## 1. Results of Cointegration Estimation

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---

### Introduction and research scope
- Focus: valuation of the real effective exchange rate (REER) and equilibrium REER (EREER) for WAEMU member countries after the 1994 CFA devaluation and the post-2002 nominal appreciation of the CFA franc (over 30 percent in nominal terms against the U.S. dollar).
- Objectives:
  - Analyze sensitivity of EREER estimates to the estimation method.
  - Estimate REER/EREER for each individual WAEMU country using single-country and panel-data econometric techniques.
- Countries in sample: Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau (listed in background), Mali, Niger, Senegal, and Togo.
- Data span: annual observations for 1970 through 2005.

### Theoretical framework and chosen fundamentals (FEER approach)
- Chosen approach: fundamentals equilibrium exchange rate (FEER) following Edwards (1989) and related FEER literature; motivated by:
  - Rejection of PPP (REER series contain a unit root).
  - Implausibility of UIP in WAEMU context.
  - FEER relevance for fixed exchange rate regimes and medium- to long-run analysis.
- FEER fundamentals used and expected signs:
  - Terms of trade (expected sign: positive)
  - Government consumption as share of GDP (expected sign: ambiguous)
  - Technological progress / relative real GDP per capita (LPROD; Balassa-Samuelson; expected sign: positive)
  - Investment to GDP (LNIR; expected sign: ambiguous a priori)
  - Openness (LOPEN; sum of exports and imports to GDP proxy; expected sign: ambiguous)
- Excluded variable: capital controls/capital inflows (long-run effect ambiguous, small in WAEMU).

### Econometric strategy and data treatment
- Single-country methods:
  - Johansen maximum likelihood VAR/VECM cointegration (multivariate).
  - ARDL/Bounds testing and single-equation ECM (Pesaran, Shin, Smith).
- Panel methods:
  - Group-mean fully modified OLS (GM-FMOLS / Pedroni).
  - Pooled mean group (PMG / Pesaran, Shin, Smith) with possibility of impulse dummy for 1994.
- Treatment of fundamentals for EREER construction:
  - Extraction of permanent components using Hodrick-Prescott (HP) filter for each fundamental.
- Unit-root testing results:
  - Country-by-country ADF tests: variables are I(1) in levels and I(0) in first differences.
  - Structural-break aware tests (Zivot-Andrews; Clemente-Montanes-Reyes): confirm nonstationarity of LREER.
  - Panel tests (Levin, Lin & Chu; Im, Pesaran & Shin): majority nonstationary in levels and stationary in first differences; exceptions LNIR and LOPEN appear stationary in levels in some panel tests.
- Cointegration testing:
  - Johansen tests: reject null of zero cointegrating vectors for all countries; typically support one cointegrating vector.
  - ARDL bounds test: WAEMU and four of seven countries confirm cointegration at the 5 percent significance level; three countries ambiguous at 5 percent but suggest cointegration at 10 percent.
  - Pedroni panel tests: null of no cointegration rejected in 3/7 tests (raw data) and 4/7 tests (time-demeaned); group tests indicate cointegration in some statistics.

### Key empirical findings — long-run relationships
- Fundamentals explain most long-run REER fluctuations: terms of trade, government consumption, productivity (LPROD), investment, openness.
- Single-country elasticities (summary):
  - Terms of trade: generally positive and significant (exceptions exist, e.g., Togo no significant effect).
  - Government consumption: often positive (appreciating) indicating spending toward nontradables in many countries; Togo exhibited depreciation effect.
  - Technological progress (LPROD): positive and significant across countries and in panel estimates (Balassa-Samuelson effect).
  - Investment (LNIR): mixed — positive in Benin; negative in Burkina Faso, Mali, Niger; GM-FMOLS shows investment negative on average.
  - Openness (LOPEN): ambiguous across estimators.
- Error-correction dynamics:
  - Error-correction coefficients negative and statistically significant in most country models, indicating stability.
  - Implied half-lives of deviations vary by country and method, e.g.:
    - Benin: half-life 7.4 (Johansen) and 3.1 (ARDL)
    - WAEMU aggregate: half-life between six months and five years depending on methodology
    - Country-specific half-lives reported range from 0.7 to 10.6 years across countries/methods.

### Panel estimation contrasts and heterogeneity
- GM-FMOLS results:
  - LPROD positive and significant in both uncorrected and time-demeaned versions.
  - LNIR negative and significant in both versions (on average).
  - Government consumption and openness significant in uncorrected data but lose significance with time-demeaned data.
- PMG results (with and without 1994 dummy):
  - Terms of trade and LPROD positive and significant with and without 1994 dummy.
  - Inclusion of 1994 impulse dummy changes long-run parameters for several variables (e.g., government spending).
  - Hausman tests: mixed evidence on long-run homogeneity — some fundamentals (productivity, openness) appear homogeneous, others (terms of trade) do not.
- Implication: PMG’s long-run homogeneity assumption may misrepresent country-specific relationships when heterogeneity is present; GM-FMOLS averages heterogeneous long-run vectors and may not represent any particular country’s EREER precisely.

### Real misalignments in 2006 — ranges and uncertainty
- General conclusion: significant uncertainty across estimators; no country has unanimous evidence across all estimators for over- or undervaluation in 2006.
- Selected 2006 estimated misalignment ranges across estimators:
  - Benin:
    - Single-country implied undervaluation about 3 to 17 percent (2006).
    - Panel estimators range about 0 to 12 percent undervaluation depending on model variant.
  - Burkina Faso:
    - Single-country overvaluation prior to 1994 (6 to 15 percent).
    - 2006 single-country suggests REER may be overvalued by about 9 percent.
    - Panel estimators suggest undervaluation ranging from about 1 to 24 percent.
  - Côte d’Ivoire:
    - 2006 single-country: Johansen ~3 percent overvaluation; ARDL ~6 percent undervaluation.
    - Panel range from 14 percent undervaluation to 53 percent overvaluation depending on estimator.
  - Mali:
    - 2006 single-country range from 6 percent undervaluation to 16 percent overvaluation.
    - Panel estimates range from 24 percent undervaluation to 6 percent overvaluation.
  - Niger:
    - 2006 single-country suggests overvaluation from 4 to 10 percent.
    - PMG with 1994 dummy yields 11 percent overvaluation.
    - FMOLS panel estimators range from 22 percent undervaluation to 1 percent overvaluation.
  - Senegal:
    - 2006 single-country estimates range from 4 percent undervaluation to 9 percent overvaluation.
    - Panel estimates range from 6 percent overvaluation to 23 percent undervaluation.
  - Togo:
    - 2006 single-country: Johansen aligned, ARDL 6 percent overvaluation.
    - Panel models mostly indicate overvaluation except FMOLS demeaned; pre-1994 overvaluation across estimators.
  - WAEMU aggregate:
    - Single-country estimators suggest some overvaluation.
    - PMG estimators suggest a 15 to 26 percent overvaluation in 2006.
    - FMOLS panel models range from 15 percent undervaluation to 21 percent overvaluation.
- Table 3 summary for 2006 (All Estimators column — percentage of estimators indicating Over Valuation / Under Valuation / Aligned (|misalignment| < 5 percent)):
  - Benin: Over Valuation 17% / Under Valuation 50% / Aligned 33%
  - Burkina Faso: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Côte d’Ivoire: Over Valuation 33% / Under Valuation 33% / Aligned 33%
  - Mali: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Niger: Over Valuation 67% / Under Valuation 17% / Aligned 17%
  - Senegal: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Togo: Over Valuation 67% / Under Valuation 17% / Aligned 17%
  - WAEMU: Over Valuation 83% / Under Valuation 17% / Aligned 0%

### Robustness, sensitivity diagnostics and data limitations
- Method-sensitivity:
  - Johansen vs ARDL often produce different half-lives; Johansen half-lives typically longer than ARDL for the same country.
  - Panel techniques sensitive to treatment of common time effects: demeaning (GM-FMOLS) or including a 1994 impulse dummy (PMG) can dramatically change estimated EREERs.
  - PMG long-run homogeneity testable via Hausman; mixed evidence suggests heterogeneity in some fundamentals.
- Data limitations:
  - Pre-1980 series sometimes constructed via extrapolation.
  - CPI-based REER limitations: CPI may reflect import prices/agricultural sector and not whole-economy price developments.
  - REER for some countries exclude important trading partners (e.g., Niger and Benin REERs lack Nigeria).
  - Alternative real exchange rate measures largely unavailable for the sample.
- Model diagnostics (selected examples reported in source):
  - Johansen and ARDL residual diagnostics show mixed results across countries for Vector AR 1-2, Normality, Heteroskedasticity, Serial correlation, and Functional form.
  - Example diagnostic p-values (as presented):
    - Vector AR 1-2 tests: F(72,43) 1.16 [0.30]; F(72,38) 1.65 [0.05]; F(72,49) 0.93 [0.62], etc.
    - Vector Normality: Chi-square(12) 21.22 [0.05]; Chi-square(12) 37.71 [0.00]; Chi-square(12) 10.91 [0.54], etc.
    - Serial correlation: Chi-square(1) 0.35 [0.55]; Chi-square(1) 4.38 [0.04]; Chi-square(1) 5.82 [0.02], etc.
    - Heteroskedasticity: Chi-square(1) 3.77 [0.05]; Chi-square(1) 0.86 [0.35]; Chi-square(1) 0.02 [0.89], etc.
  - Panel unit-root test representative results:
    - Levin & Lin rho (Levels): -0.87 I(1)
    - Im, Pesaran and Shin ADF-t (Levels): -1.22 I(1)
    - Levin & Lin rho (Differences): -24.50 ** I(0)
    - Im, Pesaran and Shin ADF-t (Differences): -13.86 ** I(0)

### Policy implications and conclusions
- Core empirical conclusions:
  - Fundamentals (terms of trade, government consumption, investment, productivity, openness) account for most long-run REER behavior.
  - Significant uncertainty exists about the path of the EREER and the degree of misalignment due to estimator choice and data treatment.
  - For many countries (Côte d’Ivoire, Mali, Senegal, Togo) single-country estimators are inconclusive about current misalignment.
- Policy recommendations and cautions:
  - Perform formal robustness analysis across econometric techniques; do not rely on a single estimator.
  - Compare panel and single-country results: panel estimates useful but should be cross-checked against single-country estimators to assess representativeness.
  - Be cautious with averaged cointegrating vectors: GM-FMOLS averages can mask country-specific responses; PMG’s homogeneity assumption can be invalid for some fundamentals.
  - Monitor deviations: short-term REER deviations revert to equilibrium, but persistent one-sided deviations should prompt evaluation of balance of payments pressures, reserve adequacy, structural competitiveness indicators, and market perceptions.
  - If deviations are sizeable and persistent under a fixed exchange rate regime, consider demand-side management and/or real exchange rate action to restore balance.
- Limitations acknowledged:
  - The analysis does not provide statistical error bands for the EREER series.
  - The study does not explore alternative theoretical models of the EREER beyond the FEER approach; noted as areas for future research.

*Source: _wp07194*

### 1. Results of Cointegration Estimation .................................................................................

### 1. Results of Cointegration Estimation

### Sections
- 1. Results of Cointegration Estimation ....................................................................................21
- 2. Results of Panel Estimations................................................................................................24
- 3. Evidence of Exchange Rate Misalignment in 2006 .............................................................38

### Figures
- 1. Benin: Actual and Equilibrium Exchange Rates, 1970–2006 .............................................28
- 2. Burkina Faso: Actual and Equilibrium Exchange Rates, 1970–2006..................................29
- 3. Côte D’Ivoire: Actual and Equilibrium Exchange rates, 1970–2006 ..................................31
- 4. Mali: Actual and Equilibrium Exchange Rates, 1970–2006 ...............................................32
- 5. Niger: Actual and Equilibrium Exchange Rates, 1970–2006 ..............................................33
- 6. Senegal: Actual and Equilibrium Exchange Rates, 1970–2006 ..........................................34
- 7. Togo: Actual and Equilibrium Exchange Rate, 1970–2006 ................................................36
- 8. WAEMU: Actual and Equilibrium Exchange Rates, 1970–2006 .......................................37

### Appendices
- A. Variable Definitions and Sources .......................................................................................41
- B. Cointegration, Unit Root Tests and Model Diagnostics .....................................................42

*Source: _wp07194 - 1. Results of Cointegration Estimation .................................................................................*

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

### _wp07194 - References..............................................................................................................

### Introduction and research scope
- Focus: valuation of the real effective exchange rate (REER) and equilibrium REER (EREER) for WAEMU member countries after the 1994 CFA devaluation and the post-2002 nominal appreciation of the CFA franc (over 30 percent in nominal terms against the U.S. dollar).
- Objectives:
  - Analyze sensitivity of EREER estimates to the estimation method (not to alternative theoretical models).
  - Estimate REER/EREER for each individual WAEMU country using single-country and panel-data econometric techniques.
- Countries in sample (WAEMU): Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal, and Togo (note: the analysis focuses on individual WAEMU countries; Guinea-Bissau is listed as a WAEMU member in background material).
- Data span: annual observations for 1970 through 2005.

### Theoretical framework and chosen fundamentals (FEER approach)
- Chosen approach: fundamentals equilibrium exchange rate (FEER) based on Edwards (1989) and related FEER literature; motivated by:
  - Rejection of PPP (REER series contain a unit root).
  - Implausibility of UIP in WAEMU context (single commodity exports, capital controls, lack of forward FX markets).
  - FEER relevance for fixed exchange rate regimes and medium- to long-run analysis.
- FEER fundamentals used:
  - Terms of trade (expected sign: positive)
  - Government consumption as share of GDP (expected sign: ambiguous)
  - Technological progress / relative real GDP per capita (Balassa-Samuelson effect; expected sign: positive)
  - Investment to GDP (expected sign: ambiguous a priori)
  - Openness (sum of exports and imports to GDP proxy; expected sign: ambiguous)
- Excluded variable: capital controls/capital inflows (long-run effect ambiguous, small in WAEMU).

### Econometric strategy and data treatment
- Single-country methods:
  - Johansen maximum likelihood VAR/VECM cointegration (multivariate).
  - ARDL/Bounds testing and single-equation ECM (Pesaran, Shin, Smith).
- Panel methods:
  - Group-mean fully modified OLS (GM-FMOLS / Pedroni).
  - Pooled mean group (PMG / Pesaran, Shin, Smith) with possibility of impulse dummy for 1994.
- Treatment of fundamentals for EREER construction:
  - Extraction of permanent components using Hodrick-Prescott (HP) filter for each fundamental (consistent across methods).
- Unit-root testing:
  - Country-by-country: ADF tests indicate variables are I(1) in levels and stationary in first differences.
  - Structural-break aware: Zivot and Andrews (1992) and Clemente, Montanes, and Reyes (1998) confirm nonstationarity of LREER.
  - Panel tests: Levin, Lin and Chu (2002) and Im, Pesaran and Shin (2003) variants—majority of series nonstationary in levels and stationary in first differences; exceptions LNIR and LOPEN appear stationary in levels in some panel tests.
- Cointegration testing:
  - Johansen tests: reject null of zero cointegrating vectors for all countries; typically do not reject at most one cointegrating vector versus more than one (with some exceptions).
  - ARDL bounds test: WAEMU and four of seven countries confirm cointegration at the 5 percent significance level; other three are ambiguous at 5 percent but suggest cointegration at 10 percent.
  - Pedroni panel tests: null of no cointegration rejected in 3/7 tests (raw data) and 4/7 tests (time-demeaned); group tests allowing heterogeneity indicate cointegration in some statistics.

### Key empirical findings (long-run relationships)
- Fundamentals explain most long-run REER fluctuations: terms of trade, government consumption, productivity (LPROD), investment, openness.
- Single-country elasticities (summary):
  - Terms of trade: generally positive and significant (exceptions exist, e.g., Togo no significant effect).
  - Government consumption: often positive (appreciating) indicating spending toward nontradables in many countries—ambiguity where spending composition unknown; Togo exhibited depreciation effect implying spending toward tradables.
  - Technological progress (LPROD): positive and significant (Balassa-Samuelson effect) across countries and in panel estimates.
  - Investment: mixed—positive in Benin (shifts spending to nontradables); negative in Burkina Faso, Mali, Niger (shifts spending to tradables); panel GM-FMOLS shows investment negative on average.
  - Openness: ambiguous; positive in some country estimates and panel PMG (uncorrected), negative in other single-country ARDLs.
- Error-correction dynamics:
  - Error-correction coefficients negative and statistically significant in most country models, indicating stability.
  - Implied half-lives of deviations vary by country and method, e.g.:
    - Benin: half-life 7.4 (Johansen) and 3.1 (ARDL)
    - WAEMU aggregate: half-life between six months and five years depending on methodology
    - Country-specific half-lives reported across Table 1 range from 0.7 to 10.6 years for different countries/methods.

### Panel estimation contrasts and heterogeneity
- GM-FMOLS (group-mean FMOLS) results (uncorrected vs time-demeaned):
  - Productivity positive and significant in both versions.
  - Investment negative and significant in both versions (on average).
  - Government consumption and openness significant in uncorrected data but lose significance with time-demeaned data.
- PMG results (with and without 1994 dummy):
  - Terms of trade and productivity positive and significant with and without 1994 dummy.
  - Inclusion of 1994 impulse dummy changes estimated long-run parameters for several variables (e.g., government spending).
  - PMG allows Hausman tests for long-run homogeneity: mixed evidence—some fundamentals (productivity, openness) appear homogeneous, others (terms of trade) do not.
- Key implication: panel estimators imposing long-run homogeneity (PMG) may misrepresent country-specific relationships when heterogeneity is present; GM-FMOLS averages heterogeneous long-run vectors and may not represent any particular country’s EREER precisely.

### Real misalignments: ranges and uncertainty (selected 2006 assessments)
- General conclusion: significant uncertainty across estimators; no country has unanimous evidence across all estimators for over- or undervaluation in 2006.
- Examples of 2006 estimated misalignments (ranges reported across estimators):
  - Benin: single-country implied undervaluation about 3 to 17 percent (2006); panel estimators range about 0 to 12 percent undervaluation depending on model variant.
  - Burkina Faso: single-country overvaluation prior to 1994 (6 to 15 percent); 2006 single-country suggests REER may be overvalued by about 9 percent; panel estimators suggest undervaluation ranging from about 1 to 24 percent.
  - Côte d’Ivoire: 2006 single-country estimates conflict—Johansen suggests about 3 percent overvaluation; ARDL suggests 6 percent undervaluation; panel range from 14 percent undervaluation to 53 percent overvaluation depending on estimator.
  - Mali: 2006 estimates range from 6 percent undervaluation to 16 percent overvaluation across single-country methods; panel estimates range from 24 percent undervaluation to 6 percent overvaluation.
  - Niger: 2006 single-country suggests overvaluation from 4 to 10 percent; PMG with 1994 dummy yields 11 percent overvaluation; FMOLS panel estimators range from 22 percent undervaluation to 1 percent overvaluation.
  - Senegal: 2006 single-country estimates range from 4 percent undervaluation to 9 percent overvaluation; panel estimates range from 6 percent overvaluation to 23 percent undervaluation.
  - Togo: 2006 single-country: Johansen aligned, ARDL 6 percent overvaluation; panel models mostly indicate overvaluation except FMOLS demeaned; pre-1994 overvaluation across estimators.
  - WAEMU aggregate: single-country estimators suggest some overvaluation; PMG estimators suggest a 15 to 26 percent overvaluation in 2006; FMOLS panel models range from 15 percent undervaluation to 21 percent overvaluation.
- Table 3 (summary for 2006): shows percentage of estimators indicating overvaluation, undervaluation, or aligned (aligned defined as less than 5 percent misaligned). Key entries (All Estimators column):
  - Benin: Over Valuation 17% / Under Valuation 50% / Aligned 33%
  - Burkina Faso: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Côte d’Ivoire: Over Valuation 33% / Under Valuation 33% / Aligned 33%
  - Mali: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Niger: Over Valuation 67% / Under Valuation 17% / Aligned 17%
  - Senegal: Over Valuation 33% / Under Valuation 50% / Aligned 17%
  - Togo: Over Valuation 67% / Under Valuation 17% / Aligned 17%
  - WAEMU: Over Valuation 83% / Under Valuation 17% / Aligned 0%

### Robustness and sensitivity diagnostics
- Method-sensitivity:
  - Single-country (Johansen vs ARDL) often produce different implied half-lives; Johansen half-lives typically longer than ARDL for the same country.
  - Panel techniques sensitive to treatment of common time effects: demeaning (GM-FMOLS) or including a 1994 impulse dummy (PMG) can dramatically change estimated EREERs.
  - PMG imposing long-run homogeneity is testable via Hausman; mixed evidence suggests homogeneity holds for some parameters but not others (e.g., terms of trade heterogeneous).
- Data limitations highlighted:
  - Pre-1980 series sometimes constructed via extrapolation.
  - CPI-based REER limitations: CPI may reflect import prices/agricultural sector and not whole-economy price developments; REER for some countries excludes important trading partners (e.g., Niger and Benin REERs lack Nigeria).
  - Alternative real exchange rate measures largely unavailable for the sample.

### Policy implications and conclusions
- Core findings:
  - Fundamentals (terms of trade, government consumption, investment, productivity, openness) account for most long-run REER behavior.
  - Significant uncertainty exists about the path of the EREER and the degree of misalignment due to estimator choice and data treatment.
  - For many countries (Côte d’Ivoire, Mali, Senegal, Togo) even single-country estimators are inconclusive about current misalignment.
- Policy recommendations and cautions:
  - Robustness: Modeling exchange rate misalignment requires formal robustness analysis across econometric techniques; do not rely on a single estimator.
  - Compare panel and single-country results: Panel estimates can be useful but should be compared with single-country estimators to check representativeness.
  - Be cautious with average cointegrating vectors: GM-FMOLS averages can mask country-specific responses; PMG’s homogeneity assumption can be invalid for some fundamentals.
  - Monitor deviations: Short-term REER deviations revert to equilibrium, but persistent one-sided deviations should prompt close evaluation (balance of payments pressures, reserve adequacy, structural competitiveness indicators, market perceptions).
  - Policy action: If deviations are sizeable and persistent, demand-side management and/or real exchange rate action may be required to restore balance under a fixed exchange rate regime.
- Limitations acknowledged by authors:
  - The analysis does not provide statistical error bands for the EREER series and does not explore alternative theoretical models of the EREER beyond the FEER approach; these are noted as areas for future research.

*Source: _wp07194 - References..............................................................................................................*

### Appendix A

### Appendix A

### Variable definitions and data coverage
- Dataset: annual data series (1970–2006) for Togo, Senegal, Mali, Niger, Burkina Faso, Côte d’Ivoire, and Benin.
- Note: Guinea Bissau was excluded from the sample because it joined WAEMU only in 1997.
- Variables, definitions, and sources:
  - LREER: Natural logarithm of the real effective exchange rate (Index 2000=100). Source: Information Notice System (INS) and IMF staff calculations.
  - LNCGR: Natural logarithm of public consumption expenditure to GDP. Source: IMF, World Economic Outlook (WEO).
  - LTTT: Natural logarithm of terms of trade (Index 2000=100). Source: IMF, World Economic Outlook (WEO).
  - LNIR: Natural logarithm of gross capital formation to GDP. Source: IMF, World Economic Outlook (WEO).
  - LPROD: Natural logarithm of real per capita GDP relative to main trade partners, normalized to 1 in 2000 with weights as discussed above. Source: IMF, World Economic Outlook (WEO).
  - LOPEN: Sum of exports and imports to GDP. Source: IMF, World Economic Outlook (WEO).

### Construction notes and partner weights
- Regional aggregate variables for WAEMU were constructed using member country annual observations and nominal GDP weights.
- Country REERs before 1980 were unavailable in INS and were constructed based on CPI indices from the World Economic Outlook with partner weights renormalized.
- The “foreign” variable (used in calculating the productivity proxy) was calculated as the renormalized weighted average of the five trading partners based on the INS weights for the REER.
- WAEMU partner country weights: France, 0.35; United States, 0.13; Germany, 0.11; China, 0.09; Japan, 0.08; Italy, 0.08.

*Italicized source attribution line provided separately by the pipeline.*

---

### Appendix B

### Unit root tests (series-level: Table B1)
- Notes:
  - "D" denotes the difference operator.
  - The null hypothesis is unit root (or I(1)).
  - Unit root tests are based on the Augmented Dickey-Fuller test, Schartz criterion, maximum lags 9.
- Selected ADF-level and difference test results (examples as presented for countries; each entry shows ADF statistic, p-value, conclusion):
  - Example country block (left column / right column format in source):
    - ln(REER): -2.55 0.30 I(1)  /  -0.74 0.82 I(1)
    - ln(TTT): -2.65 0.26 I(1)  /  -1.77 0.39 I(1)
    - ln(CGR): -2.55 0.31 I(1)  /  -1.20 0.67 I(1)
    - ln(NIR): -2.02 0.28 I(1)  /  -1.69 0.43 I(1)
    - ln(PROD): -2.52 0.32 I(1) /  -2.82 0.20 I(1)
    - ln(OPEN): -2.21 0.21 I(1) /  -2.02 0.28 I(1)
    - Dln(REER): -6.51 0.00 I(0) / -6.92 0.00 I(0)
    - Dln(TTT): -5.20 0.00 I(0) / -7.21 0.00 I(0)
    - Dln(CGR): -3.59 0.00 I(0) / -6.95 0.00 I(0)
    - Dln(NIR): -5.33 0.00 I(0) / -5.83 0.00 I(0)
    - Dln(PROD): -3.73 0.01 I(0) / -6.87 0.00 I(0)
    - Dln(OPEN): -6.31 0.00 I(0) / -5.88 0.00 I(0)
  - Additional country blocks follow the same structure; in levels most ln(...) series are concluded as I(1) and in first differences Dln(...) as I(0) with p-values frequently 0.00.

### Panel unit root tests (Table B2)
- Tests used: Levin & Lin rho, Levin & Lin t-rho, Levin, Lin & Chu ADF, Im, Pesaran and Shin ADF-t.
- Test interpretation notes:
  - Levin and Lin (1992, 1993) and Levin, Lin and Chu (2002) tests are pooled, assume parameter homogeneity.
  - Im, Pesaran and Shin (2003) ADF-t is a group-mean test allowing parameter heterogeneity.
  - One and two asterisks indicate rejection at 10 and 5 percent, or better, respectively.
- Representative results (Levels and Differences; selected statistics shown in source):
  - Example panel entries:
    - Levin & Lin rho (Levels): -0.87 I(1)
    - Im, Pesaran and Shin ADF-t (Levels): -1.22 I(1)
    - Levin & Lin rho (Differences): -24.50 ** I(0)
    - Levin, Lin & Chu ADF (Differences): -10.30 ** I(0)
    - Im, Pesaran and Shin ADF-t (Differences): -13.86 ** I(0)
  - Other country/panel combinations show mixed level stationarity conclusions but consistent difference-level I(0) rejections of the null (stationary in differences).

### Cointegration tests (Table B3 and Table B4)
- Johansen Cointegration Tests and ARDL Cointegration Tests were applied across country series.
- Notes:
  - Small sample cointegration tests also indicate the presence of one cointegrating vector for each estimation.
  - Asymptotic critical value bounds obtained from Pesaran and Pesaran (1997) under the specification of intercept and no trend for k=5, at the 5 % significance level.
- Representative Johansen test trace and maximum-eigen results (examples from source):
  - Togo (example rows):
    - None *115.45 0.00 / 55.54 0.00
    - At most 1 59.91 0.24 / 26.16 0.31
    - At most 2 33.75 0.52 / 19.13 0.40
    - At most 3 14.62 0.80 / 9.86 0.76
    - At most 4 4.75 0.83 / 4.34 0.80
    - At most 5 0.27 0.61 / 0.27 0.61
  - Across countries, the tests suggest presence of cointegration (presence of one cointegrating vector indicated).
- ARDL Bounds test examples (from source, reported with F-statistic and bounds):
  - Example ARDL Bounds test F-statistics:
    - 6.42 with Lower Bound 2.62 and Upper Bound 3.79
    - 17.93 with Lower Bound 2.62 and Upper Bound 3.79
    - 4.41 with Lower Bound 2.62 and Upper Bound 3.79
    - 4.99 with Lower Bound 2.62 and Upper Bound 3.79
    - 3.54 with Lower Bound 2.62 and Upper Bound 3.79
    - 3.45 with Lower Bound 2.62 and Upper Bound 3.79
    - 14.69 with Lower Bound 2.62 and Upper Bound 3.79
    - 3.59 with Lower Bound 2.62 and Upper Bound 3.79

### Panel cointegration tests (Table B4)
- Tests and notable statistics (one- and two-asterisk significance notation retained):
  - Panel v-stat (non-parametric): -0.21
  - Panel rho-stat (non-parametric): 0.47
  - Panel PP-stat (non-parametric): -1.86 **
  - Panel ADF-stat (parametric): -1.01
  - Group rho-stat (non-parametric): 0.77
  - Group PP-stat (non-parametric): -2.39 **
  - Group ADF-stat (parametric): -1.60 *
  - Additional panel block (source):
    - Panel v-stat (non-parametric): 0.72
    - Panel rho-stat (non-parametric): -0.63
    - Panel PP-stat (non-parametric): -3.03 **
    - Panel ADF-stat (parametric): -2.14 **
    - Group rho-stat (non-parametric): 0.38
    - Group PP-stat (non-parametric): -2.87 **
    - Group ADF-stat (parametric): -2.09 **
- Notes:
  - All tests are one sided and statistics are N(0,1) under the null of no cointegration.
  - Panel variance statistic diverges to positive infinity under the alternative; other statistics diverge to negative infinity under the alternative.
  - One and two asterisks indicate rejection at 10 and 5 percent respectively.

### Model diagnostics (Table B5)
- Diagnostics reported for Johansen and ARDL residuals across WAEMU and each country (Benin, Burkina Faso, Côte d'Ivoire, Mali, Niger, Senegal, Togo).
- Selected diagnostic test statistics and p-values (p-values in brackets as presented):
  - Vector AR 1-2 test:
    - F(72,43) 1.16 [0.30]
    - F(72,11) 1.34 [0.31]
    - F(72,43) 1.32 [0.16]
    - F(72,38) 1.65 [0.05]
    - F(72,49) 0.81 [0.79]
    - F(72,38) 1.33 [0.17]
    - F(72,38) 1.59 [0.06]
    - F(72,49) 0.93 [0.62]
  - Vector Normality test:
    - Chi-square(12) 21.22 [0.05]
    - Chi-square(12) 37.71 [0.00]
    - Chi-square(12) 19.48 [0.08]
    - Chi-square(12) 18.45 [0.10]
    - Chi-square(12) 18.48 [0.10]
    - Chi-square(12) 18.66 [0.10]
    - Chi-square(12) 10.91 [0.54]
    - Chi-square(12) 20.14 [0.62]
  - Vector hetero test:
    - Chi-square(252) 236.33 [0.75]
    - Chi-square(252) 494.87 [0.61]
    - Chi-square(252) 265.82 [0.26]
    - Chi-square(252) 240.74 [0.68]
    - Chi-square(252) 248.97 [0.54]
    - Chi-square(252) 269.79 [0.21]
    - Chi-square(252) 255.42 [0.43]
    - Chi-square(252) 257.13 [0.62]
  - Serial correlation:
    - Chi-square(1) 0.35 [0.55]
    - Chi-square(1) 4.38 [0.04]
    - Chi-square(1) 0.01 [0.92]
    - Chi-square(1) 1.47 [0.70]
    - Chi-square(1) 0.07 [0.80]
    - Chi-square(1) 5.82 [0.02]
    - Chi-square(1) 1.99 [0.16]
    - Chi-square(1) 0.08 [0.78]
  - Functional form:
    - Chi-square(1) 0.04 [0.84]
    - Chi-square(1) 7.51 [0.01]
    - Chi-square(1) 0.27 [0.60]
    - Chi-square(1) 3.40 [0.07]
    - Chi-square(1) 0.07 [0.80]
    - Chi-square(1) 1.36 [0.24]
    - Chi-square(1) 1.59 [0.21]
    - Chi-square(1) 5.33 [0.02]
  - Normality:
    - Chi-square(2) 0.29 [0.89]
    - Chi-square(2) 1.68 [0.43]
    - Chi-square(2) 1.07 [0.59]
    - Chi-square(2) 1.69 [0.43]
    - Chi-square(2) 0.39 [0.83]
    - Chi-square(2) 0.11 [0.94]
    - Chi-square(2) 1.34 [0.51]
    - Chi-square(2) 1.53 [0.47]
  - Heteroskedasticity:
    - Chi-square(1) 3.77 [0.05]
    - Chi-square(1) 0.86 [0.35]
    - Chi-square(1) 1.87 [0.17]
    - Chi-square(1) 1.78 [0.18]
    - Chi-square(1) 0.12 [0.73]
    - Chi-square(1) 0.02 [0.89]
    - Chi-square(1) 0.86 [0.35]
    - Chi-square(1) 0.73 [0.39]

- Overall diagnostic interpretation (as presented in the source): p-values are indicated in brackets and results vary across countries; several diagnostics (normality, heteroskedasticity, serial correlation, functional form) show mixed evidence across country models.

*Italicized source attribution line provided separately by the pipeline.*

### References

### _wp07194 - References

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