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---

### I. Introduction — scope, concept and empirical scope
- Context:
  - Easy financing conditions after the Global Financial Crisis contributed to rising indebtedness of Emerging Markets (EMs). The Covid-19 pandemic raises the realization risk of these vulnerabilities.
- Focus:
  - Empirically explore determinants and consequences of overshooting in large depreciations, answering:
    - (i) what pre-shock settings are associated with large exchange rate overshooting?
    - (ii) what does overshooting tell us about the output consequences of large depreciations?
- Conceptual insight:
  - Overshooting = maximum real depreciation − ex-post equilibrium depreciation.
  - Overshooting viewed as a wedge between balance sheet (BaS) and expenditure switching effects; for a given equilibrium depreciation, higher overshooting signals a relatively stronger BaS effect and foreshadows larger output loss.
- Empirical scope:
  - Analysis of 122 large depreciations since 1980 finds:
    - (i) overshooting driven by BaS-related factors: high external debt, low reserves, low trade openness;
    - (ii) overshooting-based BaS measures foreshadow post-depreciation output losses;
    - (iii) BaS dissipates over time while expenditure switching gains strength.

### II. Dynamics of contractionary depreciations (mechanisms)
- Mechanisms driving the balance sheet effect:
  - Currency mismatches (liabilities in FX, assets/revenues in local currency).
  - Financial frictions: net worth constraint, banks’ VaR rules, margin constraints on foreign creditors.
- Key processes after an adverse shock:
  - Debtor deleveraging → depreciation reduces net worth → risk premium rises → credit demand falls.
  - Domestic credit crunch: banks shed local assets to maintain VaR.
  - Sudden stop: foreign creditors cut exposures to meet margins.
  - Fire sales and reduced foreign credit amplify depreciation and output decline.
- Mitigants:
  - Trade openness provides a natural hedge; larger tradable sector reduces sudden stop likelihood.
- Why expenditure switching is delayed:
  - Dominant currency pricing; rational expectations and uncertainty; financial rigidities; structural rigidities.
- Dynamic implication:
  - BaS is fast and most binding at maximum depreciation; expenditure switching is slow. Real exchange rate overshooting signals relative strength of BaS and foreshadows output losses.

### III. Simple empirical setup (core equations and identification)
- Dependent variable:
  - output loss = negative deviation from pre-crisis trend (lloss_T = −Δy_T).
- Core conceptual expressions (preserve notation and numeric relationships as in source):
  - lloss_T = −τΔE_equil + βΔE_max * d_T−1  (conceptual)
  - ΔE_max ≡ ΔE_equil + ΔE_overshoot
  - Dornbusch overshooting under UIP: ΔE_overshoot = λ ΔE_equil
  - Overshooting-based BaS measure: lloss_T = −τΔE_equil + β((1+λ)/λ) ΔE_overshoot * d_T−1
  - Allowing for risk premium R: ΔE_overshoot = λ ΔE_equil + R
  - Extended: lloss_T = −τΔE_equil + β((1+λ)/λ) ΔE_overshoot * d_T−1 − β(1/λ) R * d_T−1
- General econometric forms used:
  - ΔE_overshoot,ET = λ ΔE_equil,ET + R(A_T−1, d_T−1) + ξ_ET, with R′(A)<0, R′(d)>0
  - lloss_ET = −τΔE_equil,ET + β((1+λ)/λ) ΔE_overshoot,ET * d_E,T−1 − β(1/λ) R(A_E,T−1, d_E,T−1) * d_E,T−1 + ε_iT

### IV. Testable hypotheses
- RER overshooting increases with equilibrium depreciation (Dornbusch overshooting).
- Overshooting increases with pre-shock debt level.
- Overshooting decreases with level of development (proxy for financial frictions).
- Output loss decreases with equilibrium depreciation (medium term); short-term effect may be weak.
- Output loss rises with overshooting*debt (captures BaS strength).
- Output loss increases with level of development (debt intolerance).

### V. Empirical strategy and dataset construction
- Estimation approach:
  - Cross-section OLS regressions; two- and three-stage least squares presented to address endogeneity.
- Identification:
  - Use lagged values for key variables (especially external debt) to reduce reverse causality concerns.
- Large depreciations dataset:
  - Subset of Culiuc and Deb (2020).
  - Monthly bilateral exchange rate vis-à-vis the U.S. dollar on a three-month rolling basis.
  - Four inclusion criteria (thresholds separate for AE and EMs): three-month growth, acceleration relative to previous three months, acceleration relative to preceding year average, significant year-on-year depreciation.
  - Thresholds used (example values reported):
    - ee̅_e = 0.15 (15%)
    - ee̅_eeee = 0.10 (10%)
    - ee̅_eeqq = 0.10 (10%)
    - ee̅_qqqq = 0.21 (21%)
  - Algorithm identifies a three-month window; month with largest contribution pinpoints onset.
  - After filtering, sample reduced to 185 large depreciation episodes; analysed sample covers 122 episodes; 96 of 122 episodes classified as stable.
- Episode metrics and definitions:
  - Analysis window: months t through t+23 (two-year window).
  - Ex-post equilibrium defined as average REER in months t+17 through t+23.
  - Overshooting = maximum depreciation − equilibrium depreciation.
  - Stability: REER peaks not later than t+17 and trend-stabilizes by t+23 (HP filter λ = 400; stable if peaks before t+23 or depreciates by no more than 2.5 percent in months t+18 through t+23).
  - Output loss: deviation of real GDP from pre-shock trend (HP-filtered real GDP for years T−10 through T−1), expressed in percent of T−1 GDP; loss computed for years T through T+4; focus on T+1.

### VI. Stylized facts (sample-level patterns)
- EMs exhibit larger maximum depreciation, equilibrium depreciation and overshooting than AEs.
- REER typically peaks around the third quarter after onset.
- Some 80 percent of episodes are stable.
- Median output loss in T+1 is similar across AEs and EMs; EMs show higher variance.

### VII. Determinants of REER overshooting (OLS findings)
- General result:
  - Strong support for Dornbusch-type overshooting in stable episodes: each percentage point of additional equilibrium depreciation associated with about 1/4 percentage point additional overshooting (relationship strong in stable subsample).
- Selected reported coefficients (from Table 2; preserve reported numeric entries as presented):
  - Equilibrium depreciation (percent): 0.060 0.061 0.038 0.048 0.275** 0.224* 0.230* 0.240*
  - Peg (T-1): 12.538** 13.450** 14.048** 15.849** 17.075** 16.821**
  - Reserves (percent GDP, T-1): -0.134* -0.191** -0.188** -0.140 -0.186** -0.179**
  - Trade openness (X+M in percent GDP, T-1): -0.110** -0.173*** -0.181*** -0.122*** -0.172*** -0.176***
  - External ST Debt (percent GDP, T-1): 0.0064.723** -0.0573.910*
  - PPP GDP/capita * External ST Debt: -0.004** -0.004*
  - Constant: 18.84*** 24.19*** 32.68*** 29.58*** 18.76*** 24.82*** 32.28*** 29.47***
  - Observations (as presented): 14112693931111017575
  - R2 (as presented): 0.0100.1020.1370.1620.0870.1990.2390.257
- Interpretation:
  - Currencies coming off a peg experience larger overshooting.
  - Larger pre-shock reserves reduce overshooting.
  - Trade openness lowers overshooting.
  - External short-term debt matters once interacted with income per capita: an additional percentage point of external ST debt associated with 4 to 5 percentage points higher overshooting; higher GDP/capita reduces this effect.

### VIII. Overshooting-based BaS measure and output loss
- Variable of interest:
  - Balance sheet effect measure = overshooting × external short-term debt (ΔE_overshoot * d_T−1).
- Bivariate relationships:
  - Overshooting and external ST debt separately vs. output loss in T+1 show weak relationships; overshooting*debt shows a strong positive relationship with output loss in T+1 (84 episodes with non-zero external ST debt plotted).
- Comparison of BaS measures (Table 3):
  - Max depreciation * External ST Debt/GDP yields smaller coefficient and lower t-statistics (e.g., 0.002* (0.001)).
  - Overshooting * External ST Debt/GDP yields much larger coefficients and higher significance (e.g., 0.018*** (0.004)).
  - Fit improves when using overshooting-based measure (R² reported by column: 0.04, 0.16, 0.136, 0.151, 0.052, 0.182, 0.148, 0.152).
- Interpretation:
  - Overshooting better captures the risk premium component and the strength of BaS.

### IX. Main results: overshooting*debt interaction (Table 4) and marginal effects
- Main regularities:
  - Overshooting * External ST Debt/GDP (T-1) remains highly significant and persistent across specifications.
  - Equilibrium depreciation does not reduce output loss immediately (becomes expansionary over medium term).
  - Stand-alone external ST debt term often has a negative estimated coefficient.
  - PPP GDP/capita (Log) positive: richer countries see larger output losses.
- Selected coefficients (Table 4, preserve numeric entries):
  - Overshooting * External ST Debt/GDP (T-1): 0.023*** (0.003), 0.025*** (0.004), 0.025*** (0.009), 0.024*** (0.003), 0.026*** (0.004), 0.025*** (0.009)
  - External ST Debt (percent GDP, T-1): -0.113*** (0.025), -0.214*** (0.056), -0.223** (0.102), -0.116*** (0.028), -0.244*** (0.061), -0.253** (0.100)
  - PPP GDP/capita (Log, T-1): 0.080* (0.042), 0.079* (0.042), 0.100** (0.045), 0.100** (0.045)
  - Observations: 88, 88, 88, 71, 71, 71
  - R²: 0.179, 0.307, 0.307, 0.203, 0.375, 0.375
- Marginal effects (using specification 3 from Table 4):
  - Impact of overshooting on output is not significant below the 50th percentile of external ST debt (just under 5 percent of GDP).
  - At the 75th percentile (around 9 percent of GDP), an additional standard deviation of overshooting (around 5 p.p.) is associated with 1.7 percent of GDP larger output loss in the year following the shock.

### X. Domestic demand vs. exports (sectoral channels)
- Hypothesis:
  - BaS depresses output mainly via domestic demand, especially investment; export sector is better hedged.
- Findings (Figures 12 and 13):
  - At the 75th percentile of external ST debt:
    - One additional percentage point of overshooting associated with a loss of 0.9 percent of pre-depreciation domestic demand.
    - Comparable effect on output loss is 0.2 percent.
  - Relationship between overshooting and non-oil export loss significant only at very high percentiles of external ST debt.
  - When overshooting is low, external ST debt associated with expansion (negative loss) of non-oil exports.

### XI. Medium-term dynamics (T through T+4)
- Regression horizons: T through T+4 (Annex Table 4).
- Key patterns (Figure 14):
  - Impact of pre-shock debt and overshooting is persistent and increases through T+2.
  - BaS causes level drop in GDP and affects early growth rates.
  - Confidence bands widen beyond T+2 (increasing dispersion).
  - Equilibrium depreciation coefficient goes from roughly zero in T to statistically significant negative over the medium term (larger equilibrium depreciations are expansionary over medium term).

### XII. Extended results and robustness (Section E and Annexes)
- Additional controls (Table 5) and findings:
  - Dual banking/currency crises raise output loss by around 5 percentage points of pre-shock GDP; overshooting*debt term remains significant.
  - Pre-crisis non-FDI portfolio inflows are a strong predictor of output loss.
  - Improvements in ToT associated with lower output loss.
  - Domestic credit growth (p.p. GDP change T-3 to T-1) is a strong predictor: each additional percentage point increase associated with 0.316 percent higher output loss in T+1.
  - Overshooting * domestic credit growth positive and significant.
- Robustness exercises:
  - Restricted samples (exclude top decile BaS, alternative episode definitions, annual REER definitions) leave overshooting*debt positive and often significant.
  - Alternative overshooting measures (eight variants) yield overshooting*debt coefficients typically within 0.022–0.025; ex-ante misalignment specification yields 0.016 but remains significant.
  - Ex-ante vs ex-post magnitudes: means ex-ante = 9.3 and ex-post = 20; medians ex-ante = 9.5 and ex-post = 16.2.
  - Eliminating true outliers leaves results intact.

### XIII. Importance of banking crises and dual crises
- Dual currency-banking crises:
  - Exhibit larger output losses than currency-only episodes.
  - Controlling for banking crises does not affect significance of overshooting*debt and only marginally reduces its magnitude.
  - Dual crises dominate relationship between BaS = REER overshooting * ST debt/GDP (T-1) and GDP Loss (T+1) (R² = 0.19 for the scatter with 84 episodes).

### XIV. Endogeneity concerns and IV estimation (2SLS and 3SLS)
- Endogeneity:
  - Pervasive when exchange rate movement measures are explanatory.
  - Overshooting both manifests and perpetuates the BaS; OLS correlations support thesis but do not establish causality.
- Instrumental-variable approach:
  - Equations (8) and (9) motivate 2SLS and 3SLS: one equation for overshooting magnitude (first stage) and one for output loss; 3SLS accommodates two-way causality.
- IV results (Table 6):
  - 2SLS and 3SLS produce overshooting*external ST debt/GDP (T-1) coefficients of 0.030 to 0.044 depending on estimator and sample (larger than OLS ~0.025).
  - Other OLS findings (negative impact of ST debt; positive impact of GDP/capita on output loss) survive under 2SLS and 3SLS.
  - Conclusion: OLS likely provides lower-bound estimates; IV estimates reinforce main findings.

### XV. Conclusions and policy implications
- Empirical support:
  - Magnitude of real exchange rate overshooting driven by BaS factors: high external ST debt, low reserves, low trade openness.
  - Overshooting-based BaS measures are powerful predictors of output loss in large depreciations; effect persistent and affects domestic demand more than exports.
  - Findings robust to controls, alternative estimators, sample restrictions, proxies for currency mismatches, and overshooting definitions.
  - BaS dissipates over medium term; expenditure switching takes time.
- Policy-relevant interpretations:
  - Negative correlation between overshooting and subsequent output does not imply optimal policy is to resist overshooting.
  - Pre-existing settings to contain overshooting: flexible exchange rate, ample reserves.
  - Overshooting not damaging if not associated with currency mismatches (high external ST debt); large REER movements need not be feared if mismatches limited.
  - Baseline overshooting definition uses 20/20 hindsight; ex-ante misalignment estimates unlikely to guide policy accurately.
  - Avoiding dual currency-banking crises is likely the best defense against large output losses.
- Potential policy implication (to be further investigated):
  - Large depreciation may reduce output primarily by destabilizing the financing sector; crisis interventions should focus on preserving financial stability rather than broad FX intervention.
  - Scarce reserves might be better used to raise the probability of preserving financial stability (e.g., FX emergency liquidity to well-capitalized banks) rather than broad FX market intervention.

### XVI. Directions for future research
- Incorporate crisis policy interventions into empirical analysis, identifying reasonably exogenous policy measures.
- Build a theoretical model combining financial frictions (giving rise to BaS) and rigidities that delay/attenuate expenditure switching.

### XVII. Annex highlights — inclusion criteria and robustness summaries
- ANNEX 2 — identification criteria (four required conditions; three-month rolling window):
  - Criterion thresholds used:
    - ee̅_e = 15%
    - ee̅_eeee = 10%
    - ee̅_eeqq = 10%
    - ee̅_qqqq = 21%
  - Formal conditions based on three-month growth, accelerations and year-on-year significance.
- ANNEX 3 — robustness:
  - Restricted samples (exclude top 10% BaS) reduce coefficient on BaS to 0.020 (vs 0.025 baseline) but remains significant at 5 percent.
  - Alternative overshooting measures (8 tested): overshooting*debt coefficient remains significant (typical range 0.022–0.025); ex-ante misalignment specification yields 0.016.
- Annex Table 1 and associated tables:
  - Interaction Overshooting * External ST Debt/GDP (T-1) positive and frequently statistically significant across many tables and horizons (examples: 0.025***, 0.024***, 0.011***, 0.035***, 0.058** depending on specification and horizon).
  - External ST Debt (percent GDP, T-1) typically negative and significant (examples: -0.220**, -0.149***, -0.209***).
  - PPP GDP/capita (Log, T-1) typically positive and often significant (examples: 0.079*, 0.045*, 0.080*).

*Source: wpiea2020060-print-pdf (IMF Working Paper content provided)*

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

### wpiea2020060-print-pdf - References .............................................................................................................

### References
- References ................................................................................................................................29

### Annex 1. Debt Intolerance as Consequence of Financial Frictions
- Annex 1. Debt Intolerance as Consequence of Financial Frictions .........................................33

### Annex 2. Criteria for Inclusion of Large Depreciation Episodes
- Annex 2. Criteria for Inclusion of Large Depreciation Episodes ............................................34

### Annex 3. Additional Robustness
- Annex 3. Additional Robustness..............................................................................................36
  - A. Restricted Samples ........................................................................................................36
  - B. Alternative Measures of Overshooting .........................................................................36

*Source: wpiea2020060-print-pdf - References .............................................................................................................*

### Annex Figures and Tables ...............................................................................................

### Annex Figures and Tables

### I. Introduction
- Context: Easy financing conditions after the Global Financial Crisis contributed to rising indebtedness of Emerging Markets (EMs). The Covid-19 pandemic—sharp declines in global demand, terms of trade shocks and tightening of global financial conditions—raises the realization risk of these vulnerabilities.
- Focus: Empirically explore determinants and consequences of overshooting in large depreciations, answering:
  - (i) what pre-shock settings are associated with large exchange rate overshooting?
  - (ii) what does overshooting tell us about the output consequences of large depreciations?
- Conceptual insight: Overshooting—the difference between maximum real depreciation and ex-post equilibrium depreciation—can be viewed as a wedge between the balance sheet (BaS) and expenditure switching effects. For a given real equilibrium depreciation, higher overshooting signals a relatively stronger BaS effect and foreshadows a larger output loss.
- Empirical scope: Analysis of 122 large depreciations since 1980 shows that:
  - (i) the size of overshooting is driven by factors associated with the balance sheet effect (high external debt, low reserves, low trade openness),
  - (ii) overshooting-based measures of the balance sheet effect foreshadow post-depreciation output losses, and
  - (iii) the balance sheet effect gradually dissipates, while expenditure switching simultaneously gains strength.

### II. The dynamics of contractionary depreciations
- Mechanisms driving the balance sheet effect:
  - Currency mismatches from liabilities denominated in FX while assets/revenues are in local currency.
  - Financial frictions: net worth constraint (Bernanke and Gertler, 1989), banks’ VaR rules, and margin constraints on foreign creditors.
- Key processes following an adverse shock:
  - Debtor deleveraging: depreciation reduces net worth, raises risk premium, lowers demand for credit.
  - Domestic credit crunch: banks shed local assets to maintain VaR probabilities.
  - Sudden stop: foreign creditors cut exposures to meet margin constraints.
  - Fire sales and reduction in foreign credit exacerbate depreciation and output decline.
- Factors that mitigate the balance sheet effect:
  - Trade openness provides a natural hedge; larger tradable sector reduces sudden stop likelihood.
- Reasons expenditure switching is delayed:
  - Dominant currency pricing (exports invoiced in FX limit immediate competitiveness gains).
  - Rational expectations and uncertainty damp investment response.
  - Financial rigidities (scarce financing post-depreciation).
  - Structural rigidities (labor/product market frictions, weak property rights, lack of complementary inputs).
- Dynamic implication: The balance sheet effect is most binding at maximum depreciation (fast), while expenditure switching responds more slowly (slow). Real exchange rate overshooting signals the relative strength of the balance sheet effect and foreshadows future output losses.

### III. A simple empirical setup (core equations and identification)
- Dependent variable: output loss (negative deviation from pre-crisis trend).
- Baseline representation (as in the paper):
  - LLOSS_T = −ΔY_T = −τΔE_equil * Y_T−1 + β(ΔE_max * D_T−1)  (conceptual expression)
  - Expressed in percent of T−1 output:
    - lloss_T = −Δy_T = −τΔE_equil + βΔE_max * d_T−1, where d = D/Y × 100  (equation (2))
  - Decomposition of maximum depreciation:
    - ΔE_max ≡ ΔE_equil + ΔE_overshoot  (equation (3))
  - Dornbusch overshooting under UIP:
    - ΔE_overshoot = λ ΔE_equil  (equation (4))
  - Combining gives an overshooting-based BaS measure:
    - lloss_T = −τΔE_equil + β((1+λ)/λ) ΔE_overshoot * d_T−1  (equation (5))
- Allowing for risk premium (R) and departure from UIP (CIP and endogenous risk premium):
  - ΔE_overshoot = λ ΔE_equil + R  (equation (6))
  - lloss_T = −τΔE_equil + β((1+λ)/λ) ΔE_overshoot * d_T−1 − β(1/λ) R * d_T−1  (equation (7))
- General econometric forms used for testing:
  - ΔE_overshoot,ET = λ ΔE_equil,ET + R(A_T−1, d_T−1) + ξ_ET, with R′(A)<0, R′(d)>0  (equation (8))
  - lloss_ET = −τΔE_equil,ET + β((1+λ)/λ) ΔE_overshoot,ET * d_E,T−1 − β(1/λ) R(A_E,T−1, d_E,T−1) * d_E,T−1 + ε_iT  (equation (9))

### IV. Testable hypotheses derived from the setup
- RER overshooting increases with equilibrium depreciation (Dornbusch overshooting).
- Overshooting increases with pre-shock debt level (strength of balance sheet effect).
- Overshooting decreases with level of development (proxy for financial frictions).
- Output loss decreases with equilibrium depreciation, although the short-term effect may be weak given delayed expenditure switching.
- Output loss rises with overshooting*debt, which captures the BaS effect’s strength.
- Output loss increases with level of development (a consequence of debt intolerance).

### V. Empirical strategy notes
- Estimation approach: cross-section OLS regressions are used to test hypotheses.
- Identification: use of lagged values for key variables (particularly external debt) to reduce reverse causality concerns.
- Variables and measures referenced explicitly in the setup:
  - Overshooting (ΔE_overshoot), equilibrium depreciation (ΔE_equil), maximum depreciation (ΔE_max).
  - External short-term debt (D_T−1), debt-to-output ratio d = D/Y × 100.
  - Development proxy A_T−1 (income/capita).
  - Coefficients to be estimated: τ, β, λ.

*Source: wpiea2020060-print-pdf - Annex Figures and Tables*

### section VI concludes with the presentation of two- and three-stage least squares results,

### Output implications of exchange rate overshooting (section VI)

### Summary of estimation approach and data limitations
- The section concludes with the presentation of two- and three-stage least squares results, which only reinforce main findings.
- Alternative estimation techniques are impractical given the data:
  - The event study nature of the study rules out time series analysis.
  - The small number of large depreciations per country (most have just one) rules out panel techniques.

### Large depreciations dataset (construction and sample)
- Dataset: subset of Culiuc and Deb (2020) large depreciation episodes.
- Construction steps:
  - (i) Identifying the onset of large depreciation episodes.
  - (ii) Characterizing key parameters of each episode (maximum and equilibrium depreciations, overshooting, etc.).
- Identification:
  - Use monthly bilateral exchange rate vis-à-vis the U.S. dollar on a three-month rolling basis.
  - Four criteria (expanding Frankel and Rose (1996) for higher-frequency data):
    1. Large (above the 푒푒̅
푒푒 cutoff).
    2. Accelerating relative to previous three-month period (푒푒̅
푒푒푒푒 cutoff).
    3. Accelerating relative to average depreciation in preceding year (푒푒̅
푒푒푞푞 cutoff).
    4. Significant on a year-on-year basis (푒푒̅
푞푞푞푞 cutoff).
  - Thresholds identified separately for advanced economies (AE) and Emerging and developing markets (EMs):
    - Table 1. Criteria cutoffs
      - Cutoff Advanced economies Emerging and developing markets
      - 푒푒̅
푒푒 0.10 0.15
      - 푒푒̅
푒푒푒푒 0.10 0.10
      - 푒푒̅
푒푒푞푞 0.10 0.10
      - 푒푒̅
푞푞푞푞 0.15 0.21
  - The algorithm identifies a three-month window; the month with largest contribution is used to pinpoint onset.
- Sample sizes and filtering:
  - After eliminating episodes where REER and output dynamics are unlikely to be driven by the processes discussed in section II, sample reduced to 185 large depreciation episodes.
  - Analysed sample covers 122 episodes (data availability constraints).
  - Stable episodes: 96 of the total of 122 episodes are classified as stable.

### Characterizing episodes: metrics and definitions
- Analysis window: two-year window following onset (months 푡푡 through 푡푡+23).
- Key metrics: maximum depreciation, equilibrium depreciation, overshooting, stability, output loss.
- Baseline equilibrium definition (following Cavallo et al. (2005)):
  - Ex-post equilibrium defined as average REER in months 푡푡+17 through 푡푡+23.
  - Overshooting = maximum depreciation − equilibrium depreciation (Δ퐸퐸
표표푠푠 = 퐸퐸
푚푚푚푚퐸퐸 − 퐸퐸
푒푒푒푒).
- Stability definition (Culiuc and Deb (2020)):
  - An episode is stable if: (i) REER peaks not later than 푡푡+17, (ii) REER trend-stabilizes by 푡푡+23.
  - Trend computed with Hodrick-Prescott filter with a 휆휆 = 400; trend considered stable if it either (i) peaks before 푡푡+23 or (ii) depreciates by no more than 2.5 percent in months 푡푡+18 through 푡푡+23.
- Output loss measurement:
  - Output loss defined as deviation of real GDP from pre-shock trend, expressed in percent of 푇푇−1 GDP.
  - Pre-shock trend: HP-filtered real GDP for years 푇푇−10 through 푇푇−1, using trend growth in 푇푇−1.
  - Loss computed for years 푇푇 through 푇푇+4.
  - Empirical analysis focuses on 푇푇+1 (typically year with largest output loss).
- Stylized facts (summary from figures and Annex Table 1):
  - EMs exhibit larger maximum depreciation, equilibrium depreciation and overshooting than AEs.
  - REER typically peaks around the third quarter after onset.
  - Some 80 percent of episodes are stable.
  - Median output loss in 푇푇+1 is similar across AEs and EMs, with EMs exhibiting higher variance.

### Determinants of REER overshooting (OLS results and interpretation)
- General result:
  - Strong support for Dornbusch-type overshooting in stable depreciation episodes: overshooting increases with equilibrium depreciation; each percentage point of additional equilibrium depreciation is associated with about ¼ percentage point of additional overshooting (relationship strong in stable subsample but not statistically significant for overall sample that includes unstable episodes).
- Table 2 (OLS regressions on REER overshooting) — selected reported coefficient values (as presented):
  - Equilibrium depreciation (percent): 0.060 0.061 0.038 0.048 0.275** 0.224* 0.230* 0.240*
    - Robust standard errors shown in parentheses in the source.
  - Peg (T-1): 12.538** 13.450** 14.048** 15.849** 17.075** 16.821**
  - Reserves (percent GDP, T-1): -0.134* -0.191** -0.188** -0.140 -0.186** -0.179**
  - Trade openness (X+M in percent GDP, T-1): -0.110** -0.173*** -0.181*** -0.122*** -0.172*** -0.176***
  - External ST Debt (percent GDP, T-1): 0.0064.723** -0.0573.910*
  - PPP GDP/capita * External ST Debt: -0.004** -0.004*
  - Constant: 18.84*** 24.19*** 32.68*** 29.58*** 18.76*** 24.82*** 32.28*** 29.47***
  - Observations (as presented): 14112693931111017575
  - R2 (as presented): 0.0100.1020.1370.1620.0870.1990.2390.257
- Interpretation of key determinants:
  - Currencies coming off a peg experience larger overshooting.
  - Larger pre-shock official reserves reduce magnitude of overshooting.
  - Trade openness lowers overshooting (serves as a natural hedge against balance sheet effect).
  - Measures of capital account liberalization do not appear to affect overshooting (results not shown).
  - External short-term debt matters once interacted with income per capita:
    - External short-term debt leads to higher overshooting, but less so for richer countries.
    - Reported interpretation: an additional percentage point of external ST debt is associated with 4 to 5 percentage points higher overshooting, while an additional standard in the GDP/capita is associated with a 2 percentage point lower overshooting at the mean level of external ST debt (7 percent of GDP).
- Model fit and caveats:
  - Relatively low R2 suggests many other factors matter.
  - Policies implemented after episode onset likely affect overshooting; pervasive endogeneity makes it impossible to assess policy impacts with simple OLS here (left for subsequent work).

### Overshooting-based balance sheet effect and output loss
- Variable of interest for output implications:
  - Balance sheet effect measure = overshooting × short-term external debt (Δ퐸퐸
표표푠푠 ∗ 푑푑
푇푇−1).
- Bivariate relationships (illustrated in Figure 9 from the source):
  - Left charts: scatter plots of overshooting and of external short-term debt separately vs. output loss in 푇푇+1.
  - Right chart: strong positive relationship between overshooting*debt and output loss in 푇푇+1 (plots include 84 large depreciation episodes with non-zero external short term debt; individual episodes identified by 3-letter ISO code and 2-digit year).
- Subsequent analysis tests whether overshooting*external ST debt is the appropriate measure linking depreciation magnitude to output loss (the only other comparable study cited is Cavallo et al. (2005)).

*Source: wpiea2020060-print-pdf - section VI concludes with the presentation of two- and three-stage least squares results, (https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020060-print-pdf.pdf)

### section III; their   main explanatory variable is maximum depreciation*external debt.

### section III; their   main explanatory variable is maximum depreciation*external debt.

### Comparison of balance sheet effect measures
- Main explanatory variable discussed: maximum depreciation * external debt.
- Table 3 comparison:
  - Specifications 1 and 5 use the maximum depreciation measure of the balance sheet effect.
  - Specifications 2 and 6 use the overshooting-based measure.
  - The coefficient for the overshooting-based measure is larger and has much higher t-statistics (4.7 vs. 1.8).
  - Fit of the regression improves considerably when using the overshooting-based measure.
- Reported regression fit/statistics (from Table 3 and related notes):
  - Note: Robust standard errors in parentheses. *, **, *** indicate significance at 10, 5 and 1 percent levels respectively.
  - R² = 0.02 (presented earlier in the section)
  - Selected coefficient estimates (Table 3):
    - Equilibrium depreciation (percent): -0.005 (0.032), -0.000 (0.027), -0.006 (0.027), -0.020 (0.021), 0.048 (0.041), 0.040 (0.034), 0.020 (0.050), 0.017 (0.049)
    - Max depreciation * External ST Debt/GDP (T-1): 0.002* (0.001), 0.002* (0.001)
    - Overshooting * External ST Debt/GDP (T-1): 0.018*** (0.004), 0.019*** (0.004)
    - Overshooting * External ST Debt on RMB/GDP (T-1): 0.012*** (0.002), 0.012*** (0.003)
    - Overshooting * External Bank Debt/GDP (T-1): 0.029*** (0.005), 0.028*** (0.006)
    - Constant: 4.374** (1.690), 2.059 (1.826), 1.615 (2.016), 1.524 (2.236), 3.414* (2.010), 0.818 (2.175), 0.572 (2.492), 0.575 (2.862)
  - Observations by column: 88, 86, 96, 87, 71, 71, 55, 54 (as presented in the Table 3 block)
  - R² by column: 0.04, 0.16, 0.136, 0.151, 0.052, 0.182, 0.148, 0.152

- Interpretation provided in text:
  - Maximum depreciation gives little indication of the magnitude of the risk premium component of the depreciation and has lower variance because all episodes have high maximum depreciations by construction.
  - Overshooting better captures the risk premium, which ultimately reflects the strength of the balance sheet effect.
  - Short-term debt, short-term debt on remaining maturity basis (RMB) and external bank debt produce similar results; short-term debt on original maturity is used henceforth because it is available for a larger sample.

### Main results (Table 4): overshooting*debt interaction and other covariates
- Summary statements:
  - The overshooting*debt interaction term remains highly significant and persistent across specifications.
  - Equilibrium depreciation does not reduce output loss in the immediate aftermath of depreciation (this changes over the medium term).
  - The stand-alone external short-term debt term has a negative estimated coefficient.
  - PPP GDP/capita (Log) has a positive estimated coefficient: richer countries see larger output losses.
  - Adding overshooting (stand-alone) does not improve fit; its coefficient is not significant and the interaction coefficient remains unchanged.
- Selected coefficient estimates (from Table 4):
  - Equilibrium depreciation (percent): -0.000 (0.027), -0.006 (0.029), -0.005 (0.030), 0.038 (0.035), 0.033 (0.041), 0.036 (0.039)
  - Overshooting * External ST Debt/GDP (T-1): 0.023*** (0.003), 0.025*** (0.004), 0.025*** (0.009), 0.024*** (0.003), 0.026*** (0.004), 0.025*** (0.009)
  - External ST Debt (percent GDP, T-1): -0.113*** (0.025), -0.214*** (0.056), -0.223** (0.102), -0.116*** (0.028), -0.244*** (0.061), -0.253** (0.100)
  - PPP GDP/capita (Log, T-1): 0.080* (0.042), 0.079* (0.042), 0.100** (0.045), 0.100** (0.045)
  - Overshooting (percent): -0.010 (0.088), -0.010 (0.087)
  - Constant: 2.09 (1.79), -70.95* (39.60), -70.63* (38.94), 0.8 (2.13), -91.35** (42.53), -90.89** (41.99)
  - Observations: 88, 88, 88, 71, 71, 71
  - R²: 0.179, 0.307, 0.307, 0.203, 0.375, 0.375

- Quantification via marginal effects (Figure 10 and accompanying text):
  - Using specification 3 from Table 4:
    - Impact of overshooting on output is not significant below the 50th percentile of external short-term debt (just under 5 percent of GDP).
    - At the 75th percentile of the preferred debt measure (around 9 percent of GDP), an additional standard deviation of overshooting (around 5 p.p.) is associated with 1.7 percent of GDP larger output loss in the year following the shock.

- Relationship between overshooting and debt:
  - Since overshooting increases with external short-term debt, the two generally go together; overshooting is only damaging when combined with significant currency mismatches.

### Domestic demand vs. exports (Section C)
- Hypothesis: balance sheet effect depresses output by affecting domestic demand, with investment particularly hit; export sector is naturally hedged and should be better insulated.
- Empirical findings (Figures 12 and 13, all episodes):
  - At the 75th percentile of external short-term debt:
    - One additional percentage point of overshooting is associated with a loss of 0.9 percent of the pre-depreciation level of domestic demand.
    - The comparable effect on output loss is 0.2 percent.
  - The relationship between overshooting and non-oil exports loss becomes statistically significant only at very high percentiles of external short-term debt.
  - When overshooting is low, external short-term debt is associated with an expansion (negative loss relative to pre-shock trend) of non-oil exports.

### Medium-term dynamics of output loss (Section D)
- Regression horizons: from T through T+4 (Annex Table 4).
- Key patterns (Figure 14):
  - The impact of pre-shock debt and the magnitude of overshooting are highly persistent and increasing through T+2.
  - The balance sheet effect causes both a level drop in GDP and affects the rate of growth in the early years.
  - Confidence bands widen beyond T+2, indicating increasing dispersion of outcomes.
  - The coefficient on equilibrium depreciation goes from roughly zero in T to a statistically significant negative over the medium term; larger equilibrium depreciations are expansionary, but only over the medium term.

### Extended results and robustness (Section E)
- Table 5 introduces additional controls:
  - Specification 1 adds a dummy for large depreciations that coincide with banking crises (Laeven and Valencia, 2018); dual crises raise output loss by around 5 percentage points of pre-shock GDP but do not affect the overshooting*debt term’s significance.
  - Specification 2 adds non-FDI flows cumulated over the three pre-shock years; pre-currency crises portfolio inflows are a strong predictor of output loss.
  - Specification 3 includes trading partner growth and change in the terms of trade; improvements in ToT are associated with lower output loss.
- Selected estimates from Table 5 (all episodes):
  - Equilibrium depreciation (percent): -0.015 (0.024), -0.028 (0.018), -0.029 (0.020), -0.015 (0.023), -0.014 (0.028), 0.024 (0.038), -0.003 (0.037)
  - Overshooting * External ST Debt/GDP (T-1): 0.021*** (0.004), 0.030*** (0.005), 0.024*** (0.004), 0.019*** (0.004), 0.020*** (0.004)
  - External ST Debt (percent GDP, T-1): -0.203*** (0.054), -1.001** (0.416), -0.241*** (0.046), -0.285*** (0.078), -0.363*** (0.076)
  - PPP GDP/capita (Log, T-1): 0.081* (0.042), 0.136*** (0.042), 0.080** (0.038), 0.078* (0.040), 0.069* (0.040), 0.032 (0.023), 0.024 (0.023)
  - Dual Banking/currency crisis: 4.859* (2.526), 4.531 (2.982), 3.289 (2.986), 5.841** (2.545), 5.179** (2.334), 3.057 (2.565)
  - Non-FDI Capital inflows (% GDP, cumulated T-3 to T-1): 0.283* (0.157)
  - Trading partner GDP (% change, T-1 to T+1): -0.886 (0.640), -0.769 (0.481)
  - ToT (% change, T-1 to T): -0.300* (0.168), -0.371*** (0.114)
  - Domestic credit to private sector (p.p. GDP change, T-3 to T-1): 0.316*** (0.090), 0.038 (0.083), -0.011 (0.084)
  - Overshooting * Dom. credit to priv. sect. (p.p. GDP change, T-3 to T-1): 0.017*** (0.006), 0.015*** (0.004)
  - Constant: -73.00* (39.93), -123.13*** (40.12), -69.12* (36.90), -72.34* (38.05), -62.71* (37.61), -28.11 (22.47), -17.80 (22.94)
  - Observations: 887, 980, 868, 511, 910, 3 (as presented),  -- R²: 0.321, 0.461, 0.481, 0.350, 0.411, 0.280, 0.455

- Additional robustness:
  - Change in private credit/GDP (p.p. change T-3 to T-1) is a strong predictor: each additional percentage point increase is associated with 0.316 percent higher output loss in T+1.
  - Overshooting*credit growth is positive and significant at the 1 percent level when replacing debt-based BaS with credit growth-based measure.
  - Sub-sample checks, alternative overshooting and equilibrium depreciation measures, and exclusions of outliers confirm main findings. An ex-ante misalignment–based measure is a poor predictor of ex-post equilibrium depreciation.

### Importance of banking crises (Section F)
- Dual currency-banking crises:
  - Exhibit larger output losses than currency-only episodes.
  - Controlling for banking crises does not affect the significance of the overshooting*debt coefficient and only marginally reduces its magnitude.
  - Dual crises dominate the relationship between the overshooting-based measure of the BaS effect and output loss (Figure 15).
- Figure 15 notes:
  - Chart includes 84 large depreciations with non-zero external short term debt.
  - R² = 0.19 for the scatter relating BaS = REER overshooting * ST debt/GDP (T-1) to GDP Loss (T+1).

*Source: wpiea2020060-print-pdf - section III; their   main explanatory variable is maximum depreciation*external debt.*

### Annex Table 4 specifications 6 through 10 rerun the medium-term output loss regressions for

### wpiea2020060-print-pdf - Annex Table 4 specifications 6 through 10 rerun the medium-term output loss regressions for

### Main empirical findings (dual crises excluded)
- Annex Table 4 specifications 6 through 10 rerun the medium-term output loss regressions for a subsample that excludes dual crises; across years the coefficient on the overshooting*debt term is no longer statistically significant.
- The left panel in Figure 16:
  - shows the marginal effect of overshooting retains the expected sign over the medium term, but loses in magnitude and significance.
  - shows the expansionary effect of equilibrium depreciation—negative effect on output loss—is left intact.
- Note on Figure 16:
  - Dotted lines indicate 90 percent confidence intervals.
  - Marginal effects are computed from specifications 6 through 10 in Annex Table 4.
  - Marginal effects for overshooting are computed at the average value of external short term debt.
- Banking crises account for a third of the sample and should not be interpreted as outliers.
- Elimination of true outliers—episodes with largest overshooting*debt—leaves results intact (Annex 4).

### Endogeneity concerns and estimation strategy
- Endogeneity is pervasive when exchange rate movement measures are explanatory variables; the relationship from overshooting to output loss is not necessarily causal.
- Overshooting:
  - is a manifestation of the processes underlying the balance sheet effect,
  - is at the same time an element perpetuating the balance sheet effect.
- Establishing a simple correlation between overshooting and output loss via OLS is sufficient to support the paper’s thesis, but not addressing endogeneity questions estimated coefficients.
- Equations (8) and (9) in section III set up two- and three-stage least square (2SLS and 3SLS) regressions:
  - one equation for the magnitude of overshooting (first stage in 2SLS),
  - one for output loss.
- 3SLS is more suitable when agents infer from fundamentals that output loss will be significant and thereby push the currency to depreciate further, allowing for two-way causality.
- Table 6 results:
  - 2SLS and 3SLS estimations produce coefficients on overshooting*external ST debt/GDP (T-1) of 0.030 to 0.044, depending on estimator and sample.
  - These coefficients are considerably larger than OLS regressions (~0.025).
  - Other OLS findings (negative impact of ST debt; positive impact of GDP/capita on output loss) survive under 2SLS and 3SLS.
  - For 3SLS regressions, endogenous variables include overshooting, output loss and overshooting*external ST debt.
  - Standard errors are reported in parentheses; *, **, *** indicate significance at 10, 5 and 1 percent levels respectively.
- Conclusion on endogeneity:
  - The relationship between the overshooting-based BaS and output loss is not due to OLS’s inherent weaknesses in dealing with endogeneity.
  - OLS likely provides lower-bound estimates of the link between the overshooting-based BaS and output loss.

### Key coefficients, sample and fit statistics (as presented)
- Equilibrium depreciation (percent): 0.048, -0.096, 0.044, -0.005, 0.240*, -0.033, 0.231**, 0.087 (standard errors in parentheses where reported).
- External ST Debt (percent GDP, T-1): 4.605**, -0.363*, 5.224*, -0.416***, 3.747*, -0.423*, 4.453, -0.461*** (standard errors reported in table).
- Peg (T-1): 14.143**, -4.199, 15.704**, 16.953**, -5.685, 19.576*** (standard errors reported).
- Reserves (percent GDP, T-1): -0.175**, 0.088, -0.261, -0.178**, 0.130, -0.289.
- Trade openness (X+M in percent GDP, T-1): -0.186***, 0.069, -0.182**, -0.178***, 0.067, -0.156*.
- PPP GDP/capita * External ST Debt: -0.004**, -0.005*, -0.004*, -0.004.
- Overshooting (percent): 0.325, -0.134, 0.279, -0.223 (standard errors reported).
- Overshooting * External ST Debt/GDP (T-1): 0.030**, 0.041***, 0.034**, 0.044*** (standard errors reported).
- PPP GDP/capita (Log, T-1): 0.126***, 0.114***, 0.129***, 0.114***.
- Constant terms: 29.73***, -126.08**, 30.40***, -100.95***, 29.61***, -128.87**, 29.49***, -101.00*** (standard errors reported).
- Observations: 9383, 8383, 7567, 6767, 67 (as presented in table).
- R-squared values presented: 0.160, 0.373, 0.173, 0.344, 0.256, 0.419, 0.274, 0.337.

### Conclusions and policy implications
- Core hypothesis tested: real exchange rate overshooting signals the relative strength of the balance sheet and expenditure switching effects.
- Empirical support:
  - The magnitude of real exchange rate overshooting is driven by factors associated with the balance sheet effect: high external short-term debt, low reserves, low trade openness.
  - Overshooting-based measures of the balance sheet effect are a powerful predictor of output loss in large depreciation episodes; the effect is persistent and affects domestic demand stronger than exports.
  - The finding is robust to additional controls, alternative estimation techniques, sample restrictions, various proxies for currency mismatches, and definitions of overshooting.
  - The balance sheet effect dissipates over the medium term, while expenditure switching takes time to materialize.
- Policy-relevant interpretations:
  - Overshooting being negatively correlated with subsequent output does not imply it is optimal to resist overshooting.
  - Pre-existing policy settings likely to help contain overshooting: flexible exchange rate, ample reserves.
  - Overshooting is not damaging if not associated with currency mismatches (proxied by high external short-term debt); large real exchange rate movements need not be feared if mismatches are limited.
  - Baseline definition of overshooting uses 20/20 hindsight; ex-ante misalignment estimates are unlikely to provide accurate guidance.
  - Overshooting is most damaging when accompanied by a banking crisis; avoiding a dual crisis is likely the best defense against large output losses.
- Potential policy implication (to be further investigated):
  - Large depreciation may reduce output primarily by destabilizing the financing sector, suggesting crisis interventions should focus on preserving financial stability rather than resisting overshooting.
  - Scarce international reserves might be better used to raise the probability of preserving financial stability (e.g., providing FX emergency liquidity assistance to well-capitalized banks) rather than broad FX market intervention, because broad interventions help all market participants close currency mismatches and only a portion of used reserves eases domestic balance sheet strains.
  - Confirming this interpretation would inform integrated policy frameworks; endogeneity complicates definitive views and requires incorporating policy interventions—particularly on the financial sector side—into the analysis.

### Directions for future research
- Add crisis policy interventions into the empirical analysis, identifying reasonably exogenous policy measures.
- Underpin the empirical analysis with a theoretical model combining financial frictions that give rise to the balance sheet effect and rigidities that delay and attenuate expenditure switching (Basu et al. (2020) provide necessary ingredients).

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020060-print-pdf.pdf*

### ANNEX 2. CRITERIA FOR INCLUSION OF LARGE DEPRECIATION EPISODES

### ANNEX 2. CRITERIA FOR INCLUSION OF LARGE DEPRECIATION EPISODES

### Identification criteria (four required conditions)
- Data basis: log series of the end-of-period monthly bilateral exchange rate vis-à-vis the US dollar.
- Criterion 1 — The depreciation must be large:
  - Δee_e,E, the three-month (quarterly) growth, must be above ee̅_e, the 90th percentile cutoff.
  - Formal condition: Δee_e,E = ee_E − ee_E–3 > ee̅_e, where ee_E = ln(E/E) and ee̅_e = PP90(Δee_e).
  - Threshold used: ee̅_e = 15%.
- Criterion 2 — The depreciation must accelerate relative to the previous period:
  - Δee_eee, the 3 month-on-3 month depreciation acceleration, must be above the 90th percentile, but not exceed ee̅_e.
  - Formal condition: Δee_eeee,E = (ee_E − ee_E–3) − (ee_E–3 − ee_E–6) > ee̅_eeee, where ee̅_eeee = min(PP90(|Δee_eeee|), ee̅_e).
  - Threshold used: ee̅_eeee = 10%.
- Criterion 3 — The depreciation must accelerate relative to the average in the preceding year:
  - Δee_eeqq, the 3-month-on-preceding year’s average depreciation (expressed in terms of three month), must be above the 90th percentile, but not exceed ee̅_e.
  - Formal condition: Δee_eeqq,E = (ee_E − ee_E–3) − (ee_E–3 − ee_E–15)/4 > ee̅_eeqq, where ee̅_eeqq = min(PP90(|Δee_eeqq|), ee̅_e).
  - Threshold used: ee̅_eeqq = 10%.
- Criterion 4 — The depreciation must be significant on an annual basis:
  - The year-on-year depreciation in at least one of the first six months into the episode must be above the 75th percentile.
  - Formal condition: Δee_qqqq,E = ee_s − ee_s–12 > ee̅_qqqq for at least one l = (t −2, t+6), where ee̅_qqqq = PP75(Δee_qqqq).
  - Threshold used: ee̅_qqqq = 21%.
- Note: The shaded three-month rolling window is used to assess these four criteria.

### Exclusions from the episode sample (rationale-based filters)
- Developing markets are excluded because they are less exposed to private capital flows.
- Episodes with nominal peak depreciation exceeding 1,000 percent within the 24 months from onset (to eliminate hyper- and very high inflation cases).
- Episodes in transition economies between 1987 and 1996 (driven by massive structural transformations).
- Episodes with peak NEER depreciation under 10 percent (to exclude cases where interlinked countries depreciated together vis-à-vis the dollar but dollar transactions and debt were limited).
- GFC-era episodes where in the second year the currency is more appreciated to the dollar than pre-shock (the GFC represented a brief but large appreciation episode of the US dollar).

### Threshold summary (as used in figures)
- ee̅_e = 15%
- ee̅_eeee = 10%
- ee̅_eeqq = 10%
- ee̅_qqqq = 21%

---

### ANNEX 3. ADDITIONAL ROBUSTNESS

### A. Restricted samples (sensitivity tests)
- Eliminating outliers:
  - Top 10 percent of observations by magnitude of the balance sheet effect (overshooting*debt in specification 1 and overshooting*credit growth in specification 2) are removed.
  - Result: the coefficient on the BaS falls to 0.020 versus 0.025 in Table 4 specification 2, but remains significant at the 5 percent level.
  - Credit growth–based BaS (specification 2) results are even stronger relative to the full sample (Table 5 specification 6).
- Identifying episodes on annual bilateral exchange rate series (specifications 3 and 4):
  - Subset also flagged using Laeven and Valencia (2013) currency-crisis definition: a nominal depreciation vis-à-vis the U.S. dollar of at least 30 percent in a year that is also at least 10 percentage points higher than the rate in the year before.
  - Result: coefficients on the BaS terms remain identical to baseline and are significant at the 1 percent level.
- Identifying episodes on annual REER series (specifications 5 and 6):
  - Uses the Chapter 3 IMF (2015b) approach (large depreciations on annual REER).
  - Result: coefficients on both measures of the BaS are slightly higher than under baseline specifications.

### B. Alternative measures of overshooting (definitions tested and empirical findings)
- Eight alternative overshooting measures tested (specifications and illustrations referenced in Annex Table 7 and Annex Figure 6):
  1. Peak REER minus REER in month t+23 (ex-post equilibrium, Cavallo et al. (2005)) — specifications 2 & 10.
  2. Peak REER minus the post-max minimum (equilibrium = minimum REER within 24 months following peak) — specifications 3 & 11.
  3. Peak REER minus trend REER in month t+23:
     - HP-filtered trend (specifications 4 & 12); HP filter parameter: λ = 400.
     - Christiano-Fitzgerald (CF) trend (specifications 5 & 13); CF filters out stochastic cycles below 2 and above 24 months.
  4. Maximum positive deviation from trend (specifications 6 & 14 for HP trend and 7 & 15 for CF trend) — captures early large spikes above trend.
  5. Peak REER minus ex-ante REER misalignment (specifications 8 & 16):
     - Ex-ante equilibrium computed via an augmented Balassa-Samuelson regression (Bluedorn et al. (2013) implementation of Rodrik (2008)) with country and year fixed effects and EBA regressors: terms of trade, trade openness, trading partner GDP, dependency ratio and population growth.
     - Overshooting = maximum depreciation − ex-ante equilibrium level.
- Empirical consistency:
  - Across all eight measures, the coefficient on the overshooting*debt term remains significant at least at the 5 percent level.
  - Point estimates of the overshooting*debt coefficient remain within 0.022–0.025 for all but the ex-ante specification.
  - Specification 8 (ex-ante misalignment) exhibits a lower coefficient on overshooting*debt: 0.016, but it remains significant at the 1 percent level.
- Comparison of ex-ante vs ex-post magnitudes:
  - Means: ex-ante = 9.3 and ex-post = 20.
  - Medians: ex-ante = 9.5 and ex-post = 16.2.
  - Interpretation: lower estimated ex-ante misalignments produce larger measured overshooting and hence a lower estimated coefficient on the BaS term.
- Discussion and hypotheses:
  - Possible causes for lower ex-ante misalignments: misspecified Balassa-Samuelson regression or ex-ante misalignments being ill-suited for extreme cases.
  - Speculative mechanism: fire-sale of domestic assets to foreigners can reduce net IIP; NIIP is a key determinant of external balance equilibrium (IMF’s EBA), so the depreciation itself may endogenously raise the equilibrium REER.
  - The hypothesis requires additional testing (e.g., crises can also yield NIIP improvements via debt restructurings).

---

*Source: wpiea2020060-print-pdf - ANNEX 2. CRITERIA FOR INCLUSION OF LARGE DEPRECIATION EPISODES*

### Annex Table 1. Key summary statistics of large depreciation episodes

### wpiea2020060-print-pdf - Annex Table 1. Key summary statistics of large depreciation episodes

### Overview
- Annex Table 1 lists peak month and maximum depreciation (LCU/USD Rate and REER) for numerous large depreciation episodes across Advanced Economies and Emerging Markets, alongside external debt and private credit statistics in T-1, and episode attributes (Stable, ST Debt, STRM Debt, Credit/GDP 3-yr change).
- Summary sample statistics (across episodes) reported:
  - Mean (or share in percent): 1495.1945.125.020.178.7%7.011.26.25.257.4%50.8%
  - Median: 1452.4730.317.612.84.58.14.75.3
  - 25th percentile: 639.1318.46.55.71.65.3-1.3-0.5
  - 75th percentile: 23112.61655.929.326.110.313.912.211.2
  - Standard deviation: 8.198.47.446.737.923.28.29.414.711.8

### Key statistics by episodes (representative entries)
- Advanced Economies (examples):
  - Australia 02/1985: LCU/USD Peak month 1736.3, Max Dep 1851.24, REER Peak month 3.97, Max Dep =Eq Dep + Overshooting Stable 7.30, ST Debt, percent GDP 2.4, STRM Debt, percent GDP -3.70, Credit/GDP 3-yr change 1
  - Iceland 03/2008: LCU/USD Rate Peak month 8116.1, Max Dep 861.15, REER Peak month 2.38, Max Dep =Eq Dep + Overshooting Stable 8.81, ST Debt, percent GDP 53.29, STRM Debt, percent GDP 1.6, Credit/GDP 3-yr change 15.5, Episode 11
  - United Kingdom 08/2008: LCU/USD Rate Peak month 639.5, Max Dep 518.3, REER Peak month 13.4, Max Dep =Eq Dep + Overshooting Stable 4.9, ST Debt, percent GDP 132.9, STRM Debt, percent GDP 11.0, Episode 11
- Emerging Markets (examples):
  - Argentina 01/2002: LCU/USD Rate Peak month 5275.2, Max Dep 5265.4, REER Peak month 168.69, Max Dep =Eq Dep + Overshooting Stable 6.8, ST Debt, percent GDP 110.8, STRM Debt, percent GDP 16.6, Credit/GDP 3-yr change -3.3, Episode 15.7.11
  - Brazil 03/2012: LCU/USD Rate Peak month 2242.3, Max Dep 1726.9, REER Peak month 24.1, Max Dep =Eq Dep + Overshooting Stable 2.8, ST Debt, percent GDP 11.3, STRM Debt, percent GDP 3.4, Credit/GDP 3-yr change 12.37.601
  - Turkey 11/2016: LCU/USD Rate Peak month 21106.7, Max Dep 2258.0, REER Peak month 37.4, Max Dep =Eq Dep + Overshooting Stable 20.60, ST Debt, percent GDP 13.9, STRM Debt, percent GDP 19.1, Credit/GDP 3-yr change 13.64.700

### Regression findings (Annex Table 3; Annex Table 5; Annex Table 7)
- Key cross-cutting result: interaction term Overshooting * External ST Debt/GDP (T-1) is positive and often statistically significant, indicating overshooting is less damaging—or associated with smaller T+1 output losses—when external short-term debt/GDP is higher (coefficients and significance levels reported across specifications):
  - Annex Table 3 (All episodes / Stable episodes only):
    - Overshooting * External ST Debt/GDP (T-1): 0.025*** (All; GDP T+1, column 1), 0.026*** (Stable; GDP T+1, column 4)
    - Coefficient standard errors: (0.009) in Annex Table 3 columns 1 and 4.
  - Annex Table 5 (Extended specifications, All devaluation episodes):
    - Overshooting * External ST Debt/GDP (T-1): 0.011*** (T+1, column 1), 0.024*** (T+2, column 2), 0.035*** (T+3, column 3), 0.058** (T+4, column 4), 0.070** (TT+1 through TT+4 combined, column 5).
    - Standard errors example: (0.003) for T+1 in column 1.
  - Annex Table 7 (alternative REER equilibrium/overshooting definitions):
    - Overshooting * External ST Debt/GDP (T-1) coefficients remain positive and highly significant across definitions (e.g., 0.024***, 0.023***, 0.022***, 0.024***, 0.023***, 0.022**, 0.025**, 0.016*** in All episodes columns 1–8).
    - Standard errors typically around (0.004)–(0.005) in many specifications.
- External ST Debt (percent GDP, T-1) typically has a negative and statistically significant coefficient:
  - Annex Table 3: -0.220** (GDP T+1, column 1), standard error (0.102).
  - Annex Table 5: -0.149*** (T+1, column 1), -0.209*** (T+2, column 2), -0.315** (T+3, column 3); standard errors reported (e.g., (0.041) for T+1).
  - Annex Table 7: coefficients negative and significant across specifications, e.g., -0.209*** (column 1), -0.255*** (column 2), -0.680*** (column 3).
- PPP GDP/capita (Log, T-1) is typically positive and often statistically significant:
  - Annex Table 3: 0.079* (GDP T+1, column 1), standard error (0.042).
  - Annex Table 5: 0.045* (T+1, column 1), 0.080* (T+2, column 2), 0.167* (T+3, column 3).
  - Annex Table 7: 0.080* (column 1), 0.082* (column 2), 0.108** (column 3).
- Selected constants, observations, and fit statistics:
  - Annex Table 3 observations: 887 (column 1), 670 (column 2), 716 (column 3); R2: 0.297, 0.284, 0.055 respectively for columns 1–3; for stable episodes R2: 0.363, 0.355, 0.042 for columns 4–6.
  - Annex Table 5 observations: 978 (T+1, col 1), 878 (T+2, col 2), 737 (T+3, col 3), 706 (T+4, col 4), 605 (combined, col 5); R2 range 0.170 to 0.311 across columns 1–3 and up to 0.300 for later columns. Stable episodes show similar observation counts with R2 up to 0.356.
  - Annex Table 7 observations vary by definition; All episodes examples: 888 (col 1), 882 (col 2); R2 examples: 0.296, 0.293.

### Robustness, extensions, and restricted samples
- Results are robust to:
  - Alternative definitions of equilibrium depreciation and overshooting (Annex Table 7): positive and significant Overshooting * External ST Debt/GDP (T-1) persists.
  - Extended horizons (T through T+4) in Annex Table 5: interaction remains positive and significant for multiple horizons.
  - Restricted samples and exclusions (Annex Table 6): Overshooting * External ST Debt/GDP (T-1) remains positive and often statistically significant across specifications, including when excluding top decile events and specific crisis episodes.
- Additional covariates and interactions included in extended specifications (Annex Table 5 and other tables):
  - Dual Banking/currency crisis (example coefficient 5.346*, standard error (2.968) in some specifications) shows positive association with GDP Loss (T+1) in certain specifications.
  - Non-FDI Capital inflows (% GDP, cumulated T-3 to T-1): coefficient 0.298* (standard error (0.174)) in a specification.
  - ToT (% change, T-1 to T): -0.344* (standard error (0.181)) in one specification; -0.342*** (standard error (0.116)) in another.
  - Domestic credit to private sector (p.p. GDP change, T-3 to T-1) and its interaction with Overshooting show positive and significant coefficients in several specifications (e.g., 0.357*** and interaction 0.019*** respectively in one set).

### Data sources and coverage (Annex Table 2)
- Core variables and sources with time coverage:
  - Large depreciation year, Maximum REER depreciation, Equilibrium REER depreciation, REER overshooting, Depreciation episode stability: Culiuc and Deb (2020), 1980-2018.
  - Real GDP, Real GDP/Capita in PPP USD, External short-term debt (and related external debt series), Non-FDI liabilities, Non-oil exports volume, Real domestic demand, International reserves, Terms-of-trade, Trade openness: World Economic Outlook, 1980-2018.
  - Domestic credit to private sector: Financial Stability Indicators, 1980-2018.
  - Exchange rate regime: Klein and Shambaugh (2010), 1980-2018 (extrapolated).
  - Banking crisis year: Laeven and Valencia (2018), 1980-2017.
  - Trading partner GDP growth: Cubeddu et al. (2014), 1980-2018 (updated).
  - PPP price factor: Penn World Tables 9.1, 1980-2017.
  - Old age dependency ratio, Population growth: World Development Indicators, 1980-2018.

*Source: wpiea2020060-print-pdf - Annex Table 1. Key summary statistics of large depreciation episodes*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020060-print-pdf.pdf_