## 0.04 percentage points once intra-year exchange rate fluctuations are accounted for, but this

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### Key quantitative findings
- Differential magnitude:
  - The differential is "0.04 percentage points once intra-year exchange rate fluctuations are accounted for".
  - The differential is "0.6 percentage points lower in countries that experienced depreciations above the 99th percentile of the full sample".
- Large nominal depreciations (above the 99th percentile) — estimation implications:
  - Debt projections could have been underestimated by about "0.9 percentage points of GDP" in the year of the large nominal depreciation if intra-year exchange rate valuation effects were not properly accounted for.
  - Debt-stabilizing primary balances could have been overestimated by about "1.5 percentage points of GDP" in the same circumstance.

### Analytical focus and methods
- Section II: introduces the basic above-the-line public debt accumulation equation when intra-year exchange rate fluctuations are considered.
- Section III: discusses the analytics to assess policy-relevant implications (IRGD and DSPB).
- Section IV: introduces a novel dataset to quantify the relevance of intra-year exchange rate valuation effects.

### Core equations and adjustments (high-level)
- Baseline gross public debt identity (nominal terms):
  - D_t = (e_t^eop D_t^f + D_t^d) + e_t^eop i_t^f D_{t-1}^f + i_t^d D_{t-1}^d − PB_t + OF_t. (equation (1))
- Correction recognizing intra-year conversion of foreign-currency interest flows (average vs end-of-period rate):
  - D_t = (e_t^eop D_t^f + D_t^d) + e_t^{avg} i_t^f D_{t-1}^f + i_t^d D_{t-1}^d − PB_t + OF_t + SF_t. (equation (2))
- Stock-flow adjustment term:
  - SF_t = (e_t^eop − e_t^{avg})(D_t^f − D_{t-1}^f). (leads to equation (3))
- Valuation-adjusted average nominal effective interest rate:
  - i_t^{iyxr} = [α_{t-1}(1+i_t^f)(1+ε_t^{eop}) e_t^{avg}/e_t^{eop} + (1−α_{t-1})(1+i_t^d)]/(1−α_t γ_t) − 1. (equation (4))
  - γ_t ≡ (1 − e_t^{avg}/e_t^{eop})
- Simplified no intra-year XR case (e_t^{avg}/e_t^{eop} = 1):
  - i_t^{no_iyxr} = α_{t-1}(1+i_t^f)(1+ε_t^{eop}) + (1−α_{t-1})(1+i_t^d) − 1. (equation (5))
- Debt-to-GDP change with and without intra-year XR:
  - With intra-year XR:
    - d_t^{iyxr} − d_{t-1}^{iyxr} = [1+i_t^{iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{iyxr} + 1/(1−α_t γ_t)(−pb_t + of_t). (equation (6))
  - Without intra-year XR:
    - d_t^{no_iyxr} − d_{t-1}^{no_iyxr} = [1+i_t^{no_iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{no_iyxr} − pb_t + of_t. (equation (7))

### Policy-related metrics: IRGD and DSPB
- IRGD definitions:
  - IRGD_t^{iyxr} = (1 + i_t^{iyxr})/[(1+g_t)(1+π_t)] − 1. (equation (8))
  - IRGD_t^{no_iyxr} = (1 + i_t^{no_iyxr})/[(1+g_t)(1+π_t)] − 1. (equation (9))
- DSPB definitions (at previous-period debt level):
  - DSPB_t^{iyxr} = [1 + i_t^{iyxr}]/[(1+g_t)(1+π_t)] − 1) [1 − α_t γ_t] d_{t-1}^{iyxr} + of_t. (equation (10))
  - DSPB_t^{no_iyxr} = [1 + i_t^{no_iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{no_iyxr} + of_t. (equation (11))
- Numerical illustrative scenario (parameters and outcomes):
  - Parameters: α_t = 0.6, i_t^f = i_t^d = 0.05, g_t = π_t = 0.03, pb_t = −0.1, of_t = 0.05; α_{t+1} expected to be 0.7.
  - Exchange rates: period t: e_t^{avg} = 1.25 LC$/US$, e_t^{eop} = 1.50 LC$/US$; period t+1: e_{t+1}^{avg} = 2.25 LC$/US$, e_{t+1}^{eop} = 3.00 LC$/US$.
  - Valuation-adjusted nominal effective interest rates: i_{t+1}^{iyxr} = 65.5 percent and i_{t+1}^{no_iyxr} = 68.0 percent.
  - IRGD outcomes: IRGD_{t+1}^{iyxr} = 56.0 percent and IRGD_{t+1}^{no_iyxr} = 58.4 percent.
  - Debt projection from initial d_{t-1} = 0.5: d_{t}^{iyxr} = 96.2 and d_{t}^{no_iyxr} = 94.2 percent of GDP.
  - DSPB results: DSPB_{t+1}^{iyxr} = 28.1 percent of GDP and DSPB_{t+1}^{no_iyxr} = 34.2 percent of GDP.
  - Interpretation: ignoring intra-year valuation effects would have led to an underestimation of debt levels and an overestimation of the primary balance needed to stabilize debt at the previous-period level under this parameterization.
- General insight: differences between average and end-of-period exchange rates (e_t^{avg}/e_t^{eop} ≠ 1) can materially affect IRGD, DSPB, and debt projections depending on exchange rate path, α_t, and fiscal flows.

### Dataset (novel assembly) — coverage and descriptive statistics
- Data sources: IMF’s World Economic Outlook (WEO), April 2020 release, augmented with IMF’s MAC DSA dataset to decompose gross public debt and effective interest rates into local and foreign currency components.
- Sample coverage: 82 advanced and emerging economies reporting a positive share of public debt denominated in foreign currency during 2008–19.
- Sample exclusions and restrictions: low-income countries excluded due to lack of currency-of-denomination and effective nominal interest rate data for gross public debt; final sample restricted to observations with non-missing effective interest rates in local and foreign currencies.
- Key descriptive statistics from Table 1 (sample 2008–19; Obs = 574):
  - Total gross public debt / GDP: Mean 51.54, Std Dev 27.55, Min 7.60, Max 172.18.
  - Gross public debt in FX / total debt: Mean 38.78, Std Dev 24.12, Min 0.03, Max 97.98.
  - Gross public debt in LC / total debt: Mean 61.22, Std Dev 24.12, Min 2.02, Max 99.97.
  - Eff. nominal interest rate on FX debt: Mean 3.91, Std Dev 2.35, Min -1.04, Max 30.91.
  - Eff. nominal interest rate on LC debt: Mean 6.50, Std Dev 3.21, Min -1.93, Max 19.17.
  - Real GDP growth: Mean 3.13, Std Dev 2.80, Min -9.77, Max 11.34.
  - GDP deflator inflation: Mean 4.59, Std Dev 6.49, Min -20.19, Max 51.51.
  - Primary balance / GDP: Mean -0.80, Std Dev 3.42, Min -16.10, Max 16.38.
  - Nominal exchange rate depreciation: Mean 4.42, Std Dev 12.40, Min -17.30, Max 104.14.
  - Avg to end-of-period XR (ratio): Mean 0.98, Std Dev 0.05, Min 0.68, Max 1.11.
- Aggregate observation: on average about 39 percent of total debt is denominated in foreign currency (roughly about 20 percent of GDP). Effective interest rates in FX are lower than in LC on average. Average primary deficit is 0.8 percent of GDP; average nominal GDP growth about 7.7 percent annually. Mean avg-to-end-of-period exchange rate ratio is 0.98, consistent with trend depreciation.

### Empirical results — intra-year exchange rate fluctuations
- Subsample avg/end XR ratio (Figure 1 summary):
  - Full sample mean of avg/end XR ratio = 0.98.
  - For significant nominal appreciations, average ratio = 1.04.
  - For significant nominal depreciations, average ratio = 0.89.
  - Footnote: restricting to 1st and 99th percentiles yields mean ratios of 1.09 and 0.78, respectively.

### Empirical results — IRGD (Table 2 summary; IRGD in percentage points; Obs = 574)
- Full sample mean IRGD^{iyxr} = -0.41 and IRGD^{no_iyxr} = -0.38; Nom growth mean = 7.83.
- By income group:
  - HICs (28 countries, 161 obs): IRGD^{iyxr} = 0.80, IRGD^{no_iyxr} = 0.80; Nom growth mean = 4.66.
  - UMICs (35 countries, 231 obs): IRGD^{iyxr} = 0.03, IRGD^{no_iyxr} = 0.09; Nom growth mean = 8.09.
  - LMICs (19 countries, 182 obs): IRGD^{iyxr} = -2.04, IRGD^{no_iyxr} = -2.00; Nom growth mean = 10.30.
- Extreme depreciation subsets:
  - Nom depr below 1st pctile (5 obs): IRGD = -6.22 (both measures); Nom growth = 6.23.
  - Nom depr below 10th pctile (35 countries, 57 obs): IRGD^{iyxr} = -5.30, IRGD^{no_iyxr} = -5.35; Nom growth = 8.20.
  - Nom depr above 90th pctile (29 countries, 57 obs): IRGD^{iyxr} = 6.08, IRGD^{no_iyxr} = 6.28; Nom growth = 12.84.
  - Nom depr above 99th pctile (5 obs): IRGD^{iyxr} = 15.28, IRGD^{no_iyxr} = 15.84; Nom growth = 24.98.
- Interpretation: for the average country, accounting for intra-year exchange rate fluctuations reduces IRGD by about 0.04 percentage points on average. Heterogeneity exists: reductions up to 0.20 or 0.57 percentage points in countries with significant nominal depreciations. Valuation-adjusted nominal effective interest rates tend to be lower once intra-year differences are included.

### Empirical results — stock-flow adjustment, debt projections, and DSPB
- Stock-flow adjustment (s_f) statistics (Table 3; Obs = 574; percent of GDP):
  - Full sample mean stock-flow adjustor = 0.02, Std Dev = 0.21, Min = -0.99, Max = 3.53.
  - HICs (28 countries, 161 obs): Mean 0.00, Std Dev 0.07, Min -0.28, Max 0.47.
  - UMICs (35 countries, 231 obs): Mean 0.03, Std Dev 0.31, Min -0.99, Max 3.53.
  - LMICs (19 countries, 182 obs): Mean 0.02, Std Dev 0.11, Min -0.25, Max 0.81.
  - Subsamples by depreciation percentiles:
    - Nom depr below 1st pctile (5 obs): Mean -0.03, Std Dev 0.09, Min -0.14, Max 0.09.
    - Nom depr below 10th pctile (35 countries, 57 obs): Mean -0.03, Std Dev 0.07, Min -0.33, Max 0.19.
    - Nom depr above 90th pctile (29 countries, 57 obs): Mean 0.20, Std Dev 0.62, Min -0.99, Max 3.53.
    - Nom depr above 99th pctile (5 obs): Mean 1.22, Std Dev 1.59, Min -0.13, Max 3.53.
- Counter-factual one-year-ahead projection exercise (method):
  - Assume WEO-reported debt levels are generated by a process including intra-year valuation effects (equation (6)); derive implicit of_t; compare one-year-ahead projections using (6) vs (7) starting from equal initial d_{t-1}.
- Counter-factual findings:
  - For episodes with large nominal depreciations (above 90th/99th percentiles), average stock-flow adjustment ~ 1.2 percent of GDP (99th percentile subsample mean = 1.22 percent).
  - Ignoring intra-year valuation effects would have led to underestimation in debt projections by about 0.9 percentage points of GDP on average for large depreciation cases.
  - Examples of larger differences: Argentina 2018: 1.6 ppts of GDP; Surinam 2016: 3.3 ppts of GDP.
  - For cases with nominal depreciations below the 1st percentile, the stock-flow adjustment term is generally low or negative, implying minor miscalculations in debt projections.
- DSPB implications: differences in estimated DSPB are sizable for large depreciation episodes, with DSPB overestimated if intra-year valuation effects are ignored.

### Intuition and illustrative cases
- Argentina 2018 (illustrative intuition):
  - Large currency depreciation such that e_{t}^{avg}/e_{t}^{eop} < 1.
  - Including intra-year valuation effects:
    - Automatic debt dynamics portion of change in debt is lower due to a lower interest rate-growth differential.
    - Contribution of the primary deficit and other net debt-creating flows to change in debt is higher because new debt is added at the lower average exchange rate relative to end-period rate.
    - Net effect: a higher change in the debt stock projected in Argentina in 2018 if intra-year valuation effects are included.
  - Debt-stabilizing primary balance needed in 2018 to stabilize debt at 2017 level would have been lower when intra-year exchange rate fluctuations are included.

### Mean nominal effective interest rates (Table 4 summary; percent; averages 2008–19)
- By income group and subsamples:
  - HICs (28 countries, 161 obs): i_iyxr Mean 5.30, i_no_iyxr Mean 5.31, i_fisc Mean 4.81.
  - UMICs (35 countries, 231 obs): i_iyxr Mean 7.83, i_no_iyxr Mean 7.89, i_fisc Mean 5.59.
  - LMICs (19 countries, 182 obs): i_iyxr Mean 7.83, i_no_iyxr Mean 7.88, i_fisc Mean 5.53.
  - Full sample (82 countries, 574 obs): i_iyxr Mean 7.12, i_no_iyxr Mean 7.16, i_fisc Mean 5.35.
  - Nom depr below 1st pctile (5 countries, 5 obs): i_iyxr Mean -0.52, i_no_iyxr Mean -0.52, i_fisc Mean 6.40.
  - Nom depr below 10th pctile (35 countries, 57 obs): i_iyxr Mean 2.36, i_no_iyxr Mean 2.30, i_fisc Mean 5.54.
  - Nom depr above 90th pctile (29 countries, 57 obs): i_iyxr Mean 19.42, i_no_iyxr Mean 19.66, i_fisc Mean 6.67.
  - Nom depr above 99th pctile (5 countries, 5 obs): i_iyxr Mean 44.30, i_no_iyxr Mean 45.03, i_fisc Mean 7.83.
- Conclusion from Table 4: i_iyxr < i_no_iyxr generally, except for countries with nominal depreciations below the 1st percentile. Average nominal effective interest rates from fiscal statements, i_fisc, cannot be used directly to assess debt dynamics unless adjusted for exchange rate valuation effects.

### Illustrative country-level decompositions (selected entries from Tables 5 and 6; percent of GDP)
- With intra-year valuation effects (selected):
  - BRA2016: Stock 78.31, Change 15.74, Automatic dynamics 4.85, Contribution primary deficit 0.27, Contribution other flows 0.61, Stock-flow adjustment -0.01, DSPB 5.48.
  - POL2017: Stock 50.60, Change -3.63, Automatic dynamics -4.90, Contribution primary deficit -0.10, Contribution other flows 1.36, Stock-flow adjustment -0.08, DSPB -3.62.
  - ARG2018: Stock 86.06, Change 28.95, Automatic dynamics 16.43, Contribution primary deficit 2.81, Contribution other flows 9.71, Stock-flow adjustment 12.20, DSPB 21.02.
  - AGO2018: Stock 89.00, Change 19.74, Automatic dynamics 12.42, Contribution primary deficit -7.60, Contribution other flows 14.92, Stock-flow adjustment 0.54, DSPB 24.18.
  - SUR2016: Stock 76.07, Change 32.72, Automatic dynamics 12.90, Contribution primary deficit 7.38, Contribution other flows 12.44, Stock-flow adjustment 3.53, DSPB 22.21.
- Without intra-year valuation effects (selected):
  - BRA2016: Stock 78.31, Change 15.73, Automatic dynamics 4.85, Contribution primary deficit 0.27, Contribution other flows 0.62, DSPB -5.46.
  - ARG2018: Stock 84.42, Change 27.31, Automatic dynamics 17.24, Contribution primary deficit 2.26, Contribution other flows 7.81, Stock-flow adjustment -25.05.
  - AGO2018: Stock 88.93, Change 19.67, Automatic dynamics 13.20, Contribution primary deficit -6.72, Contribution other flows 13.20, Stock-flow adjustment -26.39.
  - SUR2016: Stock 72.79, Change 29.43, Automatic dynamics 12.06, Contribution primary deficit 6.47, Contribution other flows 10.91, Stock-flow adjustment -22.97.
- Note: Tables 5 and 6 present full country/year level decompositions, including the stock-flow adjustment term and DSPB calculated using (10) and (11).

### Policy implications and conclusions
- Because public sectors often hold liabilities denominated in foreign currency, periods of heightened exchange rate volatility can lead to substantial revaluations of liabilities when measured in local currency and/or as a share of GDP.
- Careful consideration of how exchange rate fluctuations affect foreign currency denominated flows and stocks is critical for assessing public debt evolution.
- Accounting practice recommendation: debt-related stocks and flows denominated in foreign currency should be converted to local currency using end-of-period rates for stocks and average exchange rates for flows, as envisaged in public finance manuals.
- Inclusion of the stock-flow adjustment term stemming from intra-year exchange rate fluctuations:
  - May materially affect computation of public debt over time, interest rate-growth differentials, and debt-stabilizing primary balances.
  - Is critical to accurately project public debt levels and associated policy indicators that inform risk of debt distress.

### Suggested extensions for future work
- Increase empirical coverage to include low-income countries to quantify the size of the stock-flow adjustment term across a larger sample.
- Assess how intra-year exchange rate fluctuations might affect medium-term debt targets, particularly where average and end-of-period exchange rates have diverged substantially.
- Use assessment of intra-year valuation effects to determine fiscal consolidation paths consistent with medium-term debt objectives.

*Source: IMF Working Paper (wpiea2020261-print-pdf).*

### 0.04 percentage points once intra-year exchange rate fluctuations are accounted for, but this

### wpiea2020261-print-pdf - 0.04 percentage points once intra-year exchange rate fluctuations are accounted for, but this

### Key quantitative findings
- The differential is "0.04 percentage points once intra-year exchange rate fluctuations are accounted for".
- The differential is "0.6 percentage points lower in countries that experienced depreciations above the 99th percentile of the full sample".
- In countries with large nominal depreciations (above the 99th percentile), estimations suggest:
  - Debt projections could have been underestimated by about "0.9 percentage points of GDP" in the year of the large nominal depreciation if intra-year exchange rate valuation effects were not properly accounted for.
  - Debt-stabilizing primary balances could have been overestimated by about "1.5 percentage points of GDP" in the same circumstance.

### Analytical focus and methods
- Section II introduces the basic above-the-line public debt accumulation equation when intra-year exchange rate fluctuations are considered.
- Section III discusses the analytics to assess policy-relevant implications.

*Source: wpiea2020261-print-pdf - 0.04 percentage points once intra-year exchange rate fluctuations are accounted for, but this*

### Section IV introduces a novel dataset to quantify the relevance of intra-year exchange rate

### Section IV introduces a novel dataset to quantify the relevance of intra-year exchange rate valuation effects

### II. Public sector debt dynamics — key formulation and adjustments
- Baseline gross public debt identity (nominal terms):  
  D_t = (e_t^eop D_t^f + D_t^d) + e_t^eop i_t^f D_{t-1}^f + i_t^d D_{t-1}^d − PB_t + OF_t. (equation (1) in source)
- Correction recognizing intra-year conversion of foreign-currency interest flows (average vs end-of-period rate):  
  D_t = (e_t^eop D_t^f + D_t^d) + e_t^{avg} i_t^f D_{t-1}^f + i_t^d D_{t-1}^d − PB_t + OF_t + SF_t. (equation (2))
- Stock-flow adjustment term defined to reconcile flow/stock conversion differences:  
  SF_t = (e_t^eop − e_t^{avg})(D_t^f − D_{t-1}^f). Leading to equation (3) which explicitly adds the valuation adjustment term.
- Valuation-adjusted average nominal effective interest rate (includes capital gains/losses on principal due to exchange rate movements):  
  i_t^{iyxr} = [α_{t-1}(1+i_t^f)(1+ε_t^{eop}) e_t^{avg}/e_t^{eop} + (1−α_{t-1})(1+i_t^d)]/(1−α_t γ_t) − 1. (equation (4))  
  - γ_t ≡ (1 − e_t^{avg}/e_t^{eop})
- Simplified case when e_t^{avg}/e_t^{eop} = 1 gives equation (5):  
  i_t^{no_iyxr} = α_{t-1}(1+i_t^f)(1+ε_t^{eop}) + (1−α_{t-1})(1+i_t^d) − 1.
- Debt-to-GDP change expressions with and without intra-year exchange rate (equations (6) and (7)):  
  - With intra-year XR: d_t^{iyxr} − d_{t-1}^{iyxr} = [1+i_t^{iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{iyxr} + 1/(1−α_t γ_t)(−pb_t + of_t). (equation (6))  
  - Without intra-year XR: d_t^{no_iyxr} − d_{t-1}^{no_iyxr} = [1+i_t^{no_iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{no_iyxr} − pb_t + of_t. (equation (7))

### III. Policy-related implications — IRGD and DSPB
- Interest rate-growth differential (IRGD) definitions:  
  IRGD_t^{iyxr} = (1 + i_t^{iyxr})/[(1+g_t)(1+π_t)] − 1. (equation (8))  
  IRGD_t^{no_iyxr} = (1 + i_t^{no_iyxr})/[(1+g_t)(1+π_t)] − 1. (equation (9))
- Debt-stabilizing primary balance (DSPB) at previous-period debt level:  
  DSPB_t^{iyxr} = [1 + i_t^{iyxr}]/[(1+g_t)(1+π_t)] − 1) [1 − α_t γ_t] d_{t-1}^{iyxr} + of_t. (equation (10))  
  DSPB_t^{no_iyxr} = [1 + i_t^{no_iyxr}]/[(1+g_t)(1+π_t)] − 1) d_{t-1}^{no_iyxr} + of_t. (equation (11))
- Numerical illustrative scenario (parameters and outcomes):  
  - Parameters assumed in example: α_t = 0.6, i_t^f = i_t^d = 0.05, g_t = π_t = 0.03, pb_t = −0.1, of_t = 0.05; α_{t+1} expected to be 0.7.  
  - Exchange rates: period t: e_t^{avg} = 1.25 LC$/US$, e_t^{eop} = 1.50 LC$/US$; period t+1: e_{t+1}^{avg} = 2.25 LC$/US$, e_{t+1}^{eop} = 3.00 LC$/US$.  
  - Valuation-adjusted nominal effective interest rates: i_{t+1}^{iyxr} = 65.5 percent and i_{t+1}^{no_iyxr} = 68.0 percent.  
  - IRGD outcomes: IRGD_{t+1}^{iyxr} = 56.0 percent and IRGD_{t+1}^{no_iyxr} = 58.4 percent.  
  - Debt projection from initial d_{t-1} = 0.5: d_{t}^{iyxr} = 96.2 and d_{t}^{no_iyxr} = 94.2 percent of GDP.  
  - DSPB results: DSPB_{t+1}^{iyxr} = 28.1 percent of GDP and DSPB_{t+1}^{no_iyxr} = 34.2 percent of GDP.  
  - Interpretation: ignoring intra-year valuation effects would have led to an underestimation of debt levels and an overestimation of the primary balance needed to stabilize debt at the previous-period level under this parameterization.
- General insight: differences between average and end-of-period exchange rates (e_t^{avg}/e_t^{eop} ≠ 1) can materially affect IRGD, DSPB, and debt projections depending on exchange rate path, α_t, and fiscal flows.

### IV. Dataset (novel assembly)
- Data sources: IMF’s World Economic Outlook (WEO), April 2020 release, augmented with IMF’s MAC DSA dataset to decompose gross public debt and effective interest rates into local and foreign currency components.
- Sample coverage: 82 advanced and emerging economies reporting a positive share of public debt denominated in foreign currency during 2008–19.
- Notes: low-income countries excluded due to lack of currency-of-denomination and effective nominal interest rate data for gross public debt; final sample restricted to observations with non-missing effective interest rates in local and foreign currencies.

- Key descriptive statistics from Table 1 (sample 2008–19, in percent unless otherwise noted; Obs = 574):  
  - Total gross public debt / GDP: Mean 51.54, Std Dev 27.55, Min 7.60, Max 172.18.  
  - Gross public debt in FX / total debt: Mean 38.78, Std Dev 24.12, Min 0.03, Max 97.98.  
  - Gross public debt in LC / total debt: Mean 61.22, Std Dev 24.12, Min 2.02, Max 99.97.  
  - Eff. nominal interest rate on FX debt: Mean 3.91, Std Dev 2.35, Min -1.04, Max 30.91.  
  - Eff. nominal interest rate on LC debt: Mean 6.50, Std Dev 3.21, Min -1.93, Max 19.17.  
  - Real GDP growth: Mean 3.13, Std Dev 2.80, Min -9.77, Max 11.34.  
  - GDP deflator inflation: Mean 4.59, Std Dev 6.49, Min -20.19, Max 51.51.  
  - Primary balance / GDP: Mean -0.80, Std Dev 3.42, Min -16.10, Max 16.38.  
  - Nominal exchange rate depreciation: Mean 4.42, Std Dev 12.40, Min -17.30, Max 104.14.  
  - Avg to end-of-period XR (ratio): Mean 0.98, Std Dev 0.05, Min 0.68, Max 1.11.
- Aggregate observations: on average about 39 percent of total debt is denominated in foreign currency (roughly about 20 percent of GDP). Effective interest rates in FX are lower than in LC on average. Average primary deficit is 0.8 percent of GDP; average nominal GDP growth about 7.7 percent annually. Mean avg-to-end-of-period exchange rate ratio is 0.98, consistent with trend depreciation.

### V. Results — empirical findings
A. Evidence on intra-year exchange rate fluctuations
- Subsample analysis (Figure 1): for country/year observations with nominal depreciations below the 10th percentile (58 observations) and above the 90th percentile (58 observations):  
  - Full sample mean of avg/end XR ratio = 0.98.  
  - For significant nominal appreciations, average ratio = 1.04.  
  - For significant nominal depreciations, average ratio = 0.89.  
  - Footnote: restricting to 1st and 99th percentiles yields mean ratios of 1.09 and 0.78, respectively.

B. Evidence on interest rate-growth differentials (IRGD)
- Table 2 results (sample 2008–19; IRGD in percentage points; full sample Obs = 574):  
  - Full sample mean IRGD^{iyxr} = -0.41 and IRGD^{no_iyxr} = -0.38; Nom growth mean = 7.83.  
  - HICs (28 countries, 161 obs): IRGD^{iyxr} = 0.80, IRGD^{no_iyxr} = 0.80; Nom growth mean = 4.66.  
  - UMICs (35 countries, 231 obs): IRGD^{iyxr} = 0.03, IRGD^{no_iyxr} = 0.09; Nom growth mean = 8.09.  
  - LMICs (19 countries, 182 obs): IRGD^{iyxr} = -2.04, IRGD^{no_iyxr} = -2.00; Nom growth mean = 10.30.  
  - Extreme depreciation subsets:  
    - Nom depr below 1st pctile (5 obs): IRGD = -6.22 (both measures); Nom growth = 6.23.  
    - Nom depr below 10th pctile (35 countries, 57 obs): IRGD^{iyxr} = -5.30, IRGD^{no_iyxr} = -5.35; Nom growth = 8.20.  
    - Nom depr above 90th pctile (29 countries, 57 obs): IRGD^{iyxr} = 6.08, IRGD^{no_iyxr} = 6.28; Nom growth = 12.84.  
    - Nom depr above 99th pctile (5 obs): IRGD^{iyxr} = 15.28, IRGD^{no_iyxr} = 15.84; Nom growth = 24.98.
- Interpretation: for the average country, accounting for intra-year exchange rate fluctuations reduces IRGD by about 0.04 percentage points on average. Heterogeneity exists: reductions up to 0.20 or 0.57 percentage points in countries with significant nominal depreciations. Valuation-adjusted nominal effective interest rates tend to be lower once intra-year differences are included.

C. Evidence on stock-flow adjustment, debt projections, and DSPB
- Stock-flow adjustment (s_f) computed per footnote 10 formula; Table 3 (sample 2008–19, in percent of GDP, Obs = 574):  
  - Full sample mean stock-flow adjustor = 0.02, Std Dev = 0.21, Min = -0.99, Max = 3.53.  
  - HICs (28 countries, 161 obs): Mean 0.00, Std Dev 0.07, Min -0.28, Max 0.47.  
  - UMICs (35 countries, 231 obs): Mean 0.03, Std Dev 0.31, Min -0.99, Max 3.53.  
  - LMICs (19 countries, 182 obs): Mean 0.02, Std Dev 0.11, Min -0.25, Max 0.81.  
  - Subsamples by depreciation percentiles:  
    - Nom depr below 1st pctile (5 obs): Mean -0.03, Std Dev 0.09, Min -0.14, Max 0.09.  
    - Nom depr below 10th pctile (35 countries, 57 obs): Mean -0.03, Std Dev 0.07, Min -0.33, Max 0.19.  
    - Nom depr above 90th pctile (29 countries, 57 obs): Mean 0.20, Std Dev 0.62, Min -0.99, Max 3.53.  
    - Nom depr above 99th pctile (5 obs): Mean 1.22, Std Dev 1.59, Min -0.13, Max 3.53.
- Counter-factual one-year-ahead projection exercise (method): assume WEO-reported debt levels are generated by process including intra-year valuation effects (equation (6)); derive implicit of_t; then compare one-year-ahead projections using (6) vs (7) starting from equal initial d_{t-1}.
- Key counter-factual findings (Figures 3 and 4 and Appendix B referenced):  
  - For episodes with large nominal depreciations (above 90th/99th percentiles), average stock-flow adjustment ~ 1.2 percent of GDP (99th percentile subsample mean = 1.22 percent).  
  - Ignoring intra-year valuation effects would have led to underestimation in debt projections by about 0.9 percentage points of GDP on average for large depreciation cases.  
  - Examples of larger differences: Argentina 2018: 1.6 ppts of GDP; Surinam 2016: 3.3 ppts of GDP.  
  - For cases with nominal depreciations below the 1st percentile, the stock-flow adjustment term is generally low or negative, implying minor miscalculations in debt projections.
- DSPB implications: differences in estimated DSPB would be sizable for large depreciation episodes, leading to overestimated DSPB if intra-year valuation effects are ignored (details illustrated in Figures 4 and Appendix B).

*Source: Author’s calculations based on IMF’s WEO and MAC DSA databases (from wpiea2020261-print-pdf, Section IV–V).*

### 1.5 ppts of GDP on average (Figure 4, Panel B and Appendix B), with differences that are

### 1.5 ppts of GDP on average (Figure 4, Panel B and Appendix B), with differences that are

### Key analytical framework and equations
- Derived country/year observation identity:
  - 표푓௧ = 푑௧௜௬௫௥(1−훼௧훾௧)−(ଵା௜೟೔೤ೣೝ(ଵା௚೟)(ଵାగ೟))(1−훼௧훾௧)푑௧ିଵ௜௬௫௥+푝푏௧, where 푑௧௜௬௫௥ is the gross debt level reported by WEO for every country during 2007–19.
- When assessing observed data, 표푓௧ subsumes a pure residual capturing non-identifiable debt-creating flows from accounting issues (e.g., cash vs accrual accounting), cross-exchange rate fluctuations when more than one foreign currency is involved, intra-year exchange rate fluctuations not properly captured at annual frequency, etc.
- Full decomposition of changes in public debt to GDP ratio (from (6)):
  - 푑௧௜௬௫௥ − 푑௧ିଵ௜௬௫௥ = [ (1+푖௧௜௬௫௥)(1+푔௧)(1+휋௧) − 1 ] 푑௧ିଵ௜௬௫௥ − 1/(1−훼푡훾푡) 푝푏௧ + 1/(1−훼푡훾푡) 표푓௧.  (Equation (12))
  - Without intra-year valuation effects (from (7)):
    - 푑௧௡௢_௜௬௫௥ − 푑௧ିଵ௡௢_௜௬௫௥ = [ (1+푖௧௡௢_௜௬௫௥)(1+푔௧)(1+휋௧) − 1 ] 푑௧ିଵ௡௢_௜௬௫௥ − 푝푏௧ + 표푓௧.  (Equation (13))
  - Adjusted nominal effective interest rate that includes intra-year exchange rate differences (from (14)):
    - 횤̂௧௜௬௫௥ = 훼௧ିଵ(1+푖௧௙푒௧௔௩௚/푒௧௘௢௣)(1+휀௧௘௢௣)+(1−훼௧ିଵ)(1+푖௧ௗ)−1.

### Intuition and illustrative case (Argentina 2018)
- In 2018 Argentina experienced a large currency depreciation such that 푒௧௔௩௚/푒௧௘௢௣ < 1.
- Including intra-year valuation effects:
  - Automatic debt dynamics portion of change in debt is lower due to a lower interest rate-growth differential.
  - Contribution of the primary deficit and other net debt-creating flows to change in debt is higher because new debt (including foreign currency debt) is added at the lower exchange rate 푒௧௔௩௚ relative to 푒௧௘௢௣.
  - Net effect: a higher change in the debt stock projected in Argentina in 2018 if intra-year valuation effects are included.
- Debt-stabilizing primary balance needed in 2018 to stabilize debt at 2017 level would have been lower when intra-year exchange rate fluctuations are included, because flow primary surplus reduces more debt when converted at the lower average exchange rate 푒௧௔௩௚ relative to end-period rate 푒௧௘௢௣.

### Empirical findings and magnitudes
- Stock-flow adjustment stemming from intra-year exchange rate fluctuations can be sizable, particularly for countries with large currency fluctuations and sizable foreign currency debt.
- Figure and table references (Figures 3–4; Tables 4–6) document that inclusion of the stock-flow adjustment affects:
  - Computation of public debt over time.
  - Interest rate-growth differential.
  - Debt-stabilizing primary balance.
  - Accuracy of public debt projections and indicators of debt distress risk.
- Specific observations:
  - Table 4 (average 2008–19, percent) — mean nominal effective interest rates:
    - HICs (28 countries, 161 obs): i_iyxr Mean 5.30, i_no_iyxr Mean 5.31, i_fisc Mean 4.81.
    - UMICs (35 countries, 231 obs): i_iyxr Mean 7.83, i_no_iyxr Mean 7.89, i_fisc Mean 5.59.
    - LMICs (19 countries, 182 obs): i_iyxr Mean 7.83, i_no_iyxr Mean 7.88, i_fisc Mean 5.53.
    - Full sample (82 countries, 574 obs): i_iyxr Mean 7.12, i_no_iyxr Mean 7.16, i_fisc Mean 5.35.
    - Nom depr below 1st pctile (5 countries, 5 obs): i_iyxr Mean -0.52, i_no_iyxr Mean -0.52, i_fisc Mean 6.40.
    - Nom depr below 10th pctile (35 countries, 57 obs): i_iyxr Mean 2.36, i_no_iyxr Mean 2.30, i_fisc Mean 5.54.
    - Nom depr above 90th pctile (29 countries, 57 obs): i_iyxr Mean 19.42, i_no_iyxr Mean 19.66, i_fisc Mean 6.67.
    - Nom depr above 99th pctile (5 countries, 5 obs): i_iyxr Mean 44.30, i_no_iyxr Mean 45.03, i_fisc Mean 7.83.
  - Table 4 conclusion: 푖௧௜௬௫௥ < 푖௧௡௢_௜௬௫௥ generally, except for countries with nominal depreciations below the 1st percentile.
  - Average nominal effective interest rates from fiscal statements, 푖௧௙௜௦௖, cannot be used directly to assess debt dynamics unless adjusted for exchange rate valuation effects.

### Illustrative country-level projections (selected entries from Tables 5 and 6)
- With intra-year valuation effects (selected rows, percent of GDP):
  - BRA2016: Stock of gross public debt 78.31, Change in gross public debt 15.74, Automatic debt dynamics 4.85, Contribution primary deficit 0.27, Contribution other flows 0.61, Stock-flow adjustment -0.01, DSPB 5.48.
  - POL2017: Stock 50.60, Change -3.63, Automatic dynamics -4.90, Contribution primary deficit -0.10, Contribution other flows 1.36, Stock-flow adjustment -0.08, DSPB -3.62.
  - ARG2018: Stock 86.06, Change 28.95, Automatic dynamics 16.43, Contribution primary deficit 2.81, Contribution other flows 9.71, Stock-flow adjustment 12.20, DSPB 21.02.
  - AGO2018: Stock 89.00, Change 19.74, Automatic dynamics 12.42, Contribution primary deficit -7.60, Contribution other flows 14.92, Stock-flow adjustment 0.54, DSPB 24.18.
  - SUR2016: Stock 76.07, Change 32.72, Automatic dynamics 12.90, Contribution primary deficit 7.38, Contribution other flows 12.44, Stock-flow adjustment 3.53, DSPB 22.21.
- Without intra-year valuation effects (selected rows, percent of GDP):
  - BRA2016: Stock 78.31, Change 15.73, Automatic dynamics 4.85, Contribution primary deficit 0.27, Contribution other flows 0.62, Stock-flow adjustment (not shown), DSPB -5.46.
  - ARG2018: Stock 84.42, Change 27.31, Automatic dynamics 17.24, Contribution primary deficit 2.26, Contribution other flows 7.81, Stock-flow adjustment -25.05, DSPB (not shown in this excerpt).
  - AGO2018: Stock 88.93, Change 19.67, Automatic dynamics 13.20, Contribution primary deficit -6.72, Contribution other flows 13.20, Stock-flow adjustment -26.39.
  - SUR2016: Stock 72.79, Change 29.43, Automatic dynamics 12.06, Contribution primary deficit 6.47, Contribution other flows 10.91, Stock-flow adjustment -22.97.
- Note: Tables 5 and 6 present full country/year level decompositions, including the stock-flow adjustment term and debt-stabilizing primary balances (DSPB) calculated using (10) and (11), respectively.

### Policy implications and conclusions
- Because public sectors often hold liabilities denominated in foreign currency, periods of heightened exchange rate volatility can lead to substantial revaluations of liabilities when measured in local currency and/or as a share of GDP.
- Careful consideration of how exchange rate fluctuations affect foreign currency denominated flows and stocks is critical for assessing public debt evolution.
- Accounting practice: debt-related stocks and flows denominated in foreign currency should be converted to local currency using end-of-period rates for stocks and average exchange rates for flows, as envisaged in public finance manuals.
- Inclusion of the stock-flow adjustment term stemming from intra-year exchange rate fluctuations:
  - May materially affect computation of public debt over time, interest rate-growth differentials, and debt-stabilizing primary balances.
  - Is critical to accurately project public debt levels and associated policy indicators that inform risk of debt distress.
- Suggested extensions for future work:
  - Increase empirical coverage to include low-income countries to quantify the size of the stock-flow adjustment term across a larger sample.
  - Assess how intra-year exchange rate fluctuations might affect medium-term debt targets, particularly where average and end-of-period exchange rates have diverged substantially.
  - Use assessment of intra-year valuation effects to determine fiscal consolidation paths consistent with medium-term debt objectives.

### Appendix highlights
- Appendix A summarizes mean values of effective nominal interest rates 푖௧௜௬௫௥, 푖௧௡௢_௜௬௫௥, and 푖௧௙௜௦௖ (the latter derived per footnote 9).
- Appendix B provides decomposition of changes in public debt to GDP ratios, identifying three additive contributors: (i) automatic debt dynamics (interest rate-growth differential on previous stock), (ii) effect of primary balance, and (iii) effect of other net debt-creating flows. Equations (12) and (13) specify these contributors with and without intra-year valuation effects.

*Source: IMF Working Paper (wpiea2020261-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020261-print-pdf.pdf_