## _wp0932 — Box 1: An Overview of CGER Exchange Rate Assessment Methodologies

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### Major components and structure
- Tables included: 1. Panel Regression Results using Midpoint of CGER Assessment; 2. Panel Regression Results using MB Misalignment Estimate; 3. Evaluation Diagnostics using MB Estimates; 4. Panel Regression Results using CA Norm; 5. Country Coverage of the Expanded CGER Exercise; 6. Regression Results using Midpoint of CGER Assessment; 7. Regression Results using Individual CGER Methodologies; 8. Regression Results using Midpoint of CGER Assessment, Different Horizons.
- Figures included: 1. Mean Prediction Error; 2. Scatterplots of Realized vs. Predicted Changes in REER; 3. Undconditional Scatterplots, 27 CGER Countries; 4. Conditional Scatterplots using Midpoint of CGER Assessment.
- Box: 1. An Overview of CGER Exchange Rate Assessment Methodologies.
- Appendices: 1. Pooled Regression Results; 2. Description of Diagnostic Statistics; 3. Data Appendix.

### Background and objective
- Since 1997, CGER has conducted biannual exchange rate assessments from a multilateral perspective.
- Coverage expanded: initial G-7; 1998 added six industrial countries; 2006 expanded to 27 advanced and emerging market economies.
- Equilibrium notion: internal balance (zero output gap) and external balance (equilibrium current account and sustainable net external position).
- Objective of the paper: evaluate predictive power of CGER assessments by comparing estimated misalignments (different vintages and methodologies) to subsequent real effective exchange rate (REER) movements; performance metric is degree to which subsequent movements reduce the misalignment.

### CGER methodologies (three complementary approaches)
- Macroeconomic balance (MB) approach:
  - Calculates difference between the current account balance projected over the medium term at prevailing exchange rates and an estimated equilibrium current account balance (“CA norm”).
  - CA norm is a function of demographic factors (population growth and old-age dependency), fiscal balance, level and growth rate of output per capita.
  - Uses country-specific elasticities of the current account with respect to the real exchange rate to obtain required exchange rate adjustment.
- Reduced-form equilibrium real exchange rate (ERER) approach:
  - Estimates statistical relationship between REER and fundamentals (net foreign asset (NFA) position, relative productivity differentials, terms of trade).
  - Misalignment = estimated equilibrium REER (based on medium-term projections of fundamentals) minus current REER.
- External sustainability (ES) approach:
  - Calculates difference between the current account projected over the medium term at prevailing exchange rates and the balance that would stabilize the NFA position at a benchmark level.
  - Uses same elasticities as MB to translate gap into REER adjustment.

### Combination rules for CGER assessments
- If the average of the three misalignments is within five percent of zero, or if all three misalignments are less than 10 percent in absolute value, currency is assessed to be broadly in line with fundamentals.
- Otherwise:
  - If all three estimates are within 10 percentage points of each other, use the approximate midpoint of the three estimates as the assessment.
  - If the estimates are at least 10 percentage points apart, report a range encompassing all three estimates.

### Caveats, data limits, and convergence evidence
- CGER assessments target medium-term equilibrium (not short-term forecasts); misalignments can be persistent.
- For G-7 countries the longest sample yields at most 18 usable observations per country (bi-annual assessments 1997–2005, using a 3-year prediction window to 2008).
- Error-correction models suggest slow convergence with estimated convergence half-life of about 2½ years.

### Predictive-power evaluation — key summary findings
- Overall:
  - Misalignment assessments for advanced economies contain predictive power for subsequent REER movements, especially over a 5-year horizon.
  - Predictive power is stronger after controlling for changes in fundamentals.
  - At individual-country level, CGER assessments outperform a random-walk benchmark for roughly half the countries in the sample.
  - Assessments exhibit high systematic errors: currencies assessed as undervalued tend to remain undervalued; currencies assessed as overvalued tend to remain overvalued, even over 5 years.
- Current account predictive evidence:
  - Estimated deviations of current accounts from equilibrium predict subsequent CA movements over 3- and 5-year horizons; movements tend to reduce estimated gaps.
  - Effects larger over longer horizons and when controlling for changes in fundamentals.

### Evaluation results — mean prediction error and panel regressions
- Full-sample mean prediction error ranges between +0.6 percent and -3.2 percent and is not significantly different from zero using a Student’s t-test.
- Panel regression basic specification: subsequent log REER change (3- or 5-year horizon) regressed on estimated misalignment with country fixed effects; extended specification adds change in estimated equilibrium exchange rate (change in fundamentals).
- Key panel fixed-effects coefficients (reported across specifications):
  - Using midpoint of CGER assessment (Table 1):
    - Misalignment from Midpoint of Assessment (β1): -0.55, -0.70, -0.80, -0.82
    - Change in MB Fundamentals: 0.52, 0.38
    - Observations: 165, 165, 121, 121
    - R-squared: 0.14, 0.44, 0.27, 0.47
  - Using MB misalignment point estimates (Table 2):
    - Misalignment from MB estimates (β1): -0.47, -0.86, -0.83, -1.07
    - Change in MB Fundamentals: 0.63, 0.52
    - Observations: 185, 185, 141, 141
    - R-squared: 0.09, 0.50, 0.29, 0.63
- Interpretation:
  - β1 is significantly negative in all specifications: higher assessed overvaluation (undervaluation) associated with larger subsequent depreciation (appreciation).
  - Magnitude of β1 generally larger at 5-year horizon than 3-year horizon.
  - Coefficient on change in fundamentals (β2) is positive; controlling for fundamentals amplifies effect of misalignments on REER movements.

### Individual-country diagnostics (MB point estimates, Table 3)
- Diagnostic statistics:
  - Mean square error (MSE) decomposed into bias, variance, and covariance components.
  - Direction-of-change statistic: proportion of instances where realized REER change had the same sign as predicted.
  - Theil’s U-Statistic: ratio of CGER MSE to random-walk MSE; U < 1 indicates CGER outperforms random walk.
- Selected outcomes:
  - Direction-of-change: MB estimates correctly predict direction for 4 of 11 countries at 3-year horizon and 8 of 11 at 5-year horizon.
  - Proportion of observations in correct quadrants:
    - 3-year horizon: 64 percent
    - 5-year horizon: 69 percent
  - U-statistic (5-year horizon): CGER misalignment estimates outperform random walk for 5 out of 11 currencies; four of these five have U-statistics significantly different from one by Diebold-Mariano test.
  - MSE decomposition highlights large bias component for several currencies (e.g., U.S. dollar and Japanese yen), indicating persistence of misalignments.
- Selected individual MSE levels (3-year horizon):
  - Australian Dollar MSE: 283.34
  - Canadian Dollar MSE: 44.01
  - Danish Krone MSE: 31.67
  - Japanese Yen MSE: 847.58
  - U.S. Dollar MSE: 811.59
- Selected individual MSE levels (5-year horizon):
  - Australian Dollar MSE: 426.98
  - Canadian Dollar MSE: 106.53
  - Danish Krone MSE: 11.80
  - Japanese Yen MSE: 984.09
  - U.S. Dollar MSE: 573.28
- Significance testing:
  - Direction-of-change significance assessed with binomial distribution p = 0.5.
  - Diebold-Mariano statistic compares MSEs to random-walk benchmark; labels: “Equal”, “CGER”, “RW” indicate significance outcomes.

### Evaluating current account movements (MB CA Norm) — panel regression highlights (Table 4)
- Regression regressing actual CA change on deviation from CA norm and change in CA norm.
- Key estimates:
  - Deviation from CA Norm (β1): -0.76, -1.03, -0.68, -0.85
  - Change in CA Norm: 0.61, 0.42
  - Observations: 163, 163, 130, 130
  - R-squared: 0.39, 0.56, 0.54, 0.69
- Interpretation:
  - Current accounts away from their norm tend to move toward eliminating the gap.
  - Effect larger over longer horizons and when controlling for changes in fundamentals.

### Cross-sectional analysis and expanded coverage (Fall 2006 overhaul)
- Fall 2006 expansion to 27 advanced and emerging market economies representing 90 percent of world GDP and 80 percent of world trade (versus 70 percent and 60 percent using only 11 advanced economies).
- MB and ERER methodologies re-estimated on larger country set; ES methodology added.
- Cross-sectional findings:
  - Short-run determinants (short-term interest rate differentials) and changes in fundamentals were important drivers of recent exchange rate movements.
  - After controlling for short-run drivers and fundamental changes, exchange rates closed about two-thirds of the estimated gap over the past two years.
  - Midpoint of CGER assessment range performs better than individual misalignment estimates.

### Analysis of convergence between Fall 2006 CGER assessments and REER movements (July 2006–September 2008)
- Unconditional relationship: initial comparison does not support unconditional convergence; unconditional best-fit lines mostly flat.
- Regression specifications:
  - A. Unconditional (equation (6)): change in REER on misalignment measures.
  - B. Controls for change in estimated equilibrium REER (equation (7)).
  - C. Controls for fundamentals and interest rate differential (equation (8)); IR differential = country short-term rate minus world rate proxied by average of U.S., euro area, Japan short-term rates.
- Key regression coefficients using midpoint of Fall 06 CGER (Tables 6 and 8; Figure 4) — Change in REER (July 06–Sep 08):
  - Midpoint of Fall 06 CGER:
    - Unconditional: -0.02 [0.14]
    - Controlling fundamentals: -0.47 [2.65]**
    - Controlling fundamentals + IR differential: -0.71 [4.06]***
  - Change in MB fundamentals: 0.34 [1.74]* (col 2), 0.44 [2.87]** (col 3)
  - Change in ERER fundamentals: 0.61 [3.55]*** (col 2), 0.53 [3.71]*** (col 3)
  - IR differential vis-a-vis G-3, July 06: 1.31 [3.28]***
  - Constant: 5.15 [2.04]* (col 1), 1.39 [0.54] (col 2), -2.64 [1.22] (col 3)
  - Observations: 27 (col 1), 22 (col 2), 22 (col 3)
  - R-squared: 0.00 (col 1), 0.50 (col 2), 0.72 (col 3)
- Interpretation:
  - Controlling for fundamentals and interest rate differentials makes the CGER coefficient more negative and statistically significant.
  - Size implication: "for each percentage point of assessed overvaluation, currencies depreciated by 0.7 percentage points on average over the past two years, controlling for other factors." (coefficient = -0.71)
  - IR differential positive and significant (1.31): higher interest rate currencies tended to appreciate—consistent with carry-trade profitability; caution advised about incorporating short-term rates into medium-term CGER.

### Results using individual misalignment estimates (Table 7)
- MB misalignment (col 1/2/3): -0.13 [1.15], -0.32 [2.03]*, -0.45 [3.08]***
  - Change in MB fundamentals: 0.48 [3.32]***, 0.56 [4.96]***
  - IR differential vis-a-vis G-3 (col 3): 1.18 [4.48]***
  - Observations: 27/27/27; R-squared: 0.02/0.39/0.59
- ERER misalignment (col 1/2/3): 0.03 [0.18], -0.46 [2.28]**, -0.55 [2.56]**
  - Change in ERER fundamentals: 0.90 [4.52]***, 0.87 [4.34]***
  - IR differential vis-a-vis G-3 (col 3): 0.79 [2.16]**
  - Observations: 22/22/22; R-squared: 0.00/0.39/0.48
- ES misalignment (col 1/2/3): 0.03 [0.18], -0.14 [1.29], -0.25 [2.36]**
  - Change in ES fundamentals: 0.61 [4.99]***, 0.70 [6.80]***
  - IR differential vis-a-vis G-3 (col 3): 1.15 [4.63]***
  - Observations: 24/24/24; R-squared: 0.00/0.61/0.79
- Summary: individual-misalignment results qualitatively similar to midpoint but often smaller in magnitude and significance.

### Robustness to horizon and timing (Table 8)
- Re-estimated column 3 specification for different end dates (Midpoint coefficient and robust t-statistic):
  - End = Sep-08 (July 06–Sep 08): -0.71 [4.06]***
  - End = Jul-08 (July 06–Jul 08): -0.77 [4.70]***
  - End = Mar-08 (July 06–Mar 08): -0.43 [2.70]**
  - End = Sep-07 (July 06–Sep 07): -0.18 [1.99]*
- Other coefficients across horizons (selected):
  - Change in MB fundamentals: 0.44 [2.87]**, 0.48 [4.36]***, 0.36 [2.65]**, 0.32 [3.22]*** (for Sep-08, Jul-08, Mar-08, Sep-07 respectively)
  - Change in ERER fundamentals: 0.53 [3.71]***, 0.61 [4.25]***, 0.32 [1.93]*, 0.36 [2.34]**
  - IR differential vis-a-vis G-3, July 06: 1.31 [3.28]***, 1.32 [3.64]***, 0.82 [2.23]**, 0.77 [3.68]***
  - Observations: 22 for each horizon; R-squared: 0.72, 0.76, 0.53, 0.71 respectively.
- Interpretation:
  - Large fall 2008 movements contributed to reversion toward equilibrium, but earlier end points (Jul-08) produce even larger coefficients.
  - Coefficient magnitude and significance decline as forecast horizon shortens but remain negative and often significant.

### Pooled regressions and persistence (Appendix I highlights)
- Pooled regression selected estimates (Misalignment from Midpoint (β1)):
  - -0.06 [0.59], -0.17 [3.41]***, -0.18 [0.79], -0.24 [3.09]**
  - Change in MB Fundamentals: 0.59 [4.63]***, 0.69 [5.02]***
  - Observations: 165, 165, 121, 121; R-squared: 0.01, 0.37, 0.03, 0.48
- Findings:
  - Misalignments and current account gaps are persistent.
  - CGER predicts direction (overvalued → depreciate; undervalued → appreciate) but magnitudes of REER movements are often smaller than misalignments; currencies tend to remain overvalued or undervalued even over 5 years.
  - Prediction errors show substantial systematic bias at individual-country level.

### Diagnostic metrics and data notes (Appendices II and III)
- Diagnostics:
  - MSE: average squared deviation of expected REER change from realized change (k = 3 or 5).
  - Theil’s U-Statistic: ratio of model MSE to random walk MSE.
  - MSE decomposition into bias (UM), variance (US), covariance (UC) proportions; UM indicates systematic error.
  - Direction of Change Statistic: proportion where realized REER change had same sign as expected; benchmark 0.5 with Binomial p-values.
  - Diebold-Mariano statistic: compares predictive accuracy against random walk using MSE loss; lag choices use 1 lag and automatic Schwarz criterion.
- Data construction:
  - Exchange rate assessments and misalignment estimates from historical bi-annual CGER notes (presented to IMF Managing Director from March 1997; circulated to Executive Board from March 2001).
  - Actual REER changes from monthly REER data in IMF INS database; base months identified from CGER notes; horizons: 3-year and 5-year for panel regressions; July 2006–September 2008 for cross-section.
  - CA/GDP changes from IMF WEO database; Norway’s first three observations dropped as outliers (CA/GDP rises from zero in 1998 to 15 percent in 2000); inclusion yields qualitatively similar results.
  - Changes in fundamentals computed as differences in equilibrium REERs between periods; equilibrium REERs derived using MB (or ERER for cross-section) misalignments and INS REER.
  - Short-term interest rate differentials from IMF Research Department’s GDS database; for Pakistan and Poland, IFS used where GDS lacks data.

### Conclusion — main takeaways
- Overall findings support CGER exchange rate assessments.
- Predictive power: estimated REER misalignments and current account gaps predict future REER movements and current accounts, especially over longer horizons and after accounting for changes in fundamentals.
- Conditional convergence: after accounting for short-term determinants and fundamentals changes, exchange rates move toward reducing assessed misalignments.
- Persistence: misalignments and CA gaps are very persistent; magnitudes of subsequent REER movements often smaller than misalignments, producing substantial systematic prediction bias at individual-country level.
- Open question: reasons for persistence of misalignments over the medium term remain for future research.

*Source: _wp0932 — Box 1: An Overview of CGER Exchange Rate Assessment Methodologies.*

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

### _wp0932 - References..............................................................................................................

### Major components and structure
- Tables included:
  - 1. Panel Regression Results using Midpoint of CGER Assessment
  - 2. Panel Regression Results using MB Misalignment Estimate
  - 3. Evaluation Diagnostics using MB Estimates
  - 4. Panel Regression Results using CA Norm
  - 5. Country Coverage of the Expanded CGER Exercise
  - 6. Regression Results using Midpoint of CGER Assessment
  - 7. Regression Results using Individual CGER Methodologies
  - 8. Regression Results using Midpoint of CGER Assessment, Different Horizons
- Figures included:
  - 1. Mean Prediction Error
  - 2. Scatterplots of Realized vs. Predicted Changes in REER
  - 3. Undconditional Scatterplots, 27 CGER Countries
  - 4. Conditional Scatterplots using Midpoint of CGER Assessment
- Box:
  - 1. An Overview of CGER Exchange Rate Assessment Methodologies
- Appendices:
  - 1. Pooled Regression Results
  - 2. Description of Diagnostic Statistics
  - 3. Data Appendix

### Background on CGER assessments
- Since 1997, the IMF Consultative Group on Exchange Rate issues (CGER) has conducted biannual exchange rate assessments from a multilateral perspective.
- Initial coverage: the G-7 economies: Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States.
- 1998 expansion: six more industrial countries — Australia, Denmark, New Zealand, Norway, Sweden, and Switzerland.
- 2006 expansion: coverage expanded more substantially to include 27 advanced and emerging market economies.
- The notion of equilibrium underpinning CGER is one of internal and external balance:
  - Internal balance: associated with a zero output gap.
  - External balance: associated with an “equilibrium” current account balance (estimated as a function of economic fundamentals) and with a sustainable net external (asset or liability) position.
- Reduced-form relationships between the real exchange rate and macroeconomic fundamentals have also been employed as a measure of misalignment.
- An overview of the different methodologies used by CGER is provided in Box 1.

### Objective of the paper
- To evaluate the predictive power of the CGER assessments of exchange rate misalignments.
- Method: compare estimated misalignments (based on different vintages of CGER assessments) to subsequent movements in the respective countries’ real effective exchange rate (REER).
- Performance metric: the degree to which subsequent movements are in the direction of reducing the misalignment.

### Empirical approach and horizons
- For assessments of advanced economies (longest sample): panel approach used, with comparisons made for both 3-year and 5-year horizons.
- For the wider set of advanced and emerging market economies included since 2006: a cross-sectional analysis of exchange rate movements between 2006 and 2008 is performed instead.

### Confidentiality and data disclosure
- CGER exchange rate assessments are classified by the IMF as “Strictly Confidential,” due to potential market sensitivity of IMF views on exchange rate misalignments (although CGER assessments do not necessarily reflect the IMF’s official view on exchange rates).
- As a result, the paper does not provide information on assessed misalignments for specific countries.
- The methodologies used by CGER are public (see, for example, Lee et al. 2008), and interested parties can produce similar misalignment estimates based on publicly available information.

*Source: _wp0932 - References..............................................................................................................*

### Box 1: An Overview of CGER Exchange Rate Assessment Methodologies

### Box 1: An Overview of CGER Exchange Rate Assessment Methodologies

### Methodologies Used
- Three complementary methodologies currently in use:
  - Macroeconomic balance (MB) approach:
    - Calculates difference between the current account balance projected over the medium term at prevailing exchange rates and an estimated equilibrium current account balance (“CA norm”).
    - CA norm is a function of medium-term determinants of the savings-investment balance (demographic factors: population growth and old-age dependency; fiscal balance; level and growth rate of output per capita).
    - The exchange rate adjustment that would eliminate this difference over the medium term is obtained using country-specific elasticities of the current account with respect to the real exchange rate.
  - Reduced-form equilibrium real exchange rate (ERER) approach:
    - Estimates a statistical relationship between the real exchange rate and fundamentals such as the net foreign asset (NFA) position, relative productivity differentials between tradable and nontradable sectors, and the terms of trade.
    - Misalignment = estimated equilibrium REER (based on medium-term projections of fundamentals) minus current REER.
  - External sustainability (ES) approach:
    - Calculates the difference between the current account projected over the medium term at prevailing exchange rates and the balance that would stabilize the NFA position of the country at some benchmark level.
    - Uses same elasticities as MB to translate the difference into a real exchange rate adjustment over the medium term.

### Combining the Three Estimates
- Combination rules:
  - If the average of the three misalignments is within five percent of zero, or if all three misalignments are less than 10 percent in absolute value, the currency is assessed to be broadly in line with fundamentals.
  - Otherwise:
    - If all three estimates are within 10 percentage points of each other, use the approximate midpoint of the three estimates as the assessment.
    - If the estimates are at least 10 percentage points apart, report a range encompassing all three estimates.

### Caveats and Conceptual Notes
- CGER assessments:
  - Are assessments of the current REER relative to an equilibrium based on medium-term projections of fundamentals, not short-term forecasts.
  - Can reflect persistent deviations; misalignments can be persistent and often are.
  - Can be narrowed or closed by movements in fundamentals without any change in the real exchange rate.
- Data limitations:
  - For G-7 countries the longest sample yields at most 18 usable observations per country (bi-annual assessments from 1997 to 2005, when using a 3-year prediction window to 2008).
  - Caution advised when interpreting individual-country diagnostic statistics that rely on large-sample asymptotics.
- Convergence evidence:
  - Error-correction models suggest slow convergence of actual REER to equilibrium REER with an estimated convergence half-life of about 2½ years.

### Predictive-Power Evaluation: Summary of Findings
- Overall predictive evidence:
  - Exchange rate misalignment assessments for advanced economies contain predictive power over subsequent REER movements, especially over a 5-year horizon.
  - Predictive power is stronger after controlling for changes in fundamentals over the prediction horizon.
  - At the individual-country level, CGER assessments outperform a benchmark random-walk model for roughly half of the countries in the sample.
  - However, assessments exhibit very high systematic errors: currencies assessed as undervalued tend to remain undervalued, and currencies assessed as overvalued tend to remain overvalued, even over a 5-year horizon.
- Current account predictive evidence:
  - Estimated deviations of current accounts from their equilibrium values predict subsequent movements in current account balances over 3- and 5-year horizons; movements tend to be in the direction of eliminating estimated gaps.
  - Effects are more pronounced over longer horizons and after controlling for changes in fundamentals.

### Evaluation Results — Mean Prediction Error and Panel Regressions
- Mean prediction error:
  - Full-sample mean prediction error ranges between +0.6 percent and -3.2 percent and is not significantly different from zero using a Student’s t-test.
  - Country-level mean prediction errors are large and of opposite signs across countries; systematic country-specific prediction errors reflect persistence of misalignments.
- Panel regression specifications:
  - Basic specification: subsequent log REER change (3- or 5-year horizon) regressed on estimated misalignment (with country fixed effects).
  - Extended specification: adds change in estimated equilibrium exchange rate (change in fundamentals).
- Key estimated coefficients (panel fixed-effects):
  - Using midpoint of CGER assessment (Table 1):
    - Misalignment from Midpoint of Assessment (β1): -0.55, -0.70, -0.80, -0.82 (reported across specifications)
    - Change in MB Fundamentals: 0.52, 0.38
    - Observations: 165, 165, 121, 121 (across columns)
    - R-squared: 0.14, 0.44, 0.27, 0.47
  - Using MB misalignment point estimates (Table 2):
    - Misalignment from MB estimates (β1): -0.47, -0.86, -0.83, -1.07 (reported across specifications)
    - Change in MB Fundamentals: 0.63, 0.52
    - Observations: 185, 185, 141, 141 (across columns)
    - R-squared: 0.09, 0.50, 0.29, 0.63
  - Interpretation:
    - β1 is significantly negative in all specifications: higher assessed overvaluation (undervaluation) associated with larger subsequent depreciation (appreciation).
    - Magnitude of β1 generally larger at 5-year horizon than 3-year horizon.
    - Coefficient on change in fundamentals (β2) is positive, as expected; controlling for fundamentals makes the effect of misalignments on REER movements more pronounced.

### Individual-Country Diagnostics
- Data constraints:
  - For each country at most 18 observations (biannual assessments 1997–2005).
- Diagnostic statistics used:
  - Mean square error (MSE) decomposed into bias, variance, and covariance components.
  - Direction-of-change statistic: proportion of instances where realized REER change had the same sign as predicted by misalignment.
  - Theil’s U-Statistic: ratio of CGER MSE to random-walk MSE; value < 1 indicates CGER outperforms random walk.
- Selected diagnostic outcomes (MB point estimates, Table 3, summary):
  - Direction-of-change: MB estimates correctly predict direction for 4 of 11 countries at 3-year horizon and 8 of 11 at 5-year horizon.
  - Proportion of observations in correct quadrants (scatterplot):
    - 3-year horizon: 64 percent
    - 5-year horizon: 69 percent
  - U-statistic (5-year horizon): CGER misalignment estimates outperform random walk for 5 out of 11 currencies (value of U-statistic < 1). Four of these five have U-statistics significantly different from one by Diebold-Mariano test.
  - MSE decomposition highlights large bias component for several currencies (e.g., U.S. dollar and Japanese yen), indicating persistence of misalignments.
  - Examples of individual MSE levels reported in Table 3 (3-year horizon, selected):
    - Australian Dollar MSE: 283.34
    - Canadian Dollar MSE: 44.01
    - Danish Krone MSE: 31.67
    - Japanese Yen MSE: 847.58
    - U.S. Dollar MSE: 811.59
  - At the 5-year horizon selected MSEs:
    - Australian Dollar MSE: 426.98
    - Canadian Dollar MSE: 106.53
    - Danish Krone MSE: 11.80
    - Japanese Yen MSE: 984.09
    - U.S. Dollar MSE: 573.28
- Notes on significance testing:
  - Direction-of-change significance assessed using a binomial distribution with p = 0.5.
  - Diebold-Mariano statistic used to compare MSEs against random walk benchmark; “Equal” indicates differences not significant, “CGER” indicates CGER has significantly lower MSE, “RW” indicates random walk has significantly lower MSE.

### Evaluating Current Account Movements (MB CA Norm)
- Regression specification analogous to REER evaluation regresses actual change in CA on deviation from CA norm and change in CA norm.
- Key panel regression estimates (Table 4):
  - Deviation from CA Norm (β1): -0.76, -1.03, -0.68, -0.85 (across specifications)
  - Change in CA Norm: 0.61, 0.42
  - Observations: 163, 163, 130, 130 (across columns)
  - R-squared: 0.39, 0.56, 0.54, 0.69
- Interpretation:
  - Current accounts away from their norm tend to move toward eliminating the gap.
  - Effect is larger over longer horizons and more pronounced when controlling for changes in fundamentals.

### Cross-Sectional Analysis and Expanded Coverage
- Fall 2006 CGER overhaul:
  - Country coverage expanded to 27 advanced and emerging market economies, representing 90 percent of world GDP and 80 percent of world trade (compared to 70 percent and 60 percent using only the 11 advanced economies).
  - MB and ERER methodologies re-estimated using a larger set of countries; ES methodology added.
- Cross-sectional findings (summary):
  - Short-run determinants (short-term interest rate differentials) and changes in fundamentals have been important drivers of recent exchange rate movements.
  - After controlling for these short-run drivers and fundamental changes, exchange rates moved in the direction predicted by CGER, closing about two-thirds of the estimated gap over the past two years.
  - The midpoint of the CGER assessment range performs better than individual misalignment estimates, supporting the value of a complementary set of methodologies.

*Source: Box 1, “An Overview of CGER Exchange Rate Assessment Methodologies,” _wp0932 (IMF)._

### Box 1 for a summary).

### _wp0932 - Box 1 for a summary)

### Analysis of convergence between REER movements and Fall 2006 CGER assessments
- Objective: assess whether REERs have converged toward equilibrium values estimated in the Fall 2006 CGER exercise—i.e., whether currencies assessed as overvalued depreciated and those assessed as undervalued appreciated—using exchange rate movements between July 2006 (reference for Fall 2006) and September 2008 (reference for Fall 2008).
- Approach: examine unconditional relationships between Fall 2006 CGER assessments and REER changes between July 2006 and September 2008, using both the midpoint of the CGER assessment range and the three individual misalignment estimates used by CGER (MB, ERER, ES).
- Unconditional finding: initial comparison does not support unconditional convergence toward CGER’s estimated equilibrium; unconditional best-fit lines are mostly flat (Figure 3).
- Caveats to unconditional correlations:
  - Horizon mismatch: REER movements examined over a two-year horizon, while CGER targets the medium term typically defined as five years (the WEO forecast horizon).
  - Short-run determinants: need to control for short-run determinants such as interest rates.
  - Fundamentals may have changed since Fall 2006, altering the equilibrium REER and required adjustment.

### Regression specifications and controls
- Three specifications estimated:
  - A. Unconditional (equation (6)): change in REER (July 2006–Sept 2008) on misalignment measures. Expect 0,0 10 <≈ ββ.
  - B. Controlling for changes in fundamentals (equation (7)): adds change in estimated equilibrium REER. Expect 0,0,0 210 ><≈ βββ.
  - C. Controlling for fundamentals and interest rates (equation (8)): adds interest rate differential (country short-term rate minus world rate proxied by average of U.S., euro area, Japan short-term rates). Expect 0,0,0 210 ><≈ βββ.
- Note on interest rate differential: uncovered interest parity suggests negative correlation with REER changes, but most empirical evidence (e.g., Burnside et al. (2007)) finds a positive correlation.

### Key regression results (midpoint of CGER assessment, Tables 6 and 8; Figure 4)
- Controls used: change in MB fundamentals, change in ERER fundamentals, IR differential vis-a-vis G-3 (July 06).
- Regression coefficients (Change in REER, July 06–Sep 08; using midpoint of Fall 06 CGER):
  - Midpoint of Fall 06 CGER: -0.02 (unconditional), -0.47 (controlling fundamentals), -0.71 (controlling fundamentals + IR differential)
    - Robust t statistics: [0.14] (col 1), [2.65]** (col 2), [4.06]*** (col 3)
  - Change in MB fundamentals: 0.34 (col 2), 0.44 (col 3)
    - Robust t statistics: [1.74]*, [2.87]**
  - Change in ERER fundamentals: 0.61 (col 2), 0.53 (col 3)
    - Robust t statistics: [3.55]***, [3.71]***
  - IR differential vis-a-vis G-3, July 06: 1.31 (col 3)
    - Robust t statistic: [3.28]***
  - Constant: 5.15 (col 1), 1.39 (col 2), -2.64 (col 3)
    - Robust t statistics: [2.04]*, [0.54], [1.22]
  - Observations: 27 (col 1), 22 (col 2), 22 (col 3)
  - R-squared: 0.00 (col 1), 0.50 (col 2), 0.72 (col 3)
- Interpretation:
  - Once changes in fundamentals and interest rate differentials are controlled for, the coefficient on the CGER assessment becomes more negative and statistically significant.
  - The size of the coefficient implies speed of convergence: "for each percentage point of assessed overvaluation, currencies depreciated by 0.7 percentage points on average over the past two years, controlling for other factors." (coefficient = -0.71)
  - Interest rate differential positive and significant (1.31): higher interest rate currencies tended to appreciate over the period—consistent with documented forward premium puzzle / carry trade profitability.
  - Authors caution against incorporating short-term interest rate differentials into CGER, since CGER assesses medium-term equilibrium and short-term rates may not reflect medium-term fundamentals; unwinding of carry trades suggests instability.

### Results using individual CGER misalignment estimates (Table 7)
- Using MB misalignment:
  - MB Misalignment, Fall 06 CGER: -0.13 (col 1), -0.32 (col 2), -0.45 (col 3)
    - Robust t statistics: [1.15], [2.03]*, [3.08]***
  - Change in MB fundamentals: 0.48 (col 2), 0.56 (col 3)
    - Robust t statistics: [3.32]***, [4.96]***
  - IR differential vis-a-vis G-3, July 06: 1.18 (col 3) [4.48]***
  - Observations: 27/27/27; R-squared: 0.02/0.39/0.59
- Using ERER misalignment:
  - ERER Misalignment, Fall 06 CGER: 0.03 (col 1), -0.46 (col 2), -0.55 (col 3)
    - Robust t statistics: [0.18], [2.28]**, [2.56]**
  - Change in ERER fundamentals: 0.90 (col 2), 0.87 (col 3)
    - Robust t statistics: [4.52]***, [4.34]***
  - IR differential vis-a-vis G-3, July 06: 0.79 (col 3) [2.16]**
  - Observations: 22/22/22; R-squared: 0.00/0.39/0.48
- Using ES misalignment:
  - ES Misalignment, Fall 06 CGER: 0.03 (col 1), -0.14 (col 2), -0.25 (col 3)
    - Robust t statistics: [0.18], [1.29], [2.36]**
  - Change in ES fundamentals: 0.61 (col 2), 0.70 (col 3)
    - Robust t statistics: [4.99]***, [6.80]***
  - IR differential vis-a-vis G-3, July 06: 1.15 (col 3) [4.63]***
  - Observations: 24/24/24; R-squared: 0.00/0.61/0.79
- Summary: results using individual misalignment estimates are qualitatively similar to using the midpoint but often smaller in magnitude and significance.

### Robustness to horizon and timing (Table 8)
- Re-estimated column 3 specification for different end dates:
  - End = Sep-08 (July 06–Sep 08): Midpoint coefficient = -0.71 [4.06]***
  - End = Jul-08 (July 06–Jul 08): Midpoint coefficient = -0.77 [4.70]***
  - End = Mar-08 (July 06–Mar 08): Midpoint coefficient = -0.43 [2.70]**
  - End = Sep-07 (July 06–Sep 07): Midpoint coefficient = -0.18 [1.99]*
- Other coefficients across horizons:
  - Change in MB fundamentals: 0.44 / 0.48 / 0.36 / 0.32 with robust t stats [2.87]**, [4.36]***, [2.65]**, [3.22]***
  - Change in ERER fundamentals: 0.53 / 0.61 / 0.32 / 0.36 with robust t stats [3.71]***, [4.25]***, [1.93]*, [2.34]**
  - IR differential vis-a-vis G-3, July 06: 1.31 / 1.32 / 0.82 / 0.77 with robust t stats [3.28]***, [3.64]***, [2.23]**, [3.68]***
  - Observations: 22 for each horizon; R-squared: 0.72, 0.76, 0.53, 0.71 respectively.
- Interpretation:
  - Large exchange rate movements in fall 2008 contributed to reversion toward equilibrium, but using earlier end points (Jul-08) produces even larger and more significant coefficients on CGER assessment.
  - Coefficient magnitude and significance decline as the forecast horizon shortens (e.g., to 20 or 14 months), but remain negative and in several cases significant.

### Pooled regression and persistence (Appendix I highlights)
- Pooled regression results (selected):
  - Misalignment from Midpoint (β1): -0.06 / -0.17 / -0.18 / -0.24 with t stats [0.59], [3.41]***, [0.79], [3.09]**
  - Change in MB Fundamentals: 0.59 / 0.69 with t stats [4.63]***, [5.02]***
  - Observations vary: 165, 165, 121, 121; R-squared vary: 0.01, 0.37, 0.03, 0.48
- Findings on persistence:
  - Exchange rate misalignments and current account gaps are persistent.
  - CGER misalignments predict direction of subsequent REER movements (overvalued → depreciate; undervalued → appreciate) but magnitudes of REER movements are often smaller than misalignments, so currencies tend to remain overvalued or undervalued even over a 5-year horizon.
  - Prediction errors exhibit substantial systematic bias at the individual country level.

### Diagnostic metrics and data notes (Appendices II and III)
- Diagnostic statistics used:
  - MSE: defined as average squared deviation of expected REER change from realized change (k = 3 or 5).
  - Theil’s U-Statistic: ratio of model MSE to random walk MSE.
  - Decomposition of MSE into bias (UM), variance (US), covariance (UC) proportions; UM indicates systematic error.
  - Direction of Change Statistic: proportion where realized REER change had same sign as expected; benchmark 0.5 with Binomial p-values shown.
  - Diebold-Mariano statistic: compares predictive accuracy against random walk using MSE loss and lag choices (1 lag and automatic Schwarz criterion).
- Data sources and construction:
  - Exchange rate assessments, misalignment estimates, current account norms from historical bi-annual CGER notes (presented to IMF Managing Director biannually beginning March 1997; circulated to IMF Executive Board from March 2001).
  - Actual REER changes constructed using monthly REER data from IMF INS database; reference periods specified in bi-annual CGER notes used to identify base months; changes over 3-year and 5-year horizons for panel regressions; July 2006 to September 2008 used for cross-section.
  - Current account to GDP changes constructed using CA and nominal GDP in U.S. dollars from IMF WEO database; Norway’s first three observations dropped as outliers (CA/GDP rises from zero in 1998 to 15 percent in 2000) though inclusion yields qualitatively similar results.
  - Changes in fundamentals computed as differences in equilibrium REERs between two periods; equilibrium REERs derived using MB (or ERER for cross-section) misalignment estimates and INS REER.
  - Short-term interest rate differentials from IMF Research Department’s GDS database; for Pakistan and Poland, IFS used where GDS lacks short-term rate data.

### IV. Conclusion — main takeaways
- General assessment: overall findings generally support CGER exchange rate assessments.
- Predictive power: estimated REER misalignments and current account gaps have predictive power for future REER movements and current accounts, especially over longer horizons and after accounting for changes in fundamentals.
- Conditional convergence: after accounting for short-term determinants and fundamentals changes, exchange rates move toward reducing assessed misalignments.
- Persistence: misalignments and CA gaps are very persistent; magnitudes of subsequent REER movements often smaller than misalignments, producing substantial systematic prediction bias at individual country level.
- Open question: reasons for persistence of misalignments over the medium term are left for future research.

*Source: _wp0932 - Box 1 for a summary).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0932.pdf_