## _wp09258

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---

### Introduction: scope and data coverage
- Purpose: analyze the impact of institutional factors on financial sector development in Sub-Saharan Africa (SSA) using Data Envelopment Analysis (DEA).
- Sample and timing:
  - 37 of 44 SSA countries included in the study (data limitations excluded Chad, Comoros, Congo Democratic Republic of Congo, Equatorial Guinea, Gambia, Guinea, and Guinea-Bissau).
  - Analysis uses information as of 2007; most required indicators were not available for 2008.
- Contextual indicators cited:
  - Of the 27 SSA countries in the Global Competitiveness Index of the World Economic Forum, 24 score below 4.
  - According to the Heritage Foundation Index of Economic Freedom, 38 of the 44 SSA countries are considered either “mostly unfree” or “repressed.”
- Data sources: Beck, et al 2000 (revised 2009), Doing Business 2008, Finance for All? 2007, Governance Matters 2009, national authorities and IMF staff estimates.
- Missing-value handling:
  - ROE for Benin, Central African Republic, Republic of Congo, Eritrea, and Togo use 2006 as the best proxy.
  - NPL for Eritrea for 2006 is taken as the best proxy.
  - Three countries (Mali, São Tomé and Príncipe, and Togo) had negative ROE replaced with a very small positive number.

### Institutions and financial sector development: literature synthesis and relevance for SSA
- Theoretical and empirical consensus:
  - Financial development linked to long-term economic growth (e.g., Levine 2003; Levine et al. 2000; Beck 2006).
  - Empirical studies show a strong positive relationship between financial depth and growth in SSA (e.g., Gelbard and Pereira Leite 1999).
- Institutional determinants emphasized:
  - Property rights and contractual institutions (Acemoglu and Johnson 2005; Djankov, MacLiesh, and Shleifer 2007).
  - Legal origin and protection of private property (La Porta et al. 1997, 1998).
  - Political stability and political economy considerations (Roe and Siegel 2009; Rajan and Zingales 2003).
  - Information sharing, creditor rights, and enforcement (Djankov et al. 2007).
- SSA-specific findings from prior work:
  - Lack of borrower information, corruption, and political instability identified as main challenges in West Africa (Demetriades and Fielding 2009).
  - Financial liberalization, stronger legal institutions, legal origin, lower inflation, and increased information sharing contribute to development in SSA (McDonald and Schumacher 2007).
  - Financial depth is shallow in SSA partly due to lack of infrastructure for screening and monitoring borrowers (Demetriades, et al 2009).
  - Development of local financial markets enhances the impact of aid (Nkusu and Sayek 2004).

### Empirical approach: DEA methodology and modeling choices
- Rationale for DEA:
  - DEA is non-parametric, does not impose a functional form, works well with small samples, and does not require distributional assumptions about inefficiency.
  - Focuses on revealed best-practice frontiers and yields relative efficiency measures for decision making units (DMUs).
- DEA advantages highlighted:
  - Focus on individual observations rather than population averages.
  - Simultaneous use of multiple outputs and inputs in different units.
  - No restriction on the functional form of the transformation relationship.
  - Generates a single aggregate measure of each DMU’s utilization of inputs to produce outputs and provides projections to the frontier.
  - Value-free weighting; Pareto optimality and best-practice focus.
- Limitations and sensitivities:
  - Results sensitive to choice of inputs and outputs and to proxies for unobservable institutional factors.
  - Potential omitted variables (e.g., legal origin, democracy, ownership).
  - DEA assumes data are error free; differences attributed to resource/tool mixes and managerial effectiveness.
- DEA formulation and computation:
  - Efficiency scores bounded between zero and one; fully efficient units have score of one.
  - The linear programming problem is solved n times (once per DMU) to obtain relative efficiency scores.
  - The source provides the explicit linear program transformations and notation used for the study.

### Model specification: inputs, outputs, and implementation details
- Inputs (institutional proxies):
  - Depth of Credit Information (Credit Information index).
  - Legal Rights of Borrowers (Legal Rights index).
  - Political Stability No Violence (Political Stability index).
  - Control of Corruption (Corruption index).
- Outputs (financial development indicators):
  - Total credit/Gross domestic product (Financial Depth).
  - Access (composite measure of access to financial services).
  - Return on Equity (ROE, Profitability).
  - Nonperforming loans/total loans (NPL, Asset quality).
- Two model runs:
  - Four-input model: the four institutional proxies as inputs and the four financial indicators as outputs to assess efficiency of financial systems given institutional levels.
  - Constant-input model: a constant input (the number 1) with the four outputs to represent equal initial opportunities across countries and produce a composite measure of financial sector “quality.”
- Variable definitions (exact from source):
  - y1o - is the depth credit information index (Credit Information) for country o
  - y2o - is the legal rights of borrowers (Legal Rights) for country o
  - y3o - is the political stability no violence (Political Stability) for country o
  - y4o - is the control of corruption (Corruption) for country o
  - x1o - is the total credits/gross domestic product (Financial Depth) for country o
  - x2o - is a composite measure of access to financial services (Access) for country o
  - x3o - is the return on equity (ROE) for country o
  - x4o - is nonperforming loans/total loans (NPL) for country o
  - “o” takes all the values from 1 to 37 as the model is run for each country analyzed.
- Interpretation strategy:
  - Compare outcomes of both models and input structure to assess the role of institutions via differences between the two models’ outcomes.
  - DEA yields virtual multipliers u_r and v_i as unknowns derived from solving the linear programs.
- Data vintage note:
  - All data are as of December 31, 2007, except the ROE and NPL proxies noted above and the access index exception noted in Appendix III.

### Data: country-level inputs and outputs (selected entries preserved exactly)
- Sample entries (values preserved exactly as in source):
  - Angola: 5 42.03761.37988.3% 24 23.6%2.9%
  - Benin: 2 32.88152.010916.4% 32 8.9%9.0%
  - Botswana: 5 73.33843.402919.2% 47 60.1%0.1%
  - Burkina Faso: 2 32.58782.100514.8% 26 6.8%19.4%
  - Burundi: 2 21.07771.450723.1% 17 26.4%18.8%
  - Cameroon: 3 32.10561.57368.9% 24 24.8%13.3%
  - Cape Verde: 4 33.50733.263744.9% 40 31.4%13.4%
  - Central African Republic: 3 30.72371.59916.7% 19 43.8%30.4%
  - Congo, Rep. of: 3 30.23921.23102.3% 27 76.0%3.0%
  - Côte d’Ivoire: 5 43.33762.887614.1% 24 14.8%21.4%
  - Eritrea: 1 21.45732.000226.1% 12 48.2%44.0%
  - Ethiopia: 3 40.77581.802718.8% 14 28.4%10.1%
  - Gabon: 3 32.69961.653211.1% 39 32.3%7.0%
  - Ghana: 1 72.71712.332129.4% 16 26.2%8.7%
  - Kenya: 5 101.40521.557823.2% 10 27.4%14.1%
  - Lesotho: 1 82.53722.30699.1% 17 31.6%1.7%
  - Liberia: 1 41.35312.089612.8% 11 4.4%16.4%
  - Madagascar: 1 22.45062.35129.4% 21 60.3%9.1%
  - Malawi: 1 82.48951.758413.7% 21 39.6%4.1%
  - Mali: 2 32.37162.072614.9% 22 0.0%10.7%
  - Mauritius: 3 43.26022.906871.6% 44 26.4%2.4%
  - Mozambique: 4 22.86962.009112.8% 12 47.7%2.6%
  - Namibia: 5 83.39782.686241.4% 28 44.9%2.8%
  - Niger: 2 32.05861.61358.2% 31 14.8%21.2%
  - Nigeria: 1 80.42811.495117.2% 14 13.1%8.4%
  - Rwanda: 3 22.30502.405910.3% 23 12.4%18.4%
  - São Tomé and Príncipe: 1 32.78242.020631.0% 14 0.0%26.6%
  - Senegal: 2 32.32022.088820.8% 27 14.3%18.6%
  - Seychelles: 1 33.50932.534934.8% 41 23.2%2.3%
  - Sierra Leone: 1 42.20221.48114.4% 13 36.1%31.7%
  - South Africa: 7 92.67702.8216142.1% 46 18.1%1.4%
  - Swaziland: 5 62.60322.032718.3% 34 14.1%6.4%
  - Tanzania: 1 82.43032.058612.0% 4 29.0%6.3%
  - Togo: 2 32.08091.522918.0% 28 0.0%13.8%
  - Uganda: 1 71.35921.75337.4% 20 31.4%4.1%
  - Zambia: 1 92.73471.898110.1% 14 34.1%8.4%
  - Zimbabwe: 1 81.20141.89813.9% 34 73.8%6.4%

### Summary statistics (preserved exactly)
- Inputs and outputs summary:
  - Minimum: 1.00 2.000.241.232.3% 4.00 0.0%0.1%
  - Average: 2.54 4.762.222.0621.4% 24.05 28.3%11.9%
  - Median: 2.00 4.002.432.0114.8% 23.00 26.4%9.0%
  - Maximum: 7.00 10.003.513.40142.1% 47.00 76.0%44.0%
- Notes on ranges:
  - Depth of Credit Information index ranges from 1 to 7.
  - Legal Rights of Borrowers ranges 0 to 10.
  - Political Stability and Control of Corruption indices range 0 to 5.
  - Access can be between 0 and 100.
  - Higher index values indicate better performance for these indices.
  - *Research was done in 2007, based on surveys done in 2003–04.

### DEA results: impact of institutions on financial sector development (Appendix IV)
- DEA outcome columns: With 4 Inputs; With a Constant; Difference; Qualitative assessment
- Results (each line preserved exactly as in source):
  - 1 Angola 0.7738 0.51064 0.2632 Moderate
  - 2 Benin 0.8303 0.68142 0.1489 Weak
  - 3 Botswana 1.0000 1.00000 - Strong/Outlier
  - 4 Burkina Faso 0.6941 0.55391 0.1402 Moderate
  - 5 Burundi 0.7471 0.47121 0.2759 Moderate
  - 6 Cameroon 0.6794 0.51064 0.1687 Moderate/Weak
  - 7 Cape Verde 1.0000 0.85598 0.1440 Strong
  - 8 Central African Republic 0.6612 0.61067 0.0506 Outlier
  - 9 Congo, Rep. of 1.0000 1.00000 - Outlier
  - 10 Côte d’Ivoire 0.4867 0.51137 (0.0247) Moderate
  - 11 Eritrea 1.0000 0.76674 0.2333 Weak
  - 12 Ethiopia 0.6026 0.47040 0.1322 Strong
  - 13 Gabon 1.0000 0.82979 0.1702 Moderate
  - 14 Ghana 0.9348 0.49879 0.4360 Weak
  - 15 Kenya 0.5413 0.48089 0.0604 Moderate/Weak
  - 16 Lesotho 0.7531 0.47196 0.2811 Weak
  - 17 Liberia 0.5469 0.23547 0.3115 Weak
  - 18 Madagascar 1.0000 0.83384 0.1662 Moderate/Weak
  - 19 Malawi 0.8476 0.59824 0.2494 Moderate
  - 20 Mali 0.6109 0.46911 0.1418 Weak
  - 21 Mauritius 1.0000 0.94542 0.0546 Strong
  - 22 Mozambique 0.9346 0.69023 0.2444 Weak
  - 23 Namibia 0.6111 0.80861 (0.1975) Moderate
  - 24 Niger 0.9569 0.65957 0.2973 Moderate/Weak
  - 25 Nigeria 1.0000 0.49986 0.5001 Outlier
  - 26 Rwanda 0.8441 0.48951 0.3546 Weak
  - 27 São Tomé and Príncipe 0.7892 0.30224 0.4870 Weak
  - 28 Senegal 0.7623 0.57614 0.1861 Moderate/Weak
  - 29 Seychelles 1.0000 0.87546 0.1245 Strong
  - 30 Sierra Leone 0.6898 0.49296 0.1969 Weak
  - 31 South Africa 1.0000 1.00000 - Strong
  - 32 Swaziland 0.7510 0.72416 0.0268 Moderate
  - 33 Tanzania 0.5993 0.44164 0.1577 Weak
  - 34 Togo 0.9233 0.59687 0.3264 Weak
  - 35 Uganda 0.6881 0.48288 0.2052 Moderate
  - 36 Zambia 0.6212 0.49749 0.1238 Moderate/Weak
  - 37 Zimbabwe 1.0000 1.00000 - Outlier

### Key analytical considerations and policy implications
- Core proposition:
  - Quantify the contribution of institutional factors (corruption, political stability, contract enforcement, information availability) to financial sector development (depth, access, operational quality, profitability) at the country level using DEA.
- Aggregate conclusions from DEA modeling:
  - (i) for six countries in the sample the influence of institutional factors on financial sector development is strong;
  - (ii) for nine countries this influence is moderate;
  - (iii) for six other countries the effect moderate to weak;
  - (iv) for twelve countries the influence of institutions on financial sector development is weak.
  - There are four cases that are outliers where no clear conclusions can be drawn.
- Empirical findings:
  - Institutional factors influence financial systems through various direct and indirect channels.
  - All four institutional factors included in the model have a similar significance among SSA countries in affecting financial sector development.
  - Financial sector development in the sample is characterized more by ROE and NPLs than by Financial Depth and Access.
  - Improvements in institutional factors in SSA countries would influence Financial Depth and Access more than ROE and NPL.
  - Depth of Credit Information has the strongest impact on NPL.
    - Policy implication: consider setting up credit registries, increasing transparency, and increasing the amount of shared information to reduce NPL.
  - Access is often determined mostly by Political Stability and partially by Legal Rights of Borrowers.
  - Some countries exhibit large gaps among institutional factors, indicating a need to prioritize improvements in the weakest institutions.
  - Low levels of financial development also depend on non-institutional and other institutional factors not examined in the paper.
- Caveats for policymakers:
  - Results depend on chosen proxies and DEA specification; omitted institutional variables and bidirectional causality between financial development and institutions need attention.
  - Empirical outcomes are sensitive to data quality; improving statistical and administrative data collection should be part of reform strategies.

### Suggested extensions and further research directions
- Micro-level (bank-level) DEA to measure financial advancement per bank and examine heterogeneity by ownership, size, age, or other bank characteristics.
- Regional or global extensions: apply similar analysis to other regions (North Africa, Middle East, Central Asia, Eastern Asia, and Latin America) or to all developing countries for inter- and intra-regional comparisons.
- Use other institutional factors and financial sector development measures to test the importance of different institutional characteristics or address country-specific characteristics.
- Apply DEA over different time periods to measure the impact of institutional reforms over time.

*Source: content as provided from _wp09258 - References and Appendices (all data and quotations are from the supplied document).*

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

### _wp09258 - References

### Introduction: scope and data coverage
- Purpose: analyze the impact of institutional factors on financial sector development in Sub-Saharan Africa (SSA) using Data Envelopment Analysis (DEA).
- Contextual facts and scope:
  - Of the 27 SSA countries in the Global Competitiveness Index of the World Economic Forum, 24 score below 4.
  - According to the Heritage Foundation Index of Economic Freedom, 38 of the 44 SSA countries are considered either “mostly unfree” or “repressed.”
  - The analysis uses information as of 2007; most required indicators were not available for 2008.
  - Due to data limitations, only 37 of 44 SSA countries are included in the study.
- Data sources: Beck, et al 2000 (revised 2009), Doing Business 2008, Finance for All? 2007, Governance Matters 2009, national authorities and IMF staff estimates.

### Institutions and financial sector development: literature synthesis and relevance for SSA
- Theoretical and empirical consensus:
  - Financial development is linked to long-term economic growth (references include Levine 2003; Levine et al. 2000; Beck 2006).
  - Empirical studies (e.g., Gelbard and Pereira Leite 1999) show a strong positive relationship between financial depth and growth in SSA.
- Institutional determinants emphasized in the literature:
  - Property rights and contractual institutions (Acemoglu and Johnson 2005; Djankov, MacLiesh, and Shleifer 2007).
  - Legal origin and protection of private property (La Porta et al. 1997, 1998).
  - Political stability and political economy considerations (Roe and Siegel 2009; Rajan and Zingales 2003).
  - Information sharing, creditor rights, and enforcement (Djankov et al. 2007).
- SSA-specific findings from prior studies:
  - Lack of borrower information, corruption, and political instability identified as main challenges in West Africa (Demetriades and Fielding 2009).
  - Financial liberalization, stronger legal institutions, legal origin, lower inflation, and increased information sharing contribute to development in SSA (McDonald and Schumacher 2007).
  - Financial depth (credit to private sector/GDP) is shallow in SSA not necessarily because of borrower creditworthiness but because of lack of infrastructure for screening and monitoring borrowers (Demetriades, et al 2009).
  - Development of local financial markets enhances the impact of aid (Nkusu and Sayek 2004).

### Empirical approach: DEA methodology and modeling choices
- Rationale for DEA:
  - DEA is non-parametric, does not impose a functional form between dependent and independent variables, works well with small samples, and does not require distributional assumptions about inefficiency.
  - DEA focuses on revealed best-practice frontiers and yields relative efficiency measures for decision making units (DMUs).
- DEA advantages and characteristics highlighted:
  - Focus on individual observations rather than population averages.
  - Simultaneous use of multiple outputs and inputs stated in different units.
  - No restriction on functional form of production/transformation relationship.
  - Generates a single aggregate measure of each DMU’s utilization of inputs to produce outputs.
  - Provides projections for moving DMUs below the frontier onto the frontier.
  - Value-free weighting (no a priori weights or prices required).
  - Pareto optimality and focus on best-practice frontiers.
- Limitations and sensitivities:
  - DEA results are very sensitive to the choice of inputs and outputs.
  - Use of proxies for unobservable institutional factors may affect accuracy.
  - Potential omitted variables (e.g., legal origin, democracy, ownership) could influence results but are limited by model/data constraints.
  - The DEA assumes data are error free; differences among DMUs are attributed to resource/tool mixes and managerial effectiveness.

### Model specification: inputs, outputs, and implementation details
- Inputs (institutional proxies):
  - Existence of reliable information (Credit Information index).
  - Contract enforcement (Legal Rights index).
  - Political stability (Political Stability: no violence).
  - Degree of corruption (Control of Corruption).
- Outputs (financial development indicators):
  - Financial depth (Total credit/Gross domestic product).
  - Access (composite measure of access to financial services).
  - Profitability (Return on Equity, ROE).
  - Asset quality (Nonperforming loans/total loans, NPL).
- Two model runs:
  1. Four-input model: institutional proxies as inputs and the four financial indicators as outputs to assess efficiency of financial systems given institutional levels.
  2. Constant-input model: a constant input (the number 1) with the four outputs to represent equal initial opportunities across countries and produce a composite measure of financial sector “quality.”
- Interpretation strategy:
  - Use outcomes of both models and the input structure to assess the role of institutions by considering differences between the two models’ outcomes.
  - DEA yields virtual multipliers u_r and v_i as unknowns derived from solving the linear programs.
- Mathematical representation (as provided in source):
  - The four-input model and the constant-input model formulations are explicitly given (matrix/linear programming forms with constraints and variables as in the source).
- Variable definitions (exact as in source):
  - y1o - is the depth credit information index (Credit Information) for country o
  - y2o - is the legal rights of borrowers (Legal Rights) for country o
  - y3o - is the political stability no violence (Political Stability) for country o
  - y4o - is the control of corruption (Corruption) for country o
  - x1o - is the total credits/gross domestic product (Financial Depth) for country o
  - x2o - is a composite measure of access to financial services (Access) for country o
  - x3o - is the return on equity (ROE) for country o
  - x4o - is nonperforming loans/total loans (NPL) for country o
  - “o” takes all the values from 1 to 37 as the model is run for each country analyzed.
- Data vintage and missing-value handling:
  - All data are as of December 31, 2007, except:
    - ROE for Benin, Central African Republic, Republic of Congo, Eritrea, and Togo use 2006 as the best proxy for missing information.
    - NPL for Eritrea for 2006 is taken as the best proxy for missing information.

### Key analytical considerations and implications for policy priorities
- Core analytical proposition:
  - Quantify the contribution of institutional factors (corruption, political stability, contract enforcement, information availability) to financial sector development (depth, access, operational quality, profitability) at the country level using DEA.
- Policy-relevant insights emphasized in the text:
  - Institutional reforms matter for financial sector deepening; countries should prioritize institutional changes that contribute more to financial sector development.
  - Political stability, contract enforcement, availability of borrower information, and control of corruption are highlighted as priority institutional areas.
  - Given SSA-specific constraints (weak institutions, data limitations), policy sequencing and prioritization are important—reforms should target the institutional determinants that most efficiently translate into improved financial depth, access, operational quality, and profitability.
- Caveats for policymakers:
  - Results depend on chosen proxies and the DEA model specification; omitted institutional variables and bidirectional causality between financial development and institutions need attention.
  - Empirical outcomes are sensitive to data quality; hence, improving statistical and administrative data collection should be part of reform strategies.

*Source: content as provided from _wp09258 - References (all data and quotations are from the supplied document).*

### Appendix III). Another exception applies to the access index that was calculated in 2007, but

### _wp09258 - Appendix III). Another exception applies to the access index that was calculated in 2007, but

### Results (DEA models, 37 SSA countries)
- Sample composition and exclusions:
  - The study includes 37 SSA countries.
  - Excluded countries due to missing data: Chad, Comoros, Congo Democratic Republic of Congo, Equatorial Guinea, Gambia, Guinea, and Guinea-Bissau.
- General modeling notes:
  - As the standard model assumes non-negative inputs and outputs, scales of Political Stability, No Violence and Control of Corruption have been changed.
  - Three countries (Mali, São Tomé and Príncipe, and Togo) had negative ROE and those numbers were replaced with a very small positive number (per Bowlin (1998) this should not affect model outcome).
  - Countries are pooled into groups based on the difference of outcomes of the two models to structure presentation.
- Countries fully efficient in both models (prominent results; well-developed institutional factors and relatively well-developed financial sector):
  - Botswana: good institutional structure (best performance in terms of the Corruption index), relatively high ROE, lowest NPL ratio; Legal Rights, Financial Depth and NPL ratio are significant.
  - South Africa: all indicators are “balanced” (no obvious outliers); stands out as having effective institutional factors for fostering financial development.
  - Republic of Congo and Zimbabwe: outliers with shallow financial sectors (low Credit/GDP ratio) and extreme values in binding variables; Republic of Congo is worst in SSA with Political Stability and Corruption indices; Zimbabwe among the worst with very low Credit Information and Political Stability indices.
- Countries with absolute difference between two models > 0 and < 0.1:
  - Côte d’Ivoire: underdeveloped financial sector; good control of corruption results in low ROE and high NPL ratio (counterintuitive; may reflect poor data quality or country-specific factors).
  - Swaziland: institutional factors have moderate influence; significant variables include Credit Information, Legal Rights, ROE, and NPL ratios.
  - Central African Republic: Political Stability is critical, resulting in poor ROE and one of the worst NPL ratios; considered an outlier.
  - Mauritius: institutional system has strong influence; fully efficient in the first model with well-established institutional factors.
  - Kenya: leading in Credit Information and Legal Rights but Political Stability is an obstacle for Access and NPLs; positive and negative institutional influences neutralize overall effect.
- Countries with absolute difference between two models in range 0.1–0.2:
  - Zambia: binding factors are Legal Rights and Political Stability; significant but not sole determinants of financial sector development.
  - Seychelles: institutional factors have significant effect on financial sector development.
  - Ethiopia: reducing corruption would strongly increase Access and lower NPLs.
  - Burkina Faso: relatively good institutions but uneven financial sector; Credit Information and Corruption constrain ROE and NPLs which are poor.
  - Benin and Mali: similar to Burkina Faso but institutions do not affect financial sector development much, suggesting other factors determine poor ROE and NPLs.
  - Cape Verde: fully efficient in the first model; institutional factors exert considerable influence but high NPL ratio is not explained by modelled institutional factors.
  - Tanzania: financial sector not sensitive to institutional factors; ranks high in Legal Rights and Political Stability but bottom in Access; institutional factors have limited impact.
  - Madagascar and Gabon: fully efficient in first model; moderate institutional influence; Political Stability and Financial Depth are constraints.
  - Cameroon and Senegal: institutions affect financial sector development moderately; Credit Information is main constraint on improving ROE and NPL ratios.
  - Namibia: institutions very well developed; financial sector measures are high but institutional measures are even better relative to others.
- Countries with absolute difference between two models > 0.2:
  - Uganda: moderate influence of institutions; Legal Rights affecting ROE.
  - Malawi: sound Legal Rights and Political Stability, but other institutional parameters inhibit financial sector advancement.
  - Angola: moderate influence; Credit Information, Legal Rights, and Political Stability rank high and drive overall financial sector characteristics.
  - Burundi: moderate influence; unlike most countries Credit Information and Corruption do not shape NPL ratio.
  - Niger and Togo: relatively underdeveloped institutions; institutional factors exert some influence but certain outputs (Access in Niger; ROE and NPLs in Togo) are not affected by institutional factors.
  - Nigeria: outlier; fully efficient in the first model and has the largest difference between the two models; very poor institutional environment except for a high ranking in Legal Rights.
  - Sierra Leone, Eritrea, Mozambique, Lesotho, Liberia, Rwanda, Ghana, and São Tomé and Príncipe: institutional factors have very limited influence on financial sector development; at least one institutional factor ranks high but does not contribute to system development; have average institutional structures but at least one or two bad financial sector characteristics likely with non-institutional roots.
  - Eritrea: fully efficient in the first model but an outlier with underdeveloped institutional system and the worst NPL ratio.

### Conclusions, policy implications, and possible extensions
- Aggregate conclusions from DEA modeling:
  - (i) for six countries in the sample the influence of institutional factors on financial sector development is strong;
  - (ii) for nine countries this influence is moderate;
  - (iii) for six other countries the effect moderate to weak;
  - (iv) for twelve countries the influence of institutions on financial sector development is weak.
  - There are four cases that are outliers where no clear conclusions can be drawn.
- Key empirical implications and findings:
  - Institutional factors influence financial systems through various direct and indirect channels.
  - Institutional improvements are typically slow due to limited resources and constraints (limited knowledge base, limited financial resources, cultural factors).
  - All four institutional factors included in the model have a similar significance among SSA countries in affecting financial sector development.
  - Financial sector development in the sample is characterized more by ROE and NPLs than by Financial Depth and Access, possibly reflecting large variation of these measures in SSA countries.
  - Improvements in institutional factors in SSA countries would influence Financial Depth and Access more than ROE and NPL.
  - Depth of Credit Information has the strongest impact on NPL.
    - Policy implication: countries aiming to reduce NPL via institutional changes should consider setting up credit registries, increasing transparency, and increasing the amount of shared information.
  - Access is often determined mostly by Political Stability and partially by Legal Rights of Borrowers.
  - Some countries (e.g., Kenya and Zambia) exhibit large gaps among institutional factors analyzed, indicating a need to prioritize improvements in the weakest institutions.
  - Low levels of financial development also depend on non-institutional and other institutional factors not examined in the paper.
- Suggested extensions and further research directions:
  - Micro-level (bank-level) analysis using DEA to measure financial advancement per bank, allowing more precise and detailed results and examination of heterogeneity by ownership, size, age, or other bank characteristics.
  - Regional or global extensions: apply similar analysis to other regions (North Africa, Middle East, Central Asia, Eastern Asia, and Latin America) or to all developing countries for inter- and intra-regional comparisons.
  - Use other institutional factors and financial sector development measures to test the importance of different institutional characteristics or to address country-specific characteristics.
  - Apply DEA over different time periods to measure the impact of institutional reforms over time.

*Source: IMF working paper content (Appendix III, Results, Conclusions, and References).*

### Appendix 1. Data Envelopment Analysis (DEA)

### _wp09258 - Appendix 1. Data Envelopment Analysis (DEA)

### DEA methodology and definition
- DEA is multi-factor non-parametric analysis used to measure the relative efficiency of decision making units (DMU) in input-output terms.
- Origin and extensions:
  - Charnes, Cooper, and Rhodes (CCR) (1978).
  - Banker, Charnes, and Cooper (BCC) (1984).
- Approach:
  - Uses linear programming to map a non-parametric surface frontier over the data points to determine efficiencies of each DMU relative to the frontier.
  - Efficiency scores are bounded between zero and one; fully efficient units have an efficiency score of one.
  - The efficiency score indicates how efficient a DMU is in transforming input factors into output measures, compared to other DMUs in the study.
- Efficiency concept (Cooper, et al (2004) definition):
  - “A DMU is to be rated as fully (100 percent) efficient on the basis of available evidence if and only if the performances of other DMUs do not show that some of its inputs or outputs can be improved without worsening some of its other inputs or outputs.”

### DEA formulation (multiple inputs and outputs)
- Representation of multi-input/multi-output to virtual input/output:
  - InputsofSumWeighted
    OutputsofSumWeighted
    Efficiency
    ___
    ___
    
- Notation and assumptions:
  - There are n DMUs.
  - Each DMU uses m different inputs to produce s different outputs.
  - DMU j uses amount x_ij of input i and produces amount y_rj of output r.
  - x_ij ≥ 0 and y_rj ≥ 0 and each DMU should have at least one positive input and one positive output.
- Linear programming formulation (as presented):
  - 
    
    i
    ioi
    r
    roro
    xvyuvuh/),(max 
    1/
    
    i
    iji
    r
    rjr
    xvyu
    j=1,...,n; ir,; 0,
    ir
    vu   (1)
  - Converted linear program (Charnes et al,1978):
    - 0,
      1
      0
      ),(max
      1
      11
      1
      
      
      
      
      
      
      
      
      
      
      ir
      m
      i
      ioi
      m
      i
      iji
      s
      r
      rjr
      s
      r
      roro
      vu
      xv
      xvyu
      yuvuh
       (2) 
      j=1,...,n; ir,

- Computational procedure:
  - The problem is solved n times (once for every single DMU) to obtain relative efficiency scores.
  - Each DMU selects combinations of inputs and outputs that maximize its efficiency.
  - If a DMU obtains an efficiency score of 1 in problem (2), it is efficient according to the DEA definition above.

### Data description (Appendix II)
- Notes on data:
  - 1/ Information on some of the countries was missing in these databases and estimates of national authorities and IMF staff have been taken to complete those holes.
  - *2/ This research has been done in 2007, but is based on the results of surveys done in 2003–04.
- Variables and descriptions (as listed):
  - Depth of Credit Information Index: The depth of credit information index measures rules affecting the scope, accessibility and quality of credit information available through either public or private credit registries. Source: Doing Business.
  - Legal rights of borrowers: The strength of legal rights index measures the degree to which collateral and bankruptcy laws protect the rights of borrowers and lenders and thus facilitate lending. Source: Doing Business.
  - Political Stability No Violence: Measuring perceptions of the likelihood that the government will be destabilized or overthrown by unconstitutional or violent means, including politically-motivated violence and terrorism. Source: Governance Indicators.
  - Control of Corruption: Measuring perceptions of the extent to which public power is exercised for private gain, including both petty and grand forms of corruption, as well as “capture” of the state by elites and private interests. Source: Governance Indicators.
  - Private Credit/GDP (Size 1/): Private credit by deposit money banks and other financial institutions/GDP. Source: Financial Structure Dataset 2009.
  - Access (2/): Composite measure of access to financial services — percentage of the adult population with access to an account with a financial intermediary. Source: Finance for All? Policy Research Report.
  - Return on Equity (Profitability 1/): Average return on assets (Net Income/Total Equity). Source: National authorities and IMF staff estimates.
  - Nonperforming loans / Total Loans (Operational quality 1/): Portion of nonperforming loans in the overall portfolio. Source: National authorities and IMF staff estimates.

### Data used (Appendix III) — selected country-level inputs and outputs (as provided)
- For each country the table lists: Depth Credit Information Index; Legal Rights of Borrowers; Political Stability No Violence; Control of Corruption; Total Credit (Total Advances)/GDP; Access; Return on Equity; NPLs to Total Gross Loans.
- Sample entries (preserving exact values as in source):
  - Angola: 5 42.03761.37988.3% 24 23.6%2.9%
  - Benin: 2 32.88152.010916.4% 32 8.9%9.0%
  - Botswana: 5 73.33843.402919.2% 47 60.1%0.1%
  - Burkina Faso: 2 32.58782.100514.8% 26 6.8%19.4%
  - Burundi: 2 21.07771.450723.1% 17 26.4%18.8%
  - Cameroon: 3 32.10561.57368.9% 24 24.8%13.3%
  - Cape Verde: 4 33.50733.263744.9% 40 31.4%13.4%
  - Central African Republic: 3 30.72371.59916.7% 19 43.8%30.4%
  - Congo, Rep. of: 3 30.23921.23102.3% 27 76.0%3.0%
  - Côte d’Ivoire: 5 43.33762.887614.1% 24 14.8%21.4%
  - Eritrea: 1 21.45732.000226.1% 12 48.2%44.0%
  - Ethiopia: 3 40.77581.802718.8% 14 28.4%10.1%
  - Gabon: 3 32.69961.653211.1% 39 32.3%7.0%
  - Ghana: 1 72.71712.332129.4% 16 26.2%8.7%
  - Kenya: 5 101.40521.557823.2% 10 27.4%14.1%
  - Lesotho: 1 82.53722.30699.1% 17 31.6%1.7%
  - Liberia: 1 41.35312.089612.8% 11 4.4%16.4%
  - Madagascar: 1 22.45062.35129.4% 21 60.3%9.1%
  - Malawi: 1 82.48951.758413.7% 21 39.6%4.1%
  - Mali: 2 32.37162.072614.9% 22 0.0%10.7%
  - Mauritius: 3 43.26022.906871.6% 44 26.4%2.4%
  - Mozambique: 4 22.86962.009112.8% 12 47.7%2.6%
  - Namibia: 5 83.39782.686241.4% 28 44.9%2.8%
  - Niger: 2 32.05861.61358.2% 31 14.8%21.2%
  - Nigeria: 1 80.42811.495117.2% 14 13.1%8.4%
  - Rwanda: 3 22.30502.405910.3% 23 12.4%18.4%
  - São Tomé and Príncipe: 1 32.78242.020631.0% 14 0.0%26.6%
  - Senegal: 2 32.32022.088820.8% 27 14.3%18.6%
  - Seychelles: 1 33.50932.534934.8% 41 23.2%2.3%
  - Sierra Leone: 1 42.20221.48114.4% 13 36.1%31.7%
  - South Africa: 7 92.67702.8216142.1% 46 18.1%1.4%
  - Swaziland: 5 62.60322.032718.3% 34 14.1%6.4%
  - Tanzania: 1 82.43032.058612.0% 4 29.0%6.3%
  - Togo: 2 32.08091.522918.0% 28 0.0%13.8%
  - Uganda: 1 71.35921.75337.4% 20 31.4%4.1%
  - Zambia: 1 92.73471.898110.1% 14 34.1%8.4%
  - Zimbabwe: 1 81.20141.89813.9% 34 73.8%6.4%

### Summary statistics (Appendix III)
- Inputs and outputs summary (Minimum, Average, Median, Maximum — values preserved exactly):
  - Minimum: 1.00 2.000.241.232.3% 4.00 0.0%0.1%
  - Average: 2.54 4.762.222.0621.4% 24.05 28.3%11.9%
  - Median: 2.00 4.002.432.0114.8% 23.00 26.4%9.0%
  - Maximum: 7.00 10.003.513.40142.1% 47.00 76.0%44.0%
- Note:
  - 1/ The range for the Depth of Credit Information index is from 1 to 7. For the index of Legal Rights of Borrowers the range is 0 to 10. The range for indices of Political Stability and Control of Corruption is 0 to 5. Access can be anything between 0 and 100. In all these cases the higher the index value the better the performance of the country. The other three indicators don’t have strict ranges.
  - *2/ This research has been done in 2007, but is based on the results of surveys done in 2003–04.

### DEA results: Impact of institutions on financial sector development (Appendix IV)
- Columns: With 4 Inputs; With a Constant Difference Impact; (Difference) ; Qualitative assessment
- Results (each line preserved exactly as in source):
  - 1 Angola 0.7738 0.51064 0.2632 Moderate
  - 2 Benin 0.8303 0.68142 0.1489 Weak
  - 3 Botswana 1.0000 1.00000 - Strong/Outlier
  - 4 Burkina Faso 0.6941 0.55391 0.1402 Moderate
  - 5 Burundi 0.7471 0.47121 0.2759 Moderate
  - 6 Cameroon 0.6794 0.51064 0.1687 Moderate/Weak
  - 7 Cape Verde 1.0000 0.85598 0.1440 Strong
  - 8 Central African Republic 0.6612 0.61067 0.0506 Outlier
  - 9 Congo, Rep. of 1.0000 1.00000 - Outlier
  - 10 Côte d’Ivoire 0.4867 0.51137 (0.0247) Moderate
  - 11 Eritrea 1.0000 0.76674 0.2333 Weak
  - 12 Ethiopia 0.6026 0.47040 0.1322 Strong
  - 13 Gabon 1.0000 0.82979 0.1702 Moderate
  - 14 Ghana 0.9348 0.49879 0.4360 Weak
  - 15 Kenya 0.5413 0.48089 0.0604 Moderate/Weak
  - 16 Lesotho 0.7531 0.47196 0.2811 Weak
  - 17 Liberia 0.5469 0.23547 0.3115 Weak
  - 18 Madagascar 1.0000 0.83384 0.1662 Moderate/Weak
  - 19 Malawi 0.8476 0.59824 0.2494 Moderate
  - 20 Mali 0.6109 0.46911 0.1418 Weak
  - 21 Mauritius 1.0000 0.94542 0.0546 Strong
  - 22 Mozambique 0.9346 0.69023 0.2444 Weak
  - 23 Namibia 0.6111 0.80861 (0.1975) Moderate
  - 24 Niger 0.9569 0.65957 0.2973 Moderate/Weak
  - 25 Nigeria 1.0000 0.49986 0.5001 Outlier
  - 26 Rwanda 0.8441 0.48951 0.3546 Weak
  - 27 São Tomé and Príncipe 0.7892 0.30224 0.4870 Weak
  - 28 Senegal 0.7623 0.57614 0.1861 Moderate/Weak
  - 29 Seychelles 1.0000 0.87546 0.1245 Strong
  - 30 Sierra Leone 0.6898 0.49296 0.1969 Weak
  - 31 South Africa 1.0000 1.00000 - Strong
  - 32 Swaziland 0.7510 0.72416 0.0268 Moderate
  - 33 Tanzania 0.5993 0.44164 0.1577 Weak
  - 34 Togo 0.9233 0.59687 0.3264 Weak
  - 35 Uganda 0.6881 0.48288 0.2052 Moderate
  - 36 Zambia 0.6212 0.49749 0.1238 Moderate/Weak
  - 37 Zimbabwe 1.0000 1.00000 - Outlier

*Appendix 1. Data Envelopment Analysis (DEA), _wp09258

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09258.pdf_