## wp17236

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### Major findings and contributions
- Constructs novel indices of financial inclusion from micro-level Findex data to capture both the level and the distribution of financial access in a country.
- Uses representative GALLUP/Findex samples of about 1,000 individuals per country, totaling about 146,000 observations on over 140 countries, 34 of which are from sub-Saharan Africa.
- Uses the 2011 Findex wave for empirical analysis because income inequality data are available with a lag and up to 2013; indices are constructed for both 2011 and 2014.
- Key empirical associations:
  - Inequality in financial access is strongly associated with income inequality (Figure 1; reported R² = 0.2688 for the plotted relationship).
  - The level of financial inclusion (micro-based measure) does not appear to be significantly related to income inequality once controls are included.
  - Unequal financial access both overall and between men and women is significantly and robustly related to greater income inequality at the country level.
- Stylized distributional pattern:
  - Inequality in financial access follows a Kuznets-type relationship: at lower average intensities of financial access, increases in financial inclusion are driven by higher intensity of use by a smaller share of the population, exacerbating inequality; after a turning point, further increases are driven by broader access, lowering inequality in financial inclusion.

### Data and measurement
- Primary data source: World Bank’s Findex dataset (GALLUP surveys), two waves available: 2011 and 2014.
- Findex advantages:
  - Individual-level focus permits construction of a synthetic, micro-based measure of financial inclusion that captures both access and intensity of use across a broad range of financial services.
  - Allows derivation of Gini coefficients of inequality of financial access from microdata (Box 1: Deriving a Gini-Index of Financial Access).
- Constructed indices:
  - 2011 Financial Inclusion Index: 8 questions (Q1, Q3a, Q3b, Q8b, Q13a, Q14a, Q15a-Q15b, Q15a1a-Q15a1c); responses Yes/No/missing.
  - 2014 Financial Inclusion Index: 12 questions plus emergency funds question (Q1, Q3, Q4, Q6, Q9, Q11, Q14, Q16, Q18a, Q20, Q21a, Q24); responses Yes/No/missing except Q24 with categorical responses combined into two categories (“Very or somewhat possible”; “Not very or at all possible”).
  - Charts and analysis presented for the 2014 index; charts using the 2011 index are qualitatively similar.
- Inequality measure:
  - Inequality of financial access derived from standard Gini-coefficient calculation using individual financial access scores from Global Findex 2011 survey data.
  - Key formulas preserved:
    - GINI(X) = −2 Cov( X / μ(X), (1 − F(X)) )
    - CONC(X,Y) = −2 Cov( X / μ(X), (1 − G(Y)) )
    - GINI(X; v) = −v Cov( X / μ(X), (1 − F(X))^(v−1) )  (standard Gini corresponds to v = 2)
  - Fractional rank procedure described for unit-record data ensures Gini estimate independence from sample size when using { (Fi, yi, wi) }.

### Methodology: correspondence analysis and index construction
- Individual-level scores constructed using correspondence analysis (CA); Joint Correspondence Analysis (JCA) tested and used for robustness.
- Interpretation and properties:
  - CA outputs analogous to PCA but display chi-square distances; origin is the “center of gravity” (average response); main horizontal axis explains about 90 percent of variation.
  - Responses indicating having financial access lie on the right half; “missing” and “no” answers cluster on the left.
  - A “Yes” response to credit/debit cards lies far right (relatively rare and associated with different response patterns).
  - Individual inclusion score approximated as the sum of x-axis positions of an individual’s responses; higher score = access to more and rarer services.
- Caveats in CA interpretation:
  - Rarer services implicitly treated as indicating higher inclusion (robustness tests including/excluding such questions yielded broadly similar results).
  - Input/output qualitative; quantitative interpretation of intermediate score distances depends on chi-square metric assumptions.
  - Selection of questions based on authors’ judgement; multiple combinations tested for robustness.

### Distributional patterns and relationship with development
- Distribution of individual scores:
  - Highly skewed towards low-level scores.
  - Country-level scores are highly scattered across income groups.
  - 2014 index: higher value bins represent higher financial inclusion; intensity at higher levels relatively equally distributed; low inclusion concentrated in two bins driven by low-income countries, particularly sub-Saharan Africa.
- Aggregate relationship with development:
  - Financial inclusion scores closely related to countries’ level of development: low-income countries at lower scores and high-income countries at higher scores.

### Empirical findings on inequality and income inequality
- Main empirical result:
  - Inequality in access to financial services is positively and significantly related to income inequality.
  - It is the degree of inequality of access — rather than the level of access — that is associated with income inequality.
  - Gender differences in financial access explain a substantial share of overall inequality in financial inclusion (decomposition shows up to 30 percent driven by inequality across genders).
- Regression specification summarized:
  - Gini_i = FinInequality_i + Structural_i + Policies_i + ε_i
    - Gini_i: World Bank’s Gini coefficient (four-year averages 2010-13 used).
    - FinInequality_i: overall inequality in financial access (expected positive).
    - Structural_i: log real GDP per capita, share of agriculture in GDP, etc.
    - Policies_i: openness to trade, inflation, rural electricity access, average years of schooling (and squared), gender inequality index, financial development.
  - Estimation method: ordinary least squares.

### Selected regression coefficients and model statistics (Table 2, selected)
- Dependent Variable: Gini Coefficient (WDI)
- Inequality in financial access:
  - Column (1): 0.324*** (0.069)
  - Column (2): 0.346*** (0.063)
  - Column (3): 0.266*** (0.069)
  - Column (4): 0.271*** (0.071)
- Log real GDP per capita:
  - (1): -0.096 (0.096)
  - (2): -0.080 (0.084)
  - (3): -0.215* (0.116)
  - (4): -0.048 (0.150)
- Share of agriculture in GDP:
  - (1): -0.004*** (0.001)
  - (2): -0.004*** (0.001)
  - (3): -0.004*** (0.001)
  - (4): -0.004*** (0.001)
- Inflation:
  - (1): -0.003*** (0.001)
  - (2): -0.002 (0.002)
  - (3): -0.002 (0.002)
- Human capital:
  - (3): 0.183* (0.106)
  - (4): 0.194* (0.110)
- Human capital squared:
  - (3): -0.041** (0.018)
  - (4): -0.042** (0.019)
- Gender inequality index:
  - (3): 0.237** (0.094)
  - (4): 0.211** (0.094)
- Financial development:
  - (3): 0.066 (0.065)
  - (4): 0.079 (0.065)
- Access to electricity, rural:
  - (4): -0.081 (0.051)
- Constant:
  - (1): 1.014** (0.439)
  - (2): 0.961** (0.381)
  - (3): 1.166** (0.542)
  - (4): 0.393 (0.662)
- Observations:
  - (1): 84
  - (2): 84
  - (3): 76
  - (4): 76
- R-squared:
  - (1): 0.42
  - (2): 0.45
  - (3): 0.61
  - (4): 0.62
- Robust standard errors in parentheses; significance: *** p<0.01, ** p<0.05, * p<0.1

### Robustness checks and additional empirical evidence
- Interaction terms of financial access inequality with income-group dummies: interactions insignificant in most cases, suggesting the link is not significantly different across income groups; exception: using market Gini shows stronger link for low-income countries in some specs.
- Results robust to other inequality measures: market Gini, top 10 and top 20 income percentiles.
- Results robust to inclusion of regional dummies.
- Gender-gap analyses:
  - Including female-to-male financial access ratio: a higher ratio significantly related to lower income inequality (Annex Table 4).
  - Regressing overall inequality on gender gap and including residual plus gender gap: greater gender inequality in financial access strongly associated with higher income inequality beyond other drivers.
- Index sensitivity:
  - Excluding some index components does not significantly alter results; correlations between original index and streamlined indices remain high (correlations reported such as 0.990***, 0.991***, 0.987***, 0.963*** for various exclusions).

### Policy implications and recommendations
- Policies should prioritize broad-based access to a range of financial services across the population rather than focusing solely on raising average levels of financial inclusion.
- Reducing participation costs and barriers that prevent the poor and women from accessing financial services can help reduce income inequality; expanding services primarily for those already included may increase inequality until access widens.
- Reducing the gender gap in financial access would promote greater income equality.
- Addressing non-financial drivers of gender gaps (e.g., labor force participation, education, legal discrimination, social norms) is important because such gaps contribute to gender differences in financial inclusion and hence to income inequality.
- Further research recommended:
  - Better identification of channels through which gender inequality in financial access affects income inequality.
  - Use of individual-level longitudinal data to understand drivers of financial inclusion and exclusion and linkages with other gender gaps.

### Limitations and caveats
- Findex data limitations:
  - Lack of a time dimension limits econometric strategies and controls for endogeneity; individuals are not traceable between waves.
  - No household-level information beyond basic individual characteristics; missing variables include marital status, head of household status, number of dependents.
- Index and CA caveats:
  - Relative rarity of some services treated as higher inclusion may reflect income/ infrastructure differences rather than intrinsic inclusion quality; robustness tests addressed this.
  - CA-based scores are qualitative in nature; interpretation of intermediate score distances depends on metric assumptions.
  - Question selection based on authors’ judgement; multiple combinations tested for robustness.

### Annex highlights
- Annex I: Correspondence Analysis
  - CA provides chi-square distance-based embedding of categorical responses; inertia and SVD used to find principal axes.
  - MCA and JCA described; JCA used to address diagonal-dominance issues in the indicator cross-product matrix.
- Annex II: Country lists
  - Whole sample, Emerging and Developing Markets subset, and Sub-Saharan Africa list provided (country names preserved in the source).
- Annex III: Variable definitions and sources
  - Structural, policy, infrastructure, and financial variables defined; sources include SWIID 5.0, World Bank, Penn World Table 8.0, UNDP, Sahay and others (2015), among others.
- Annex IV: Robustness tables
  - Selected robustness coefficients and model-fit statistics reported (examples include inequality-in-financial-access coefficients 0.271**, 0.210*, 0.331***, 0.556, -0.577, 25.21* across different models; sample sizes and R-sq values as reported).

*Source: wp17236 - 1. Questions used to construct the financial inclusion index (excerpts provided from the IMF PDF).*

### 1. Questions used to construct the financial inclusion index ...................................................10

### wp17236 - 1. Questions used to construct the financial inclusion index ...................................................10

### Major findings and contributions
- Constructs novel indices of financial inclusion from micro-level Findex data to capture both the level and the distribution of financial access in a country.
- Uses representative GALLUP/Findex samples of about 1,000 individuals per country, totaling about 146,000 observations on over 140 countries, 34 of which are from sub-Saharan Africa.
- Uses the 2011 Findex wave for empirical analysis because income inequality data are available with a lag and up to 2013; indices are constructed for both 2011 and 2014.
- Key empirical associations:
  - Inequality in financial access is strongly associated with income inequality (Figure 1; reported R² = 0.2688 for the plotted relationship).
  - The level of financial inclusion (as per the micro-based measure) does not appear to be significantly related to income inequality once controls are included.
  - Unequal financial access both overall and between men and women is significantly and robustly related to greater income inequality at the country level.
- Stylized distributional pattern:
  - Inequality in financial access follows a Kuznets-type relationship: at lower average intensities of financial access, increases in financial inclusion are driven by higher intensity of use by a smaller share of the population, exacerbating inequality. After a turning point, further increases are driven by broader access, lowering inequality in financial inclusion.

### Literature synthesis (selected points preserved from source)
- Finance and inequality:
  - Early theoretical models: financial development can enhance growth and reduce inequality by relaxing information and transaction costs that disproportionately bind the poor (Galor and Zeira 1993; Aghion and Bolton 1997; Galor and Moav 2004).
  - Non-linear/Kuznets-type models: distributional effects of financial development depend on economic development stage (Greenwood and Jovanovic 1990; Townsend and Ueda 2006).
  - Evidence that financial development can disproportionately boost incomes of the poorest quintile and reduce inequality (Beck, Demirguc-Kunt and Levine 2007); sub-Saharan African panel evidence suggests inequality declines with financial sector development (Batuo and others 2010).
  - Mechanisms may be indirect (e.g., via labor market effects) rather than direct access to credit (Beck, Levine and Levkov 2007; Giné and Townsend 2004).
  - Recent work emphasizes financial access/inclusion as a broader concept beyond depth (Dabla Norris and others 2015a; Sahay and others 2015). Dabla Norris and others (2015a) highlight that policies focused on reducing participation costs to increase access can reduce inequality, while relaxing borrowing constraints can initially increase inequality; Sahay and others (2015) document a positive relationship between the gender gap in account holding and income inequality.
- Gender gaps:
  - Systematic gender bias in financial inclusion is well documented (Allen and others 2012; Demirguc-Kunt, Klapper and Singer 2013).
  - Gender inequality in education and economic opportunities reduces growth and increases income inequality, especially in low-income countries (Klasen 1999; Klasen and Lamanna 2009; Amin et al. 2015; Gonzales and others 2015b; Hakura and others 2016; IMF 2015; World Bank 2011).
  - After controlling for observable individual characteristics, gender remains significantly related to usage of financial services in developing countries; legal discrimination and gender norms may explain cross-country variation (Demirguc-Kunt, Klapper and Singer 2013).
- Integration:
  - Inequality in financial access—including gender gaps in financial inclusion—can affect income inequality directly (by enabling economic participation and access to productive tools) and indirectly (by interacting with gender gaps in education, health, and labor force participation).

### Data and measurement insights
- Primary data source: World Bank’s Findex dataset (GALLUP surveys) with representative samples of 1,000 individuals per country; two waves available to date: 2011 and 2014.
- Findex advantages:
  - Individual-level focus permits construction of a synthetic, micro-based measure of financial inclusion that captures both access and intensity of use across a broad range of financial services.
  - Allows derivation of Gini coefficients of inequality of financial access from microdata (Box 1: Deriving a Gini-Index of Financial Access; correspondence-analysis-based components shown in Figures).
- Complementarity:
  - Findex complements supply-side datasets (IMF Financial Access Survey, World Bank Enterprise Surveys) by focusing on individuals rather than institutions or aggregate depth measures.

### Policy-relevant implications (derived from analysis in the content)
- Policies should target more equal access to a broad range of financial services across the population rather than focusing solely on raising average levels of financial inclusion.
- Reducing participation costs and barriers that prevent the poor and women from accessing financial services can help reduce income inequality; conversely, policies that primarily deepen access for those already included may increase inequality until broader access is achieved.
- Addressing non-financial drivers of gender gaps (e.g., labor force participation, education, legal discrimination, social norms) is important because such gaps contribute to gender differences in financial inclusion and hence to income inequality.

*Source: wp17236 - 1. Questions used to construct the financial inclusion index (excerpts provided from the IMF PDF).*

### 21.      Notwithstanding the advantages of the Findex data, they have some limitations.

### 21. Notwithstanding the advantages of the Findex data, they have some limitations.

### Limitations of the Findex data
- Lack of a time dimension limits possible econometric methodologies, plausible controls for endogeneity, and analysis of how financial inclusion changes over time and how these changes affect macroeconomic outcomes.
- Individuals are not traceable between different Findex waves.
- No household-level information beyond basic individual characteristics (age, gender, education, income and formal employment status). Missing household variables include marital status, whether the person surveyed is head of household, and number of dependents—information that would enable more in-depth analysis of drivers and impacts of financial inclusion worldwide.

### Constructing a Novel Index of Financial Inclusion
- Micro-level Findex information used to construct country-aggregates of financial inclusion for the 2011 and 2014 Findex waves.
- Individual-level scores constructed using correspondence analysis (the principal component analysis equivalent for categorical data).
- Selection criteria for questions entering the index:
  - (i) be directly related to financial access, and
  - (ii) not include information on individuals’ personal characteristics or environment to avoid biasing empirical estimations.
- Selected questions capture access to and use of formal financial services.
- 2011 Financial Inclusion Index: 8 questions related to access to financial infrastructure and use of financial services.
  - Questions included: Q1 Has an account at a financial institution/post office/MFI; Q3a If has a debit card; Q3b If has a credit card; Q8b If has an account, uses electronic payments; Q13a Saved at financial institution in the last 12 months; Q14a Borrowed from financial institution in the last 12 months; Q15a-Q15b Has loan from financial institution for home purchase or construction; Q15a1a-Q15a1b Q15a1c Has used mobile phone to pay bills, send money or receive money.
  - Possible responses: Yes/No/missing.
- 2014 Financial Inclusion Index: 12 questions plus a question on general accessibility to financing (availability of emergency funds).
  - Questions included: Q1 Has an account; Q3 If has a debit card, card is in own name; Q4 If has a debit card, used card in the last 12 months; Q6 If has a credit card, used card in the last 12 months; Q9 If has an account, made deposit into account in the last 12 months; Q11 If has an account, made withdrawal in the last 12 months; Q14 If has an account, made transaction with mobile phone; Q16 Made Internet Payments; Q18a Saved at financial institution in the last 12 months; Q20 Borrowed from financial institution in the last 12 months; Q21a Has loan from financial institution for house, apartment, or land; Q24 Possibility of coming up with emergency funds.
  - Possible responses: Yes/No/missing, except Q24: Very possible/Somewhat Possible/Not very possible/Not at all possible/missing.
  - Note: Modified Q24 responses—“Very possible” and “Somewhat Possible” combined as “Very or somewhat possible”; “Not very possible” and “Not at all possible” combined as “Not very or at all possible”.
- Charts and analysis presented for the 2014 index; charts using the 2011 index are qualitatively similar.
- Correspondence analysis interpretation:
  - Outputs similar to Principal Component Analysis but charts display chi-square distances; distances between points describe qualitative differences.
  - Origin is the “center of gravity” representing the “average” response; main axis is the horizontal axis.
  - Responses indicating having financial access are on the right half of the plane; “Missing” and “no” answers cluster on the left-hand side.
  - Having a credit/debit card appears on the far right of the x-axis because (1) relatively few individuals have them and (2) those who answered “Yes” also answered their entire questionnaire quite differently from the “average”.
  - A “Yes” response to “Do you have access to emergency funds?” appears between the origin and having access to credit cards.
  - The principal horizontal axis helps explain about 90 percent of the variation in the data.
  - The second principal axis (vertical) explains an additional 5 percent of the variation and is therefore not relevant for the analysis.
- Interpretation of individual inclusion scores:
  - Individual’s inclusion score defined as approximately the sum of the x-axis positions of the responses in the correspondence analysis.
  - Higher inclusion score indicates access to more services and access to rarer services than those in the “center”.
  - Co-occurrence implies proximity: responses often answered together appear close; different response options from the same question cannot appear together for an individual.

### Distributional Patterns and Relationship with Development
- Distribution of individual scores:
  - Highly skewed towards low-level scores.
  - Country-level scores are highly scattered across countries’ income groups.
  - Figure 4 (2014 index) shows higher value bins represent higher financial inclusion; intensity of financial inclusion relatively equally distributed at higher levels, but concentrated in two bins on the low inclusion side—mainly driven by low-income countries, particularly sub-Saharan African ones.
  - The distribution for the 2011 index shows a similarly skewed picture.
- Aggregate relationship with development:
  - Financial inclusion scores closely related to countries’ level of development.
  - Figure 5 shows clustering of countries’ financial inclusion level by income level: low-income countries at lower scores and high-income countries at higher scores.

### Assumptions and Caveats
- Relatively rarer services implicitly assumed to indicate “higher” levels of financial inclusion; this may not be the case because higher technology services may correlate with higher average income, infrastructure, and capital. Robustness tests including/excluding such questions yielded broadly similar results.
- The origin is defined as the location in the point-cloud centered by the normalized column totals; a synthetic dataset could produce a different center corresponding to a different set of “average” responses.
- Extreme points in the dataset correspond to answering “Yes” or “No” to all questions; alternative datasets could alter extremity of least/most inclusive scores.
- Input and output are qualitative, making quantitative interpretation of differences in “degree of inclusion” difficult. An individual with a score of 1 (all services) unambiguously has access to more services than one with a score of 0 (no services), but comparing distances between intermediate values depends on acceptance of assumptions imposed by the chi-square metric and other caveats.
- Selection of questions based on authors’ judgement; many combinations tested for robustness with broadly similar results. Several “rarer” responses were included to increase index resolution.

### Constructing an Index of Inequality in Financial Access
- Inequality measure derived from the standard Gini-coefficient calculation using individual financial access scores from Global Findex 2011 survey data.
- Procedure covers covariance-based expressions for the generalized Gini; concentration coefficients convenient for calculations from unit-record data.
- Figure 6 shows inequality in financial access varies strongly across countries (darker shades and higher Gini depict higher inequality).
- Box 1: Deriving a Gini-Index of Financial Access (formulas and methodology preserved)
  - GINI(X) = −2 Cov( X / μ(X), (1 − F(X)) )
    - Where X is a random variable with mean μ(X) and F(X) is its cumulative distribution function.
  - CONC(X,Y) = −2 Cov( X / μ(X), (1 − G(Y)) )
    - Where G(Y) is the cumulative distribution function of Y; CONC(X,Y) reflects concentration of X on observations with high ranks in Y.
  - Generalized Gini (S-Gini) as covariance:
    - GINI(X; v) = −v Cov( X / μ(X), (1 − F(X))^(v−1) )
    - Where v is a parameter tuning degree of ‘aversion to inequality’. The standard Gini corresponds to v = 2.
  - Fractional ranks calculation for sample { (yi, wi) }:
    - Denote distinct values y1* < y2* < ... < yK* and weighted proportions πk* = ( Σ wi 1(yi = yk*) ) / ( Σ wi ).
    - Fractional rank for yk*: Fk* = Σ_{j=0}^{k−1} πj* + 0.5 πk*, with π0* = 0.
    - Each observation associated with fractional rank Fk* = Σ Fk* 1(yi = yk*)_{k=1}^K.
    - Resulting Gini estimate independent of sample/population size when plugging { (Fi, yi, wi) } into standard sample covariance formula.

### Empirical Patterns of Inequality
- Inequality in financial access follows a Kuznets-type relationship:
  - At lower levels of average financial inclusion, increases in average scores appear mainly driven by a smaller group intensifying use of financial services; inequality increases.
  - At later stages, after a turning point, increases in average scores are mainly driven by additional people joining the financial system; extensity increases and inequality decreases.
- Gender contribution:
  - Gender inequality in financial inclusion explains a substantial share of overall inequality in financial inclusion.
  - Decomposition shows up to 30 percent of inequality in financial access is driven by inequality across genders.
  - Decomposition components (Equation 1):
    - G = Gw + Gnb + Gt
      - Gw is the Within component (inequality among males + inequality among females).
      - Gnb is the net between component capturing contribution of gender inequality.
      - Gt represents the transvariation contribution.

### Testing the Link Between Inequality in Financial Access and Income Inequality — Specification
- Regression specification (equation (2)):
  - Gini_i = FinInequality_i + Structural_i + Policies_i + ε_i
    - Gini_i: World Bank’s Gini coefficient of income inequality in country i (World Bank Development Indicators 2016). Four-year averages (2010-13) used due to data scarcity. Other inequality measures used in robustness checks (top income levels, market Gini).
    - FinInequality_i: measure of overall inequality in financial access; expected positive association with income inequality. Interaction with income-level indicators to test differentiated effects by development level.
    - Structural_i: structural country characteristics (log of income per capita, share of agricultural production in total production). Share of agricultural output expected negatively associated with income inequality. Robustness checks include share of rural population and growth in dependency ratios.
    - Policies_i: country-level policies (openness to trade, quality of macroeconomic management proxied by inflation, level of infrastructure measured by percent of rural population with access to electricity). Expected negative associations with income inequality. Average years of schooling included with squared term to capture non-linear effect. Aggregate measure of gender inequality included (expected positive association with income inequality). Financial sector development may be positively associated with income inequality if credit is concentrated and financial inclusion lags financial deepening.
- Estimation method: ordinary least squares.

*Source: Global Findex, and authors’ calculations (from the supplied content).*

### 32.      Inequality in financial access.

### 32.      Inequality in financial access.

### Major empirical findings
- Inequality in access to financial services is positively and significantly related to income inequality.
- It is the degree of inequality—instead of the level—of access to financial services that is related with income inequality (the level of financial inclusion does not enter the specification significantly).
- A significant share of inequality in financial access is driven by gender differences in financial access.

### Table 2: Factors associated with income inequality (selected coefficients)
- Dependent Variable: Gini Coefficient (WDI)
- Inequality in financial access:
  - Column (1): 0.324*** (0.069)
  - Column (2): 0.346*** (0.063)
  - Column (3): 0.266*** (0.069)
  - Column (4): 0.271*** (0.071)
- Log real GDP per capita:
  - (1): -0.096 (0.096)
  - (2): -0.080 (0.084)
  - (3): -0.215* (0.116)
  - (4): -0.048 (0.150)
- Log real GDP per capita squared:
  - (1): 0.002 (0.005)
  - (2): 0.001 (0.005)
  - (3): 0.010 (0.006)
  - (4): 0.001 (0.008)
- Share of agriculture in GDP:
  - (1): -0.004*** (0.001)
  - (2): -0.004*** (0.001)
  - (3): -0.004*** (0.001)
  - (4): -0.004*** (0.001)
- Openness to trade:
  - (1): -0.000* (0.000)
  - (2): -0.000 (0.000)
  - (3): -0.000 (0.000)
  - (4): -0.000 (0.000)
- Inflation:
  - (1): -0.003*** (0.001)
  - (2): -0.002 (0.002)
  - (3): -0.002 (0.002)
- Human capital:
  - (3): 0.183* (0.106)
  - (4): 0.194* (0.110)
- Human capital squared:
  - (3): -0.041** (0.018)
  - (4): -0.042** (0.019)
- Gender inequality index:
  - (3): 0.237** (0.094)
  - (4): 0.211** (0.094)
- Financial development:
  - (3): 0.066 (0.065)
  - (4): 0.079 (0.065)
- Access to electricity, rural:
  - (4): -0.081 (0.051)
- Constant:
  - (1): 1.014** (0.439)
  - (2): 0.961** (0.381)
  - (3): 1.166** (0.542)
  - (4): 0.393 (0.662)
- Observations:
  - (1): 84
  - (2): 84
  - (3): 76
  - (4): 76
- R-squared:
  - (1): 0.42
  - (2): 0.45
  - (3): 0.61
  - (4): 0.62
- Robust standard errors in parentheses
- Significance: *** p<0.01, ** p<0.05, * p<0.1

### Other determinants (signs and significance)
- Higher share of agriculture in GDP is associated with lower income inequality (negative and significant).
- Higher human capital levels are associated with lower income inequality when human capital levels reached a critical size (human capital positive and human capital squared negative and significant in some specifications).
- Higher levels of overall gender inequality are positively related to income inequality (gender inequality index positive and significant in columns 3–4).
- Better macroeconomic management, proxied by the inflation rate, is associated with lower levels of income inequality (inflation negative and significant in column 1).
- Other variables—openness to trade, access to electricity, financial development—enter with expected signs but are not significant at standard levels in many specifications.

### Robustness checks (summary)
- Inclusion of interaction terms of financial access inequality with low-income, middle-income, and high-income dummies: insignificant interactions in most cases, suggesting the link between financial access inequality and income inequality is not significantly different across income groups (columns 1–3). Exception: when using the market Gini instead of the World Bank Gini, the link appears stronger for low-income countries (column 4).
- Results robust to using other inequality measures: market Gini, top 10 and top 20 income percentiles.
- Results robust to inclusion of regional dummies.
- Gender gaps in access to finance:
  - Including the ratio of female-to-male financial access directly: a higher ratio is significantly related to lower income inequality (Annex Table 4, columns 1–2).
  - To isolate gender effects, overall inequality in financial access was regressed on the gender gap and the residual included jointly with the gender gap: greater gender inequality in financial access is strongly associated with higher income inequality beyond other drivers (Annex Table 4, columns 3–4).
- Testing exclusion of some index components: excluding certain components does not significantly alter the index; correlations between the original index and streamlined indices are below 0.95 (Annex Table 5).
- Results robust to including other regressors such as the share of the rural population or the level of the financial access index.

### Conclusions and policy recommendations
- The study finds a particularly important role for inequality in access to financial services in explaining income inequality, with a significant share of that inequality driven by gender differences in financial access.
- The association is stronger for the distribution of financial access across the population than for the overall level of financial development or overall financial inclusion.
- Policy implications:
  - Policies that foster broad-based access to a range of financial services across the population would promote greater income equality.
  - Policies aiming at reducing the gender gap in financial access would also promote greater income equality.
- Further research needed:
  - More work is required to better understand channels through which gender inequality in financial access affects income inequality.
  - Going back to individual-level data would help understand drivers of financial inclusion and exclusion, and linkages between gender gaps in financial inclusion and other gender gaps (education, labor force participation).
  - Authors indicate plans to address some questions in further research (Deléchat and others, forthcoming).

*Source: wp17236 - 32.      Inequality in financial access.*

### Annex I: Correspondence Analysis

### Annex I: Correspondence Analysis

### Motivation and context
- Categorical variables often lack comparable scale and distance properties across different question types (e.g., multi-choice vs. binary responses).
- Correspondence Analysis (CA) gives nominal variables a notion of distance, enabling simultaneous, agnostic treatment of multiple categorical variables via Singular Value Decomposition (SVD).
- CA is established in biometrics, psychometrics, marketing, ecology, and computational sciences.
- The paper utilized Joint Correspondence Analysis (JCA), a variant of CA, for robustness (results broadly similar to Multiple Correspondence Analysis (MCA)).

### Simple Correspondence Analysis — conceptual steps
- Start from a contingency table cross-tabulating responses (example: two questions each with three responses: “yes”, “no”, and “missing”).
- Notation from the example contingency table:
  - n_rc is the number of respondents who made response r and c.
  - n_r+ and n_+c are the row and column sums, respectively.
  - n_++ is the grand total.
- Chi-squared distance between two columns c and c′:
  - d_{χ^2}(c,c′) = sqrt( sum_{r=1}^R n_{++}/n_{r+} ( n_{rc}/n_{+c} − n_{rc′}/n_{+c′} )^2 ).
- Chi-squared distance of a response c to the “average” response c*:
  - d_{χ^2}^2(c,c*) = sum_{r=1}^R n_{++}/n_{r+} ( n_{rc}/n_{+c} − n_{r+}/n_{++} )^2 .
- Inertia (weighted total deviation from center):
  - Inertia = sum_{c=1}^J ( n_{+c}/n_{++} ) d_{χ^2}^2(c,c*), where J is the number of columns.
- Interpretation:
  - If rows and columns are independent, all column points coincide and the data cloud is a single point.
  - Analogous to PCA, CA finds a lower-dimensional subspace that maximizes total inertia; SVD is applied to get a rank K ≤ min(M−1, N−1) approximation.

### Multiple Correspondence Analysis (MCA) and Joint Correspondence Analysis (JCA)
- Construct a complete disjunctive N x Q indicator matrix Z (N individuals, Q question-response categories); entries 1 if that response chosen, 0 otherwise.
- Cross-product B = Z^T Z produces a Q x Q matrix of pairwise cross-tabulations across all possible responses.
- B is centered and standardized (using marginal totals) to obtain S; S is then analyzed via the CA algorithm.
- MCA issue: diagonals of B (self-cross-tabulations) can unduly influence inertia measures.
- JCA addresses the diagonal problem by iteratively fitting using only the off-diagonal values of B.
- This paper tested both MCA and JCA; JCA was ultimately used for robustness.

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### Annex II: List of Countries Included in the Sample

- Whole Sample includes: Albania, Algeria, Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahrain, Bangladesh, Belarus, Belgium, Benin, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Chad, Chile, China, Colombia, Congo, Dem. Rep., Congo, Rep., Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, Dominican Republic, Ecuador, Egypt, Arab Rep., El Salvador, Estonia, Finland, France, Gabon, Georgia, Germany, Ghana, Greece, Guatemala, Guinea, Haiti, Honduras, Hong Kong, SAR, China, Hungary, India, Indonesia, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Korea, Rep., Kuwait, Kyrgyz Republic, Latvia, Lebanon, Lithuania, Luxembourg, Macedonia, FYR, Madagascar, Malawi, Malaysia, Mali, Malta, Mauritania, Mauritius, Mexico, Moldova, Mongolia, Montenegro, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Pakistan, Panama, Peru, Philippines, Poland, Portugal, Romania, Russian Federation, Rwanda, Saudi Arabia, Senegal, Serbia, Sierra Leone, Singapore, Slovak Republic, Slovenia, South Africa, Spain, Sri Lanka, Sudan, Sweden, Tajikistan, Tanzania, Thailand, Togo, Turkey, Turkmenistan, Uganda, Ukraine, United Arab Emirates, United Kingdom, United States, Uruguay, Uzbekistan, Venezuela, RB, Vietnam, Yemen, Rep., Zambia, Zimbabwe.

- Emerging and Developing Markets list (subset): Albania, Algeria, Angola, Argentina, Armenia, Azerbaijan, Bahrain, Bangladesh, Belarus, Benin, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Chad, Chile, China, Colombia, Congo, Dem. Rep., Congo, Rep., Costa Rica, Croatia, Dominican Republic, Ecuador, Egypt, Arab Rep., El Salvador, Gabon, Georgia, Ghana, Guatemala, Guinea, Haiti, Honduras, Hungary, India, Indonesia, Iraq, Jamaica, Jordan, Kazakhstan, Kenya, Kuwait, Kyrgyz Republic, Lebanon, Macedonia, FYR, Madagascar, Malawi, Malaysia, Mali, Mauritania, Mauritius, Mexico, Moldova, Mongolia, Montenegro, Nepal, Nicaragua, Niger, Nigeria, Pakistan, Panama, Peru, Philippines, Poland, Romania, Russian Federation, Rwanda, Saudi Arabia, Senegal, Serbia, Sierra Leone, South Africa, Sri Lanka, Sudan, Tajikistan, Tanzania, Thailand, Togo, Turkey, Turkmenistan, Uganda, Ukraine, United Arab Emirates, Uruguay, Uzbekistan, Venezuela, RB, Vietnam, Yemen, Rep., Zambia, Zimbabwe.

- Sub-Saharan Africa list: Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Chad, Congo, Dem. Rep., Congo, Rep., Gabon, Ghana, Guinea, Kenya, Madagascar, Malawi, Mali, Mauritius, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zambia, Zimbabwe.

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### Annex III: List of Variables (selected definitions and sources)

- Structural Characteristics
  - Gini coefficient: Net inequality, source SWIID 5.0.
  - World Bank Gini coefficient: WB Gini coefficient, source World Bank.
  - Log of real GDP per capita: Log of real GDP divided by population, source Penn World Table 8.0.
  - Agriculture to GDP: Agriculture, value added (% of GDP), source World Bank.

- Policies
  - Trade to GDP: Sum of import and exports as share of GDP, source World Bank.
  - GII: Gender Inequality Index, source UNDP and Gonzales and others (2015b).
  - Government consumption expenditure to GDP: General government final consumption expenditure (% of GDP), source World Bank.
  - ICRG composite risk rating: International Country Risk Guide Composite Political, Financial, Economic Risk Rating (CPFER) = 0.5 ((Political Risk + Financial Risk + Economic Risk) Ranging from Very High Risk (00.0 - 49.5) to Very Low Risk (80.0 - 100). The higher the points, the lower the risk.

- Infrastructure
  - Electricity access: Access to electricity (% of population), source World Bank.
  - Rural electricity access: Access to rural electricity (% of rural population), source World Bank.

- Financial variables
  - Intensity of financial inclusion within country: Correspondence-analysis constructed index of financial inclusion, covering 12 dimensions of financial inclusion; IMF staff calculation from World Bank Findex 2014 dataset.
  - Inequality of financial access: Within-country gini-coefficient of the intensity of financial inclusion; IMF staff calculation from the calculated individual financial inclusion scores using World Bank Findex 2014 dataset.
  - Financial Development: Financial Development Index covering financial markets and institutions in their depth, access and efficiency; source Sahay and others (2015).

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### Annex IV: Robustness Checks — Key empirical results (selected coefficients and model statistics)

- Table 1. Testing the Link Between Inequality in Financial Access and Income Inequality, by Income Group
  - Inequality in financial access coefficients (models 1–6): 0.271**, 0.210*, 0.331***, 0.556, -0.577, 25.21*.
  - Interaction terms and dummies (selected):
    - *low-income: 0.01755, 52.59* (appear with model-specific coef/SE).
    - *middle-income: 0.07658.881 (as shown).
    - *high-income: -0.209, -32.95 (as shown).
  - Structural/controls (selected coefficients and signs as reported):
    - Log real GDP per capita: -0.312, -0.0999, -0.0598, -18.94, 17.67, 3.879.
    - Log real GDP per capita squared: 0.0139, 0.00231, -0.000405, 0.878, -1.19, -0.552.
    - Share of agriculture in GDP: -0.00388*, -0.00452**, -0.00378*, -0.480*, -0.491**, -0.390**.
    - Gender inequality index: 0.189, 0.228, 0.319*; 2.826, 14.77, 9.42 in other specifications.
    - Financial development: 0.0713, 0.0875, 0.108; 6.411, 12.7, 14.57 in market-Gini specifications.
  - Sample size and fit:
    - N = 76 (models as listed).
    - R-sq: 0.631, 0.63, 0.648, 0.350, 0.44, 0.489.
    - adj. R-sq: 0.553, 0.553, 0.575, 0.20, 0.31, 0.37.

- Table 2. Different Measures of Income Inequality (selected)
  - Inequality in financial access (columns): 0.556, -0.577, 25.21*, 15.45*, 17.12* (for Market Gini and top-share measures).
  - Selected control coefficients (as reported):
    - Share of agriculture in GDP: -0.480*, -0.491**, -0.390**, -0.295*, -0.344*.
    - Inflation: -0.293*, -0.172, -0.182, -0.167, -0.164.
    - Gender inequality index: 2.826, 14.77, 19.42, 23.18**, 24.76**.
  - Sample sizes and fit:
    - N = 70 (Market Gini specs), N = 59 (top-share specs).
    - R-sq: 0.35, 0.44, 0.489, 0.674, 0.681.

- Table 3. Regional Dummies (selected)
  - Inequality in financial access coefficients across regional specifications: 0.252***, 0.256***, 0.177*, 0.253***, 0.160*.
  - Regional dummies (selected significance):
    - Sub-Saharan Africa: 0.0326, 0.0942*.
    - Middle East and North Africa: -0.176***, -0.0812**.
    - Latin America and the Caribbean: 0.103***, 0.128***.
    - Euro Area: 0.00079, 0.00369.
  - Selected controls:
    - Share of agriculture in GDP: -0.00375*, -0.00440**, -0.00367*, -0.00432**, -0.00188.
    - Financial development: 0.0831, 0.119*, 0.141**, 0.0752, 0.201***.
  - Sample size and fit:
    - N = 76 for all specifications.
    - R-sq: 0.633, 0.674, 0.732, 0.625, 0.802.
    - adj. R-sq: 0.563, 0.611, 0.681, 0.554, 0.753.

- Table 5. Correlations between Different Indices of Financial Access Inequality
  - Correlation matrix entries (selected):
    - Main index with Excluding debit card: 0.990***.
    - Main index with Excluding credit card: 0.991***.
    - Main index with Excluding home loan: 0.987***.
    - Main index with Excluding debit card, credit card and home loan: 0.963***.
    - Excluding debit card with Excluding credit card: 0.977***.
    - Excluding debit card with Excluding home loan: 0.966***.
    - Excluding credit card with Excluding home loan: 0.976***.
    - Robust standard errors and significance codes: *** p<0.01, ** p<0.05, * p<0.1.

- Table 4 and additional correlations and robustness specifications are reported in the annex tables with standard errors in parentheses and significance indicators as shown.

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*Source: wp17236 - Annex I: Correspondence Analysis (IMF Working Paper pdf content provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17236.pdf_