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---

### I. Main updates to the EBA methodology (2022)
- EBA methodology updated in 2022 for the 2022 External Sector Report (ESR).
- Main refinements to the CA model:
  - refinement of variables included in the models;
  - a Bayesian Model Averaging (BMA) procedure to exclude non-robust variables;
  - sample expanded from 49 to 52 economies (added Bangladesh, Romania and Vietnam);
  - complementary tools added for pension-system features, updated labor and product market regulations analysis for a subsample, and a new methodology for estimating measurement and accounting biases in the CA.
- REER-Index and REER-Level models updated to use refined variables and the BMA procedure.
- Revised estimates of the semi-elasticity between the CA and the REER account for reactions of both the trade balance and the income balance.
- Core empirical finding: EBA CA gaps are associated with future CA and REER movements in the expected way; adjustment speed depends on initial CA balance and income level.

### II. EBA CA model — formulation, estimation, and key elasticities
- Model formulation (notation preserved from source):
  - 퐶퐴
    ௜௧
    = 훼+퐶
    ௜௧
    ᇱ
    훽+퐹
    ௜௧
    ′휆+푃
    ௜௧
    ′훾+푒
    ௜௧
- Variable groups:
  - 퐶
    ௜௧
    : cyclical and temporary factors;
  - 퐹
    ௜௧
    : medium-term macroeconomic and structural fundamentals;
  - 푃
    ௜௧
    : policy variables;
  - 푒
    ௜௧
    : zero-mean, normally distributed regression residual, assumed AR(1).
- Data and estimation:
  - sample: 52 countries, annual data for the 1986-2019 period;
  - estimation: pooled Generalized Least Squares (GLS) with a panel-wide AR(1) correction.
- Key estimated effects (preserve exact values as reported):
  - Output gap: 1 percent increase in relative output gap reduces CA by about 0.35 percentage points of GDP.
  - Commodity terms-of-trade gap interacted with openness: 1 percent terms-of-trade improvement in a country with openness 0.5 → CA increases by 0.15 percentage points of GDP.
  - Lagged annual change in REER (annual log-change): 1 percent appreciation → CA decreases by 0.02 percentage points of GDP.
  - Lagged NFA-to-GDP ratio: estimated coefficient 0.04.
  - Output per worker (lagged, relative to frontier): 1 percent increase → CA increases by about 0.03 percent of GDP.
  - Expected real GDP growth (5 years ahead): 1 percentage point increase → CA lowers by about 0.3 percent of GDP.
  - Exhaustible oil and natural gas reserves (adjusted energy balance): 1 percent of GDP increase → CA increases by about 0.3 percent of GDP (relevant for 9 of 52 economies).
- Policy variables (deviations from GDP-weighted global average):
  - Fiscal policy (cyclically-adjusted general government overall balance, instrumented): estimated coefficient 0.3.
  - Health spending (lagged, public health spending relative to GDP): 1 percent of GDP increase → CA reduces by about 0.3 percentage points of GDP.
  - Foreign exchange intervention (FXI) × capital controls (FARI): 1 percent of GDP in FX purchases → CA improves by 0.12 percent of GDP for the median country of the FARI distribution.
  - Credit gap: 1 percent of GDP increase in the credit gap → CA deteriorates by 0.1 percent of GDP.

### III. Model selection, instrumentation, and robustness procedures
- Variable selection:
  - Bayesian Model Averaging (BMA); variable considered robust if posterior inclusion probability (PIP) > 50 percent.
- Endogeneity and instruments:
  - Fiscal policy and FXI instrumented; instruments include global factors (lags of world real GDP growth, world output gap, world cyclically-adjusted fiscal balance, U.S. corporate credit spread) and country-specific features (lagged GDP per capita, lagged output gap, lagged fiscal balance differences from trade-weighted partners, exchange rate regime, democracy index).
- Treatment of terms-of-trade:
  - Terms-of-trade gaps constructed via band-pass filtering of 42 commodity price series and aggregated using country-specific trade weights; oil and gas balance computed using long-term trend prices.
- Measurement issues:
  - Treatment of NFA components and measurement biases (nominal interest income, retained earnings on portfolio equity) discussed in Annex III and Section VII.A.

### IV. Robustness exercises (Section III.D) — NFA decomposition, demographics, capital mobility, FXI, credit gap
- NFA decomposition (replace aggregated NFA with components: reserves, portfolio equity, FDI, external debt):
  - R-squared rises with decomposition.
  - Large estimated coefficient on reserves is hard to interpret.
  - Evidence of endogeneity; coefficients on other fundamentals and policy variables weaken.
  - Conclusion: decomposed NFA not adopted.
- Demographic polynomials (third-order polynomial approximation):
  - Estimated parameters not statistically significant; model fit does not improve.
  - Conclusion: retain original demographic block from Cubeddu and others (2019).
- Capital mobility alternatives:
  - De jure: KAOPEN (Chinn-Ito) used instead of FARI → coefficients and fit very similar; drawback: KAOPEN reestimated each data update.
  - De facto measures (three measures following Bayoumi and others, 2015): (i) (external assets + liabilities)/GDP; (ii) BOP financial share flows as percent of BOP total flows; (iii) BOP financial share flows as percent of GDP. Winsorization and high-openness indicators tested.
  - Findings: estimated coefficients similar, model fit worsens with de facto measures, inclusion probability of FXI × capital controls interaction falls below 50% threshold.
  - Conclusion: retain FARI (de jure) interacting with instrumented FXI.
- FXI measurement and instrumentation:
  - FXI proxied by transaction-based change in reserves plus comparable derivative operations; when BOP data not available, change in stock of reserves used.
  - Instruments: global accumulation of reserves measure; reserve adequacy measure linked to M2 defined as (M2-reserves)/GDP relative to emerging market group average; EMDE dummy.
- Credit gap:
  - Credit gap defined as credit-to-GDP ratio minus its long-term trend estimated with one-sided HP filter; penalty parameter = 1,600.
  - For some countries two-sided HP used in initial years.
  - Finding: 1 percent of GDP increase in credit gap → 0.1 percent of GDP deterioration in CA.

### V. Model fit, exclusions, and implications for normative interpretation
- Goodness of fit:
  - Refined model R-squared ≈ 53 percent.
  - Absolute sum of residuals falls by about 10% relative to previous model (a 1% of GDP gap previously becomes a 0.9% of GDP gap).
- Exclusions to preserve normative interpretation:
  - Country fixed effects and lagged CA excluded despite improving fit because they attribute variation to persistent cross-country differences and would capture persistent policy distortions.
- Implication:
  - Retain aggregated NFA, original demographic block, and FARI for interaction with instrumented FXI to preserve interpretability and robustness.

### VI. Complementary tools (Section VII): measurement biases, pensions, product and labor market regulations
- Three complementary tools to interpret EBA residuals:
  1. Measurement and accounting biases (inflation differential bias; portfolio equity retained earnings bias) — updated methodology in Annex III.
  2. Pension system features — analysis summarized in Annex IV.
  3. Labor and product market regulations — updated analysis for advanced economy subsample; data limitations preclude full model inclusion.

- Measurement and accounting biases (Annex III):
  - Two main biases under BPM6:
    1. Inflation bias: nominal interest income recorded includes compensation for expected inflation → systematic bias in NIIP valuation changes.
    2. Portfolio equity retained earnings bias: retained earnings on portfolio equity not recorded symmetrically in income flows → bias in income balance.
  - Retained earnings estimation:
    - Retain stock and flow methods; drop hybrid method.
    - New corporate saving method introduced combining national accounts and foreign portfolio holdings data; corporate saving approach complements stock and flow methods.
  - Final adjustor to EBA model results averages stock, flow, and corporate saving approaches; more granular data can refine estimates.

- Pensions (Annex IV):
  - Datasets: Koomen and Wicht (KW) for 49 economies (1986-2016); OECD Pensions at a Glance for 51 OECD and G20 economies (2005-2021).
  - Coverage proxy: 1 − self-employment share.
  - Main quantitative findings:
    - Adding pension indicators explains between 1.7 and 8.6 percent of the variation of EBA CA model residuals.
    - Baseline EBA CA equation R-squared ≈ 52 percent.
    - Relation stronger for mandatory FF replacement rates than PAYG; stronger at higher coverage rates.
    - Illustration: a 10-percentage point rise in mandatory FF replacement rate → 0.41 percentage point of GDP rise in CA balance at sample average coverage; at coverage one standard deviation higher (18 percentage points) effect = 0.57 percentage point of GDP.
  - Key coefficients and statistics (Annex Table 1, exact values preserved):
    - PAYG replacement rate #: 0.956 (column 1), 1.145 (column 2); standard errors (0.675), (0.769).
    - Mandatory FF replacement rate #: 3.083*** (column 1), 4.087*** (column 2); standard errors (0.895), (1.006).
    - Coverage rate #: 2.397** (column 1), -1.611 (column 2), 5.080*** (column 3), -2.139 (column 4), 4.812*** (column 5), -1.988 (column 6); standard errors (1.027), (2.171), (1.559), (3.824), (1.510), (3.779).
    - Mandatory FF replacement rate × Coverage rate #: 9.354*** (standard error (2.573)).
    - Mandatory replacement rate #: 3.026** (column 3), 3.818*** (column 4); standard errors (1.266), (1.359).
    - Voluntary replacement rate #: -5.009* (column 3), -1.072 (column 4), -4.437 (column 5), -1.716 (column 6); standard errors (2.911), (3.819), (2.749), (3.754).
    - Mandatory replacement rate × Coverage rate #: 15.428*** (standard error (5.927)).
    - Mandatory public replacement rate #: 2.590** (column 5), 1.936 (column 6); standard errors (1.150), (1.338).
    - Mandatory private replacement rate #: 7.083*** (column 5), 3.762* (column 6); standard errors (1.735), (1.938).
    - Mandatory private replacement rate × Coverage rate #: 51.287*** (standard error (11.305)).
    - Constants: 0.068, 0.067, -0.477, 0.098, -0.715**, -0.212; standard errors (0.208), (0.205), (0.384), (0.521), (0.358), (0.521).
    - Observations: 1,254; 1,254; 484; 484; 475; 475.
    - R-squared: 0.017; 0.025; 0.044; 0.062; 0.072; 0.086.
    - Number of economies: 49; 49; 36; 36; 36; 36.
  - Interpretation and policy use:
    - Results do not warrant formal adjustors to normative EBA CA benchmarks but can aid interpretation of residuals and policy advice.
    - Considerable uncertainty in estimates; replacement rates are theoretical projections subject to construction assumptions.

- Product and labor market regulations (Annex V / Annex Tables):
  - Data: OECD PMR and EPL indicators for 22 AEs, years 1998–2018; indicators scaled 0–6.
  - Estimated relations (selected exact values):
    - Product market regulation (overall): coefficient -0.018 (standard error (0.9838)); not statistically significant.
    - Legal barriers to entry: coefficient 0.773 (standard error (0.6128)); sign suggests deregulation associated with lower CA but not statistically significant.
    - Labor market regulation (combined indicator): coefficients -0.408 (standard error (0.2803)) and -0.722** (standard error (0.2958)).
    - Observations: 484 and 352; number of economies: 22 and 22; R-squared: 0.003 and 0.011.
  - Interpretation:
    - Some structural indicators not strongly associated with CA balances in this sample.
    - Easing legal barriers to entry associated with lower CA balance (consistent with expectations) but not strongly significant.
    - Easing some labor market regulations associated with higher CA balance.
    - Effects are country-specific; structural reform impacts on CA depend on reform mix and persistence.

### VII. Properties of EBA CA gaps adjustments (Annex material)
- Multilateral consistency: CA gaps adjusted so they add to zero across EBA sample.
- Dynamics and half-life:
  - EBA CA gaps tend to persist but converge toward zero when regression coefficient 훼 < 0.
  - Half-life definition: HL(X) = − ln(2)/ln(1 + α).
- Empirical setup:
  - Sample: 48 economies from baseline EBA regression (Ireland excluded; Bangladesh, Romania, Vietnam added only in 2022).
  - Subperiods: 2012–19 (actual assessments), 1987–2019 (backward application).
  - Panel regression: X_{i,t} − X_{i,t−1} = α X_{i,t−1} + ε_{i,t}.
- Key half-life estimates and heterogeneity (exact values preserved):
  - IMF staff current account gaps (2012–19, ESR sample) half-life: 6.9 years.
  - EBA gaps half-lives: 4.7 years (whole period) and 5.7 years (2012–19).
  - Half-lives between 4.7 and 6.7 years correspond to α between −0.098 and −0.138.
  - Deficit emerging economies: half-life 1.5 years.
  - Advanced surplus economies: half-life 6.4 years.
  - Crisis episodes: deficits adjust faster in crises (2.1 years) versus normal times (5.5 years).
  - Wage bargaining regimes: decentralized bargaining half-life 3.7 years; centralized bargaining half-life 10.8 years.
- Drivers of adjustment:
  - Adjustment mainly driven by changes in actual current accounts or cyclically adjusted current account balances.
  - Changes in EBA norms modestly contribute; changes in norms mainly linked to NFA variable.
- Policy gaps, residuals, and contribution to adjustment:
  - Policy gaps half-life: 2.7 years.
  - EBA CA gaps half-life: 4.7 years.
  - Residuals half-lives: 4.5 years (surplus), 2.2 years (deficit).
  - Policy gaps aligned with overall external gaps in about two-thirds of cases.
  - Closing policy gaps in 2019 would change absolute value of EBA gaps by 0.1 percent of country GDP on average.
  - Closing fiscal gaps would reduce overall EBA gap by $150 billion; closing credit gap would increase overall EBA gap by $125 billion.
- REER prediction:
  - Initial EBA CA gaps associated with future REER adjustments with correct sign.
  - REER index gaps derived from EBA adjust similarly to observed REER.
  - No statistically significant association between changes in REER level gaps and initial EBA CA gaps.
- Implication:
  - EBA gaps adjust slowly and asymmetrically; residuals require careful interpretation; policy advice should consider alignment of policy gaps with CA gaps.

### VIII. Annex I — commodity long-term prices and oil/gas reserves variable
- Commodity terms-of-trade gap construction:
  - Commodity super-cycle defined as frequencies in 20-70 years range.
  - Two-step decomposition: Christiano-Fitzgerald band-pass filter to isolate CSC20_70_{k,t}; Butterworth high-pass filter (parameter 40) to distinguish long-term trend from short-term fluctuations.
  - Log price decomposition: ln P_{k,t} = LTT_{k,t} + CSC20_70_{k,t} + STF_{k,t}.
  - Commodity price gap: gap_{k,t} = CSC20_70_{k,t} + STF_{k,t} = ln P_{k,t} − LTT_{k,t}.
  - Aggregation: commoTOTgap_{i,t} = Σ_k (ω_{k,i,t}^{exports} − ω_{k,i,t}^{imports}) × gap_{k,t}, multiplied by openness ratio.
  - Price series extended backward using World Bank Pink Sheet, Pfaffenzeller and others (2007), Jacks (2013) dataset, Schwerhoff and Stuermer (2015) dataset.
  - Historical series extended between 2021 and 2027 using WEO forecasts; beyond 2027 (up to 2032) using a no-change assumption.
- Oil and Natural Gas Reserves variable:
  - Purpose: capture income from exhaustible resources and temporariness of endowments.
  - Formal (textual) definition preserved:
    - Oil&Gas_{i,t} = Σ_k { (1/3) Σ_{s=0}^{2} (X_{k,i,t−s} / Y_{i,t−s}) × corrective_factor_{k,t−s} } × temp_{k,i,t} / temp_{Norway,2010,k}
      - X_{k,i,t}: nominal oil and gas net exports (if positive; zero otherwise).
      - Y_{i,t}: nominal GDP.
      - Corrective_factor = exp(−gap_{k,t}).
      - temp = ratio of current extraction to proven reserves in volume terms, relative to Norway in 2010.
  - Rationale: value net exports at long-term prices and smooth volumes with 3-year moving average to enhance structural interpretation.
  - Note: climate/decarbonization uncertainty may alter effective proven reserves; lower effective reserves → higher temporariness → higher CA norms for exporters.

### IX. Annex II — Benchmarks for Policy Variables (P*)
- P* represent desirable medium-term policy levels aimed at domestic objectives.
- Fiscal P*: cyclically-adjusted fiscal balance consistent with debt-stabilizing primary balance and long-term aging costs.
- Public health spending P*: guided by regression including PPP GDP per capita, current old-age dependency ratio, and income inequality; staff can justify different levels.
- Capital controls P*: cross-country average level = 0.29 in 2019 (index 0–1), or a country’s actual level, whichever is smaller.
- FXI P*: normally set to zero over medium term once reserves adequate; nonzero desirable level possible if reserves well below ARA metric.
- Credit gap P*: typically zero.

### X. Annex III — measurement biases (details)
- Inflation bias estimation unchanged from prior methodology.
- Portfolio equity retained earnings:
  - Stock and flow methods retained; hybrid method discontinued.
  - New corporate saving method uses national accounts and foreign portfolio holdings to allocate corporate saving to foreign investors; asset-side computed as CPIS-weighted sum of partner countries’ retained earnings.
  - Final adjustor averages stock, flow, and corporate saving estimates; granular data can refine estimates.

### XI. Annex IV — pensions (data, estimation, interpretation)
- Data sources: KW dataset (49 economies, 1986–2016), OECD Pensions at a Glance (51 economies, 2005–2021).
- Coverage proxy: 1 − self-employment share.
- Pension indicators explain between 1.7 and 8.6 percent of variation in EBA CA residuals.
- R-squared of baseline EBA CA equation ≈ 52 percent.
- Stronger relations for mandatory FF replacement rates and at higher coverage rates.
- Results used for interpretation rather than formal adjustors due to uncertainties.

*Source: wpiea2023047-print-pdf — IMF Working Papers 2022 Update of the EBA Methodology (selected sections and annex material as provided).*

### References .............................................................................................................

### wpiea2023047-print-pdf - References

### Figures
- 1. The IMF’s External Sector Assessment Process ................................................................................ 6
- 2. EBA Models: Summary of Explanatory Variables in EBA CA, REER Index and REER Level Models .......................................................................................................................................... 18
- 3. Estimated CA-REER Semi-Elasticities, EBA Sample ....................................................................... 25
- 4. IMF Staff and EBA CA Gaps Adjustment: Estimated Half-Lives ...................................................... 33

### Tables
- 1. Description of External Sector Assessment Categories ................................................................... 35
- 2. EBA Data Sources ............................................................................................................................ 36
- 3. Countries in EBA Models ................................................................................................................ 37
- 4. Estimation Results: EBA Current Account Model ........................................................................... 38
- 5. Previous EBA Current Account Models .......................................................................................... 39
- 6. EBA Current Account Model Fit ...................................................................................................... 40
- 7. Robustness Checks on NFA, Demographics.................................................................................. 41
- 8. Robustness Checks on Capital Mobility .......................................................................................... 42
- 9. Estimation Results: EBA REER Models ......................................................................................... 43
- 10. Estimation Results: EBA REER Models (Comparison with Previous Models) ............................... 44
- 11. Estimation Results: Exports and Imports Medium-Run Elasticities ................................................ 45
- 12. EBA Gaps Adjustment: Changes in CA Balances or Changes in the Norm? ................................. 45
- 13. EBA Gaps Adjustment: Contribution of Policy Gaps and Residuals .............................................. 45
- 14. EBA Gaps: REER Adjustment ........................................................................................................ 46

### Annexes
- I. Measuring Commodity Long-Term Prices ....................................................................................... 47
  - A.  Construction of the Commodity Terms-of-Trade Gap ............................................................. 47
  - B.  Construction of the Oil and Natural Gas Reserves Variable ................................................... 49
- II. Benchmarks for Policy Variables (P*) .............................................................................................. 50
- III. Measurement Biases ....................................................................................................................... 51
- IV. Pension Systems and Current Accounts ......................................................................................... 54
  - A.  Data and Related Caveats ...................................................................................................... 54
  - B.  Estimation Results ................................................................................................................... 55
  - C.  Contribution to CA Balances ................................................................................................... 56
- V. Measuring the Effects of Structural Policies ..................................................................................... 58

### Annex Figures
- 1. Oil Price Decomposition and Price Gap ............................................................................................ 48
- 2. Allocation of Corporate Profits in the National Accounts .................................................................. 51

### Annex Tables
- 1. EBA CA Model Residuals and Pension System Parameters ........................................................... 57

*Source: wpiea2023047-print-pdf - References (IMF Working Paper PDF content list).*

### 2. EBA CA Model Residuals and OECD Product and Labor Market Rigidities .................................................

### 2. EBA CA Model Residuals and OECD Product and Labor Market Rigidities

### I. Introduction — scope and main updates
- EBA methodology updated in 2022 for the 2022 External Sector Report (ESR).
- Main refinements to the CA model:
  - refinement of variables included in the models;
  - a Bayesian Model Averaging (BMA) procedure to exclude non-robust variables;
  - an expanded sample of economies (panel size increased from 49 to 52 economies with the addition of Bangladesh, Romania and Vietnam);
  - complementary tools for assessing the relationship between CA balances and pension system features, an update of the labor and product market regulations analysis for a subsample with necessary data, and a new methodology for estimating measurement and accounting biases in the CA.
- REER-Index and REER-Level models also updated to use refined variables and the BMA procedure.
- Revised estimates of the semi-elasticity between the CA and the REER account for reactions of both the trade balance and the income balance.
- The core question examined: how much estimated current account (CA) gaps based on EBA are associated with future external adjustment; main result: EBA CA gaps are associated with future CA and REER movements in the expected way, with adjustment speed depending on initial CA balance and income level.

### II. Overview of the External Sector Assessment Process
- The CA model is the workhorse for external sector assessments, providing a cyclical-adjusted CA gap by comparing an economy’s CA to its CA benchmark.
- Multilateral consistency: CA gaps are adjusted so they add up to zero across the EBA sample.
- CA-implied REER gap is calculated using the CA-REER elasticity; REER models can complement this when the CA-implied REER gap does not capture currency fluctuations.
- Staff judgement combines model outputs, alternative indicators (e.g., unit labor costs REER, export shares), the ES approach, and country-specific numerical adjustors (e.g., measurement issues, pandemic effects, one-off shocks).
- EBA methodology is applied to the 52 largest economies that are not commodity exporters or financial centers; the world average refers to the GDP-weighted average of the 52 countries in the EBA sample, which represent over 90 percent of global GDP.
- The EBA CA model generally receives greater weight than REER models because CA balances are less volatile and more directly related to the medium-term external position.

### III. The EBA CA Model — formulation and estimation
- Model equation (notation preserved from source):
  - 퐶퐴
    ௜௧
    = 훼+퐶
    ௜௧
    ᇱ
    훽+퐹
    ௜௧
    ′휆+푃
    ௜௧
    ′훾+푒
    ௜௧
- Variable groups:
  - 퐶
    ௜௧
    : cyclical and temporary factors;
  - 퐹
    ௜௧
    : medium-term macroeconomic and structural fundamentals;
  - 푃
    ௜௧
    : policy variables;
  - 푒
    ௜௧
    : zero-mean, normally distributed regression residual, assumed AR(1).
- Most variables are measured relative to the GDP-weighted world average.
- Endogeneity and timing:
  - fiscal policy and foreign exchange intervention are instrumented;
  - health spending, annual change in the REER, and some fundamentals (net foreign asset position, productivity) are lagged.
- Estimation sample and method:
  - sample: 52 countries using annual data for the 1986-2019 period;
  - estimation: pooled Generalized Least Squares (GLS) with a panel-wide AR(1) correction.

### IV. Variable blocks and key estimated effects (regression results and interpretation)
- Temporary and cyclical factors
  - Output gap (relative to world average): an increase in the relative output gap of 1 percent reduces the current account balance by about 0.35 percentage points of GDP.
  - Commodity terms-of-trade gap interacted with trade openness: a 1 percent terms-of-trade improvement in a country with an openness degree of 0.5 is associated with an increase in the current account balance of 0.15 percentage points of GDP.
  - Lagged annual change in the REER (annual log-change): a 1 percent appreciation is associated with a 0.02 percentage points of GDP decrease in the current account balance, holding other factors constant.
- Macroeconomic fundamentals
  - Lagged net foreign asset (NFA)-to-GDP ratio: estimated coefficient 0.04, indicating higher NFA positions are associated with higher CA balances.
  - Output per worker (lagged, relative to frontier): a 1 percent increase in relative output per worker is associated with an increase of about 0.03 percent of GDP in the current account balance.
  - Expected real GDP growth (5 years ahead): an increase of 1 percentage point in expected real growth lowers the current account by about 0.3 percent of GDP.
- Structural fundamentals
  - Demographics: model includes population growth, old-age dependency ratio (OAD), share of prime-aged savers, life expectancy of current prime-aged savers, and interaction of life expectancy with future (20 years ahead) OAD to capture static and dynamic lifecycle effects; estimated coefficients align with economic priors.
  - Institutional quality (ICRG-based proxy): a country at the 75th percentile of institutional quality can have, all else equal, a 0.5 percentage points of GDP lower current account balance compared to the median country.
  - Exhaustible oil and natural gas reserves (structural energy balance adjusted for temporariness): the estimated coefficient implies that a 1 percent of GDP increase in the adjusted energy balance increases the current account balance by about 0.3 percent of GDP. This term is relevant for 9 out of the 52 economies in the sample.
- Policy variables (all measured as deviations from the GDP-weighted global average and used for normative assessment)
  - Fiscal policy (cyclically-adjusted general government overall balance, instrumented): estimated coefficient 0.3.
  - Health spending (lagged, public health spending relative to GDP): an increase in public health expenditures of 1 percent of GDP reduces the current account by about 0.3 percentage points of GDP.
  - Foreign exchange intervention (FXI) interacted with capital controls (FARI), FXI proxied by transaction-based change in reserves plus comparable derivative operations, interaction instrumented: a 1 percent of GDP in FX purchases leads to a 0.12 percent of GDP improvement in the current account for the median country of the FARI distribution.
  - Credit gap: included to capture the relationship between credit cycles and CA/REER (credit booms associated with CA deterioration and REER appreciation).

### V. Model selection, robustness and other methodological notes
- Bayesian Model Averaging (BMA) is used to select robust explanatory variables; a variable is considered robust if posterior inclusion probability (PIP) > 50 percent.
- To address endogeneity, instruments include global factors (lags of world real GDP growth, world output gap, world cyclically-adjusted fiscal balance, U.S. corporate credit spread) and country-specific features (lagged GDP per capita, lagged output gap, lagged fiscal balance in differences from trade-weighted average across trading partners, exchange rate regime, democracy index).
- Terms-of-trade gaps constructed via band-pass filtering of 42 commodity price series and aggregated using country-specific trade weights; oil and gas balance computed using long-term trend prices to enhance structural interpretation.
- Treatment of NFA and measurement issues (e.g., nominal interest income, retained earnings on portfolio equity) discussed elsewhere (Section VII.A and Annex III in source).

*Italic source: IMF Working Papers — 2022 Update of the EBA Methodology (excerpt: "2. EBA CA Model Residuals and OECD Product and Labor Market Rigidities").*

### Section III.D for an analysis of the robustness of the model to alternative measures of capital mobility.

### Section III.D: Robustness Checks

### Overview of robustness exercises
- As part of the 2022 EBA refinements, staff explored several modifications to the CA model following recent contributions to the literature.  
- These extensions were discussed even if they were not incorporated into the model at this point.

### NFA components: replacing aggregated NFA with decomposition
- Rationale:
  - Aggregated NFA may be inadequate because its components have different rates of return; composition may affect primary income and the CA balance.
- Exercise:
  - The NFA term was replaced with its components: foreign exchange reserves, portfolio equity, FDI and external debt (see Table 7, column (2) in source).
- Findings:
  - The R-squared of the model rises when NFA is decomposed.
  - A large estimated coefficient on the stock of foreign exchange reserves is hard to interpret (reserves often include government debt of reserve-currency-issuing advanced economies that typically pay a low or even negative growth-adjusted rate of return).
  - Estimation results may reflect endogeneity: unobserved country characteristics may drive both CA and NFA composition.
  - Coefficients on other fundamentals (output per worker, demographics, institutional quality) and policy variables (including fiscal balance) weaken in the more complex specification.
- Conclusion:
  - Due to mixed results and interpretation issues, a decomposed NFA variable was not added to the CA model at this point.

### Demographic polynomials: full age-structure approximation
- Rationale:
  - Instead of using three demographic variables for specific age groups, Koomen and Wicht (2022) suggest using full population age-structure information; approximated with a third-order polynomial as proposed by Fair and Dominguez (1991).
- Exercise:
  - Static demographic variables were replaced with third-order demographic polynomials (see Table 7, column (3)).
- Findings:
  - The estimated parameters on the demographic polynomials are not statistically significant.
  - Model fit does not improve with the polynomial specification.
- Conclusion:
  - The CA model maintains the EBA demographic block introduced by Cubeddu and others (2019).

### Capital mobility: alternative de jure and de facto measures
- Importance:
  - Measuring capital mobility is important to capture effects of foreign exchange intervention (FXI) on exchange rates and the CA balance.
- De jure alternative (KAOPEN / Chinn-Ito index):
  - The KAOPEN index (Chinn and Ito, 2006) was used instead of the FARI (normalized to [0,1], and capital controls = 1 – capital openness).
  - Finding: When FARI is replaced by Chinn-Ito, coefficients and model fit are very similar to the refined model (see Table 8, column (2)).
  - Drawback: KAOPEN is reestimated each time underlying data are updated, so historical values change annually even if underlying data remain unchanged.
- De facto alternatives (following Bayoumi and others, 2015):
  - Three measures considered:
    - (i) Financial integration = (external assets + liabilities)/GDP (EWG data).
    - (ii) BOP financial share flows as percent of BOP total flows.
    - (iii) BOP financial share flows as percent of GDP.
  - Implementation notes:
    - Ratios with extreme values were also constructed with winsorization (replace observations above each year’s 95th percentile with that percentile’s value) or by converting to high openness indicators (value 1 for countries above each year’s median); qualitative results remain unchanged.
  - Findings (Table 8, columns (3)-(5)):
    - Estimated coefficients remain similar to the refined model.
    - Model fit worsens when any de facto measures are used.
    - The probability of inclusion of the interaction of FXI and capital controls falls significantly and below the 50% threshold used to assess regressor robustness.
  - Conclusion:
    - Considering these findings, the de jure capital controls index (FARI) was not replaced with de facto capital mobility proxies.

### FXI measurement and instrumentation
- FXI:
  - In a few cases where BOP data are not available, FXI is calculated with the change in the stock of reserves.
- Instrumentation of FXI and its interaction with capital controls:
  - Instrumented with:
    - A measure of global accumulation of reserves (to capture the “keeping-up-with-the-Joneses” effect).
    - A measure of reserve adequacy linked to M2, defined as (M2-reserves)/GDP relative to the average emerging market group.
    - An emerging market and developing economy dummy (to capture tendencies to accumulate reserves as part of export-led growth strategies).
  - References cited for instruments: Adler and others (2015), Bayoumi and others (2015) and Daude and others (2016).

### Financial excesses / credit gap robustness
- The model includes a credit gap measure (following BIS methodology) to capture financial excesses:
  - Defined as the difference between the credit-to-GDP ratio and its long-term trend estimated with a one-sided Hodrick-Prescott (HP) filter with a large penalty parameter.
  - Penalty parameter used for the credit cycle is 1,600 (obtained by dividing the BIS quarterly parameter of 400,000 by 44 as suggested by Ravn and Uhlig (2002)).
  - For a few countries with data limitations, a two-sided HP filter was applied in initial sample years.
- Finding:
  - A 1 percent of GDP increase in the credit gap is associated with a 0.1 percent of GDP deterioration in the current account.

### Model fit and exclusions for normative interpretation
- Goodness of fit:
  - Refined model R-squared is about 53 percent; moderately better than previous CA model (data up to 2019).
  - Absolute sum of residuals falls by about 10% relative to the previous model (a 1% of GDP gap previously becomes a 0.9% of GDP gap with the refined model).
- Exclusions to preserve normative interpretation:
  - Country fixed effects and lagged CA balance can increase fit but are excluded for the EBA exercise:
    - Country fixed effects attribute a large fraction of CA variation to cross-country differences rather than over-time changes (Chinn and Prasad, 2003).
    - Fixed effects and lagged CA may capture persistent policy distortions and would not justify desirability of persistence.
  - These exclusions penalize model fit compared to other studies but are necessary for normative analysis.

### Implications for model specification and policy-relevant estimation
- Mixed results from alternative specifications imply:
  - Retaining aggregated NFA term rather than decomposed components.
  - Maintaining the original demographic block.
  - Using the FARI (de jure capital controls) rather than de facto capital mobility measures for the interaction with FXI.
- Overall:
  - The de jure capital controls index combined with instrumented FXI preserves interpretability and model robustness in the EBA CA specification.
  - De facto proxies for capital mobility tend to worsen overall model fit and reduce robustness of the FXI × capital controls interaction.

*Source: Section III.D, wpiea2023047-print-pdf (IMF Working Paper — 2022 Update of the EBA Methodology).*

### 1. Choice of a benchmark or desired NFA-to-GDP level. In most cases, the benchmark NFA level is

### 1. Choice of a benchmark or desired NFA-to-GDP level. In most cases, the benchmark NFA level is

### Benchmark NFA choice and interpretation
- In most cases, the benchmark NFA level is set equal to the last year’s level (or the current year if it is available).
- For countries with large net debtor positions (and high sustainability risk), a benchmark NFA level consistent with a stronger external position is recommended.
- The precise benchmark for such debtor countries should be informed by:
  - estimated thresholds below which the risk of a balance-of-payments crisis increases substantially (Catão and Milesi-Ferretti, 2014), or
  - reference values, such as averages of a particular regional or country group.
- The CA balance that stabilizes the NFA position at its benchmark level should not be interpreted as a CA norm, since it is relevant only when external sustainability is a main concern.
- In cases where external sustainability is a main concern, results from the ES approach may take precedent to the EBA CA model results and guide the external sector assessments.

### Derivation of stabilizing current account balance
- The current account balance that stabilizes the NFA position at its benchmark level is derived directly from equation (18) using:
  - medium-term inflation (휋) and
  - medium-term potential growth (g)
- The medium-term values for 휋 and g are based on Fund staff forecasts.

### Estimation of the CA gap and REER adjustment
- The CA gap is defined as the difference between:
  - the cyclically-adjusted CA, using the same adjustment as in the EBA CA model (see Section III.E, equation (2)), and
  - the current account balance that would stabilize the NFA position at its benchmark level.
- The corresponding REER gap (i.e., REER adjustment needed to close the above current account gap) is derived from the current account gap using the staff-assessed REER-CA semi-elasticities, for which benchmark values are estimated (see Section V).

---

### VII. Complementary Tools — overview
- The section summarizes three complementary tools designed to support interpretation of the part of CA balances not explained by the EBA CA model (residuals), building on earlier work of Cubeddu and others (2019).
- The three tools:
  1. Estimation of measurement and accounting biases due to inflation differentials and the treatment of portfolio equity investment retained earnings in the CA.
  2. Insights into how pension parameters may contribute to CA balances for a subset of the 52 EBA economies for which the relevant indicators are available.
  3. Updated insights into the role of labor market and product market regulations, focusing on advanced economies.

### A. Measurement and Accounting Biases
- Existing CA measurement biases (inflation and portfolio equity retained earnings) will continue to be estimated by IMF staff.
- The “hybrid” approach used to estimate portfolio retained earnings (see Adler and others, 2019) is set to be dropped because:
  - it does not bring any new information (it combines the two other existing methods),
  - it lacks a clear interpretation, and
  - it can be prone to measurement issues.
- A new method developed for use in the 2022 External Sector Report:
  - combines national accounts and foreign portfolio holdings data to reapportion the share of domestic corporate saving (or undistributed profit) attributed to foreign portfolio investors,
  - complements existing methods (based on financial market data) by capturing activities of multinationals firms missing in domestic stock market data,
  - ensures consistency between the measure of retained earnings and external sector data, as both are compiled using the same SNA/BOP methodology,
  - can be complemented with more granular sectoral data shared by country authorities on a case-by-case basis.
- Further methodological details are presented in Annex III.

### B. Pensions
- Pension system characteristics that can theoretically affect private saving, national saving, and the CA balance include:
  - generosity,
  - system of financing,
  - whether participation is mandatory or voluntary,
  - share of the population covered.
- Possible effects:
  - In an economy with myopic households or liquidity constraints, moving from a voluntary approach to a mandatory system could result in higher national saving and a rise in the CA balance.
  - The relationship between pension system features and the CA is not straightforward; the overall outcome depends on how pension system parameters compare with those in the rest of the world.
- Annex IV analyzes how pension system characteristics help to explain EBA CA residuals using two different datasets and finds:
  - some pension system characteristics have implications for CA balances,
  - uncertainties associated with the estimates and methodological differences regarding the measurement of pension parameters across databases suggest the need for caution in interpreting the results.
- Conclusion on policy use:
  - Using the estimates to quantify formal adjustors to normative EBA CA benchmarks is not currently warranted.
  - The results can aid in the interpretation of EBA CA model residuals and the formulation of policy advice.

### C. Product and Labor Market Regulations
- Stringency of regulations in labor and product markets, and reforms easing them, can in principle impact saving, investment, and the CA balance.
  - Easing labor market regulation could increase export competitiveness and raise the CA balance.
  - Easing product market regulations could raise investment and reduce the CA balance.
- Introducing product and labor market regulation indicators in the EBA CA model is precluded by data limitations.
- Results for a subset of economies with the necessary data can inform policy discussions on the role of structural reforms.

*IMF WORKING PAPERS 2022 Update of the EBA Methodology*

### Annex V analyzes the effects of labor and product market regulations on the CA. Overall, while using the

### wpiea2023047-print-pdf - Annex V analyzes the effects of labor and product market regulations on the CA. Overall, while using the

### Properties of EBA CA Gaps Adjustments
- EBA produces multilaterally consistent assessments of current account (CA) balances and real effective exchange rates (REER).  
- EBA CA gaps tend to persist but show convergence toward zero over time when regression coefficient 훼 < 0 (exponential convergence absent shocks 휀).
- Half-life definition used: HL(X) = − ln(2)/ln(1 + α).

### Empirical setup and sample
- Sample: 48 economies from the baseline EBA regression (Ireland excluded; Bangladesh, Romania, Vietnam not included prior to 2022 refinements).
- Two subperiods due to data availability:
  - 2012–19: actual assessments from three subsequent vintages of EBA models and available optimal policies (P*).
  - 1987–2019: current EBA specification applied backward assuming desirable policies (P*) constant at their 2019 level.
- Panel regression estimated: X_{i,t} − X_{i,t−1} = α X_{i,t−1} + ε_{i,t}, where X represents various gap measures (IMF staff-assessed CA gaps, EBA CA gaps, CA norms, policy gaps, EBA residuals).

### Speed and pattern of CA gap adjustment (key findings)
- Regression coefficient α is generally negative and statistically significant, indicating convergence toward zero.
- Adjustment is slow overall:
  - IMF staff current account gaps (2012–19, ESR sample) half-life: 6.9 years.
  - EBA gaps half-lives: 4.7 years (whole period) and 5.7 years (2012–19).
  - Half-lives between 4.7 and 6.7 years correspond to α coefficients between −0.098 and −0.138.
- Pronounced cross-country heterogeneity:
  - Deficit emerging economies: half-life of 1.5 years.
  - Advanced surplus economies: half-life of 6.4 years.
  - Crisis episodes (Laeven and Valencia 2020, plus extended recessions): deficits adjust faster in crises (2.1 years) versus normal times (5.5 years).
  - Wage bargaining regimes: decentralized bargaining half-life 3.7 years; centralized bargaining half-life 10.8 years.
- Other factors associated with faster adjustment: more financially closed economies (based on Fiscal Analysis of Resource Industries Index) and less flexible exchange rate regimes (based on Annual Report on Exchange Arrangements and Exchange Restrictions classification).

### What drives the adjustment: actual CA vs norms
- Adjustment of EBA gaps is mainly driven by changes in actual current accounts or cyclically adjusted current account balances.
- Changes in EBA current account norms play only a modest role.
- Changes in the norm are mainly related to the net foreign assets (NFA) variable; persistent external imbalances lead to building large external positions over time.
- Asymmetries exist between surplus and deficit countries, with other fundamentals affecting surplus economies’ norms.

### Policy gaps, residuals, and their contribution to adjustment
- All policy gaps adjust over time, generally faster than the EBA CA gap:
  - Policy gaps half-life: 2.7 years.
  - EBA CA gaps half-life: 4.7 years.
- Asymmetry across policy types:
  - Fiscal gaps: adjustment slower when fiscal stance is tighter than warranted.
  - Credit gaps: adjustment slower after a credit crunch.
  - Health gaps: adjust very slowly.
  - Foreign exchange reserve gaps: adjust extremely rapidly.
- Residuals adjust relatively slowly, with half-lives of 4.5 years (surplus) and 2.2 years (deficit).
- Quantitative contribution:
  - Policy gaps contribute modestly to overall external adjustment compared with residuals (see Table 13).
  - Policy gaps are aligned with overall external gaps in about two-thirds of cases.
  - Closing policy gaps in 2019 would change the absolute value of EBA gaps in percent of GDP by 0.1 percent of country GDP on average (would be reduced in US dollar terms).
  - Closing fiscal gaps would reduce the overall EBA gap by $150 billion, whereas closing the credit gap would increase the overall EBA gap by $125 billion.

### EBA CA gaps and REER prediction
- Initial EBA CA gaps are associated with future REER adjustments with the correct sign.
- Strong positive association between initial EBA CA gaps and changes in observed REER over both sub-periods.
- REER index gaps derived from EBA adjust similarly to observed REER.
- No statistically significant association between changes in REER level gaps and initial EBA CA gaps.

### Implications and interpretation for policy advice
- EBA gaps tend to adjust over time but adjustment is slow and asymmetric; interpretation of EBA CA model residuals should account for this.
- Closing policy gaps contributes to external adjustment primarily when policy gaps and overall CA gaps are aligned; policy actions often close for domestic reasons irrespective of external impacts.
- Results do not currently warrant quantifying formal adjustors to normative EBA CA benchmarks based solely on these estimates, but findings can aid interpretation of residuals and formulation of policy advice.

### Concluding remarks and avenues for further research
- The 2022 EBA update improves conceptual framework and incorporates recent data and literature; main novelty is evaluating how estimated CA gaps associate with future external adjustment.
- Findings: CA gaps associate with future CA and REER movements; speed depends on initial CA balance and income level.
- Ongoing/future research areas include:
  - Assessment of stock imbalances and risks associated with their size and composition.
  - Determinants of corporate saving and the role of multinational companies behind large persistent CA surpluses in some advanced economies.
  - How risks of fragmentation in trade and financial systems may affect distribution of current account balances going forward.
- Progress depends on further data collection for inclusion in EBA methodology.

*IMF WORKING PAPERS 2022 Update of the EBA Methodology — Annex V material as provided.*

### Annex I. Measuring Commodity Long-Term Prices

### Annex I. Measuring Commodity Long-Term Prices

### A. Construction of the Commodity Terms-of-Trade Gap
- Rationale and filtering choice:
  - Commodity price fluctuations follow “commodity supercycles” longer than standard business cycles; therefore band-pass filters are used instead of the Hodrick-Prescott (HP) filter with smoothing parameter of λ=100 typically used for business cycle analysis at annual frequencies.
  - Commodity super-cycle defined as fluctuations in frequencies in the 20-70 years range (following Jacks, 2013).
- Sequencing of variable construction:
  - (i) Apply filtering techniques to individual commodity price series to obtain individual commodity price gaps (e.g., oil price gap, copper price gap).
  - (ii) Aggregate commodity price gaps using country-specific trade weights to build country-specific terms-of-trade gaps. This sequencing improves transparency by allowing calculation of each commodity’s contribution to the overall gap.
- Sample and data extension:
  - Price gaps calculated for a sample of 42 individual commodity price series.
  - Fund data available since 1980 are extended backwards using external datasets:
    - World Bank Commodity Price Data (The Pink Sheet): annual prices, 1960 to present, nominal US dollars.
    - Pfaffenzeller and others (2007): annual prices, 1900 to 2003, nominal US dollars.
    - Jacks (2013), updated dataset: annual real prices, 1850 to 2015, converted to nominal US dollars using US official CPI.
    - Schwerhoff and Stuermer (2015), updated dataset: annual prices, 1700 to 2018, nominal US dollars.
- Estimation and decomposition:
  - Log price decomposition for commodity k at time t: ln P_{k,t} = LTT_{k,t} + CSC20_70_{k,t} + STF_{k,t}, where:
    - LTT_{k,t} denotes the long-term trend;
    - CSC20_70_{k,t} denotes the commodity super-cycle (20-70 year frequencies);
    - STF_{k,t} denotes short-term fluctuations.
  - Two-step decomposition:
    - (i) Isolate CSC20_70_{k,t} using the Christiano-Fitzgerald band-pass filter.
    - (ii) Apply the Butterworth high-pass filter (with parameter 40) to the residual to distinguish LTT_{k,t} from STF_{k,t}.
  - Commodity price gap definition:
    - gap_{k,t} = CSC20_70_{k,t} + STF_{k,t} = ln P_{k,t} − LTT_{k,t}.
  - Aggregation into country-specific commodity terms-of-trade gap:
    - commoTOTgap_{i,t} = Σ_k (ω_{k,i,t}^{exports} − ω_{k,i,t}^{imports}) × gap_{k,t}, where country-specific Comtrade weights ω are used.
  - Final adjustment:
    - Multiply the country-specific commodity terms-of-trade gap by the openness ratio.
- Illustration and data treatment in figure:
  - Annex Figure 1 decomposes oil log prices into long-term trend (orange, dashed), commodity supercycle (blue), short-term fluctuations (red), and oil price gap (green).
  - Historical series extended between 2021 and 2027 using WEO forecasts, and beyond 2027 (up to 2032) using a no-change assumption.

### B. Construction of the Oil and Natural Gas Reserves Variable
- Purpose:
  - Capture effects of income from exhaustible resources (oil and gas) in the EBA CA model; reflect temporariness of resource endowments and saving decisions by net exporters.
- Conceptual definition:
  - The variable is an interaction of each commodity’s net external balance with a measure of its temporariness (ratio of current extraction to proven reserves, the inverse of “years-till-exhaustion”), relative to Norway in 2010.
- Steps to leverage price-gap construction:
  1. Neutralize short- and medium-term price fluctuations in net exports of oil and gas by valuing net oil and gas exports at long-term prices (using oil and gas price gaps to correct net export series to prices consistent with a zero-price gap).
  2. Adapt net exports measure: after price neutralization, apply a 3-year moving average to smooth remaining short-term fluctuations in trade volumes.
- Formal definition (textual representation of formula from source):
  - Oil&Gas_{i,t} = Σ_k { (1/3) Σ_{s=0}^{2} (X_{k,i,t−s} / Y_{i,t−s}) × corrective_factor_{k,t−s} } × temp_{k,i,t} / temp_{Norway,2010,k}
    - X_{k,i,t} denotes nominal oil and gas net exports (if positive; zero otherwise).
    - Y_{i,t} denotes nominal GDP.
    - Corrective factor = exp(−gap_{k,t}), which values external balances as if prices were at their long-term trend.
    - temp measures resource temporariness: ratio of current extraction to proven reserves in volume terms, relative to Norway in 2010.
- Rationale:
  - Insulates the oil and gas reserves variable from short- and medium-term price fluctuations, enhancing structural nature and contributing to norm stability.
- Note on climate/decarbonization uncertainty:
  - Effective extraction of proven reserves may be lower than currently thought; if “effective“ proven reserves were lower, temporariness would increase and oil/gas net exporters’ CA norms would increase, all else equal. This is flagged for future research.

### Annex II. Benchmarks for Policy Variables (P*)
- Purpose:
  - P* are normative policy benchmarks representing desirable medium-term levels of policy variables; they are set to meet medium-term domestic objectives rather than to target a specific current account level.
- Fiscal policy:
  - P* corresponds to levels of the cyclically-adjusted fiscal balance (as a share of potential GDP) deemed desirable from a medium to long-term perspective when output gaps are closed.
  - Anchors: debt-stabilizing primary balance, long-term adjustment needs given fiscal costs of aging.
  - Fiscal P* may differ from recommendations for the current year when cyclical considerations matter.
- Public health spending:
  - P* guided by benchmark estimates from a regression including (PPP-based) GDP per capita, current old-age dependency ratio, and income inequality.
  - Staff can choose actual spending levels if justified.
- Capital controls:
  - Desirable medium-term benchmark is the cross-country average level of the controls index: 0.29 in 2019 (index range 0 to 1), or a country’s actual level, whichever is smaller.
- Foreign exchange intervention (FXI):
  - Over the medium term, FXI would normally be set to zero, assuming countries reach adequate reserves (including comparable off balance-sheet FX positions) from a precautionary viewpoint.
  - In exceptional circumstances, a nonzero desirable level could be set when reserves are significantly below the IMF’s Assessing Reserve Adequacy (ARA) metric, implying reserve accumulation may be necessary over an extended period.
  - Deviations of policy gaps (P − P*) for FXI are not necessarily policy distortions; they may be appropriate responses to conditions or necessary temporary reserve build-up.
- Credit gap:
  - P* for the credit gap should be zero in most cases because credit gaps are estimated directly.
  - Adjustments considered if the credit gap estimate misrepresents financial imbalances (e.g., during financial deepening or credit busts).

### Annex III. Measurement Biases
- Two main biases in external accounts arising from statistical treatment of investment income under BPM6:
  1. Inflation bias:
    - Investment income recorded in nominal terms; for debt instruments, nominal interest income also compensates for expected inflation erosion of principal, leading to systematic bias in NIIP valuation changes.
  2. Portfolio equity retained earnings bias:
    - For FDI equity, both dividends and retained earnings are recorded in the income balance; for portfolio equity only dividends are recorded, while retained earnings are reflected in NIIP valuation changes only.
- Prior methodology and 2022 refinements:
  - Previous EBA methodology introduced complementary tools to adjust for these biases using approaches in Adler and others (2019): two approaches for inflation bias (realized inflation, forecasted inflation) and three approaches for portfolio equity retained earnings bias (stock, flow, hybrid).
  - 2022 refinements:
    - Inflation bias estimation unchanged.
    - Focused on improving portfolio equity retained earnings bias estimates:
      1. Retained flow and stock methods retained; hybrid method discontinued because it adds no new information and can introduce bias when stock and flow data are inconsistent.
         - Notation from source:
           - RE(flow) = [1 / (dy × pe)] × DIV = RE_dom_DIV × DIV
           - RE(stock) = [1 / pe − dy] × L = RE_dom_n × p × L
           - RE(hybrid) = L / pe − DIV = RE_dom_n × p × L + [ (L / n × p) . DIV_dom − DIV ]
           - dy = dividend yield ratio; pe = price-earnings ratio; DIV = dividends on portfolio equity liabilities; L = stock of portfolio equity liabilities; p and n are price and number of equities.
      2. Introduced a new corporate saving method combining national accounts and foreign portfolio holdings data (Allen and Rebillard, forthcoming).
         - Rationale: flow and stock methods assume firms with foreign shareholders have same payout ratios as domestic listed companies; corporate saving approach uses national account data and assumes similar average saving behavior across firms with different foreign ownership ratios.
         - Corporate saving approach calculation (textual):
           - Country i’s portfolio equity retained earnings bias on liability side: RE_i_L = S_i × [ (for_i × peq_i) / (for_i × peq_i + ...) ] where:
             - S_i denotes corporate saving (net of depreciation);
             - for_i denotes foreign ownership rate (percentage owned by both FDI and foreign portfolio equity investors in overall equity liabilities of the corporate sector);
             - peq_i denotes share of portfolio equity investors among foreign investors (FDI and portfolio equity).
           - Asset side calculated as CPIS-weighted sum of partner countries’ portfolio equity retained earnings on liability side; net balance RE_i = RE_i_A − RE_i_L.
         - Corporate saving estimates broadly align with stock and flow approaches but can differ where listed firms’ retained earnings deviate from overall corporate sector.
    - Adjustor to EBA model results averages the three approaches (stock, flow, corporate saving). In some cases more granular data can refine estimates.

### Annex IV. Pension Systems and Current Accounts
### A. Data and Related Caveats
- Objective:
  - Assess relation between pension system replacement and coverage rates and the part of CA balances not explained by the refined EBA CA model.
- Data sources and coverage:
  - Koomen and Wicht (KW) dataset: mandatory pension indicators for 49 economies over 1986-2016 (all in EBA sample); includes mandatory FF and PAYG replacement rates based on Bloom and others (2007) and SSA reports; missing observations filled using nearest available year and SSA reports.
  - OECD Pensions at a Glance reports: replacement rates for voluntary and mandatory schemes for 51 OECD and G20 economies spanning 2005-2021; uses OECD staff estimates for full-career average income-earning workers.
  - Coverage proxy:
    - Follows KW: proxy for coverage rate = 1 − self-employment share (self-employment share from ILO via World Bank WDI), since self-employed are more likely to be excluded from pension systems.
- Caveats:
  - Necessary pension data not available for full EBA sample of 52 economies during 1986-2019; analysis focuses on subsample with available data.
  - KW only consider mandatory systems; OECD data extends to voluntary systems.

### B. Estimation Results
- Approach:
  - Estimate relation between pension indicators and residuals from the refined EBA CA model for economies with pension data.
  - Use fitted values to estimate contribution of pension parameters to explaining CA balances.
  - Variables enter regressions in demeaned form (deviation from GDP-weighted sample average).
  - Specifications include replacement and coverage rates and their interactions, following KW.
- Findings (summary from source text):
  - The R-squared statistics indicate that the pension variables explain between [text truncates in source]. (Source presents Annex Table 4.1 with estimated relations; text indicates pension variables have explanatory power but full table/results are in Annex Table 4.1.)

*Source: Annex I–IV text from "wpiea2023047-print-pdf - Annex I. Measuring Commodity Long-Term Prices" (IMF Working Papers 2022 Update of the EBA Methodology).*

### 1.7 and 8.6 percent of the variation of EBA CA model residuals. This result represents a noticeable

### wpiea2023047-print-pdf - 1.7 and 8.6 percent of the variation of EBA CA model residuals. This result represents a noticeable

### Pension system indicators: relation to EBA CA model residuals
- Adding pension system indicators explains between 1.7 and 8.6 percent of the variation of EBA CA model residuals.
- Baseline EBA CA equation R-squared is about 52 percent.
- Proportion explained is larger for the subsample of 36 EBA economies with OECD replacement rates than for the 49 EBA economies with KW indicators.
- Relation is stronger for mandatory FF replacement rates than for PAYG rates (columns 1 and 2).
- Relation with FF rates is especially strong for economies with larger coverage rates.
- Example of economic significance (based on column 2):
  - A 10-percentage point rise in the mandatory FF replacement rate is associated with a 0.41 percentage point of GDP rise in the CA balance (0.1 × 4.08) at the sample average coverage rate.
  - When the coverage rate is one standard deviation higher (by 18 percentage points) a 10-percentage point rise in the FF replacement rate is associated with a 0.57 percentage point of GDP rise in the CA balance.
- OECD "Pensions at a Glance" results:
  - Mandatory replacement rates show a strong relation with CA balances, especially at high coverage rates (columns 3-4).
  - Voluntary replacement rates have a relatively weak relation with CA balances; estimated coefficients are statistically indistinguishable from zero.
  - OECD mandatory private replacement rates have a stronger estimated relation with the CA than mandatory public replacement rates, especially at higher pension coverage rates (columns 5-6).
  - Interpretation: mandatory private replacement rates are often FF (consistent with stronger relation); mandatory public replacement rates are often PAYG (consistent with weaker relation).

### Robustness and interpretation
- Potential concern: pension system variables correlated with other variables in EBA CA model could contaminate estimates.
- Robustness check: re-estimating the latest EBA CA equation while adding pension indicators (for subset with data) yields very similar coefficients that are economically and statistically indistinguishable from those reported in Table 4.
- Caution: replacement rates in datasets are estimates of theoretical future rates and can differ significantly depending on construction assumptions.
- Policy use: while results do not warrant directly quantifying formal adjustors to normative EBA CA benchmarks, they can aid interpretation of EBA CA model residuals and formulation of policy advice.

### Contribution to CA balances (estimation and uncertainty)
- Estimation results in Online Annex Table 4.1 can be used to estimate CA contributions from pension variables to CA balances.
- There are considerable uncertainties associated with these estimates, reflecting uncertainty in replacement rate projections and other factors.
- The results are intended to inform interpretation and policy formulation rather than to serve as formal benchmark adjustors.

### Key coefficients and statistics from Annex Table 1 (selected, exact values preserved)
- PAYG replacement rate #: 0.956 (column 1) and 1.145 (column 2) with standard errors (0.675) and (0.769).
- Mandatory FF replacement rate #: 3.083*** (column 1) and 4.087*** (column 2) with standard errors (0.895) and (1.006).
- Coverage rate #: 2.397** (column 1), -1.611 (column 2), 5.080*** (column 3), -2.139 (column 4), 4.812*** (column 5), -1.988 (column 6) with corresponding standard errors (1.027), (2.171), (1.559), (3.824), (1.510), (3.779).
- PAYG replacement rate x Coverage rate #: 4.892 (standard error (3.278)).
- Mandatory FF replacement rate x Coverage rate #: 9.354*** (standard error (2.573)).
- Mandatory replacement rate #: 3.026** (column 3) and 3.818*** (column 4) with standard errors (1.266) and (1.359).
- Voluntary replacement rate #: -5.009* (column 3), -1.072 (column 4), -4.437 (column 5), -1.716 (column 6) with standard errors (2.911), (3.819), (2.749), (3.754).
- Mandatory replacement rate x Coverage rate #: 15.428*** (standard error (5.927)).
- Voluntary replacement rate x Coverage rate #: -41.486 and -35.698 with standard errors (26.265) and (25.958).
- Mandatory public replacement rate #: 2.590** (column 5) and 1.936 (column 6) with standard errors (1.150) and (1.338).
- Mandatory private replacement rate #: 7.083*** (column 5) and 3.762* (column 6) with standard errors (1.735) and (1.938).
- Mandatory public replacement rate x Coverage rate #: 9.689* (standard error (5.255)).
- Mandatory private replacement rate x Coverage rate #: 51.287*** (standard error (11.305)).
- Constant terms: 0.068, 0.067, -0.477, 0.098, -0.715**, -0.212 with standard errors (0.208), (0.205), (0.384), (0.521), (0.358), (0.521).
- Observations: 1,254, 1,254, 484, 484, 475, 475.
- R-squared: 0.017, 0.025, 0.044, 0.062, 0.072, 0.086.
- Number of economies: 49, 49, 36, 36, 36, 36.
- Data sources: KW dataset (columns 1-2); OECD dataset (columns 3-6).

### Structural policies: product and labor market regulations and CA residuals
- Equation estimated relates EBA CA residual μ̂_{j,t} to vector S_{j,t} of regulatory stringency indicators (deviations from GDP-weighted world average).
- OECD indicators used: overall product market reforms indicator, product market sub-indicator "legal barriers to entry", and aggregated labor market regulations indicator (combines severance pay at 9 months, 4 years, and 20 years and strictness of fixed-term contract rules).
- Dataset covers PMR and EPL for years spanning 1998 to 2018 for 22 AEs; indicators run from 0 to 6 (6 = most heavily regulated). Missing observations imputed using nearest available year.
- Findings (Annex Table 5.1 / Annex Table 2):
  - Product market regulation (overall): coefficient -0.018 (standard error (0.9838)); not statistically significant; sign opposite to theoretical expectation (column 1).
  - Legal barriers to entry: coefficient 0.773 (standard error (0.6128)); lower barriers (deregulation) associated with lower CA balances, though not statistically significant at conventional levels (column 2).
  - Labor market regulation (combined indicator): coefficients -0.408 (column 1, standard error (0.2803)) and -0.722** (column 2, standard error (0.2958)).
- Observations: 484 and 352.
- Number of economies: 22 and 22.
- R-squared: 0.003 and 0.011.
- Interpretation:
  - Some structural indicators are not strongly associated with CA balances.
  - Reducing legal barriers to entry is associated with a lower CA balance (consistent with expectations) but not statistically strong in this sample.
  - Easing some labor market regulations is associated with a higher CA balance.
  - Impact of structural reforms on CA will be highly country-specific and depend on reform mix and persistence of effects; calls for granular, country-specific policy recommendations.

*Source: IMF Working Papers — 2022 Update of the EBA Methodology (content unit: wpiea2023047-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023047-print-pdf.pdf_