2023, based on information available as of October 2024.
- Robustness checks and key finding:
  - Leave-one-year-out regressions and rolling regressions starting in 2019 performed; incorporating the COVID years has a limited impact on estimation results and estimated coefficients remain broadly stable and robust.
- Impact of updates on EBA CA gaps (relative to 2024 EBA assessment):
  - For an average ESR country, data update alone explains about 50 percent of the change in absolute EBA CA gaps: 0.27 percentage points out of 0.51.
  - Data update plus coefficients re-estimated using data through 2019 explains roughly 75 percent of the change: 0.34 compared with 0.51.
  - Extending the sample from 2019 to 2023 and re‑estimating coefficients accounts for remaining 25 percent.
- Magnitude comparison with 2022 refinement:
  - 2026 refinement: average absolute change in EBA gaps ≈ 0.51 (percent of GDP) for ESR countries and 0.57 for non-ESR EBA countries.
  - 2022 refinement: average absolute change ≈ 0.67 for ESR countries and 1.03 for non-ESR EBA countries.
- Variables and sources (preserved labels):
  - CURRENT ACCOUNT — World Economic Outlook
  - Current Account — World Economic Outlook
  - Output Gap — World Economic Outlook
  - Commodity Terms of Trade — World Economic Outlook and World Integrated Trade Solution(WITS)
  - Real Effective Exchange Rate — Information Notice System (INS)
  - Net Foreign Assets (NFA) position — EWN: Lane, Milesi Ferretti and World Economic Outlook
  - Output per worker, relative to top 3 economies — World Economic Outlook
  - Expected real GDP growth (5 years ahead) — World Economic Outlook
  - Demographic variables — UN World Population Prospects, 2024 Vintage
  - Institutional Quality — International Country Risk Guide (ICRG)
  - Exhaustible Resources of Oil and Natural Gas — World Economic Outlook, WITS and BP Statistical Review of World Energy
  - Fiscal Policy — World Economic Outlook
  - Health Spending — OECD, and WDI
  - Foreign Exchange Intervention (FXI) — World Economic Outlook, Data Template on International Reserves and Foreign Currency Liquidity
  - Capital Account Openness — IMF (Baba and others, 2026)
  - Credit Gap — BIS (Credit statistics) and World Bank (Global Financial Development Database)
- Examples of historical revisions incorporated:
  - Health spending for Australia, Austria, Canada, Denmark, Finland, Germany, the Netherlands, New Zealand, Norway, Portugal, Spain, Korea, Sweden for 1986.
  - NFA for South Africa for 1987–1993.
  - REER for Egypt, Hungary, Poland for 1992.

### Improved commodity terms-of-trade (ToT) gap construction and trade weights
- Key methodological changes:
  - Replaced log-approximation of price gaps with exact calculation: gap_k,t = P_k,t / P_k,t_T − 1 = exp(lnP_k,t − lnP_k,t_T) − 1.
  - Made commodity trade weights consistent between exports and imports by using the same denominator (X_i,t + M_i,t).
- Rationale and expected effect:
  - Exact formula better captures extreme price variations (e.g., natural gas spike in 2022); changes are small in "normal times" but more suitable when commodity price changes are large.
  - Empirical note: 81.7 percent of commodity price gaps over 1986–2024 were in the [-40%; +40%] range; exact formula increases occurrence of very large positive gaps (over 1986–2024, 1.2 percent of price gaps in 70–80% range using exact calc vs. 0.2 percent with log-linear).
- Alternative trade-weight approaches evaluated (Section 1.2.4):
  - Problem with nominal weights: double-counting of price fluctuations (price enters both nominal weights and price gaps) and difficulty extrapolating current-year nominal weights.
  - Proposed volume-weights approach (deflate nominal trade by global commodity price P_k,t; deflate GDP by US CPI due to lack of USD GDP deflators); variants: volume weights, constant volumes (2015), smoothed volumes (11-year moving average).
  - Adjusted openness definition: TradeOpenness_i,t = (X_i,t + M_i,t) / GDP_i,t.
- Empirical results (preserve reported values exactly):
  - Preferred specification (column 3: exact commodity price gaps; nominal weights using common X+M denominator):
    - R-squared IV = 0.489
    - R-squared fit = 0.523
    - Root MSE = 0.032
    - Commodity ToT x trade openness coefficient = 0.392*** (0.042)
    - Output gap coefficient = -0.254*** (0.030)
  - Volume-weight specifications (columns 4–8) comparative statistics:
    - R-squared IV: 0.469, 0.468, 0.479, 0.481, 0.472
    - R-squared fit: 0.500, 0.500, 0.512, 0.512, 0.502
    - Root MSE: 0.032 for all columns
    - Commodity ToT x trade openness coefficients: 0.209*** (0.029), 0.269*** (0.031), 0.260*** (0.031), 0.247*** (0.031), 0.270*** (0.029)
    - Output gap coefficients: -0.260*** (0.031), -0.262*** (0.030), -0.261*** (0.030), -0.254*** (0.030), -0.259*** (0.030)
- Decision:
  - All tested volume-weight specifications worsened model fit relative to preferred specification (column 3); attempt to switch to volume weights was dropped.

### Coefficient changes, demographics, health spending, and NFA
- Output per worker:
  - Estimated coefficient rose from 0.034 in the 2022 model to 0.050 in the 2022 model with updated data, and is 0.044 in the refined model.
  - Interpretation: higher output per worker associated with higher CA balances (capital exporters).
- Health spending (desirable policies proxy for social safety net):
  - Coefficient becomes more negative (in absolute value): −0.298 in 2022 model → −0.408 in refined model.
  - Re-estimation using updated data raises coefficient in absolute value to −0.342 (Online Annex Table 1.1.3 Column 1); extending sample to 1986–2023 increases it further to −0.364 (Online Annex Table 1.1.3 Column 5).
  - Interpretation: stronger social safety nets reduce precautionary saving; recent shocks and aging likely reinforced effect.
- Net foreign assets (NFA):
  - Estimated coefficient on NFA declines modestly from 0.036 in 2022 model to 0.031 in refined model.
  - Even modest coefficient changes can imply large contributions for economies with sizable net creditor/debtor positions.

### Updated complementary toolboxes — overview and key results
- Toolbox purpose:
  - Provide interpretation of CA residuals and inform policy advice where structural indicators cannot be included directly in core EBA CA regression.
- Toolboxes updated: pensions, product and labor market regulations, inflation bias.

- Pension toolbox — data, estimation, and key coefficients:
  - Coverage datasets:
    - KW dataset: mandatory pension indicators for 49 economies over 1986–2016.
    - OECD Pensions at a Glance: mandatory and voluntary replacement rates for 51 OECD and G20 economies spanning 2005–2024 (analysis uses OECD staff estimates).
    - Coverage proxy: 1 minus self-employment share (ILO).
  - Caveat: cross-country comparable pension data limited; toolbox estimates not used as formal adjustors.
  - Estimation: pension indicators regressed on residuals from 2026 refined EBA CA model for 1986–2023; variables demeaned.
  - Explanatory power: R-squared between 1.0 and 5.0 percent of variation in EBA CA residuals (baseline EBA CA equation R-squared ≈ 52 percent).
  - Key coefficients (Online Annex Box Table 1.5.1a; values preserved):
    - PAYG replacement rate #: 0.255 (col 1), 0.336 (col 2) — SEs (0.706), (0.809)
    - Mandatory FF replacement rate #: 2.262*** (col 1), 2.836*** (col 2) — SEs (0.876), (0.996)
    - Coverage rate #: 2.209** (col 1), −0.068 (col 3), 5.494*** (col 4), 1.152 (col 5), 5.582*** (col 6), 0.756 (col 6)
    - Interaction Mandatory FF replacement rate x Coverage rate #: 5.497** — SE (2.715)
    - Mandatory replacement rate #: 1.543 (col 3), 2.170* (col 4) — SEs (1.206), (1.252)
    - Voluntary replacement rate #: often indistinguishable from zero
    - Mandatory private replacement rate #: 5.138*** (col 5), 2.951* (col 6) — SEs (1.672), (1.789)
    - Mandatory private replacement rate x Coverage rate #: 36.448*** — SE (11.801)
    - Observations: 1,451 (cols 1–2), 628 (cols 3–4), 619 (cols 5–6)
    - R-squared: 0.010, 0.012, 0.021, 0.030, 0.040, 0.048 respectively
    - Number of economies: 49 (cols 1–2), 36 (cols 3–6)
  - Interpretation:
    - Stronger relation between CA balances and mandatory fully funded replacement rates, especially with larger coverage.
    - Voluntary replacement rates weaker relation; mandatory private (often FF) stronger than mandatory public (often PAYG).
  - Machine learning:
    - XGBoost used as non-parametric check; yields qualitatively similar findings and higher explanatory power, with interpretability caveats.

- Product and labor market regulation toolbox — key findings:
  - Variables and results (Online Annex Box Table 1.5.2a; values preserved):
    - PMRs: LPS coefficient = 0.0049** (OECD column)
    - LMRs: EPL coefficient = −0.0048** (OECD column)
    - Effective retirement age, male = −0.0015 (not significant)
    - PMRs: SBP (WEF) coefficient = 0.0242**
    - LMRs: CLER (WEF) coefficient = 0.0508**
    - Observations: 374 (WEF), 533 (OECD)
    - R-squared: 0.026 (OECD), 0.053 (WEF)
    - Number of countries: 24 (OECD), 49 (WEF)
  - Interpretation:
    - Product market deregulation linked to lower CA balances.
    - Stricter labor market regulation lowers CA balances; greater labor–employer cooperation associated with higher CA balances.
    - Structural variables explain 2–5 percent of residual variation; useful but require country-specific judgment.

- Inflation bias toolbox — concept and role:
  - Concept: recording of investment income in nominal terms under BPM can misstate real returns when expected inflation differentials predict currency movements; this could distort CA balances (BPM6 and BPM7 acknowledge this in high-inflation cases).
  - Empirical assessment:
    - Inflation bias relevant for only a few countries (financial centers) historically.
    - Relative currency movements often driven by non-inflation factors; historical estimates volatile.
    - Multilateral consistency of corrections difficult.
  - Conclusion: findings do not support formal adjustors to normative EBA CA benchmarks; toolbox guides discussion when inflation bias may matter.

### Adjusted NFA methodology — motivation and construction
- Motivation:
  - Using actual NFA in EBA regression allows accumulated past excess CA imbalances to shift estimated norms (feedback loop); adjusted NFA aims to remove cumulated excess CA flows so past excesses do not influence future norms.
- Methodology (post-estimation iterative procedure; φ̂ denotes estimated NFA coefficient):
  - Step 1 — Baseline estimation:
    - Estimate standard EBA regression and recover CA norms ca_i,t^n = α̂ + λ̂ F_i,t + γ̂ P_i,t^* + φ̂ nfa_i,t−1.
  - Step 2 — Initialize adjusted NFA:
    - Set nfa_i,t0^b = nfa_i,t0.
    - Construct nfa_i,t0+1^b = nfa_i,t0^b / (1 + g_i,t0+1 + π_i,t0+1) + ca_i,t0+1^n + val_i,t0+1 (val = valuation term scaled by GDP).
  - Step 3 — Calculate adjusted CA norms:
    - ca_i,t^adj = ca_i,t^n − φ̂ nfa_i,t−1 + φ̂ nfa_i,t−1^b.
  - Step 4 — Iterate forward:
    - nfa_i,t+1^b = nfa_i,t^b / (1 + g_i,t+1 + π_i,t+1) + ca_i,t+1^adj + val_i,t+1.
    - Impose multilateral consistency: sum of adjusted NFAs equals zero across countries in each period.
  - Step 5 — Calculate new EBA CA gaps:
    - Define ca_i,t^cycle = ca_i,t − β̂ C_i,t.
    - New gap: ca_i,t^gap = ca_i,t^cycle − ca_i,t^adj.
    - Decomposition: ca_i,t^gap = γ̂ (P_i,t − P_i,t^*) + u_i,t + φ̂ (nfa_i,t−1 − nfa_i,t−1^b).
- Treatment of valuation changes:
  - Valuation changes added to both actual and adjusted NFA so NFA adjustment captures only cumulated excess CA flows; large and variable valuation swings are thereby prevented from forcing offsetting CA adjustments.
- Treatment of data revisions:
  - Recompute historical CA norms consistent with revised data while preserving original assessment: ca_i,t^norm,rev = ca_i,t^cyc,rev − ca_i,t^gap,published.
  - Revisions to nfa_i,t0 update starting points; NFA adjustment invariant to initial NFA level revisions.

### Implementation choices, reference case, and empirical magnitudes
- Required inputs:
  - (i) adjusted NFA in t0, (ii) sequence of adjusted CA norms ca_i,t^adj, (iii) sequence of valuation effects val_i,t, (iv) estimated parameter φ̂.
- Reference-case implementation:
  - Set t0 = 2012 (first EBA assessments of 2013).
  - For (ii) take sum of adjusted EBA CA norms plus “adjustors to the norm.”
  - For (iii) calculate valuation changes as the change in NFA not accounted for by flows.
  - For (iv) use φ̂ = 0.031 (from refined EBA CA regression).
- Empirical impacts:
  - Online Annex Figure 1.6.1 compares 2025 EBA CA gaps: refined specification (x-axis) vs. refined with NFA adjustments (y-axis); results:
    - At global level, larger negative CA gaps for countries with persistent past excess deficits and larger positive CA gaps for persistent surplus countries.
    - Country-level changes larger for economies with large debtor or creditor positions.
    - Average magnitude of EBA CA gap revisions (absolute change) from NFA adjustment: 0.71 percentage points relative to refined specification (or 0.51 percentage points GDP-weighted).
    - Data updates alone generate a similar 0.51 percentage points change relative to 2024 CA gap assessment (or 0.66 percentage points GDP-weighted).
- Mechanistic interpretation:
  - NFA adjustment equals a geometrically weighted sum of past CA gaps depreciated by nominal growth.
  - If past CA gaps have same sign as today's gap, NFA adjustment amplifies assessed excess imbalances; if no persistence, NFA adjustment uncorrelated with CA gaps.
  - Illustrative numeric example from source:
    - Constant 6 percent nominal growth (discount factor 1/1.06), half-life ≈ 12 years.
    - A country running a persistent 2 percent CA gap for 10 years accumulates nfa2022 − nfa2022^b = 0.02 × 1 − (1/1.06)10 1 − 1/1.06 = 0.02 × 7.8 = 0.156.
    - With φ̂ = 0.031, contribution to assessed CA gap ≈ 0.031 × 0.156 ≈ 0.48 percentage points.

### Memory assumptions for NFA adjustment and quantitative alternatives
- Reference choice and trade-offs:
  - Reference-case start t0 = 2012 chosen as balance between conceptual grounds, data vintage consistency, and accumulation uncertainty.
  - General regularity: extending further back increases resulting CA gaps.
- Alternative starting dates and impacts (preserve reported values):
  - Alternative 1 — three-year average anchor (2010–2012 average NFA):
    - Revises CA gaps by an average of 0.71 percentage points relative to refined specification.
    - Revises CA gaps by 0.53 percentage points GDP-weighted.
    - All ESR economies deviate less than 0.3 percent of GDP from reference case.
  - Alternative 2 — early anchor 2000 (25-year window):
    - Revises CA gaps by an average of 1.16 percentage points relative to refined specification.
    - Revises CA gaps by 1.27 percentage points GDP-weighted.
    - Only 11 economies have deviation less than 0.3 percent of GDP compared with reference case.
    - Shortcoming: requires strong assumptions about CA norms prior to 2012; 25-year window compounds estimation uncertainty.
- Rolling-window (fixed H) memory alternatives:
  - 5-year window:
    - Revises CA gaps by an average of 0.27 percentage points relative to refined specification.
    - Revises CA gaps by 0.22 percentage points GDP-weighted.
  - 10-year window:
    - Revises CA gaps by an average of 0.54 percentage points relative to refined specification.
    - Revises CA gaps by 0.40 percentage points GDP-weighted.
  - Comparing to reference case: around 42 percent of economies have deviation of less than 0.3 percent of GDP for both 5- and 10-year windows.
- Choice of historical CA_norm sequence:
  - Reference: EBA CA norms with "adjustors to the norm" (multilaterally consistent).
  - Alternative A — staff CA norms:
    - Revises CA gaps by average 0.51 percentage points relative to refined specification.
    - GDP-weighted: 0.38 percentage points.
    - 69 percent of economies deviate less than 0.3 percent of GDP from reference case.
  - Alternative B — uniform EBA specification:
    - Revises CA gaps by average 0.73 percentage points relative to refined baseline.
    - GDP-weighted: 0.66 percentage points.
    - 58 percent of economies deviate less than 0.3 percent of GDP from reference case.
- Mathematical expression preserved (equation (18) and related):
  - 푐푎푖,푡푔푎푝 = γ̂(푃푖,푡 − 푃푖,푡∗) + 푢푖,푡 + φ̂
  - 푛푓푎푖,푡푔푎푝 = γ̂(푃푖,푡 − 푃푖,푡∗) + 푢푖,푡 + φ̂ ∑푘=0
    푡−푡0−2
    푐푎푖,푡−푘−1
    (
    1+푔̅+π̅
    )
    푘

### Prudential considerations, policy advice, and alternative approaches
- Prudential concerns:
  - External sustainability concerns for large negative NFA positions should apply equally to adjusted NFAs.
  - NFA adjustment computed from accumulating CA norms may be lower than staff-judged sustainable NFA levels (e.g., relative to ARA metric); staffs can consider upward adjustments for large debtor economies.
  - Example threshold reference: European Commission MIP uses −35 percent as flag for potential risks for large debtor economies.
  - Staff judgment remains incorporated in setting desirable policies in EBA CA norms.
- Policy advice framing (Staff view):
  - Advice should continue to be anchored on the CA norm (now based on adjusted NFA), not on closing difference between adjusted and actual NFA.
  - Difference between adjusted and actual NFA is a correction term; adjusted CA norm is no longer influenced by past CA excesses.
  - Focus remains on flow variables responding to policy actions (fiscal adjustment, structural reforms).
- Discussion of alternative approaches and limitations:
  - Long-run NFA estimation (cointegration on fundamentals) did not yield robust results across broad sample; methodology constructs adjusted NFA by removing cumulated excess CA flows, not an optimal NFA*.
  - External Sustainability (ES) approach relevant for stabilization at benchmark NFA but does not remove feedback-loop motivating adjusted NFA.
  - NFA decomposition by asset class informative but would not remove normative inconsistency since lagged NFA would still enter norm.
  - "Policy-gap-only" norm sequences would create inconsistent definitions of “excess” within EBA.
  - Dropping NFA from regression would eliminate main channel capturing slow-moving steady-state fundamentals; Online Annex Box 1.6.1 reaffirms rationale for inclusion.

### Concluding assessment
- Problem identified: increasing contribution of past CA imbalances, via lagged NFA, to CA norm creates material normative inconsistency.
- Proposed solution: adjusted NFA methodology strips out past excesses, preserving EBA framework while removing feedback loop.
- Staff assessment:
  - Benefits of eliminating normative inconsistency outweigh implementation costs.
  - Resulting CA gap revisions on average comparable to other EBA methodology revisions and concentrated in persistent surplus and deficit economies.
  - Method does not derive normative NFA levels; policy advice will remain focused on CA norm (with adjusted NFA contribution).

*Source: ch1onlineannex - Section 2 (ch1onlineannex - Section 2. PDF).*

### Section 2.

### ch1onlineannex - Section 2

### 1. EBA CA Model Refinements

- The current EBA model estimates were previously based on data for the 1986–2019 period and have been updated and refined in this round.

### 1.1. Data Update and Extensions

- Data updates included:
  - Extending all series by four additional years to cover 1986–2023.
  - Adding coverage for certain variables in selected countries by incorporating historical data revisions.
  - Updating to the latest vintages of periodically revised variables—for example, demographic variables now reflect the 2024 revision of the UN World Population Prospects.
- Sample and timing:
  - The updated dataset covers a sample of 52 economies with annual data spanning 1986–2023, based on information available as of October 2024.
- Robustness checks performed:
  - Leave-one-year-out regressions to assess sensitivity to individual years (see Online Annex Table 1.1.2).
  - Rolling regressions starting in 2019, adding one year at a time, to evaluate the stability of the estimated coefficients (see Online Annex Table 1.1.3).
  - Overall finding from robustness checks: incorporating the COVID years has a limited impact on estimation results—the estimated coefficients remain broadly stable and robust.
- Impact of data updates on EBA CA gaps (relative to the 2024 EBA assessment):
  - For an average ESR country, the data update alone accounts for about 50 percent of the change in the absolute EBA current account (CA) gaps (0.27 percentage points out of 0.51).
  - When combining the data update with coefficients re-estimated using data through 2019, roughly 75 percent of the change is explained (0.34 compared with 0.51).
  - Extending the sample from 2019 to 2023 and re-estimating coefficients accounts for the remaining 25 percent (Online Annex Table 1.1.4).
- Magnitude of changes in the 2026 refinement compared with the 2022 refinement:
  - In the 2026 refinement, the data update and coefficient re-estimation result in an average absolute change in EBA gaps of about 0.51 (as a percent of GDP) for ESR countries and 0.57 for non-ESR EBA countries.
  - In the 2022 refinement, the data update and coefficient re-estimation led to average absolute changes of 0.67 for ESR countries and 1.03 for non-ESR EBA countries.
- Note on ESR country definition in this context:
  - ESR countries here refer to the 26 countries included in both the EBA CA regression and Chapter 2.

- Variables and their sources (as listed):
  - CURRENT ACCOUNT — World Economic Outlook
  - Current Account — World Economic Outlook
  - Output Gap — World Economic Outlook
  - Commodity Terms of Trade — World Economic Outlook and World Integrated Trade Solution(WITS)
  - Real Effective Exchange Rate — Information Notice System (INS)
  - Net Foreign Assets (NFA) position — EWN: Lane, Milesi Ferretti and World Economic Outlook
  - Output per worker, relative to top 3 economies — World Economic Outlook
  - Expected real GDP growth (5 years ahead) — World Economic Outlook
  - Demographic variables — UN World Population Prospects, 2024 Vintage
  - Institutional Quality — International Country Risk Guide (ICRG)
  - Exhaustible Resources of Oil and Natural Gas — World Economic Outlook, WITS and BP Statistical Review of World Energy
  - Fiscal Policy — World Economic Outlook
  - Health Spending — OECD, and WDI
  - Foreign Exchange Intervention (FXI) — World Economic Outlook, Data Template on International Reserves and Foreign Currency Liquidity
  - Capital Account Openness — IMF (Baba and others, 2026)
  - Credit Gap — BIS (Credit statistics) and World Bank (Global Financial Development Database)
- Specific historical data revisions incorporated (examples):
  - Health spending variable for Australia, Austria, Canada, Denmark, Finland, Germany, the Netherlands, New Zealand, Norway, Portugal, Spain, Korea, and Sweden for the year 1986.
  - NFA variable for South Africa for the years 1987–1993.
  - REER variable for Egypt, Hungary, and Poland for 1992.

### 1.2. Improved Commodity Terms-of-Trade Gap

- Improvements made to the construction of the commodity terms-of-trade (ToT) gap to better capture extreme price variations (for example, the natural gas price spike in 2022):
  - Replaced log-approximation of the gaps with the exact calculation formula because the log-approximation is not suited when commodity price movements are abnormally large.
  - Calculation of commodity trade weights was made more consistent between exports and imports by using the same denominator.
- Expected effect of the refinements:
  - While resulting changes are small in "normal times,” the new specification is more suitable when commodity price changes are large.
- Documentation pointers within the annex:
  - Online Annex Section 1.2.1 describes the 2022 EBA methodology for calculating the commodity terms-of-trade gap.
  - Online Annex Sections 1.2.2 and 1.2.3 lay out the refined calculations of price gaps and commodity trade weights.

*Source: ch1onlineannex - Section 2 (ch1onlineannex - Section 2. PDF).*

### Section 1.2.4 discusses alternative approaches to calculating commodity trade weights.

### ch1onlineannex - Section 1.2.4: Alternative approaches to calculating commodity trade weights

### Issues with nominal commodity trade weights (2022 EBA methodology)
- Commodity trade weights in the 2022 EBA vintage are derived from UN Comtrade nominal trade values (shares of total goods exports or imports for 42 commodities across 52 EBA countries).
- Two main problems identified:
  - Double-counting of commodity price fluctuations:
    - Price movements enter both the nominal commodity weights and the commodity price gaps, amplifying fluctuations in the computed commodity ToT variable (with potential non-linear interactions).
    - Mathematical representation shown: commoTOTvar_i,t = Σ((X_k,i,t_nominal − M_k,i,t_nominal) / GDP_i,t) · gap_k,t = Σ((X_k,i,t_volume − M_k,i,t_volume) / GDP_i,t) · (P_k,t / P_k,t0) · (P_k,t / P_k,t_T − 1).
  - Difficulty extrapolating nominal weights for the assessment year:
    - Missing current-year nominal weights require renormalized price-change-based estimations, which introduce uncertainty (e.g., which price series to use).

### Proposed volume-weights approach (attempted refinement)
- Objective: construct commodity trade weights in volume terms to avoid double-counting and improve extrapolation properties.
- Steps implemented:
  - Deflate nominal commodity trade numerators (X_k,i,t_comtrade and M_k,i,t_comtrade in US dollars) by the global commodity price P_k,t (US dollars) to obtain numerators in volume (constant USD).
  - Deflate GDP (denominator) using the US CPI index because country‑by‑country GDP deflators in US dollars were unavailable.
  - Variants implemented and reported:
    - Volume weights (as described above).
    - Constant volumes (constant 2015).
    - Smoothed volumes (average; 11-year moving average).
- Adjusted openness definition to reflect new denominators: TradeOpenness_i,t = (X_i,t + M_i,t) / GDP_i,t (instead of (X_i,t + M_i,t) / (2*GDP_i,t)) to be consistent with using X+M as denominator in commodity weight construction.

### Empirical results and decision
- Results are reported in Online Annex Table 1.2.1 (model variants columns 1–8). Key comparative statistics (preserving reported values exactly):
  - Preferred specification (column 3: exact commodity price gaps; nominal weights using common X+M denominator) records:
    - R-squared IV = 0.489
    - R-squared fit = 0.523
    - Root MSE = 0.032
    - Commodity ToT x trade openness coefficient = 0.392*** (standard error (0.042))
    - Output gap coefficient = -0.254*** (standard error (0.030))
  - Volume-weight specifications (columns 4–8) show generally worse model fit compared with the preferred specification:
    - R-squared IV values for columns 4–8: 0.469, 0.468, 0.479, 0.481, 0.472.
    - R-squared fit values for columns 4–8: 0.500, 0.500, 0.512, 0.512, 0.502.
    - Root MSE for these columns: 0.032, 0.032, 0.032, 0.032, 0.032.
    - Commodity ToT x trade openness coefficients in columns 4–8: 0.209*** (0.029), 0.269*** (0.031), 0.260*** (0.031), 0.247*** (0.031), 0.270*** (0.029).
    - Output gap coefficients in columns 4–8: -0.260*** (0.031), -0.262*** (0.030), -0.261*** (0.030), -0.254*** (0.030), -0.259*** (0.030).
- Conclusion reached in the Annex:
  - In all tested specifications using volume weights (volume; constant volumes; smoothed volumes) the fit of the EBA CA regression worsened relative to the preferred specification (column 3: weights using the common X+M denominator; and exact formula of commodity price gaps).
  - Therefore, the attempt to switch to volume weights was dropped.

### Additional relevant methodological notes (context from adjacent sections)
- Revised commodity price gap calculation:
  - The price gap is now computed exactly rather than via a log approximation: gap_k,t = P_k,t / P_k,t_T − 1 = exp(lnP_k,t − lnP_k,t_T) − 1 = exp(lngap_k,t) − 1.
  - In "normal times" the log-approximation is close: 81.7% of commodity price gaps over 1986-2024 were in the [-40%; +40%] range.
  - The exact formula prohibits commodity price gaps smaller than -100% and increases occurrence of very large positive gaps (empirical evidence: over 1986-2024, 1.2% of price gaps fell within the 70-80% range using the exact calculation, compared to 0.2% with the log-linear approximation).
- Revised trade-weight denominator:
  - Re-formulation uses X_i,t + M_i,t as common denominator for commodity export and import weights:
    - ω_k,i,t_comtrade,X = X_k,i,t_comtrade / (X_i,t_comtrade + M_i,t_comtrade)
    - ω_k,i,t_comtrade,M = M_k,i,t_comtrade / (X_i,t_comtrade + M_i,t_comtrade)
  - This leads to an equivalent representation of commodity ToT variable:
    - commoTOTvar_i,t = (X_i,t + M_i,t) / GDP_i,t · Σ( X_k,i,t_comtrade / (X_i,t_comtrade + M_i,t_comtrade) − M_k,i,t_comtrade / (X_i,t_comtrade + M_i,t_comtrade) ) · gap_k,t
    - which simplifies to commoTOTvar_i,t = Σ( X_k,i,t_comtrade / GDP_i,t − M_k,i,t_comtrade / GDP_i,t ) · gap_k,t.

*Italic source: ch1onlineannex - Section 1.2.4, Online Annex Tables and Figures (External Sector Report Chapter 1), IMF | July 2026*

### Annex Figure 1.4.3). By contrast, the demographic contribution to current account norms for emerging

### ch1onlineannex - Annex Figure 1.4.3). By contrast, the demographic contribution to current account norms for emerging

### Demographics and current account norms
- Population aging in emerging markets is well under way and, by some metrics, proceeding faster than in advanced economies.
- Convergence in key demographic variables across country groups has contributed to a narrowing of demographic contributions to current account (CA) norms and is expected to continue doing so.
- The demographic norm is adjusted to be multilaterally consistent across countries and is reported as a simple average for advanced and emerging economies.

### Output per worker and capital flows
- The estimated coefficient on output per worker increased from 0.034 in the 2022 model to 0.050 in the 2022 model with updated data, and is 0.044 in the refined model.
- Interpretation: richer economies with higher capital–labor ratios tend to export capital to poorer economies by running higher-than-otherwise current account balances; the reverse is expected for poorer countries.
- The higher coefficient when extending the sample to 2023 reflects increased capital outflows from advanced economies during 2020–2023 relative to 1986–2019 (see Online Annex Figure 1.4.4).

### Health spending (desirable policies) and precautionary saving
- The coefficient on the health spending variable becomes more negative (in absolute value), from −0.298 in the 2022 model to −0.408 in the refined model.
- Re-estimation using updated data raises the coefficient on health spending (in absolute value) to −0.342 (Online Annex Table 1.1.3 Column 1).
- Extending the sample period from 1986–2019 to 1986–2023 further increases the coefficient (in absolute value) from −0.342 to −0.364 (Online Annex Table 1.1.3 Column 5).
- Interpretation: health spending proxies for the strength of the social safety net and, through precautionary saving motives, influences aggregate saving behavior. The coefficient increase likely reflects faster-than-expected population aging and reinforcement of precautionary saving by recent global shocks (COVID-19 pandemic and the war in Ukraine).

### Net foreign assets (NFA)
- The estimated coefficient on NFA declines modestly from 0.036 in the 2022 model to 0.031 in the refined model.
- Even with a modest coefficient change, implied contributions from NFA can be quantitatively large for economies with sizable net creditor or debtor positions.

### Updated complementary toolboxes — Overview
- Toolboxes updated as part of 2026 EBA refinements include: pensions, product and labor market regulations, and inflation bias.
- Data limitations preclude direct inclusion of many structural indicators in the core EBA CA model; toolboxes inform interpretation of CA residuals and policy advice.

### Pension toolbox — data, methods, and key estimation results
- Coverage:
  - KW dataset: mandatory pension indicators for 49 economies over 1986–2016 (mandatory FF and PAYG replacement rates based on Bloom and others, 2007).
  - OECD Pensions at a Glance: mandatory and voluntary replacement rates for 51 OECD and G20 economies spanning 2005–2024; analysis uses OECD staff estimates for full-career average income-earning workers.
  - Coverage proxy: 1 minus the self-employment share (ILO annual data).
- Caveats:
  - Pension systems are complex, vary widely, and comparable cross-country data remain limited and largely confined to advanced economies.
  - Direct application of pension toolbox estimates as formal adjustors in the CA model is not warranted due to normative judgments and lack of forward-looking, consistent panel measures.
- Estimation:
  - Relation estimated between pension indicators and residuals from the 2026 refined EBA CA model for 1986–2023; variables enter demeaned (deviations from GDP-weighted sample average).
  - R-squared: pension variables explain between 1.0 and 5.0 percent of variation in EBA CA model residuals (baseline EBA CA equation R-squared ≈ 52 percent).
- Key coefficients and findings (from Online Annex Box Table 1.5.1a):
  - PAYG replacement rate #: coefficients: 0.255 (column 1), 0.336 (column 2) — standard errors (0.706), (0.809).
  - Mandatory FF replacement rate #: 2.262*** (column 1), 2.836*** (column 2) — standard errors (0.876), (0.996).
  - Coverage rate #: 2.209** (column 1), −0.068 (column 3), 5.494*** (column 4), 1.152 (column 5), 5.582*** (column 6), 0.756 (column 6) — standard errors shown in table.
  - Interaction Mandatory FF replacement rate x Coverage rate #: 5.497** — standard error (2.715).
  - Mandatory replacement rate #: 1.543 (column 3), 2.170* (column 4) — standard errors (1.206), (1.252).
  - Voluntary replacement rate #: coefficients often statistically indistinguishable from zero in presented columns.
  - Mandatory private replacement rate #: 5.138*** (column 5), 2.951* (column 6) — standard errors (1.672), (1.789).
  - Mandatory private replacement rate x Coverage rate #: 36.448*** — standard error (11.801).
  - Observations: 1,451 (columns 1–2), 628 (columns 3–4), 619 (columns 5–6).
  - R-squared: 0.010, 0.012, 0.021, 0.030, 0.040, 0.048 respectively.
  - Number of economies: 49 (columns 1–2), 36 (columns 3–6).
- Interpretation:
  - Stronger relation between CA balances and mandatory fully funded (FF) replacement rates, especially for economies with larger coverage rates.
  - Voluntary replacement rates show weaker relations with CA balances.
  - Mandatory private replacement rates (often FF) have a stronger relation with the CA than mandatory public replacement rates (often PAYG).
- Machine learning complement:
  - A supervised gradient boosting (XGBoost) algorithm is used to estimate relationships non-parametrically, accommodating unbalanced panels, incomplete data, high-dimensional variables, and non-linearities.
  - Machine learning yields qualitatively similar findings and typically higher explanatory power than OLS, but with interpretability and economic-theory consistency caveats.

### Product and labor market regulation toolbox — methods and findings
- Objective: relate EBA CA residuals to regulatory stringency indicators for economies with available OECD and WEF data.
- Variables considered:
  - Product market regulation: regulatory burdens in licensing and permits system (LPS) and starting business procedures (SBP, WEF).
  - Labor market regulation: employment protection legislation (EPL), effective retirement age for males, and degree of cooperation in labor–employer relations (CLER, WEF).
- Estimation equation: μ̂jt = α + S jt γ + ε jt , where μ̂ denotes EBA CA residual for country j in year t, and S jt is vector of regulatory deviations from GDP-weighted world average.
- Key empirical findings (Online Annex Box Table 1.5.2a):
  - PMRs: LPS coefficient = 0.0049** (OECD column).
  - LMRs: EPL coefficient = −0.0048** (OECD column).
  - Effective retirement age, male = −0.0015 (OECD column, not significant).
  - PMRs: SBP (WEF) coefficient = 0.0242**.
  - LMRs: CLER (WEF) coefficient = 0.0508**.
  - Observations: 374 (WEF), 533 (OECD) depending on specification.
  - R-squared: 0.026 (OECD), 0.053 (WEF).
  - Number of countries: 24 (OECD), 49 (WEF).
- Interpretation:
  - Deregulation in product markets (lower entry barriers) is associated with lower CA balances.
  - Stricter labor market regulations lower CA balances; greater labor–employer cooperation is associated with higher CA balances.
  - Structural variables explain between 2 and 5 percent of variation in EBA CA residuals—useful for interpretation but warrant cautious, country-specific application.
- Use in external assessments:
  - Results should be interpreted cautiously and complemented with country-specific judgment.
  - Not currently warranted to translate results into formal adjustors to normative EBA CA benchmarks; useful for interpreting residuals and informing granular policy recommendations.

### Inflation bias toolbox — concept and application
- Definition:
  - Inflation bias arises because investment income on debt securities is recorded in balance of payments nominal terms, not accounting for changes in the value of the foreign debt principal due to exchange rate movements linked to inflation differentials.
  - If lenders anticipate foreign currency depreciation, they demand higher nominal returns; anticipated appreciation leads to lower nominal returns. Under BPM recording, these nominal return differentials can systematically misstate real returns and thus CA balances.
- Theoretical link:
  - Monetary theory ties relative currency movements closely to inflation differentials; high-inflation currencies are predicted to depreciate relative to low-inflation currencies.
- Conditions for distortion:
  - For inflation bias to distort CA balances, two conditions must be satisfied (text indicates continuation in source).
- Empirical assessment and toolbox role:
  - Historical analysis in the EBA sample finds inflation bias could be relevant for only a few countries (financial centers).
  - Relative currency movements are often dominated by factors other than inflation differentials; where inflation bias could be relevant, historical estimates are volatile.
  - Ensuring multilateral consistency of inflation bias corrections is challenging.
  - Findings do not support formal adjustors to normative EBA CA benchmarks; the toolbox provides guidance for discussing inflation bias when historical evidence suggests it may matter.
- Reference to BPM guidance:
  - BPM acknowledges the possibility of inflation bias in the case of high inflation (see Chapter 11 of BPM6 and Chapter 12 of BPM7).

*Source: IMF staff calculations and accompanying text in the provided Online Annex content.*

### 1. Economies’ net foreign debt positions need to differ significantly in their exposure to higher-

### ch1onlineannex - 1. Economies’ net foreign debt positions need to differ significantly in their exposure to higher-expected-inflation currencies

### Exposure to higher-expected-inflation currencies and valuation effects
- Condition 1 (definition): The exposure of an economy j’s foreign debt position to different currencies’ expected inflation rates in year t is:
  - InfExp_jt = ∑_i π_it NFA_ij t^D_i
  - where:
    - π_it is expected inflation associated with currency i, proxied by the 5-year ahead Consensus Forecast inflation.
    - NFA_ij t^D is economy j’s net foreign debt position in currency i (expressed in percent of economy-j GDP).
- Condition 2 (expected empirical relationship): 
  - Economies that are relatively long in debt denominated in higher-expected-inflation currencies should see a systematic erosion of their net foreign debt by adverse valuation effects from exchange rates.
  - Economies that are relatively short in debt denominated in higher-expected-inflation currencies should see systematic exchange-rate valuation gains.
  - Formally, a systematically positive inflation exposure (InfExp_jt > 0) should be associated with systematically negative valuation effects eroding an economy’s foreign debt position (ValXR_jt^D < 0); while a systematically negative inflation exposure (InfExp_jt < 0) should be associated with systematically positive valuation effects (ValXR_jt^D > 0).

- Notes and caveats on inflation bias and data:
  - The BPM acknowledges the possibility of an inflation bias in the case of high inflation. Historical data in the EBA sample indicate the inflation bias could be relevant for only a few countries (i.e., financial centers).
  - Relative currency movements reflect factors other than inflation differentials, and such factors may outweigh relatively muted inflation differentials for many countries in the EBA sample.
  - Historical estimates of inflation-bias-related factors exhibit high volatility, making their role in annual external sector assessments highly uncertain.
  - Ensuring multilateral consistency of inflation bias corrections is a challenge.

### Motivation for an excess-adjusted NFA (background)
- EBA regression (equation (10)) specification:
  - ca_i,t = α + β C_i,t + λ F_i,t + γ P_i,t + φ nfa_i,t−1 + u_i,t
- Rationale for including NFA: NFA captures slow-moving steady-state relationship between the current account (CA) and NFA. In steady state:
  - ca_i,t^ss = (g_i,t^ss + π_i,t^ss) nfa_i,t^ss
  - where g is real GDP growth rate and π is inflation.
- Empirical sign: The estimated coefficient on lagged NFA is positive; debtor countries are statistically associated with CA deficits, creditors with surpluses.
- Normative inconsistency concern:
  - Actual NFA reflects both steady-state fundamentals and accumulated past excess imbalances (deviations from norms that have persisted).
  - Using actual NFA in the regression allows past excesses to shift the estimated norm, creating a feedback loop: excess imbalances accumulate into NFA positions that subsequently justify larger imbalances by shifting the CA norm.
  - The refinement constructs an adjusted NFA from accumulated CA norms to remove this feedback.

### Methodology to construct adjusted NFA (steps)
- Overall objective: Remove cumulated excess current account balances from observed NFA so that past excesses do not influence future norms. The procedure is iterative and is a post-estimation adjustment (no re-estimation of regression coefficients).

- Step 1: Baseline estimation
  - Estimate standard EBA regression and recover CA norms ca_i,t^n using desirable policies P_i,t^* and actual structural features F_i,t:
    - ca_i,t^n = α̂ + λ̂ F_i,t + γ̂ P_i,t^* + φ̂ nfa_i,t−1
- Step 2: Initialize adjusted NFA
  - Set initial adjusted NFA equal to actual NFA at baseline year: nfa_i,t0^b = nfa_i,t0.
  - Construct next-year adjusted NFA for t0+1:
    - nfa_i,t0+1^b = nfa_i,t0^b / (1 + g_i,t0+1 + π_i,t0+1) + ca_i,t0+1^n + val_i,t0+1
    - where g is real GDP growth, π is inflation, and val is the valuation term for the period scaled by GDP.
  - Valuation changes are incorporated into adjusted NFA to exclude valuation swings from impacting the gap between actual and adjusted NFA.
- Step 3: Calculate adjusted CA norms
  - Replace the contribution of nfa_i,t−1 with adjusted nfa_i,t−1^b:
    - ca_i,t^adj = ca_i,t^n − φ̂ nfa_i,t−1 + φ̂ nfa_i,t−1^b
- Step 4: Iterate forward
  - Construct subsequent year adjusted NFA:
    - nfa_i,t+1^b = nfa_i,t^b / (1 + g_i,t+1 + π_i,t+1) + ca_i,t+1^adj + val_i,t+1
  - Iterate forward using adjusted CA norms. Multilateral consistency is imposed such that the sum of adjusted NFAs equals zero across countries in each period.
- Step 5: Calculate new EBA CA gaps
  - Define cyclically-adjusted CA: ca_i,t^cycle = ca_i,t − β̂ C_i,t
  - New EBA gap: ca_i,t^gap = ca_i,t^cycle − ca_i,t^adj
  - Using the equations, the CA gap decomposes into:
    - ca_i,t^gap = γ̂ (P_i,t − P_i,t^*) [policy gap] + u_i,t [residual] + φ̂ (nfa_i,t−1 − nfa_i,t−1^b) [NFA adjustment]
  - Implication: The NFA refinement alters the EBA CA gap by adding contributions from past CA gaps via the “NFA adjustment” term, bringing consistency to the dynamic relationship between flow (CA) and stock (NFA).

- Treatment of valuation changes
  - Valuation changes are added to benchmark NFAs for three main reasons:
    - Large year-to-year valuation swings would otherwise translate directly into NFA adjustments requiring offsetting CA adjustments that may not be appropriate.
    - Valuation terms are highly variable but tend to be slowly mean-reverting.
    - When valuation effects reflect permanent differences across countries (e.g., exorbitant privilege for reserve currency issuers), they should be incorporated into adjusted NFAs.
  - Valuation changes are applied additively to both actual and adjusted NFA so the NFA adjustment captures only cumulated excess CA flows.

- Treatment of data revisions
  - To maintain internal consistency, historical CA norms are recomputed to be consistent with revised data while preserving the original assessment.
  - Revised CA norm: ca_i,t^norm,rev = ca_i,t^cyc,rev − ca_i,t^gap,published
  - On the stock side, revisions to nfa_i,t0 update the starting point for both actual and adjusted NFA; the NFA adjustment term is invariant to revisions in the initial NFA level.

### Implementation choices, reference case, and empirical results
- Implementation requires data on:
  - (i) the adjusted NFA in t0,
  - (ii) sequence of adjusted CA norms ca_i,t^adj,
  - (iii) sequence of valuation effects val_i,t, and
  - (iv) the estimated parameter for NFA in EBA, φ̂.
- Mechanical elements:
  - Valuation changes enter both actual and adjusted NFA and cancel out of the NFA adjustment.
  - The estimated parameter for NFA is fixed and taken directly from the EBA CA regression.
- Methodological choices with material trade-offs:
  - Sequence of norms and the initial start date.
- Reference-case implementation choices:
  - Set t0 = 2012 (corresponding to first EBA assessments of 2013).
  - For (ii) take the sum of adjusted EBA CA norms plus “adjusters to the norm.”
  - For (iii) calculate valuation changes as the change in NFA not accounted for by flows.
  - For (iv) use the coefficient φ̂ = 0.031 (coefficient based on the refined EBA CA regression).
- Empirical comparisons and magnitudes:
  - Online Annex Figure 1.6.1 compares EBA CA gaps for 2025 across two specifications: (i) the refined EBA specification with updated demographic block (x-axis), and (ii) the refined methodology with NFA adjustments using the implementation choices above (y-axis). (Outlier excluded.)
  - At the global level, the methodology produces larger negative CA gaps in countries with persistent past excess CA deficits, offset by larger positive CA gaps in countries with persistent past excess CA surpluses.
  - Country-level changes are larger for countries with large debtor or creditor positions.
  - The average magnitude of EBA CA gap revisions, measured as absolute change, from incorporating the NFA adjustment is 0.71 percentage points relative to CA gaps generated by the refined specification (or 0.51 percentage points GDP-weighted).
  - By comparison, data updates alone generate a similar 0.51 percentage points change relative to the 2024 CA gap assessment (or 0.66 percentage points GDP-weighted).
- Interpretation of adjusted NFA and mechanistic insight:
  - The adjusted NFA corrects assessed excess imbalances so that CA gaps are not unduly affected by past CA excesses.
  - The NFA adjustment can be expressed as a geometrically weighted sum of past CA gaps, depreciated by nominal growth.
  - If past CA gaps have the same sign as today's gap, NFA adjustment will increase assessed excess imbalances; if no persistence in CA gaps, NFA adjustments would be uncorrelated with CA gaps.
  - Illustrative mechanism: a creditor economy running a CA surplus above its norm accumulates actual NFA faster than adjusted NFA, generating a positive NFA adjustment that amplifies the assessed CA gap; symmetric logic for debtor economies.

*Source: External Sector Report Chapter 1, Online Annex (ch1onlineannex) — IMF | July 2026*

### 2012.  Memory assumptions govern the window over which past adjusted current accounts are accumulated for the NFA adjust

### ch1onlineannex - 2012. Memory assumptions govern the window over which past adjusted current accounts are accumulated for the NFA adjust

### Overview of the NFA-adjustment memory choice
- The choice of initial date t₀ and the length of the accumulation window involves trade-offs among: going as far back as possible on conceptual grounds, data vintage consistency, and accumulation uncertainty.
- Reference case: accumulation begins in 2012 (corresponding to the first EBA assessment year in 2013), chosen as a balance between these trade-offs.
- General empirical regularity: the further back in time one extends the NFA adjustment method, the larger the resulting CA gaps tend to be.

### Alternative starting dates and their quantitative effects
- Reference accumulation start: 2012.
- Alternative 1 — three-year average anchor (2010–2012 average NFA instead of single 2012 value):
  - Revises CA gaps by an average of 0.71 percentage points relative to the refined specification.
  - Revises CA gaps by 0.53 percentage points GDP-weighted.
  - Comparing EBA gaps relative to the reference case, all ESR economies have a deviation of less than 0.3 percent of GDP.
- Alternative 2 — early anchor year set at 2000 (extending window to 25 years capturing pre-2009 imbalances):
  - Revises CA gaps by an average of 1.16 percentage points relative to the refined specification.
  - Revises CA gaps by 1.27 percentage points GDP-weighted.
  - Comparing EBA gaps relative to the reference case, only 11 economies have a deviation of less than 0.3 percent of GDP.
  - Important shortcoming: requires strong assumptions about CA norms prior to 2012; 25-year window can compound estimation uncertainty.

- Mathematical expression from the source (preserved):
  - 푐푎푖,푡푔푎푝 = γ̂(푃푖,푡 − 푃푖,푡∗) + 푢푖,푡 + φ̂
  - 푛푓푎푖,푡푔푎푝 = γ̂(푃푖,푡 − 푃푖,푡∗) + 푢푖,푡 + φ̂ ∑푘=0
    푡−푡0−2
    푐푎푖,푡−푘−1
    (
    1+푔̅+π̅
    )
    푘
    (18)

### Memory length, half-life, and illustrative accumulation effects
- Example parameters:
  - Constant 6 percent nominal growth and discount factor γ = 1/(1+푔̅+휋̅) = 1/1.06.
  - Half-life of the process: approximately 12 years (ln(2)/ln(1.06) ≈ 11.9).
- Illustration of accumulated effect:
  - A country running a persistent 2 percent CA gap for a decade would accumulate an NFA adjustment contributing approximately 0.4 percentage points to its assessed CA gap.
  - Detailed numeric illustration from the source footnote:
    - If a country runs a 2-percentage point CA gap each year from 2013 to 2022 (10 years), the accumulated NFA adjustment at the end of 2022 is:
      - 푛푓푎2022 − 푛푓푎2022푏 = 0.02 ∑δ푘 9 푘=0 = 0.02 ⋅ 1 − (1/1.06)10 1 − 1/1.06 = 0.02 × 7.8 = 0.156.
      - With 휙̂ = 0.031 (the coefficient with updated data), this NFA adjustment contributes 0.031 × 0.156 ≈ 0.48 percentage points to the assessed CA gap.

### Rolling-window (fixed H) memory alternatives and quantitative impacts
- Rationale: resetting the start year every year (e.g., rolling H-year window) prevents very distant historical gaps from indefinitely affecting current assessments while maintaining the adjustment discipline.
- No formal optimal memory length; trade-off between longer windows (conceptual appeal) and limiting influence of distant past.
- Quantitative results for rolling windows:
  - 5-year window:
    - Revises CA gaps by an average of 0.27 percentage points relative to the refined specification.
    - Revises CA gaps by 0.22 percentage points GDP-weighted.
  - 10-year window:
    - Revises CA gaps by an average of 0.54 percentage points relative to the refined specification.
    - Revises CA gaps by 0.40 percentage points GDP-weighted.
  - Comparing EBA gaps relative to the reference case, around 42 percent of the economies have a deviation of less than 0.3 percent of GDP for both the 5-year and 10-year memory windows.

### Choice of historical CA_norm (풄풂풊,풕풂풅풋) sequence: trade-offs and impacts
- Reference case: EBA CA norms with "adjustors to the norm" (some economies have adjustors for IIP considerations, e.g., Spain, India, Brazil, Türkiye). These norms are multilaterally consistent across the sample and internally consistent with the rest of the EBA framework.
- Alternative A — staff CA norms (EBA CA norms with adjustors based on staff judgment):
  - Pros: incorporate full set of country-team adjustments and align with official external sector assessments.
  - Cons: only sporadically available for non-ESR countries, lack multilateral consistency across the broader sample, rely on dispersed country-team inputs that are difficult to replicate historically.
  - Quantitative effect: revises CA gaps by an average of 0.51 percentage points relative to the refined specification.
  - Quantitative effect GDP-weighted: 0.38 percentage points.
  - Comparing EBA gaps relative to the reference case: 69 percent of economies have a deviation of less than 0.3 percent of GDP.
- Alternative B — uniform EBA specification (single fixed regression applied mechanically across full sample and horizon):
  - Pros: alleviates concerns that norms shift year-on-year due to data changes or changes in the baseline EBA specification; no need to adjust any norm for historical data revisions.
  - Cons: definition changes in some policy variables across EBA methodological vintages (e.g., the credit gap) require additional assumptions for consistent series; resulting CA gaps may deviate from official EBA gaps in a given year, posing communication challenges.
  - Quantitative effect: revises CA gaps by an average of 0.73 percentage points relative to the refined baseline.
  - Quantitative effect GDP-weighted: 0.66 percentage points.
  - Comparing EBA gaps relative to the reference case: 58 percent of economies have a deviation of less than 0.3 percent of GDP.

*Source: ch1onlineannex - 2012. Memory assumptions govern the window over which past adjusted current accounts are accumulated for the NFA adjust (PDF chapter).*

### 0.3 percent of GDP (Online Annex Figure 1.6.4).

### ch1onlineannex - 0.3 percent of GDP (Online Annex Figure 1.6.4)

### Prudential considerations
- External sustainability concerns for large negative NFA positions, that have been an integral part of past EBA assessments, should equally apply to adjusted NFAs.
- There could be concern that the NFA adjustment computed based on the accumulation of CA norms may be lower than what Staff judge to be a sustainable level for the NFA, for instance, relative to the ARA metric.
- While part of these considerations should already be taken care of in EBA CA norm, it could be possible to adjust the NFA adjustments upwards to above a certain threshold for large debtor economies (see, for example, Catao and Milesi-Ferretti, 2014; Cubeddu and others, 2023).
- For instance, the European Commission’s Macroeconomic Imbalances Procedure (MIP) defines a threshold of -35 percent to flag potential risks for large debtor economies (European Commission, 2019).
- It should be noted that Staff judgment is incorporated in the setting of desirable policies in EBA CA norms.

### Online Annex Figure 1.6.4 (note)
- Title: Deviations in 2025 EBA CA Gaps under Alternative CA Norms for NFA Adjustments
- Note: Distribution of EBA CA gaps in 2025, percent of GDP, constructed as deviations from the reference case (defined as alternative CA gap – reference case CA gap).
- Definitions:
  - “Staff norms" replaces EBA norms with staff-assessed norms when accumulating the adjusted NFA.
  - "Same model" uses the EBA CA norm from a uniform specification.
- Additional details: Dashed lines on right hand side chart are means. ESR sample. CDF refers to the cumulative density function.

### Discussion of Policy Advice (1.6.5)
- The introduction of NFA adjustments can raise questions about how policy advice should be framed once the NFA refinement is implemented.
- Staff’s view:
  - Policy advice should continue to be anchored on the CA norm, now based on the adjusted NFA, rather than targeting the difference between the adjusted and the actual NFA.
  - The difference between adjusted and actual NFA simply measures a correction term for the original inconsistency between NFA and CA gaps.
  - Importantly, the resulting adjusted CA norm is no longer influenced by past CA excesses.
  - This approach maintains continuity with existing practice and focuses advice on a flow variable that responds more directly to policy actions such as fiscal adjustment or structural reforms.
- Footnote: The CA Norm is a key metric in policy discussions. Medium-term forecasts of the CA tend to converge to the norm.

### Discussion of Alternative Approaches (1.6.6)
- Long-run NFA estimation (or NFA norm):
  - Alternative: derive an optimal or long-run NFA level via cointegration techniques regressing the NFA on fundamentals (output per capita, public debt, demographic variables).
  - Empirical outcome: these regressions did not yield robust results across specifications in the broad sample.
  - Clarification: the method in this note does not derive NFA norms or an optimal NFA*; it constructs adjusted NFA by removing cumulated excess current account balances from observed NFA.
- External Sustainability approach:
  - EBA includes an external sustainability (ES) approach that determines the CA-to-GDP ratio that would stabilize the NFA-to-GDP position over the medium term at a benchmark or desired level.
  - Relevance: most relevant when NFA positions are considered excessively large and further widening would put external sustainability at risk.
  - Limitation: ES does not address the feedback-loop concern motivating the adjusted NFA; construction of NFA adjustments is not about assessing the level of the NFA but about removing the feedback loop.
  - Mechanism: The resulting NFA adjustments to the CA norm—the difference between actual and adjusted NFA multiplied by the estimated coefficient—do not contribute to CA norms, breaking the feedback loop.
- NFA decomposition approaches:
  - Proposal: modify the EBA CA regression to disaggregate the NFA regressor by asset class (reserves vs. rest of NFA, net debt vs. net equity, foreign-currency vs. domestic-currency positions).
  - Limitation: informative about composition but do not address the normative inconsistency because lagged NFA would still enter the norm and past excess CA imbalances would continue to feed into subsequent CA norms.
- “Policy-gap-only” norm sequences:
  - Proposal: restrict the norm sequence to the identified policy-gap component of the CA gap, excluding the residual.
  - Limitation: would introduce a second and inconsistent definition of “excess“ within the same EBA exercise; interpretation of residuals in EBA presumes residuals reflect mainly country-specific distortions not explicitly captured.
- Dropping the NFA:
  - Direct response to normative inconsistency: drop lagged NFA from the EBA regression.
  - Cost: would eliminate main channel for capturing slow-moving steady-state fundamentals (demographics, structural asset demand, other unobservables) whose cumulative effects are reflected in the NFA position.
  - Note: there are strong theoretical reasons to include NFA as discussed in Online Annex Box 1.6.1.

### Concluding Remarks (1.6.7)
- Issue: the increasing contribution of past CA imbalances, through the lagged NFA, in determining the CA norm has become a material concern for the EBA exercise.
- Consequence if unaddressed: subsequent CA norms will increasingly embed past excesses.
- Proposed solution: the adjusted NFA methodology strips out past excesses from contributing to the CA norm while leaving the broader EBA framework unchanged.
- Staff assessment:
  - The benefits of eliminating this normative inconsistency outweigh the implementation costs.
  - The resulting revisions to CA gaps are on average comparable to those stemming from other EBA methodology revisions and concentrated in persistent surplus and deficit economies.
  - Important: the adjusted NFA methodology does not derive a normative NFA level, and staff policy advice will not focus on closing the difference between actual and adjusted NFA.
  - Focus of external sector assessments will remain on the CA norm, which now includes an adjusted NFA contribution rather than a contribution from observed NFA.

### Online Annex Box 1.6.1 — Motivation for Including the NFA in the EBA Regression (summary)
- Purpose: outline rationale for including NFA in the EBA framework and show there is solid ground for its inclusion with a positive coefficient because it captures a slow-moving steady-state relationship.
- Key steady-state relationship (equation numbers preserved from source):
  - From law of motion of the NFA ratio, stabilizing the NFA-to-GDP ratio requires:
    - 푐푎푖,푡푠푠 =(푔푖,푡푠푠+휋푖,푡푠푠) 푛푓푎푖,푡푠푠  (1)
  - Steady-state NFA is a function of structural fundamentals and steady-state policies:
    - 푛푓푎푖,푡푠푠 = 푛푓푎푠푠(퐹푖,푡푠푠,푋푖,푡푠푠,푃푖,푡푠푠)  (2)
  - Steady-state current account represented as:
    - 푐푎푖,푡푠푠 = 휆 퐹푖,푡푠푠 + γ푃푖,푡푠푠 + 푢푖,푡푠푠  (3)
- NFA as proxy for unobservable fundamentals:
  - If we have a proxy 푛푓푎푖,푡푝 for 푛푓푎푖,푡푠푠, include it in regression:
    - 푐푎푖,푡푠푠 = 휆퐹푖,푡푠푠 + 훾푃푖,푡푠푠 + 휙 푛푓푎푖,푡푝 + 푢푖,푡푠푠  (4)
  - NFA is an imperfect proxy; conditional on 퐹푠푠 and 푃푠푠, NFA summarizes unobservable 푋푠푠 but is not sufficient statistic for entire steady-state CA.
- From steady state to observables:
  - Deviation of CA from steady state represented as:
    - 푐푎푖,푡 − 푐푎푖,푡푠푠 = 훽퐶푖,푡 + 휆(퐹푖,푡 − 퐹푖,푡푠푠) + 훾(푃푖,푡 − 푃푖,푡푠푠) + 푢푖,푡𝑑𝑒𝑣  (5)
  - Replacing (4) into (5) yields observable regression:
    - 푐푎푖,푡 = 훽퐶푖,푡 + 휆퐹푖,푡 + 훾푃푖,푡 + 휙 푛푓푎푖,푡𝑝 + 푢푖,푡𝑠푠 + 푢푖,푡𝑑𝑒𝑣  (6)
  - This is the EBA equation (see equation 1 in main text).
- Income source clarification:
  - The positive relationship between CA and NFA in steady state is a stock-flow accounting identity required to stabilize the NFA ratio in a growing economy; the return on foreign assets r does not appear in equation (1).
  - The source of income (labor or capital, domestic or foreign) does not matter for the steady-state relation; what matters is how much of total income is saved relative to investment.

*Source: Online Annex (ch1onlineannex - 0.3 percent of GDP (Online Annex Figure 1.6.4)).*

### References

### References

### Measurement, Methodology, and External Accounts
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### Valuation, Net Foreign Assets, and External Adjustment
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### Demographics, Saving, Pension Systems, and Aging
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### Trade, Trade Costs, and Gravity Literature
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### Capital Flows, Controls, and External Financing Risks
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### Productivity, Regulation, and Structural Drivers
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### Additional empirical and theoretical contributions
- Blanchard, O. J. and M. Das. 2017. “A New Index of External Debt Sustainability.” Working Paper Series WP17-13, Peterson Institute for International Economics.
- Florez-Orrego, S., M. Maggiori, J. Schreger, Z. Sun, and S. Tinda. 2024. “Global Capital Allocation.” Annual Review of Economics 16 (1), 623–653.
- Herkenhoff, Philipp, and Philip Sauré. 2021. “How Expected Inflation Distorts the Current Account and the Valuation Effect.” European Economic Review, 135, 103721.
- Santos Silva, J. M. C., and S. Tenreyro, 2006, “The log of gravity,” The Review of Economics and Statistics, 88 (4), 641–58.

*External Sector Report Chapter 1  IMF | July 2026*

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_Source: https://www.imf.org/-/media/files/publications/esr/2026/english/ch1onlineannex.pdf_