## _wp08120

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---

### Introduction: context and objectives
- Benin: small, poor West African coastal country located east of Nigeria and west of Togo; population in 2006, 7.5 million, grows nearly 3 percent a year; annual average per capita GDP growth was less than 1 percent a year for 1965–2005.
- Problem statement:
  - Despite peaceful democratization and four peaceful presidential elections since 1991, Benin has not yet attracted significant private investment.
  - Ratio of fixed investment to GDP has been found to have the most explanatory power for growth (Levine and Renelt, 1992).
  - Credibility of fiscal policy management partly explains private uncertainty about investment (Serven, 1998, 1997).
- Paper objective:
  - Investigate the nexus of public and private investment and its impact on growth in Benin.
  - Provide stylized facts and policy lessons to inform academics and policymakers on how public and private investment can impact growth and help reduce poverty in low-income countries.
- Key methodological stance:
  - Employ econometric techniques to investigate short- and long-run behavior of private investment and links to growth.
  - Use a parsimonious structural VECM in the spirit of the general-to-specific approach of Hendry (1995a, 1995b, and 2000).
  - Combine backward-looking analysis with forward-looking VAR outputs (HD, VD, IRF).

### Background and stylized facts (Benin, 1965–2006)
- Growth and investment trends:
  - Between 1965 and 2005, real GDP grew annually by an average of 3.4 percent, but annual per capita GDP increased by only 0.3 percent.
  - After the 1994 CFA franc devaluation, real GDP growth rebounded to a yearly average of 4.4 percent in 1994–2005; annual real per capita GDP increased by 1.7 percent.
  - Since 1994 private investment growth slowed: real private investment growth decelerated from an average of 14 percent a year for 1980–93 to 6.1 percent for 1994–2006.
- Sectoral and FDI observations:
  - Cotton sector: investment has been too low to cover capital depreciation.
  - FDI in the cotton sector declined from US$270 million in 1998 (11 percent of GDP) to US$251 million in 2004 (6 percent) even though total FDI inflows rose from US$33 million in 1998 to US$60 million in 2004.
  - Cotton seed production: average share of nominal GDP about 3 percent on average for 2000-05; approximately 550,000 Benin families run small farms, about 310,000 grow cotton and sell cotton seed; about 14,000 new small farmers (in net terms) enter the sector each year; average family size in rural areas is 10 people; ginning industry capacity is estimated at 600,000 tons.
- Comparative private investment (percent of GDP, 2000–05):
  - WAEMU (PPP weighted) 11.1
  - Benin 12.5
  - Burkina Faso 10.6
  - Côte d'Ivoire 7.7
  - Mali 12.1
  - Niger 5.2
  - Senegal 17.0
  - Togo 16.1
  - CEMAC (PPP weighted) 21.0
  - Cameroon 16.5
  - Central African Rep. 4.5
  - Chad 27.3
  - Congo, Republic of 16.0
  - Equatorial Guinea 41.1
  - Gabon 19.8
  - Memorandum items: WAEMU 3.0 (real GDP growth in percent), CEMAC 5.7 (real GDP growth in percent).
- Business environment constraints (Doing Business 2006):
  - World Bank’s 2006 Doing Business report ranks Benin 137 of 175 countries in ease of doing business.
  - Constraints: cumbersome licensing requirements, difficult labor market conditions, scarcity of credit, high factor costs.
  - Benin moved up only 2 points between 2005 and 2006 on Doing Business indicators; Côte d’Ivoire improved by 15 points.

### Methodology and model specification
- Estimation procedure (five steps):
  - 1. Time series analysis and unit root tests
  - 2. Unrestricted VAR specification analysis, including lag length choice and diagnostics checks for misspecification
  - 3. Cointegration analysis and exogeneity tests
  - 4. Conditional structural VECM, eliminating all insignificant variables using the PcGETS
  - 5. IRF, VD and HD analysis on the basis of step 4
- Endogenous variables (vector): (INST, GDP, PINV, CRED, GINV, TOT)
  - TOT = log of trade volume index
  - GINV = log of public investment
  - CRED = log of credit to the private sector
  - PINV = log of private investment
  - GDP = log of constant GDP at market price
  - INST = institutional strength (POLITYDEMOC = democracy – autocracy + 10, range 0–20)
- Model forms:
  - VAR in levels and VECM (error-correction) representations used.
  - Π = αβ' characterizes cointegration; rank(Π) determines number of cointegrating relations.
- Structural identification:
  - Two cointegration vectors assumed in estimation example (6 endogenous variables → 4 permanent shocks, up to 2 transitory shocks).
  - Minimum of 15 restrictions imposed for meaningful IRFs given model dimensions.

### Data, sample, and diagnostics
- Data and sample:
  - Annual data for 1965–2005 from World Bank Development Indicators 2006 and IMF International Financial Statistics of June 2006.
  - Series (except TOT and INST) at constant prices (2000 = 100).
  - Number of annual observations: 41.
- Unit root and lag choices:
  - Unit root tests indicate most variables are nonstationary (see Appendix Table 1).
  - All six variables entered with 4 lags in equation (1); based on F-statistics a 1-lag VAR seems appropriate; model generalized to 2 lags.
- VAR(2) diagnostics:
  - Tests confirm absence of serial autocorrelation and heteroscedasticity.
  - Residuals normally distributed without an ARCH effect.
  - System stable at lag 2, passing 1-up and N-down Chow tests.
- Cointegration and exogeneity:
  - Johansen LR trace test indicates 2 cointegrating equations at 5 percent significance.
  - Exogeneity test statistics:
    - TOT, CRED, and INST are only weakly exogenous.
    - GINV and GDP are weakly exogenous to the private investment long-run equation.
    - PINV is weakly exogenous to the GDP equation.
- Parsimonious structural VECM estimation:
  - Estimated by FIML with general-to-specific reduction; parameters reduced from 78 to 21.
  - Retained system of three endogenous variables (GDP, PINV, GINV) stable; equations pass normality, serial correlation, and heteroscedasticity diagnostics.

### Key empirical findings: investment–growth nexus
- Long-run relationships and elasticities:
  - Trade index (TOT) and public investment (GINV) have a positive impact on private investment (PINV) in the long run.
  - Credit to the private sector (CRED) does not have a significant long-run impact on private investment or on GDP growth (long-run insignificance imposed in cointegrating vectors).
  - Public investment and the export (trade) index have both direct and indirect effects—via private investment—on GDP growth.
  - A 1 percent increase in private investment yields an 0.3 percent long-run increase in GDP (Equation 7).
  - Long-run elasticity of private investment to public investment = 0.4.
  - Institutional quality, terms-of-trade developments, public investment, and credit to the private sector appear to have positive impacts on growth (institutional variable range 0–20).
- Short-run dynamics and speed of adjustment (ECM, 1965–2005):
  - ECM(GDP) = -0.36 (t-statistic [-2.01]**)
  - ECM(PINV) = -0.24 (t-statistic [-2.14]**)
  - Selected short-run first-lag coefficients (t-stats in brackets):
    - DTOT(-1): 0.13 [1.716]*
    - DGINV(-1): 0.12 [3.571]**, 0.14 [3.26]**, 0.16 [1.66]*
    - DPINV(-1): 0.14 [2.152]**, 0.14 [1.905]*
    - DCRED(-1): 0.22 [3.08]**, 0.15 [3.31]**, 0.11 [2.457]**
    - DGDP(-1): 0.77 [3.626]**, 0.35 [1.88]*, 0.15 [2.761]**
    - DINST(-1): 0.10 [1.84]*, 0.45 [3.11]**, 0.14 [1.76]*
    - CONSTANT: 4.23 [2.02]**, -7.98 [-2.42]**, 1.13 [2.01]**
  - Interpretation:
    - Private investment is a long-run determinant of growth but adjusts sluggishly in the short run.
    - GDP dynamic implies 27 percent of GDP’s deviation from long-run equilibrium is corrected every year, implying it takes two to three years to halve the gap.
    - No evidence of short-run crowding out of private investment by public investment; short- and long-run elasticities support crowding-in (complementarity).
    - Credit, supply factors, and institutions significantly affect private investment in the short run; limited long-run impact of credit likely reflects financial depth and short-term nature of credit in Benin.

### Variance decomposition, impulse responses, and historical decomposition
- Variance decomposition (selected horizons, structural factorization basis):
  - Year 1: Standard error 1.1867; Terms of Trade 7.000; Public Investment 10.4583; Credit to private sect. 3.7617; Private Investment 76.921; Supply Factor 11.859
  - Year 2: Standard error 1.2977; Terms of Trade 7.134; Public Investment 10.997; Credit 3.715; Private Investment 65.605; Supply Factor 12.549
  - Private investment explains about 77 percent of its own shocks immediately after a shock; GDP explains about 75 percent of its own shocks immediately after a shock.
  - Contribution of credit to private-sector forecast-error variance rises from about 3.8 percent to 12.6 percent over horizons; impact of credit on GDP forecast-error variance remains below 1 percent.
  - Supply-factor shocks have a larger impact on private investment forecast errors than terms of trade, credit, or public investment.
- Impulse response findings:
  - Private investment overreacts to its own shock; responses to other shocks are less than 1:1.
  - Response of private investment to a terms-of-trade shock is limited.
  - Response to a private-sector credit shock persists longer than to terms-of-trade shocks.
  - GDP response to a private investment shock: growth picks up in the first year after the shock; by the sixth year after a slowdown, private investment is positively correlated with marginal comovement of the output response to public investment.
  - GDP change in response to a terms-of-trade shock is more pervasive and persistent than changes to private investment or private-sector credit.
- Historical decomposition:
  - Since the 1990s public investment has become the most significant determinant of private investment.
  - Supply-factor shocks were more influential in 1975–1990; the transition to a market-oriented economy around early 1990 reduced the dominance of supply-factor influences.
  - Historical decomposition suggests private investment would have been higher if driven by positive supply factors.

### Policy implications and recommendations
- Investment complementarities and fiscal policy:
  - Public and private investment in Benin are complementary rather than mutually crowding out; both have positive short- and long-run effects on growth under certain conditions.
  - Fiscal policy should avoid or limit short-run crowding-out effects on the private sector when scaling up public investment.
  - Channeling part of additional fiscal space created by debt relief to public investment could benefit Benin in the medium term by supporting private investment and growth.
- Institutional and market reforms:
  - Significant potential exists for institutional reforms to improve the business environment, raise private investment, and invigorate growth (address licensing, labor market, credit scarcity, and factor costs).
  - Strengthening institutional and regulatory frameworks and improving economic freedom could foster private investment; Benin’s poor rating on the economic freedom index is an obstacle.
  - Reforms should address institutional weaknesses in key sectors (for example, cotton) and accelerate implementation to translate improvements into higher private investment.
- Financial sector and informal economy:
  - Credit to the private sector affects growth indirectly through private investment, but this effect is short-lived—likely because credit is short-term in Benin.
  - Informal sector importance: microfinance institutions collect about 8.3 percent of total deposits and lend on average 17.4 percent of credits; more than 70 percent of microfinance institutions operate informally.
  - Scaling up public expenditure after HIPC and MDRI relief could have significant real impacts not fully captured by the model.
- Research implications:
  - A more detailed empirical micro-foundation and externality-based analysis would be desirable to identify channels (productivity, crowding-in, crowding-out, informal sector effects) through which public investment affects growth.

### Appendix C — selected statistical test results
- Unit root tests (first differences, Dickey-Fuller; Phillips-Perron):
  - TOT: -2.23; -2.27; -6.97***; -8.91***
  - GINV: -2.2; -2.26; -2.83; -3.63**
  - PINV: -1.47; -1.46; -6.96***; -11.58***
  - GDP: -1.75; -1.72; -5.89***; -5.97***
  - CRED: -1.26; -1.48; -5.50***; -5.63***
  - INST: -2.45; -2.45; -3.26*; -3.35*
  - MacKinnon critical values: 1 percent = -4.2050; 5 percent = -3.5266; 10 percent = -3.1946
- Optimal lag diagnostics (Appendix Table 2 highlights):
  - Lag 4: 0.79730 [0.7470]
  - Lag 3: 0.92976 [0.5860]
  - Lag 2: 1.0227 [0.4759]
  - Lag 1: 1.7858 [0.0479]*
- Cointegration (Johansen trace test, Appendix Table 4):
  - Trace test indicates 2 cointegrating eqn(s) at the 0.05 level.
- Structural long-run matrix (selected coefficients, Appendix Table 6):
  - C(42): Coefficient 0.410929; Std. Error 0.047935; z-Statistic 8.572693; Prob. 0.00000
  - C(52): Coefficient 0.675861; Std. Error 0.047281; z-Statistic 14.29444; Prob. 0.00000
  - C(53): Coefficient 0.296516; Std. Error 0.024207; z-Statistic 12.24921; Prob. 0.00000
  - C(64): Coefficient 1.44096; Std. Error 0.080704; z-Statistic 17.8549; Prob. 0.00000
  - Included observations: 36 after adjustments

*Source: _wp08120 - References; IMF staff analysis drawn from the cited content unit.*

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

### _wp08120 - References ......................................................................................................................30

### Introduction: context and objectives
- Benin: small, poor West African coastal country located east of Nigeria and west of Togo; population in 2006, 7.5 million, grows nearly 3 percent a year; annual average per capita GDP growth was less than 1 percent a year for 1965–2005.
- Problem statement:
  - Despite peaceful democratization and four peaceful presidential elections since 1991, Benin has not yet attracted significant private investment.
  - Ratio of fixed investment to GDP has been found to have the most explanatory power for growth (Levine and Renelt, 1992).
  - Credibility of fiscal policy management partly explains private uncertainty about investment (Serven, 1998, 1997).
- Paper objective:
  - Investigate the nexus of public and private investment and its impact on growth in Benin.
  - Provide stylized facts and policy lessons to inform academics and policymakers on how public and private investment can impact growth and help reduce poverty in low-income countries.
- Key methodological stance:
  - Employ econometric techniques to investigate short- and long-run behavior of private investment and links to growth.
  - Use a parsimonious structural VECM in the spirit of the general-to-specific approach of Hendry (1995a, 1995b, and 2000).
  - Combine backward-looking analysis with forward-looking VAR outputs (HD, VD, IRF).

### Background and stylized facts (Benin, 1965–2006)
- Growth and investment trends:
  - Between 1965 and 2005, real GDP grew annually by an average of 3.4 percent, but annual per capita GDP increased by only 0.3 percent.
  - After the 1994 CFA franc devaluation, real GDP growth rebounded to a yearly average of 4.4 percent in 1994–2005; annual real per capita GDP increased by 1.7 percent.
  - Since 1994 private investment growth slowed: real private investment growth decelerated from an average of 14 percent a year for 1980–93 to 6.1 percent for 1994–2006.
- Sectoral and FDI observations:
  - Cotton sector is a major contributor to economic activity; investment has been too low to cover capital depreciation.
  - FDI in the cotton sector declined from US$270 million in 1998 (11 percent of GDP) to US$251 million in 2004 (6 percent) even though total FDI inflows rose from US$33 million in 1998 to US$60 million in 2004.
  - Cotton seed production average share of nominal GDP about 3 percent on average for 2000-05; approximately 550,000 Benin families run small farms, about 310,000 grow cotton and sell cotton seed; about 14,000 new small farmers (in net terms) enter the sector each year; average family size in rural areas is 10 people; ginning industry capacity is estimated at 600,000 tons.
- Comparative private investment (Text Table 1): private investment ratios (percent of GDP) 2000–05
  - WAEMU (PPP weighted) 11.1
  - Benin 12.5
  - Burkina Faso 10.6
  - Côte d'Ivoire 7.7
  - Mali 12.1
  - Niger 5.2
  - Senegal 17.0
  - Togo 16.1
  - CEMAC (PPP weighted) 21.0
  - Cameroon 16.5
  - Central African Rep. 4.5
  - Chad 27.3
  - Congo, Republic of 16.0
  - Equatorial Guinea 41.1
  - Gabon 19.8
  - Memorandum items: WAEMU 3.0 (real GDP growth in percent), CEMAC 5.7 (real GDP growth in percent).
- Private investment and growth correlation:
  - For the last five years, economic growth has been more robust in CEMAC than in WAEMU countries; differences partly explained by private investment disparities (high returns in oil sector).
  - Central African Republic (only non-oil-producing country in CEMAC) recorded real GDP growth of –0.4 percent a year on average for 2000–05 and had the lowest private investment ratio in the region.
- Business environment constraints (Text Table 2 / Doing Business 2006):
  - World Bank’s 2006 Doing Business report ranks Benin 137 of 175 countries in ease of doing business.
  - Constraints noted: cumbersome licensing requirements, difficult labor market conditions, scarcity of credit, high factor costs.
  - Benin moved up only 2 points between 2005 and 2006 on Doing Business indicators; Côte d’Ivoire improved by 15 points.
  - Doing Business 2006 rankings and changes (selected):
    - Benin: Ease of Doing Business rank 137; Registering Property rank 212; Getting Credit rank 126; Starting a Business rank -131; Dealing with Licenses rank 33; Employing Workers rank -21; other item ranks and changes as listed in Text Table 2.
  - Note: “Other WAEMU/Except Guinea-Bissau” and other country-specific Doing Business entries are reported in Text Table 2.

### Main empirical findings and policy-relevant results
- Empirical findings:
  - Private investment is a critical determinant of growth in Benin (consistent with growth-accounting studies and model results).
  - Public investment provides long-run support for private investment and growth; short-run crowding-out effects may occur.
  - Adverse shocks (for example, deteriorating terms of trade) can have long-lasting growth effects.
  - Impact of credit to the private sector has been short-lived to date.
- Policy implications and recommendations:
  - Channeling part of additional fiscal space created by debt relief to public investment could benefit Benin in the medium term by supporting private investment and growth.
  - Significant potential exists for institutional reforms to improve the business environment, raise private investment, and invigorate growth (address licensing, labor market, credit scarcity, and factor costs).
  - Reforms should address institutional weaknesses in key sectors (for example, cotton) and accelerate implementation to translate improvements into higher private investment.

### Methodology, model choice, and econometric approach
- Modeling approach:
  - Use vector autoregression (VAR) and vector error correction models (VECMs) to study dynamics and long-run equilibria.
  - Preference for structural VECM approach to capture relationships and dynamic behavior among selected economic variables.
  - Structural VARs (SVARs) and SVECMs considered depending on unit root properties.
- Outputs and their purposes (Text Table 3 mapping):
  - Cointegration relations: identify long-run determinants of private investment and growth.
  - Error correction model (representation): characterize dynamic adjustment of GDP (or private investment) toward long-run equilibrium in response to structural shocks.
  - Historical decomposition (HD): reconstruct historical trends of GDP/private investment filtering specific shocks.
  - Variance decomposition (VD): project likely contributions of private investment to GDP growth (or vice versa) under unchanged policy.
  - Impulse response function (IRF): trace dynamic behavior of private investment (or GDP) in response to various shocks.
- Small-sample considerations:
  - Control for small sample size using a retained model estimate (through PcGive).
  - Cites Juselius (2006): sample “small” vs “big” depends on amount of information in data; informative data about a long-run relation can yield good test properties even with short samples.
- Model parsimony and congruence:
  - Adopt general-to-specific reduction to ensure the data are congruent with the structural model and to avoid parameterization problems of standard VARs.
  - Use of coherent VAR outputs (HD, VD, IRF) to combine backward-looking analysis with forward-looking insights.

*Source: _wp08120 - References .............................................................................................................*

### 17.      There are five steps to the estimation process:

### 17.      There are five steps to the estimation process:

### A. Steps in the estimation process
- Five-step procedure:
  - 1. Time series analysis and unit root tests
  - 2. Unrestricted VAR specification analysis, including lag length choice and diagnostics checks for misspecification
  - 3. Cointegration analysis and exogeneity tests
  - 4. Conditional structural VECM, eliminating all insignificant variables using the PcGETS (which eliminates automatically the least significant variables)
  - 5. IRF, VD and HD analysis on the basis of step 4

### B. Variable choices and ordering
- Endogenous variables used (vector):
  - (INST, GDP, PINV, CRED, GINV, TOT) represented as ),,,( ' ttttttt INSTGDPPINVCREDGINVTOTY=
- Variable definitions and roles:
  - TOT = log of trade volume index (external factor)
  - GINV = log of public investment (proxy for fiscal variable)
  - CRED = log of credit to the private sector (proxy for financial variable)
  - PINV = log of private investment (private sector behavior)
  - GDP = log of constant GDP at market price (supply factors)
  - INST = institutional strength measured using the POLITY project alternative to Freedom House (positive change indicates stronger institutions)
- Rationale and modeling approach:
  - Time-to-build approach used to capture lag until capital stock becomes productive
  - Structural vector autoregression model (SVECM) used to capture time lags and address endogeneity
  - Choice of CRED over interest rate as financial proxy because credit to private sector better captures effectiveness of monetary policy
  - Public investment (GINV) chosen over revenue or total expenditure to focus on public vs private investment dynamics, given revenue driven by trade taxes and limited information on fiscal authority behavior
- Ordering by assumed exogeneity (most to least):
  - TOT assumed most exogenous; GDP assumed most endogenous
  - Public investment (GINV) and credit (CRED) treated as policy instruments, with CRED assumed endogenous to fiscal instrument

### C. The model specification
- General VAR and VECM representations:
  - VAR in levels: ∑_{i=1}^{p} π_i t-i + C + D_t + ε_t (equation (1) representation)
  - VECM (error-correction) form: ∑_{i=1}^{p-1} Γ_i ΔY_{t-i} + Π Y_{t-1} + C D_t + ε_t (equation (2))
  - Error-correction representation: ∑_{i=1}^{p-1} Γ_i ΔY_{t-i} + αβ' Y_{t-1} + C D_t + ε_t (equation (3))
- Cointegration characterization:
  - Π = αβ' ; rank(Π) determines number of cointegrating relations
  - If rank(Π) = r, then r cointegrating relationships; if r = 0 then ΔY_t is stationary; if r = n then Y_t is I(0)

### D. Structural model and identification
- Structural SVAR representation used for IRF and VD (equation (4) form)
- Assumptions and properties:
  - Two cointegration vectors assumed in estimation example
  - Long-run effects matrix Φ and matrices A and B involved; with 6 endogenous variables and 2 cointegration relations, long-run matrices are of rank 4 (= 6–2)
  - A and B are nonsingular
- Identification requirements for IRFs:
  - Minimum of 6*(6-1)/2 = 15 restrictions required for meaningful IRF
  - Given 2 cointegration relationships:
    - At most 2 shocks have transitory effects (or 0 have long-run impacts)
    - At least 4 = 6–2 shocks have permanent effects
    - Two transitory shocks induce 8 = 2*(6–2) independent restrictions
    - Following King et al. (1991), 2*(2–1)/2 = 1 contemporaneous restriction identity imposed
    - Data-oriented significance approach imposes 4*(4–1)/2 additional restrictions
    - Total restrictions imposed: [2*(6-2)] + [2*(2-1)/2] + [4*(4-1)/2] = 15

### Impulse response and identification issues
- IRF purpose:
  - Track path over time of change in private investment and real GDP after a one-unit shock to TOT, GINV, CRED, PINV, and GDP
- MA representation used: ∑_{j=0}^{∞} Φ_j L^j with Φ_0 = I and Φ_j → 0 as j → ∞
- Distinction between long-run impulse response Φ and short-run Φ*_j

### Variance decomposition (VD)
- VD estimates relative contribution of each structural innovation to forecast error variance of each endogenous variable
- Forecast recursion at origin T:
  - h-step ahead forecast: ∑_{i=1}^{p} π_i Y_{T-i+h}
  - Forecast error in structural innovation form: ∑_{i=0}^{h-1} Θ_i ε_{T+h-i}, where Θ_i = BA^{-1} Φ_i*
- Percentage contribution formula:
  - w_{kn}(h) = [∑_{i=0}^{h-1} Θ_{i,kn}^2] / [∑_{n=1}^{K} ∑_{i=0}^{h-1} Θ_{i,kn}^2]

### Historical decomposition (HD)
- HD decomposes forecast error into contributions from structural shocks over time windows
- For j such that T_j satisfies T_j t ≤ + ≤ ≤ 0, the decomposition sums innovations from t+1 to t+j to attribute portions of Y_{t+j} to specific shocks

### IV. Empirical evidence — A. Statistical tests and estimation details
- Data and sample:
  - Annual data for 1965–2005 from World Bank Development Indicators 2006 and IMF International Financial Statistics of June 2006
  - Series (except TOT and INST) are at constant prices (2000 = 100)
  - Number of annual observations: 41 (noted as relatively few annual observations)
- Unit root and lag choices:
  - Unit root tests indicate most variables are nonstationary (see Appendix Table 1 referenced)
  - All six variables entered with 4 lags in equation (1) specification; based on F-statistics a 1-lag VAR seems appropriate
  - Model generalized to 2 lags given limited observations and to ensure residuals are well behaved; unrestricted VAR(2) diagnostics used
- Diagnostic outcomes for VAR(2):
  - Tests confirm absence of serial autocorrelation and heteroscedasticity
  - Residuals normally distributed without an ARCH effect
  - System variables stable at lag 2, passing 1-up and N-down Chow tests (indicating system stability)
- Cointegration and exogeneity:
  - Johansen LR trace test indicates 2 cointegrating equations at 5 percent significance (see Appendix Table 3 and Appendix Figures 1 and 2 referenced)
  - Exogeneity test statistics (WETS) results:
    - TOT, CRED, and INST are only weakly exogenous
    - GINV and GDP are weakly exogenous to the private investment long-run equation
    - PINV is weakly exogenous to the GDP equation
- Parsimonious structural VECM estimation:
  - Estimated using full information maximum likelihood (FIML) with general-to-specific approach in the I(0) space
  - General-to-specific eliminates redundant or insignificant variables
  - Number of parameter estimates reduced from 78 to 21
  - Coefficient estimates improved in the parsimonious model
  - Final model diagnostics (Appendix Table 5 and Appendix Figures 3 and 4 referenced):
    - System of three endogenous variables (GDP, PINV, GINV) is stable by recursive constancy Chow tests
    - GDP, PINV, and GINV equations are normally distributed, showing no serial correlation or heteroscedasticity

*Source: _wp08120 - 17.      There are five steps to the estimation process:*

### 33.      The investment equation supports the conclusion that the trade index and public

### _wp08120 - 33.      The investment equation supports the conclusion that the trade index and public

### Key empirical findings: investment–growth nexus
- The investment equation supports the conclusion that the trade index and public investment have a positive impact on private investment in the long run.
- Credit to the private sector does not have a significant long-run impact on private investment or on GDP growth (long-run insignificance imposed in cointegrating vectors).
- Public investment and the export (trade) index have both a direct and an indirect effect—via private investment—on GDP growth.
- A 1 percent increase in private investment yields an 0.3 percent long-run increase in GDP (Equation 7).
- The long-run response (elasticity) of private investment to public investment is 0.4 (consistent with Oshikoya (1994) for Cameroon; by comparison, Oshikoya found 0.54 for Morocco, 0.61 for Mauritius, and 0.10 for pooled middle-income countries).
- Institutional quality, terms-of-trade developments, public investment, and credit to the private sector appear to have positive impacts on growth (institutional variable = POLITY DEMOC – AUTOC + 10, range 0–20).

### Short-run dynamics and speed of adjustment (Error Correction Model, 1965–2005)
- Estimated error correction coefficients:
  - ECM(GDP) = -0.36 (t-statistic [-2.01]**)
  - ECM(PINV) = -0.24 (t-statistic [-2.14]**)
- Selected short-run coefficients (first lags, t-stats in brackets):
  - DTOT(-1): 0.13 [1.716]*
  - DGINV(-1): 0.12 [3.571]**, 0.14 [3.26]**, 0.16 [1.66]*
  - DPINV(-1): 0.14 [2.152]**, 0.14 [1.905]*
  - DCRED(-1): 0.22 [3.08]**, 0.15 [3.31]**, 0.11 [2.457]**
  - DGDP(-1): 0.77 [3.626]**, 0.35 [1.88]*, 0.15 [2.761]**
  - DINST(-1): 0.10 [1.84]*, 0.45 [3.11]**, 0.14 [1.76]*
  - CONSTANT: 4.23 [2.02]**, -7.98 [-2.42]**, 1.13 [2.01]**
- Interpretation:
  - Private investment is a long-run determinant of growth but adjusts sluggishly in the short run.
  - The GDP dynamic equation implies 27 percent of GDP’s deviation from long-run equilibrium is corrected every year, implying it takes two to three years to halve the gap (half-life calculation using α = 0.27).
  - No evidence of short-run crowding out of private investment by public investment; short- and long-run elasticities support crowding-in (complementarity) in Benin.
  - Credit, supply factors, and institutions significantly affect private investment in the short run.
  - The limited long-run impact of credit may reflect financial depth and the short-term nature of credit in Benin.

### Variance decomposition and shocks
- Private investment and real GDP predominantly explain their own forecast-error variance immediately after shocks:
  - Private investment explains about 77 percent of its own shocks just after a shock.
  - GDP explains about 75 percent of its own shocks just after a shock.
- Contribution of credit to private sector on private investment forecast-error variance rises from about 3.8 percent to 12.6 percent over horizons, while its impact on GDP forecast-error variance remains below 1 percent—suggesting credit may have an indirect effect on output via private investment.
- Supply-factor shocks (labor market and investment conditions) have a larger impact on private investment forecast errors than terms of trade, credit, or public investment.
- From the provided forecast-error variance decomposition lines (selected horizons, structural factorization basis):
  - Year 1: Standard error 1.1867; Terms of Trade 7.000; Public Investment 10.4583; Credit to private sect. 3.7617; Private Investment 76.921; Supply Factor 11.859
  - Year 2: Standard error 1.2977; Terms of Trade 7.134; Public Investment 10.997; Credit 3.715; Private Investment 65.605; Supply Factor 12.549
  - (Additional horizon values are reported in the Text Table 5 in the source.)

### Historical decomposition (HD) and temporal patterns
- Since the 1990s public investment has become the most significant determinant of private investment.
- Supply-factor shocks were more influential in 1975–1990; the transition to a market-oriented economy around early 1990 reduced the dominance of supply-factor influences.
- Figure 3 (historical decomposition of private investment, 1975–2005) indicates private investment would have been higher if driven by positive supply factors; the institutional variable was not controlled for in that comparison.
- Shocks to public investment and to credit to the private sector show different persistence patterns across the historical series.

### Impulse response analysis (IRF)
- Private investment overreacts to its own shock; responses to other shocks are less than 1:1.
- The response of private investment to a terms-of-trade shock is limited.
- The response to a private-sector credit shock persists longer than to terms-of-trade shocks.
- GDP response to a private investment shock: growth picks up in the first year after the shock; by the sixth year after a slowdown, private investment is positively correlated with marginal comovement of the output response to public investment.
- Overall, GDP change in response to a terms-of-trade shock is more pervasive and persistent than changes to private investment or private-sector credit.

### Policy implications and conclusions
- The analysis, based on annual data 1965–2005 and a conditional parsimonious VECM with structural VAR outputs (HD, VD, IRF), yields the following implications:
  - Public and private investment in Benin are complementary rather than mutually crowding out; both have positive short- and long-run effects on growth under certain conditions.
  - Fiscal policy should avoid or limit short-run crowding-out effects on the private sector when scaling up public investment.
  - Strengthening institutional and regulatory frameworks and improving economic freedom could foster private investment; Benin’s poor rating on the economic freedom index is an obstacle to private investment.
  - Credit to the private sector affects growth indirectly through private investment, but this effect is short-lived—likely because credit is short-term in Benin.
  - Given the informal sector’s increasing role (microfinance institutions collect about 8.3 percent of total deposits and lend on average 17.4 percent of credits; more than 70 percent of microfinance institutions operate informally), scaling up public expenditure after HIPC and MDRI relief could have significant real impacts that are not fully captured by the model.
  - A more detailed empirical micro-foundation and externality-based analysis would be desirable to identify channels (productivity, crowding-in, crowding-out, informal sector effects) through which public investment affects growth.

### Data and variable definitions (as used in the analysis)
- Sample period: 1965–2005; 41 observations; optimal lag length = 2 in reported ECM.
- GDP: Natural log of constant GDP at market price (constant prices 2000=100). Source: World Bank Development Indicators 2006.
- GINV: Natural log of public investment (constant prices 2000=100). Source: World Bank Development Indicators 2006.
- PINV: Natural log of private investment (constant prices 2000=100). Source: World Bank Development Indicators 2006.
- CRED: Natural log of credit to the private sector (constant prices 2000=100). Source: World Bank Development Indicators 2006.
- TOT: Natural log of trade volume index (Index 2000=100). Source: World Bank Development Indicators 2006.
- INST: Variable capturing institutional strength. Source: POLITY project (POLITYDEMOC = democracy – autocracy + 10, range 0–20).

*Source: IMF staff analysis (Text and tables drawn from the cited content unit).*

### Appendix C: Statistical Tests and Results

### Appendix C: Statistical Tests and Results

### Unit Root Tests (Appendix Table 1)
- Tests presented: Dickey-Fuller test and Phillips-Perron test.
- First difference (with constant) results (Dickey-Fuller; Phillips-Perron):
  - TOT: -2.23; -2.27; -6.97***; -8.91***
  - GINV: -2.2; -2.26; -2.83; -3.63**
  - PINV: -1.47; -1.46; -6.96***; -11.58***
  - GDP: -1.75; -1.72; -5.89***; -5.97***
  - CRED: -1.26; -1.48; -5.50***; -5.63***
  - INST: -2.45; -2.45; -3.26*; -3.35*
- Levels (with constant and trend): results reported alongside first-difference entries in the table.
- MacKinnon critical values for Dickey-Fuller and Phillips-Perron test:
  - 1 percent = -4.2050; 5 percent = -3.5266; 10 percent = -3.1946
- Significance legend:
  - * Rejection of the null hypothesis (unit root) at 10 persent level
  - ** Rejection of the null hypothesis (unit root) at 5 persent level
  - *** Rejection of the null hypothesis (unit root) at 1 persent level

### Optimal Lag Length (Appendix Table 2)
- F-statistics (F(36,33) etc.) and lag-selection diagnostics:
  - Lag 4: 0.79730 [0.7470]
  - Lag 3: 0.92976 [0.5860]; Lag 3 - 4F(72,43) 1.0871 [0.3893]
  - Lag 2: 1.0227 [0.4759]; Lag 2 - 4F(108,47) 1.3715 [0.1125]
  - Lag 1: 1.7858 [0.0479]*; Lag 1 - 4F(144,48) 8.6101 [0.0000]**
- AR 1-2 test (multivariate and individual):
  - Multivariate/model AR 1-2 test: 1/1.20 [0.24]
  - LTOT: 1.28 [0.36]
  - LGINV: 1.31 [0.30]
  - LPINV: 0.05 [0.95]
  - LCRED: 1.81 [0.19]
  - LGDP: 0.93 [0.41]
  - INST: 1.32 [0.29]
- Normality tests (Chi^2):
  - Multivariate/model Normality: 2/2.33 [0.31]
  - LTOT: 1.50 [0.47]
  - LGINV: 2.69 [0.26]
  - LPINV: 2.56 [0.28]
  - LCRED: 3.98 [0.14]
  - LGDP: 4.56 [0.10]
  - INST: 0.77 [0.68]
- ARCH 1-1 tests:
  - Multivariate/model: 3/N.A.
  - LTOT: 1.02 [0.32]
  - LGINV: 0.07 [0.79]
  - LPINV: 0.01 [0.93]
  - LCRED: 0.70 [0.41]
  - LGDP: 0.46 [0.50]
  - INST: 0.01 [0.93]
- Heteroschedasticity tests:
  - Multivariate/model: 3/0.22 [1.00]
  - LTOT: 0.03 [1.00]
  - LGINV: 0.09 [1.00]
  - LPINV: 0.04 [1.00]
  - LCRED: 0.04 [1.00]
  - LGDP: 0.13 [1.00]
  - INST: 0.08 [1.00]
- Notes on test statistics:
  - 1/ F(2,24) test uses for individual variables and F(72,54) for multivarriate model statistics critical values.
  - 2/ Chi^2(2) tesr uses for individual variables and Chi^2(12) for multivarriate model statistics critical values.
  - 3/ F(1,24) test uses.
  - 4/ F(24,1) test uses for individual variables and F(252,21) for multivarriate model statistics critical values.

### Residual Analysis and Cointegration (Appendix Tables 3 and 4)
- Residual analysis of Unrestricted VAR(2) (Appendix Table 3):
  - AR 1-2 test F-statistics across lags: reported in Appendix Table 2 and 5.
- Unrestricted Cointegration Rank Tests (Appendix Table 4):
  - Trace test eigenvalues, statistics, and probabilities:
    - None: Eigenvalue 0.688911; Trace Statistic 16.62 [0.001]**
    - At most 1: Eigenvalue 0.600087; Trace Statistic 3.42 [0.023]*
    - At most 2: Eigenvalue 0.393113; Trace Statistic 9.51 [0.243]
    - At most 3: Eigenvalue 0.266572; Trace Statistic 1.03 [0.366]
    - At most 4: Eigenvalue 0.213089; Trace Statistic 9.56 [0.322]
    - At most 5: Eigenvalue 0.018623; Trace Statistic 0.7 [0.404]
  - 1/ Trace test indicates 2 cointegrating eqn(s) at the 0.05 level
  - (*) and (**) denotes rejection of the hypothesis at the 0.1 and 0.05 level respectively.
  - 41 observations from 1965 - 2005.
  - Test assumes no intercepts and no trend.
  - The test is carried with two lags in VAR(6).
- Variable-specific test statistics (Appendix Table 4):
  - DLGINV F(2,26): 1.17675 [0.33172]
  - DLPINV F(2,26): 1.0881 [0.3517]
  - DLGDPR F(2,26): 1.1891 [0.3205]
  - Overall F(18,62): 1.11169 [0.4272]
  - DLGINV Chi^2(2): 4.1666 [0.1245]
  - DLPINV Chi^2(2): 4.4208 [0.1403]
  - DLGDPR Chi^2(2): 4.6703 [0.0968]
  - Overall Chi^2(6): 5.009 [0.317]
  - DLGINV F(16,13): 0.51667 [0.8944]
  - DLPINV F(16,13): 0.55957 [0.8648]
  - DLGDPR F(16,13): 0.98801 [0.5163]
  - Overall F(96,52): 0.76737 [0.8688]

### AR, Normality, and Heteroschedasticity Tests (Appendix Table 5)
- Tests reported for endogenous variables of retained model (summary diagnostics listed in Appendix Table 2 and Table 4).
- Specific values referenced in Appendix Table 2 (see AR 1-2 test, Normality test, ARCH 1-1, Heteroschedasticity test entries).

### Structural Model / Long-Run Matrix (Appendix Table 6)
- Estimated coefficients, standard errors, z-statistics, and probabilities:
  - C(51): Coefficient 0.311774; Std. Error 0.012827; z-Statistic 24.30662; Prob. 0.00000
  - C(32): Coefficient 2.256391; Std. Error 0.154673; z-Statistic 14.58810; Prob. 0.00000
  - C(42): Coefficient 0.410929; Std. Error 0.047935; z-Statistic 8.572693; Prob. 0.00000
  - C(52): Coefficient 0.675861; Std. Error 0.047281; z-Statistic 14.29444; Prob. 0.00000
  - C(43): Coefficient -0.394492; Std. Error 0.10197; z-Statistic -3.868698; Prob. 0.00010
  - C(53): Coefficient 0.296516; Std. Error 0.024207; z-Statistic 12.24921; Prob. 0.00000
  - C(63): Coefficient -1.086297; Std. Error 0.226408; z-Statistic -4.797953; Prob. 0.00000
  - C(24): Coefficient 0.372954; Std. Error 0.060736; z-Statistic 6.141146; Prob. 0.00000
  - C(64): Coefficient 1.44096; Std. Error 0.080704; z-Statistic 17.8549; Prob. 0.00000
  - C(25): Coefficient 1.206314; Std. Error 0.058477; z-Statistic 20.6287; Prob. 0.00000
  - C(35): Coefficient 2.910962; Std. Error 0.037685; z-Statistic 77.2443; Prob. 0.00000
  - C(45): Coefficient 0.49015; Std. Error 0.042782; z-Statistic 11.45696; Prob. 0.00000
  - C(46): Coefficient 0.404006; Std. Error 0.058044; z-Statistic 6.96031; Prob. 0.00000
- Included observations: 36 after adjustments
- Model specification note: Model: Ae = Bu where E[uu']=I, and B=I

### Figures and Diagnostics (Appendix Figures 1–5)
- Appendix Figure 1: Time Series of Cointegration Vectors — fitted LTOT, fitted LGINV, fitted LCRED, fitted LPINV, fitted LGDPR (plotted across 1970, 1980, 1990, 2000 time axis; numeric tick labels shown such as 4.50, 4.75, 5.00; series scales for fitted series noted in figures).
- Appendix Figure 2: Cointegration Analysis: Recursive Eigenvalues — Ev a l1 through Ev a l5 plotted over 1995, 2000, 2005 with y-axis ticks 0.25, 0.50, 0.75.
- Appendix Figure 3: Recursive Constancy Statistics — 1up and Ndn constancy tests for DLGINV, DLPINV, DLGDPR, and CHOWs plotted over 1995–2005 with 5% critical lines.
- Appendix Figure 4: Residual Normality Tests — r:DLGINV N(0,1), r:DLPINV N(0,1), r:DLGDPR N(0,1) histograms and density markers (axis ranges shown).
- Appendix Figure 5: Benin: Historical Decomposition of GDP, 1975 - 2005 (Annual change). Figure shows:
  - Time series plotted from 1975 through 2005 with vertical axis ticks at -0.06, -0.04, -0.02, 0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12
  - Components shown in legend: Shock to terms of trade; Shock to public investment; Shock to private investment; Stochastic change in GDP; Actual change; Baseline GDP
  - Source: Staff estimate.

*Appendix C: Statistical Tests and Results*

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