## _wp10162 - 1. Summary Statistics Across Geographic and Economic Regions, 1973–2008

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---

### Introduction and purpose
- Assessments of exchange rate levels are central to IMF surveillance.
- Four methodologies applied to evaluate exchange rate levels in sub-Saharan African countries relative to fundamentals:
  - Macroeconomic balance approach (gap between current account balance and its norm; valuation determined by gap magnitude and current account elasticity to the real exchange rate).
  - Equilibrium real exchange rate approach (equilibrium REER from fundamentals; valuation as percentage deviation of observed REER from equilibrium).
  - External sustainability approach (norm current account that would stabilize net foreign assets; valuation via gap and elasticity as in macroeconomic balance approach).
  - Purchasing power parity approach (equilibrium REER from the law of one price; valuation by gap between equilibrium and observed REER).
- Methodological contrasts with prior studies:
  - Dataset covers all 182 countries the WEO reported on (including sub-Saharan Africa); CGER covered 54 economies with only South Africa from sub-Saharan Africa.
  - Estimation period extends to 2008 in chapter title context; elsewhere dataset described as drawn from annual data from 1973 through 2014.
  - Econometric technique: pooled generalized method of moments (following Vitek (2009)), versus pooled and fixed effects panel estimation in CGER.
  - Use of annual data rather than CGER’s four-year averages; additional variables include aid and remittances.

### Dataset, sources, and data adjustments
- Primary data sources:
  - WEO (IMF, 2009a) for macroeconomic variables.
  - World Bank World Development Indicators for demographics, aid, and remittances.
  - IMF Information Notice System for effective exchange rate and trade weight data.
  - IMF Balance of Payments database for net foreign asset data.
  - Uppsala Conflict Data Program (2009) for armed conflict data.
- Coverage and sample:
  - Dataset drawn from annual data for 182 economies from 1973 through 2014.
  - Chapter title references 1973–2008.
- Data exclusions and adjustments:
  - Excluded observations with negative values for nominal GDP, GDP at constant prices, government consumption, exports, imports, population, employment, exchange rate, and terms of trade.
  - Excluded observations with absolute values greater than 100 percent for dependency ratio, population growth, fiscal balance, government spending, current account balance, trade balance, and oil trade balance as a percent of GDP.
  - Trade weight data replaced by country-reported data when large discrepancies exist.

### Subsamples and econometric treatment
- Subsamples analyzed:
  - Whole sample (all available information).
  - Group of low and middle income countries (LMIC).
  - Group of sub-Saharan economies.
  - Subset of sub-Saharan economies excluding oil-exporting countries.
- Rationale and method:
  - Slope coefficients differ for sub-Saharan Africa relative to advanced economies and LMIC.
  - Estimation method: pooled generalized method of moments (GMM); LMIC and sub-Saharan estimations start from 1990.
  - Annual data used; aid and remittances included as additional variables.

### Key comparative findings (summary statistics and observations)
- Macroeconomic balances:
  - Fiscal balances, government debt, external current account, and net foreign asset (NFA) holdings of African countries are generally worse than those of LMIC; both African and LMIC groups are worse than advanced economies.
- Income and external assistance:
  - African economies are poorer than LMIC and rely more on foreign aid.
  - The mean for real GDP per capita in both the African and LMIC groups in the 2000s are lower than the mean income of advanced economies in the 1970s–80s.

### Macroeconomic Balance Approach — methodology
- Objective: compute REER adjustment to close gap between projected medium-term CAB at prevailing REER and CAB norm consistent with sustainable medium-term fundamentals.
- Estimation equation (panel, 1973–2008):
  - CAB_it = α + X_it β + Z_it δ + ε_it
  - X: relative old age dependency, relative population growth, relative income, relative income growth, relative fiscal balance, oil trade balance, initial NFA, aid inflows, remittances.
  - Z: armed conflict dummy; change (log) in oil production.
- Relative variables constructed as deviations from trade-weighted averages (trade weights spliced for 1973–1989, 1990–1995, 1996–2008).
- Estimation: panel GMM with White standard errors; samples: whole sample, LMIC, sub-Saharan Africa, sub-Saharan excluding oil exporters.

### Macroeconomic Balance Approach — key estimation results and findings
- Panel unit root tests: none of the variables have a unit root that cannot be rejected by a majority of tests.
- Whole sample and LMIC: broadly similar to CGER except:
  - Population growth: insignificant in whole and LMIC samples.
  - Relative income growth: significant and larger in whole and LMIC samples than in CGER estimates.
- Sub-Saharan Africa specific findings:
  - Demographics lack explanatory power.
  - Relative income: a 1 percent increase in relative income improves the current account balance by 0.07 percent in the sub-Saharan Africa sample (versus ≤ 0.02 percent in other samples).
  - Fiscal balance: a 1 percent fiscal-gap strengthening improves the current account balance by 1 percent in sub-Saharan Africa (versus 0.3 percent or less in other samples).
  - Aid and remittances: improve the current account balance in sub-Saharan Africa but are statistically insignificant elsewhere.
  - Change in oil production: significant and large in the African sample; insignificant in other samples.
  - Excluding oil exporters: a 1 percent decline in the oil trade balance reduces the current account balance by 1.1 percent.
  - Fiscal dominance in oil-importing African countries: a 1 percent decline in fiscal savings reduces external balance by more than 1 percent.
- Norms and underlying balance:
  - Norms calculated using restricted-model coefficients; medium-term fundamentals from October 2009 WEO database.
  - Underlying balance used: 2014 current account projection from October 2009 WEO (constant real exchange rate path, zero output gap).
- Elasticities used to translate CAB gaps into REER adjustments:
  - Import elasticity IM_RER_ε = 0.92.
  - Export elasticity X_RER_ε = -0.71.
  - CAB_RER_ε computed via CAB_RER_ε = 1 / (1 - X_RER_ε - IM_RER_ε).
  - Degree of REER change ΔRER (%) = (U_CAB - N_CAB) / CAB_RER_ε (U_CAB = underlying CAB; N_CAB = norm CAB).

### Macroeconomic Balance Approach — robustness checks
- Annual data versus nonoverlapping four-year averages: panel GMM on four-year averages yields sign, magnitude, and t-statistics similar to annual-data estimates for whole and LMIC samples; panel GMM could not be applied to the sub-Saharan sample due to data limitations.
- Outlier exclusion: excluding observations six standard deviations away from the mean does not drive coefficients or significance.
- Controls for excessive GDP growth: 0-1 dummies for two or more consecutive periods of real GDP growth higher than 10 and 15 percent do not have explanatory power.

### Equilibrium Real Exchange Rate (ERER) Approach — methodology
- Objective: measure percent deviation of REER from equilibrium estimated from medium-term fundamentals.
- Estimation equation (panel):
  - ln(RER_it) = α + X_it β + ε_it
  - X: terms of trade, relative productivity (GDP PPP per unit of labor), relative government consumption-to-GDP, NFA, aid inflows, remittance inflows.
- Theoretical expectations:
  - Terms of trade ↑ → REER appreciates.
  - Relative productivity ↑ → REER appreciates.
  - Relative government consumption ↑ → REER appreciates.
  - NFA-to-GDP ↑ → REER appreciates.
  - Aid/remittances: effect depends on productivity impacts.

### ERER Approach — estimation results and findings
- Panel GMM (restricted models):
  - Terms of trade and relative productivity are main determinants; coefficient magnitudes similar to CGER.
  - Aid inflows explanatory in GMM:
    - Whole sample: a 1 percent increase in aid inflows tends to depreciate the exchange rate by 0.9 percent.
  - African countries: coefficient magnitudes similar to whole and LMIC samples.
  - Africa (non-oil-exporting): terms of trade has smaller impact; relative productivity and aid inflows have larger effects.
- Exchange rate assessment: percent deviation of observed REER from estimated equilibrium REER.

### ERER Approach — robustness checks
- Four-year averages: sign, magnitude, and t-statistics similar to annual-data estimates for whole and LMIC.
- Controls for armed conflict and oil production: no explanatory power for REER in this approach.
- Outlier exclusion and GDP growth dummies: coefficients not driven by outliers; growth dummies lack explanatory power.

### External Sustainability Approach — methodology and findings
- Objective: compute REER adjustment required to close gap between projected CAB (no exchange rate change) and CAB norm implied by stabilizing normative NFA position.
- Norm NFA position: calibrated to most recent net international investment position observation (2008 value from IMF Balance of Payments database).
  - Exception: Botswana NFA position calculated consistent with medium-term fiscal sustainability for an exhaustible-resource exporter.
- Norm CAB that stabilizes calibrated NFA computed; gap = norm CAB − underlying CAB (underlying from 2014 WEO projection).
- REER change computed using same elasticities as macroeconomic balance approach:
  - Import elasticity = 0.92.
  - Export elasticity = -0.71.
- Country-level NFA/GDP, Nominal Growth, NORM, Underlying, GAP reported in Table 7 (tabulated in source).

### Purchasing Power Parity (PPP) Approach — methodology and findings
- Assumption: nominal exchange rates related to national price levels: E_ij = C * (P_i / P_j).
- Log form implies real exchange rate rer_it ≈ constant c in long run; equilibrium REER approximated by estimated constant and country fixed effects.
- Estimation: pooled GMM with fixed effects on annual data (1990–2008).
- Summary model fit (Table 8):
  - Whole sample: observations = 4710; adjusted R Squared = 0.26; Std Error of Regression = 0.43.
  - LMIC: observations = 2674; adjusted R Squared = 0.25; Std Error = 0.26.
  - Africa: observations = 959; adjusted R Squared = 0.28; Std Error = 0.29.
  - Africa (Non-Oil Exporting): observations = 795; adjusted R Squared = 0.27; Std Error = 0.27.
- Exchange rate assessment: percent deviation of underlying REER from PPP-based equilibrium.

### Potential for bias and limitations
- Equilibrium REERs are econometric estimates of long-run relationships and subject to econometric biases.
- All four methodologies implicitly assume macroeconomic fundamentals are sustainable.
- Import and export elasticities are not country-specific; calibrated to Isard and Faruqee (1998); mismatch with true country-specific elasticities could over- or under-magnify REER adjustment estimates.
- Under- or overvaluation does not automatically imply exchange rate adjustment is the appropriate policy response; structural or macroeconomic policies may be preferable.

### Conclusion — overall findings
- Four methodologies applied: macroeconomic balance, equilibrium real exchange rate, external sustainability, and purchasing power parity.
- Sub-Saharan African economies exhibit dynamics different from advanced economies and other LMICs.
- Notable sub-Saharan-specific quantitative findings:
  - Relative income: 1 percent → 0.07 percent CAB improvement in sub-Saharan sample.
  - Fiscal balance: 1 percent improvement → 1 percent CAB improvement in sub-Saharan sample.
  - Excluding oil exporters: a 1 percent decline in oil trade balance → 1.1 percent reduction in CAB.
  - Aid inflows (whole sample): 1 percent aid inflow → 0.9 percent REER depreciation.

### Appendix I. Unit Root Test Results — key statistics and settings
- Test settings:
  - Sample: 1973 2008.
  - Exogenous variables: Individual effects.
  - Automatic selection of lags based on AIC: 0 to 4.
  - Newey-West bandwidth selection using Bartlett kernel.
- Selected panel unit root test results (series, primary statistics, Prob., cross-sections, Obs):
  - Real Exchange Rate (Log REER): Levin, Lin & Chu t* = -10.8863; Prob. = 0.0000; Cross-sections = 178; Obs = 4328.
  - Current Account Balance (CAB-to-GDP): Levin, Lin & Chu t* = -9.59881; Prob. = 0.0000; Cross-sections = 176; Obs = 5777.
  - Relative Income per Capita: Levin, Lin & Chu t* = -5.46507; Prob. = 0.0000; Cross-sections = 174; Obs = 5478.
  - Relative Fiscal Balance: Levin, Lin & Chu t* = -9.38103; Prob. = 0.0000; Cross-sections = 150; Obs = 2821.
  - Relative Population Growth: Levin, Lin & Chu t* = -29.0869; Prob. = 0.0000; Cross-sections = 174; Obs = 5378.
  - Relative Economic Growth: Levin, Lin & Chu t* = -1.09253; Prob. = 0.1373; Cross-sections = 165; Obs = 3649.
  - Initial Net Foreign Assets (NFA/GDP): Levin, Lin & Chu t* = -37.7314; Prob. = 0.0000; Cross-sections = 53; Obs = 852.
  - Terms of Trade (Log): Levin, Lin & Chu t* = -3.29297; Prob. = 0.0005; Cross-sections = 167; Obs = 5638.
  - Oil Trade Balance (Trade Balance on Oil to GDP): Levin, Lin & Chu t* = -6.57864; Prob. = 0.0000; Cross-sections = 168; Obs = 5477.
  - Relative Dependency Ratio: Levin, Lin & Chu t* = -9.99986; Prob. = 0.0000; Cross-sections = 181; Obs = 5458.
  - Aid (Aid to GDP): Levin, Lin & Chu t* = -76.1424; Prob. = 0.0000; Cross-sections = 150; Obs = 4479.
  - Remittances (Remittances to GDP): Levin, Lin & Chu t* = -6.64636; Prob. = 0.0000; Cross-sections = 102; Obs = 2275.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10162.pdf*

### 1. Summary Statistics Across Geographic and Economic Regions, 1973–2008 .......................6

### _wp10162 - 1. Summary Statistics Across Geographic and Economic Regions, 1973–2008 .......................6

### Introduction and purpose
- Assessments of exchange rate levels are central to IMF surveillance.
- This paper applies four methodologies to evaluate exchange rate levels in sub-Saharan African countries relative to fundamentals:
  - Macroeconomic balance approach (gap between current account balance and its norm; valuation determined by gap magnitude and current account elasticity to the real exchange rate).
  - Equilibrium real exchange rate approach (equilibrium REER from fundamentals; valuation as percentage deviation of observed REER from equilibrium).
  - External sustainability approach (norm current account that would stabilize net foreign assets; valuation via gap and elasticity as in macroeconomic balance approach).
  - Purchasing power parity approach (equilibrium REER from the law of one price; valuation by gap between equilibrium and observed REER).

- Methodological differences relative to prior studies:
  - Dataset covers all 182 countries the WEO reported on (including sub-Saharan Africa); CGER covered 54 economies with only South Africa from sub-Saharan Africa.
  - Estimation period extends to 2008 in this chapter title context; elsewhere the dataset is described as drawn from annual data from 1973 through 2014.
  - Econometric technique used: pooled generalized method of moments (following Vitek (2009)), versus pooled and fixed effects panel estimation in CGER.
  - Use of annual data rather than CGER’s four-year averages; additional variables added include aid and remittances.

### Dataset, sources, and data adjustments
- Primary data sources:
  - WEO (IMF, 2009a) for macroeconomic variables.
  - World Bank World Development Indicators for demographics, aid, and remittances.
  - IMF Information Notice System for effective exchange rate and trade weight data.
  - IMF Balance of Payments database for net foreign asset data.
  - Uppsala Conflict Data Program (2009) for armed conflict data.

- Dataset coverage and sample:
  - Dataset drawn from annual data for 182 economies from 1973 through 2014.
  - The chapter title references 1973–2008.

- Data exclusions and adjustments (treated as data errors and excluded from estimation sample):
  - Negative values for nominal GDP, GDP at constant prices, government consumption, exports, imports, population, employment, exchange rate, and terms of trade.
  - Absolute values greater than 100 percent for dependency ratio, population growth, fiscal balance, government spending, current account balance, trade balance, and oil trade balance as a percent of GDP.
  - Trade weight data replaced by country-reported data whenever there is a large discrepancy.

### Subsamples and econometric treatment
- Subsamples analyzed:
  - Whole sample (all available information).
  - Group of low and middle income countries (LMIC).
  - Group of sub-Saharan economies.
  - Subset of sub-Saharan economies excluding oil-exporting countries.

- Rationale:
  - Certain economic conditions are unique to sub-Saharan and low-income countries; slope coefficients differ for sub-Saharan Africa relative to advanced economies and LMIC, implying different impacts of fundamentals in equilibrium relationships (example: fiscal accounts have about a one-to-one impact on external balance in sub-Saharan Africa, but a much smaller impact in other LMIC).

- Econometric approach:
  - Pooled generalized method of moments methodology (following Vitek (2009)), differing from CGER’s pooled and fixed effects panel estimation.
  - Use of annual data due to shorter time series availability for many non-CGER countries; aid and remittances included as additional variables due to their importance in sub-Saharan Africa.

### Key comparative findings (summary statistics and observations)
- Macroeconomic balances:
  - Fiscal balances, government debt, external current account, and net foreign asset (NFA) holdings of African countries are in general worse than those of LMIC; both African and LMIC groups are worse than advanced economies.

- Income and external assistance:
  - African economies are poorer than LMIC and rely more on foreign aid.
  - Advanced economies are significantly richer than African and LMIC groups.
  - The mean for real GDP per capita in both the African and LMIC groups in the 2000s are lower than the mean income of advanced economies in the 1970s–80s.

*Source: _wp10162 - 1. Summary Statistics Across Geographic and Economic Regions, 1973–2008 .......................6*

### 3. Variation across time and country for the advanced economies is much smaller than

### _wp10162 - 3. Variation across time and country for the advanced economies is much smaller than

### Macroeconomic Balance Approach — methodology
- Purpose: measure exchange rate under- or overvaluation by computing adjustment needed for the real exchange rate to close the gap between the projected medium-term current account balance at the prevailing REER and the current account norm consistent with sustainable medium-term macroeconomic fundamentals.
- Estimation equation (panel, 1973–2008):
  - CAB_it = α + X_it β + Z_it δ + ε_it
  - CAB_it: current account balance as a share of nominal GDP (country i, time t).
  - X: K macroeconomic fundamentals: relative old age dependency, relative population growth, relative income, relative income growth, relative fiscal balance, oil trade balance, initial NFA, aid inflows, remittances.
  - Z: control variables: armed conflict dummy; change (log) in oil production.
- Relative variables constructed as deviations from trade-weighted averages of trading partners using trade weights from the IMF Information Notice System database (trade weights for 1973–1989, 1990–1995, 1996–2008 spliced).
- Estimation method: panel generalized method of moments (GMM), White standard errors and covariance matrix; samples: whole sample, LMIC, sub-Saharan Africa, sub-Saharan Africa excluding oil exporters. LMIC and sub-Saharan estimations start from 1990.

### Macroeconomic Balance Approach — key estimation results and findings
- Panel unit root tests (Appendix): none of the variables have a unit root that cannot be rejected by a majority of the test results.
- Whole sample and LMIC estimates broadly similar to CGER (Lee et al., 2008) except for population growth and income growth:
  - Population growth: insignificant in whole and LMIC samples.
  - Relative income growth: significant and larger in whole and LMIC samples than in CGER estimates.
- Sub-Saharan Africa specific findings:
  - Demographics lack explanatory power for sub-Saharan Africa.
  - Relative income: a 1 percent increase in relative income improves the current account balance by 0.07 percent in the sub-Saharan Africa sample (versus ≤ 0.02 percent in other samples).
  - Fiscal balance: a 1 percent fiscal-gap strengthening improves the current account balance by 1 percent in sub-Saharan Africa (versus 0.3 percent or less in other samples).
  - Aid and remittances: improve the current account balance in sub-Saharan Africa but are statistically insignificant in other economies.
  - Change in oil production control: significant and large in magnitude in the African sample; insignificant in other samples.
  - Excluding oil exporters from sub-Saharan Africa increases the impact of oil trade balance on the current account: a 1 percent decline in the oil trade balance reduces the current account balance by 1.1 percent.
  - Fiscal dominance in oil-importing African countries: a 1 percent decline in fiscal savings reduces external balance by more than 1 percent.
- Current account norm and underlying balance:
  - Norms calculated using restricted-model coefficients; medium-term fundamentals taken from the October 2009 WEO database.
  - Underlying balance used: 2014 current account projection from October 2009 WEO (constant real exchange rate path, economy reaches internal equilibrium—zero output gap). Focus on 2014 as the year when external balance should be in equilibrium.
- Elasticities used to translate CAB gaps into REER adjustments:
  - Import elasticity IM_RER_ε = 0.92.
  - Export elasticity X_RER_ε = -0.71.
  - CAB_RER_ε computed as CAB_RER_ε = 1 / (1 - X_RER_ε - IM_RER_ε) (formula shown in paper).
  - Degree of REER change ΔRER (%) = (U_CAB - N_CAB) / CAB_RER_ε (U_CAB = underlying CAB; N_CAB = norm CAB).

### Macroeconomic Balance Approach — robustness checks
- Use of annual data versus nonoverlapping four-year averages:
  - Panel GMM on four-year averages yields sign, magnitude, and t-statistics quite similar to annual-data estimates for whole and LMIC samples; panel GMM could not be applied to sub-Saharan Africa sample due to data limitations.
- Outlier exclusion:
  - Re-estimated excluding observations six standard deviations away from the mean; coefficient estimates and significance levels are not driven by outliers.
- Control for excessive GDP growth:
  - Included 0-1 dummy for two or more consecutive periods of real GDP growth higher than 10 and 15 percent; these dummies do not have explanatory power.

---

### Equilibrium Real Exchange Rate (ERER) Approach — methodology
- Purpose: measure percent deviation of REER from equilibrium estimated from medium-term macroeconomic fundamentals.
- Estimation equation (panel):
  - ln(RER_it) = α + X_it β + ε_it
  - X: terms of trade, relative productivity (GDP PPP per unit of labor), relative government consumption-to-GDP, NFA, aid inflows, remittance inflows.
- Theoretical expectations:
  - Terms of trade ↑ → REER appreciates.
  - Relative productivity ↑ → REER appreciates.
  - Relative government consumption ↑ (nontradables intensive) → REER appreciates.
  - NFA-to-GDP ↑ → REER appreciates (creditor countries).
  - Aid/remittances: impact depends on productivity effects; productivity-enhancing aid/remittances can lead to REER depreciation.

### ERER Approach — estimation results and findings
- Panel GMM results (restricted models) indicate:
  - Terms of trade and relative productivity are the main determinants of equilibrium REER; coefficient magnitudes similar to CGER.
  - Aid inflows have explanatory power in GMM estimates:
    - For the whole sample: a 1 percent increase in aid inflows tends to depreciate the exchange rate by 0.9 percent (reflecting possible productivity-enhancing effect in the nontradable sector).
  - African countries: coefficient magnitudes similar to whole and LMIC samples.
  - Non-oil-exporting African countries: terms of trade has smaller impact; relative productivity and aid inflows have larger effects on equilibrium REER.
- Exchange rate under-/overvaluation measured as percent deviation of observed REER from estimated equilibrium REER.

### ERER Approach — robustness checks
- Four-year averaged data: sign, magnitude, and t-statistics similar to annual-data estimates for whole and LMIC samples.
- Controls for armed conflict and oil production: these controls do not have explanatory power in determining REER in this approach.
- Outlier exclusion and GDP growth dummies: coefficient estimates not driven by outliers; dummies for exceptional growth do not have explanatory power.

---

### External Sustainability Approach — methodology and findings
- Purpose: measure REER adjustment required to close gap between projected current account (no change in exchange rate path) and current account norm implied by a stabilizing normative NFA position.
- Norm NFA position defined by: NFA_t = (1 + g)^(n) * (CAB_t + g) ??? (equation (6) shown in text; norm NFA position can be calibrated or estimated).
- In this paper: norm NFA position calibrated to most recent net international investment position observation (2008 value from IMF Balance of Payments database). Exception: Botswana NFA position calculated consistent with medium-term fiscal sustainability for an exhaustible-resource exporter (Deléchat and Gaertner, 2008).
- Norm CAB that stabilizes calibrated NFA computed; gap = norm CAB − underlying CAB (underlying = 2014 projection from October 2009 WEO).
- REER change required to close gap computed using same elasticities as macroeconomic balance approach:
  - Import elasticity = 0.92; export elasticity = -0.71.
- Table 7 provides country-level NFA/GDP, Nominal Growth, NORM, Underlying, GAP for sub-Saharan African countries (values tabulated in source).

---

### Purchasing Power Parity (PPP) Approach — methodology and findings
- Assumption: nominal exchange rates related to national price levels: E_ij = C * (P_i / P_j).
- Log form implies real exchange rate rer_it ≈ constant c in long run; equilibrium REER approximated by estimated constant and country fixed effects.
- Estimation: pooled GMM with fixed effects on annual data (1990–2008).
- Table 8 summary results:
  - Constant estimates and fixed effects used to compute equilibrium REER for each sub-Saharan African country.
  - Number of observations and model fit: whole sample observations = 4710; adjusted R Squared = 0.26; Std Error of Regression = 0.43. LMIC: observations = 2674; adjusted R Squared = 0.25; Std Error = 0.26. Africa: observations = 959; adjusted R Squared = 0.28; Std Error = 0.29. Africa (Non-Oil Exporting): observations = 795; adjusted R Squared = 0.27; Std Error = 0.27.
- Exchange rate assessment: percent deviation of underlying REER from PPP-based equilibrium.

---

### Potential for Bias and limitations
- Equilibrium REER based on econometric estimates of long-run relationships; results subject to econometric biases and should be treated with caution.
- All four methodologies implicitly assume macroeconomic fundamentals are sustainable; e.g., macroeconomic balance equilibrium CAB may not be sustainable if fiscal balance is not sustainable.
- Import and export elasticities are not country-specific; elasticities calibrated to Isard and Faruqee (1998). If calibrated elasticities differ from true country-specific elasticities, REER adjustment estimates may be over- or under-magnified.
- Exchange rate under- or overvaluation does not automatically imply a required exchange rate adjustment; underlying structural or macroeconomic challenges may be better addressed via non-exchange-rate policies.

### Conclusion — summary of overall findings
- Four methodologies applied: macroeconomic balance, equilibrium real exchange rate, external sustainability, and purchasing power parity.
- Across methodologies and samples, sub-Saharan African economies exhibit different dynamics than advanced economies and other LMICs.
- Notable sub-Saharan Africa-specific results:
  - Relative income and fiscal balance have stronger impacts on CAB than in other samples (relative income: 1 percent → 0.07 percent CAB improvement; fiscal balance: 1 percent → 1 percent CAB improvement).
  - Aid and remittances matter more for CAB in sub-Saharan Africa than elsewhere.
  - Oil trade balance and changes in oil production are especially important in African samples; excluding oil exporters magnifies oil trade balance effects.
  - Aid inflows can be associated with REER depreciation (example: whole sample finding of 1 percent aid inflow → 0.9 percent REER depreciation), consistent with productivity effects concentrated in nontradable sector.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10162.pdf*

### Appendix I. Unit Root Test Results

### Appendix I. Unit Root Test Results

### Summary of test settings (applies to all tables)
- Sample: 1973 2008
- Exogenous variables: Individual effects
- User specified maximum lags
- Automatic selection of lags based on AIC: 0 to 4
- Newey-West bandwidth selection using Bartlett kernel

### Table 9 — Panel Unit Root Test Result for Real Exchange Rate (Series: Logarithm of REER)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -10.8863; Prob. = 0.0000; Cross-sections = 178; Obs = 4328
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -9.55476; Prob. = 0.0000; Cross-sections = 178; Obs = 4328
  - ADF - Fisher Chi-square: Statistic = 693.021; Prob. = 0.0000; Cross-sections = 178; Obs = 4328
  - PP - Fisher Chi-square: Statistic = 561.375; Prob. = 0.0000; Cross-sections = 178; Obs = 4532

### Table 10 — Panel Unit Root Test Results for Current Account Balance (Series: CAB-to-GDP)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -9.59881; Prob. = 0.0000; Cross-sections = 176; Obs = 5777
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -12.8458; Prob. = 0.0000; Cross-sections = 176; Obs = 5777
  - ADF - Fisher Chi-square: Statistic = 845.572; Prob. = 0.0000; Cross-sections = 176; Obs = 5777
  - PP - Fisher Chi-square: Statistic = 867.291; Prob. = 0.0000; Cross-sections = 176; Obs = 5949

### Table 11 — Panel Unit Root Test Result for Relative Income per Capita (with respect to weighted average of trading partners)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -5.46507; Prob. = 0.0000; Cross-sections = 174; Obs = 5478
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = 0.82176; Prob. = 0.7944; Cross-sections = 174; Obs = 5478
  - ADF - Fisher Chi-square: Statistic = 401.867; Prob. = 0.0244; Cross-sections = 174; Obs = 5478
  - PP - Fisher Chi-square: Statistic = 388.555; Prob. = 0.0660; Cross-sections = 174; Obs = 5662

### Table 12 — Panel Unit Root Test Results for Relative Fiscal Balance (Series: Relative Fiscal Balance to GDP with respect to weighted average of trading partners)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -9.38103; Prob. = 0.0000; Cross-sections = 150; Obs = 2821
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -10.8302; Prob. = 0.0000; Cross-sections = 150; Obs = 2821
  - ADF - Fisher Chi-square: Statistic = 681.891; Prob. = 0.0000; Cross-sections = 150; Obs = 2821
  - PP - Fisher Chi-square: Statistic = 694.753; Prob. = 0.0000; Cross-sections = 150; Obs = 3007

### Table 13 — Panel Unit Root Test Result for Relative Population Growth (with respect to weighted average of trading partners)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -29.0869; Prob. = 0.0000; Cross-sections = 174; Obs = 5378
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -35.0818; Prob. = 0.0000; Cross-sections = 174; Obs = 5378
  - ADF - Fisher Chi-square: Statistic = 1928.58; Prob. = 0.0000; Cross-sections = 174; Obs = 5378
  - PP - Fisher Chi-square: Statistic = 2320.50; Prob. = 0.0000; Cross-sections = 174; Obs = 5537

### Table 14 — Panel Unit Root Test Result for Relative Economic Growth (Series: Relative PPP per Capita Growth with respect to weighted average of trading partners)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -1.09253; Prob. = 0.1373; Cross-sections = 165; Obs = 3649
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -7.62501; Prob. = 0.0000; Cross-sections = 165; Obs = 3649
  - ADF - Fisher Chi-square: Statistic = 603.240; Prob. = 0.0000; Cross-sections = 165; Obs = 3649
  - PP - Fisher Chi-square: Statistic = 642.903; Prob. = 0.0000; Cross-sections = 165; Obs = 3839

### Table 15 — Panel Unit Root Test Result for Initial Net Foreign Assets (Series: Net Foreign Assets to GDP)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -37.7314; Prob. = 0.0000; Cross-sections = 53; Obs = 852
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -8.29799; Prob. = 0.0000; Cross-sections = 53; Obs = 852
  - ADF - Fisher Chi-square: Statistic = 146.426; Prob. = 0.0057; Cross-sections = 53; Obs = 852
  - PP - Fisher Chi-square: Statistic = 93.2637; Prob. = 0.8068; Cross-sections = 53; Obs = 943

### Table 16 — Panel Unit Root Test Result for Terms of Trade (Series: Logarithm of Terms of Trade)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -3.29297; Prob. = 0.0005; Cross-sections = 167; Obs = 5638
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -5.29839; Prob. = 0.0000; Cross-sections = 167; Obs = 5638
  - ADF - Fisher Chi-square: Statistic = 538.842; Prob. = 0.0000; Cross-sections = 167; Obs = 5638
  - PP - Fisher Chi-square: Statistic = 623.420; Prob. = 0.0000; Cross-sections = 167; Obs = 5776

### Table 17 — Panel Unit Root Test Result for Oil Trade Balance (Series: Trade Balance on Oil to GDP)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -6.57864; Prob. = 0.0000; Cross-sections = 168; Obs = 5477
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -4.10258; Prob. = 0.0000; Cross-sections = 168; Obs = 5477
  - ADF - Fisher Chi-square: Statistic = 494.272; Prob. = 0.0000; Cross-sections = 168; Obs = 5477
  - PP - Fisher Chi-square: Statistic = 518.009; Prob. = 0.0000; Cross-sections = 168; Obs = 5608

### Table 18 — Panel Unit Root Test Result for Relative Dependency Ratio (Series: Relative Old Age Dependency with respect to weighted average of trading partners)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -9.99986; Prob. = 0.0000; Cross-sections = 181; Obs = 5458
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -2.04896; Prob. = 0.0202; Cross-sections = 181; Obs = 5458
  - ADF - Fisher Chi-square: Statistic = 500.833; Prob. = 0.0000; Cross-sections = 181; Obs = 5458
  - PP - Fisher Chi-square: Statistic = 145.120; Prob. = 1.0000; Cross-sections = 181; Obs = 5865

### Table 19 — Panel Unit Root Test Result for Aid (Series: Aid to GDP)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -76.1424; Prob. = 0.0000; Cross-sections = 150; Obs = 4479
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = -20.5430; Prob. = 0.0000; Cross-sections = 150; Obs = 4479
  - ADF - Fisher Chi-square: Statistic = 746.075; Prob. = 0.0000; Cross-sections = 150; Obs = 4479
  - PP - Fisher Chi-square: Statistic = 828.990; Prob. = 0.0000; Cross-sections = 150; Obs = 4626

### Table 20 — Panel Unit Root Test Result for Remittance (Series: Remittances to GDP)
- Null: Unit root (assumes common unit root process)
  - Levin, Lin & Chu t*: Statistic = -6.64636; Prob. = 0.0000; Cross-sections = 102; Obs = 2275
- Null: Unit root (assumes individual unit root process)
  - Im, Pesaran and Shin W-stat: Statistic = 0.28604; Prob. = 0.6126; Cross-sections = 102; Obs = 2275
  - ADF - Fisher Chi-square: Statistic = 308.606; Prob. = 0.0000; Cross-sections = 102; Obs = 2275
  - PP - Fisher Chi-square: Statistic = 286.332; Prob. = 0.0001; Cross-sections = 102; Obs = 2420

*Appendix I. Unit Root Test Results — _wp10162 - Appendix I. Unit Root Test Results*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10162.pdf_