## _wp13139

## Source details

**Canonical URL:** [_wp13139](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13139.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13139.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13139.pdf.json)

---

### I. INTRODUCTION AND BACKGROUND
- Core premise: Income inequality has roots in unequal opportunities; access to education and health care is critical for participation in growth and avoiding economic hardship.
- Context elevating inequities as central policy issue: the 2008–09 financial crisis, high unemployment, the Arab spring, and sustained growth in low-income countries combined with still high poverty rates.
- Literature and prior findings summarized:
  - Growth–poverty and distributional impact studies (Fosu, 2011).
  - Benefit incidence analyses of health and education expenditure (Gaddah and Munro, 2011; Kamgnia, 2008).
  - Labor market and jobs gap (Leigh and Flores, 2012).
  - Fiscal expenditure allocations (Clements, Gupta, and Nozaki, 2011).
  - Berg and Ostry (2011): chronic income inequality detrimental to growth; more equal countries likely experience durable growth spells.
  - Garcia-Verdu, Selasse, and Thomas (2011): household survey approach for six SSA countries — poorest quartile saw substantial annual household per capita consumption growth in three of four high-growth countries (Ghana, Tanzania, Uganda); low-growth countries had low or negative changes (Cameroon low, Zambia negative); Mozambique results depend on deflator choice (CPI or regional price indices).
- Contribution of this paper:
  - Uses the social opportunity function to assess inclusiveness of growth by focusing on access to education and health.
  - Constructs opportunity curves over time; an outward parallel shift implies inclusive growth (increased average opportunities and increased opportunities available to the poor).
  - Applies framework to Cameroon, Ghana, Mozambique, Tanzania, Zambia and complements with growth incidence curves and an equity index of opportunity.
- High-level empirical summary:
  - Periods of growth coincide with periods of increased access — corroborates Garcia-Verdu, Selasse, and Thomas (2011).
  - Average access and distribution of education and health increased across all examined countries over time.

### II. CONCEPTUAL FRAMEWORK: THE INCLUSIVE GROWTH CONCEPT AND THE SOCIAL OPPORTUNITY FUNCTION
- Inclusive growth: ensuring economic opportunities created by growth are available to all, particularly the poor (in line with Ali and Zhuang, 2007); rapid, sustainable growth must be equitable for poverty reduction (Stuart, 2011).
- Social opportunity function framework (preserve notation and expressions):
  - Social welfare: W = W(x1, x2, ..., xn)  (equation 1.1).
  - Social opportunity function: O = O(y1, y2, ..., yn)  (equation 1.2), where yi captures opportunity of ith person.
  - Opportunity curve and average opportunity Y*(p):
    - PN(p) = Σ_i y_i / pN  (equation 1.3); with binary yi, average opportunity Y*(p) equals percentage of population with access.
  - Transfer principle: transfers from non-poor to relatively poor improve social opportunity function (inequality condition presented as equation (1.4) in source).
  - Opportunity curve classification:
    - dY*(p)/dp > 0 for 0<p<1 → upward sloping opportunity curve → not pro-poor.
    - dY*(p)/dp < 0 for 0<p<1 → downward sloping → pro-poor.
    - dY*(p)/dp = 0 for 0<p<1 → perfect equity.
  - Opportunity index (AO):
    - AO = ∫_0^p Y*(p) dp = Σ_i y_i / pN  (equation 1.5). Higher AO → greater opportunities available.
  - Equity index of opportunity (EI):
    - EI(p) = AO(p) / Y*(p)  (equation 1.6).
      - EI > 1 → downward sloping → pro-poor.
      - EI = 1 → perfect equity.
      - EI < 1 → upward sloping → not pro-poor.
  - Relationship and dynamics:
    - AO(p) = EI(p) * Y*(p)  (equation 1.7).
    - Total differential: dAO(p) = EI * dY*(p) + Y*(p) * dEI  (equation 1.8).
    - Growth becomes more inclusive if dAO(p) > 0; contributions arise from increases in average opportunities and/or improvements in equity.

### III. KEY STYLIZED FACTS ON THE EDUCATION AND HEALTH SECTORS IN SELECTED AFRICAN COUNTRIES
- Purpose: contextual background for empirical application; not a policy causality evaluation.
- Country highlights and selected numeric indicators (exact values preserved):

  - A. Cameroon (Table 1 highlights)
    - Primary education free since 2000; gross primary enrollment moved from 74.7 (1996) to 119.8 (2010).
    - School enrollment, primary (% gross): 74.7 (1996), 87.5 (2000), 109.1 (2005), 109.4 (2006), 112.8 (2007), 119.8 (2010).
    - School enrollment, primary (% net): n.a. (1996–2007), 92.4 (2010).
    - School enrollment, secondary (% gross): n.a. (1996), 27.7 (2000), 27.8 (2005), 24.3 (2006), n.a. (2007), 42.2 (2010).
    - Literacy rate, adult total (% ages 15+): n.a. (1996), 68.4 (2000), n.a., n.a., 70.7 (2007), n.a. (2010).
    - Primary completion rate, total (% relevant age group): n.a. (1996), 51.0 (2000), 52.9 (2005), 52.9 (2006), 57.1 (2007), 78.7 (2010).
    - Pupil-teacher ratio, primary: n.a. (1996), 51.9 (2000), 47.8 (2005), 44.7 (2006), 44.4 (2007), 45.5 (2010).
    - Mortality rate, under-5 (per 1,000): 148.1 (1996), 147.5 (2000), 142.1 (2005), 141.0 (2006), 139.9 (2007), 136.2 (2010).
    - Life expectancy at birth, total (years): 51.6 (1996), 50.1 (2000), 49.4 (2005), 49.6 (2006), 49.8 (2007), 51.1 (2010).

  - B. Ghana (Table 2 highlights)
    - Capitation grant since early 2005; gross primary enrollment: 77.6 (1991) to 107.3 (2011).
    - School enrollment, primary (% gross): 77.6 (1991), 80.6 (1997), 80.5 (1999), 90.3 (2005), 106.3 (2009), 107.3 (2011).
    - School enrollment, primary (% net): n.a. (1991–1999), 60.7 (1999), 66.5 (2005), 76.7 (2009), 84.0 (2011).
    - School enrollment, secondary (% gross): n.a. (1991), 27.7 (1997), 40.2 (1999), 47.2 (2005), 59.1 (2009), 58.1 (2011).
    - Primary completion rate, total (% relevant age group): 63.7 (1991), n.a. (1997), 68.0 (1999), 74.6 (2005), 86.7 (2009), 94.0 (2011).
    - Pupil-teacher ratio, primary: 29.1 (1991), n.a., 29.6 (1999), 32.8 (2005), 33.1 (2009), 31.0 (2011).
    - Mortality rate, under-5 (per 1,000): 118.5 (1991), 107.0 (1997), 101.8 (1999), 86.0 (2005), 76.6 (2009), n.a. (2011).
    - Life expectancy at birth, total (years): 57.3 (1991), 58.0 (1997), 58.1 (1999), 61.0 (2005), 63.4 (2009), n.a. (2011).

  - C. Mozambique (Table 3 highlights)
    - Strategic education plans and rapid expansion; gross primary enrollment: 66.2 (1995) to 114.2 (2009).
    - School enrollment, primary (% gross): 66.2 (1995), n.a. (1996), 69.1 (1999), 84.1 (2002), 114.1 (2008), 114.2 (2009).
    - School enrollment, primary (% net): 43.8 (1995), n.a., 52.0 (1999), 56.4 (2002), 89.2 (2008), 90.4 (2009).
    - School enrollment, secondary (% gross): 7.3 (1995), n.a., 5.2 (1999), 8.4 (2002), 20.5 (2008), 23.3 (2009).
    - Literacy rate, adult total (% ages 15+): n.a. (1995–2008), 55.0 (2009).
    - Primary completion rate, total (% relevant age group): source text notes increase from 26 percent in 1995 to 56 percent in 2009 (table entries ambiguous).
    - Pupil-teacher ratio, primary: 57.6 (1995), n.a., 61.5 (1999), 67.2 (2002), 64.0 (2008), 61.3 (2009).
    - Mortality rate, under-5 (per 1,000): 195.0 (1995), 191.0 (1996), 180.0 (1999), 169.0 (2002), 144.8 (2008), 139.6 (2009).
    - Life expectancy at birth, total (years): 45.4 (1995), 45.9 (1996), 47.0 (1999), 47.0 (2002), 48.9 (2008), 49.3 (2009).

  - D. Tanzania (Table 4 highlights)
    - PEDP abolished fees; gross primary enrollment: 68.2 (1995) to 102.3 (2010).
    - School enrollment, primary (% gross): 68.2 (1995), 68.3 (2000), 105.4 (2005), 111.4 (2008), 105.8 (2009), 102.3 (2010).
    - School enrollment, primary (% net): 48.7 (1995), 53.1 (2000), 90.8 (2005), 98.0 (2008), n.a. (2009–2010).
    - Primary completion rate, total (% relevant age group): n.a. (1995), n.a., 55.3 (1999), n.a., 102.9 (2008), 98.9 (2009).
    - Pupil-teacher ratio, primary: 36.8 (1995), 41.4 (2000), 55.9 (2005), 52.4 (2008), 53.7 (2009), 50.8 (2010).
    - Mortality rate, under-5 (per 1,000): 154.6 (1995), 130.2 (2000), 102.8 (2005), 85.4 (2008), 80.4 (2009), 92.4 (2010).
    - Life expectancy at birth, total (years): 49.6 (1995), 50.4 (2000), 53.3 (2005), 55.8 (2008), 56.6 (2009), 57.4 (2010).

  - E. Zambia (Table 5 highlights)
    - Fees eliminated for grades 1–7; gross primary enrollment: 96.6 (1990) to 115.3 (2010).
    - School enrollment, primary (% gross): 96.6 (1990), 90.8 (1994), 83.7 (1999), 107.1 (2004), 122.0 (2008), 115.3 (2010).
    - School enrollment, primary (% net): n.a. (1990), 76.9 (1994), 70.5 (1999), 86.5 (2004), 97.6 (2008), 91.4 (2010).
    - Primary completion rate, total (% relevant age group): 65.2 (1990), 74.5 (1994), 99.6 (1999), 96.5 (2004), 103.2 (2008), 103.25 (2010).
    - Pupil-teacher ratio, primary: 44.0 (1990), n.a., 60.9 (1999), 62.4 (2004), 60.5 (2008), 58.0 (2010).
    - Mortality rate, under-5 (per 1,000): 182.8 (1990), 180.7 (1994), 161.3 (1999), 142.4 (2004), 121.8 (2008), 111.0 (2010).
    - Life expectancy at birth, total (years): 47.5 (1990), 44.1 (1994), 42.0 (1999), 43.6 (2004), 47.1 (2008), 48.5 (2010).

### IV. APPLICATION OF SOCIAL OPPORTUNITY FUNCTION TO SELECTED AFRICAN COUNTRIES
- A. Household surveys and data
  - Countries and survey years:
    - Cameroon: 1996, 2001, 2007.
    - Ghana: 1991, 1998, 2005.
    - Mozambique: 1996, 2002, 2008.
    - Tanzania: 2000, 2008.
    - Zambia: 1998, 2004, 2010.
  - Variables: demographic, economic, health care, educational information at individual household member level.
  - Definitions:
    - Education access: current enrollment status consistent with ISCED 97; population restricted to official primary and secondary school age; yi = 1 if enrolled, 0 otherwise.
    - Health access: access to health "consultation" among the "sick" population; yi = 1 if accessed care, 0 otherwise.
  - Limitation: surveys do not contain information on quality of services; analysis focuses on access not quality.

- B. Empirical results — Access to primary school education
  - General findings:
    - Opportunity curves for primary enrollment are upward sloping (not pro-poor) across countries.
    - Within-country dynamics: outward shifts in opportunity curves — improved access.
    - Opportunity indices increased for all countries due to increased average opportunities and improvements in distribution.
  - Country-specific primary education outcomes (exact reported values):
    - Cameroon:
      - Average opportunity for primary-school-age population: 84 percent (1996), 84 percent (2001), 87 percent (2007).
      - Equity index of opportunity (EI): 0.91 (1996) to 0.95 (2007).
    - Ghana:
      - Average opportunity: 62.5 percent (1991), 73.4 percent (1998), 87 percent (2005).
      - EI: 0.88 (1991), 0.91 (1998), 0.98 (2005).
    - Mozambique:
      - Average opportunity: 59 percent (1996), 80 percent (2002), 95 percent (2008).
      - Equity index: 0.84 in 1996 to 0.90 in 2002 and further to 0.99 in 2008.
    - Tanzania:
      - Average opportunity: 75 percent (2000) to about 86 percent (2008).
      - EI: 0.88 (2000) to 0.97 (2008).
    - Zambia:
      - Average opportunity: 70 percent (1998) to 83 percent (2010).
      - EI: 0.83 (1998) to 0.94 (2007), then 0.91 (2010).

- C. Empirical results — Access to secondary school education
  - General:
    - Averages lower than for primary; on average access around 50 percent across the five countries.
    - Opportunity curves for secondary education are upward sloping (non-pro-poor).
    - General improvement in equality of access to secondary education across countries.
  - Country-specific secondary education outcomes (exact reported values):
    - Cameroon:
      - Average opportunity: 39 percent (1996) to 52 percent (2007).
      - EI: 0.67 (1996), 0.71 (2001), 0.77 (2007).
    - Ghana:
      - Average opportunity: 32 percent (1991) to 51 percent (2005).
      - EI: 0.80 (1991), 0.89 (2004), 0.77 (2005).
    - Mozambique:
      - Average opportunity: about 7 percent (1996) to 46 percent (2008).
      - EI: 0.42 (1996) to 1.13 (2008).
    - Tanzania:
      - Average opportunity: 17 percent (2000) to 37 percent (2008).
      - EI: 0.45 (2000) to 0.74 (2008).
    - Zambia:
      - Average opportunity: 32 percent (1998) to 56 percent (2008).
      - EI: 0.59 (1998) to 0.67 (2008).

- D. Empirical results — Access to health services
  - General:
    - Overall improvement in access to health care services driven by increases in average opportunity and improved distribution.
  - Country-specific health outcomes (exact reported values):
    - Cameroon:
      - Average opportunity: 60 percent (1996) to 88 percent (2001), then 77 percent (2007).
      - EI: 0.81 (1996) to 0.94 (2001), then 0.92 (2007).
    - Ghana:
      - Average opportunity: 55 percent (1991) to 49 percent (1998) to about 57 percent (2005).
      - EI: 0.85 (1991), 0.81 (1998), 0.89 (2005).
    - Mozambique:
      - Average opportunity: 65 percent (1996), 74 percent (2002), 77 percent (2008).
      - EI: 0.96 (1996), 0.85 (2002), 0.95 (2008).
    - Tanzania:
      - Average opportunity: 86 percent (2000) to 93 percent (2008).
      - EI: 0.92 (2000) to 0.93 (2008).
    - Zambia:
      - Average opportunity: 59 percent (1998), 77 percent (2004), 82 percent (2010).
      - EI: 0.84 (1998), 0.94 (2004), 0.98 (2010).

### METHODOLOGY HIGHLIGHTS
- Framework:
  - Social opportunity function analogous to social welfare function; combines average opportunities and distributional equity.
  - Opportunity curves used as a one-to-one representation of the social opportunity function to analyze inclusiveness quantitatively.
  - Equity index of opportunity developed to measure equity in access to education and health services.
- Dynamics:
  - Examines shifts in opportunity curves between periods; inclusiveness depends on dAO(p) = EI * dY*(p) + Y*(p) * dEI being positive.
- Data and measurement:
  - Uses household survey microdata to construct binary access variables (yi ∈ {0,1}) for enrollment and health consultation among the sick.
  - Focuses on access (not quality) due to data limitations.

### KEY CONCLUSIONS AND POLICY IMPLICATIONS
- Empirical conclusions:
  - Periods of overall growth coincided with increased access to education and health in the countries analyzed.
  - Average access and distribution have increased across countries, but equity in distribution varied across countries and over time.
  - Significant progress in primary school enrollment; secondary enrollment remains low on average (~50 percent).
  - Improvements in health sector access and distribution have been marginal in the last decade across analyzed countries.
- Policy implications and recommendations:
  - Achieving overall growth is necessary but not sufficient for inclusive growth; targeted government efforts required to create opportunities for the poor.
  - Target resources toward sectors that impact the poor most (health and education).
  - Implement better-targeted subsidies and active labor market policies that promote employment.
  - Invest early in human capital for the poor to reduce income inequalities at the source.
  - Design education and health services effectively to meet the needs of the poor segment to support sustained reforms and growth momentum.
  - Framework can be extended to access to job opportunities, finance, and land ownership; tools can guide allocation of limited government resources to needy populations to reduce inequality and poverty.

*Content based solely on _wp13139 - References .............................................................................................................*

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

### _wp13139 - References .............................................................................................................

### I. INTRODUCTION AND BACKGROUND
- Global developments elevating inequities in income and opportunities to central policy issue: the 2008–09 financial crisis, high unemployment, the Arab spring, and sustained growth in low-income countries combined with still high poverty rates.
- Core premise: Income inequality has roots in unequal opportunities; access to education and health care is critical for participation in growth and avoiding economic hardship.
- Literature and previous findings:
  - Many studies focus on whether growth reduces poverty and on the distributional impact of growth (Fosu, 2011).
  - Benefit incidence analyses of health and education expenditure (Gaddah and Munro, 2011; Kamgnia, 2008).
  - Labor market issues, closing the jobs gap (Leigh and Flores, 2012).
  - Impact of fiscal expenditure allocations (Clements, Gupta, and Nozaki, 2011).
  - Berg and Ostry (2011): chronic income inequality is detrimental to economic growth; more equal countries likely experience durable growth spells.
  - Garcia-Verdu, Selasse, and Thomas (2011): case-study household survey approach for six SSA countries (Cameroon, Ghana, Mozambique, Tanzania, Uganda, Zambia) — poorest quartile saw substantial annual household per capita consumption growth in three of four high-growth countries (Ghana, Tanzania, Uganda); low-growth countries had low or negative changes (Cameroon low, Zambia negative); Mozambique results depend on deflator choice (CPI or regional price indices).
- Contribution of this paper:
  - Uses the social opportunity function (similar to social welfare function) to assess inclusiveness of growth by focusing on access to education and health.
  - Constructs opportunity curves over time to examine dynamics: an upward parallel shift of the opportunity curve implies inclusive growth (increased average opportunities and increased opportunities available to the poor).
  - Applies social opportunity functions to Cameroon, Ghana, Mozambique, Tanzania, Zambia (same set as Garcia-Verdu et al., 2011) and complements with growth incidence curves and an equity index of opportunity measuring equity in access to education and health.
- High-level empirical result summary:
  - Periods of growth coincide with periods of increased access (opportunities) — corroborates Garcia-Verdu, Selasse, and Thomas (2011).
  - Average access and distribution of education and health increased across all examined countries over time.

### I.1 Specific empirical findings (education and health)
- Primary education:
  - Opportunity curves for primary school enrollment are upward sloping — in general access has not been pro-poor.
  - Within-country dynamics show outward shifts of opportunity curves — improved access to primary education.
  - Opportunity indices for primary education increased for all countries, underpinned by increased average opportunities and improvement in distribution (opportunity curves shifted outward).
  - Interpretation: growth process has been inclusive using access-to-education indicator.
- Secondary education:
  - Averages for secondary education are lower across all countries compared to primary; on average access is about 50 percent for all five countries.
  - Opportunity curves for secondary education are upward sloping — distribution could be considered non-pro-poor.
  - Dynamic evidence: increases in average opportunities and in distribution; outward shifts of opportunity curves for secondary education indicating inclusive growth so far, though scope remains to make growth more inclusive.
- Health care:
  - General improvement in access to health care services.
  - Improved opportunity index for health care services underpinned by increase in average opportunity and improved distribution — consistent with inclusive growth.
- Policy implication emphasized:
  - Importance of effective design and implementation of education and health services to meet needs of the poor to sustain reforms and growth momentum.
  - Framework can be extended to access to job opportunities, finance, and land ownership; tools can guide allocation of limited government resources to needy populations to reduce inequality and poverty.

### II. CONCEPTUAL FRAMEWORK: THE INCLUSIVE GROWTH CONCEPT AND THE SOCIAL OPPORTUNITY FUNCTION
- Inclusive growth concept:
  - Definitions emphasize addressing inequalities in income, assets, financial and human capital, education and health, and economic opportunities.
  - Consensus: rapid, sustainable economic growth must also be equitable for poverty reduction (Stuart, 2011).
  - High and rising income inequality can lower the poverty-reduction impact of growth and reduce growth itself (Bourguignon, 2003); inequality affects political stability and social cohesion (Berg and Ostry, 2011).
  - Inclusive growth: ensuring economic opportunities created by growth are available to all, particularly the poor (in line with Ali and Zhuang, 2007).
- Social opportunity function:
  - Inclusive growth is defined as maximization of the social opportunity function which depends on increasing average opportunities and distributing opportunities equitably.
  - The social opportunity function attaches greater weight to opportunities enjoyed by the poor — transfers from non-poor to relatively poor improve the social opportunity function (transfer principle).
- Formal definitions and equations (preserve notation and expressions as in source):
  - For n persons with incomes x1, x2, ..., xn (x1 is poorest, xn is richest), social welfare W is:
    - W = W(x1, x2, ..., xn)  (equation 1.1).
  - Social opportunity function O is:
    - O = O(y1, y2, ..., yn)  (equation 1.2), where yi captures opportunity of ith person.
  - Opportunity curve and average opportunity Y*(p):
    - PN(p) = Σ_i y_i / pN  where yi is binary (1 if ith person has access, 0 otherwise) and p is cumulative percentage of population (equation 1.3).
    - Given binary yi, average opportunity Y*(p) equals percentage of population with access.
  - Transfer principle condition:
    - If ∂^2 O / ∂y_i ∂y_j > < 0 ? (presented in source as inequality (1.4) reflecting improvement when transferring opportunity to poorer person).
  - Opportunity curve analogous to Lorenz curve; slope of Y*(p) measures marginal change in access when adding more non-poor persons to pN.
  - Classification:
    - If dY*(p)/dp > 0 for 0<p<1 → upward sloping opportunity curve → not pro-poor (favors non-poor).
    - If dY*(p)/dp < 0 for 0<p<1 → downward sloping → pro-poor.
    - If dY*(p)/dp = 0 for 0<p<1 → perfect equity.
  - Opportunity index (AO) — area under opportunity curve:
    - AO = ∫_0^p Y*(p) dp = Σ_i y_i / pN  (equation 1.5).
    - Higher AO implies greater opportunities available to the population.
  - Equity index of opportunity (EI):
    - EI(p) = AO(p) / Y*(p)  (equation 1.6).
    - Interpretation:
      - EI > 1 → downward sloping opportunity curve → pro-poor.
      - EI = 1 → perfect equity.
      - EI < 1 → upward sloping opportunity curve → not pro-poor.
  - Relationship:
    - AO(p) = EI(p) * Y*(p)  (equation 1.7).
    - Total differential:
      - dAO(p) = EI * dY*(p) + Y*(p) * dEI  (equation 1.8).
    - Growth becomes more inclusive if dAO(p) > 0. Contributions to inclusiveness come from increases in average opportunities (first term) and/or improvements in equity (second term).

### III. KEY STYLIZED FACTS ON THE EDUCATION AND HEALTH SECTORS IN SELECTED AFRICAN COUNTRIES
- Purpose: provide context for empirical results using opportunity curve, opportunity index, and equity index. Paper does not evaluate policy causality; provides background for Section IV empirical application.

- A. Cameroon (selected indicator highlights from Table 1; World Bank WDI)
  - Policy and trends:
    - Primary school education free since 2000; 10-year education policy adopted in 2006 emphasizing universal primary education, access, quality, private sector partnerships, governance improvements.
    - Gross primary enrollment increased from about 88 percent in 2000 to about 120 percent in 2010.
    - Secondary school enrollment increased from about 28 percent to 42 percent in same period.
    - Removal of primary school fees in 2000 appears to have spurred enrollment increases.
  - Quality and indicators:
    - Pupil-teacher ratio (primary and secondary) remains fairly high despite declines.
    - Literacy rate marginally increased from around 68 percent in 2000 to about 71 percent in 2007.
    - Primary completion rate moved from 51 percent in 2000 to 79 percent in 2010.
  - Health:
    - Public and private sectors provide health services; government defines policy and manages system.
    - Primary health care policy emphasized universal accessibility and community cofinancing/comanagement (policy dates back to 1980s; Cameroon Ministry of Public Health, 1992).
    - Reforms introduced user charges and promoted comanagement, decentralization, cost-recovery since June 1990.
    - Mortality rate (under 5) fell from 148 per 1,000 live births in 1996 to 136 in 2010.
    - Life expectancy fell slightly from 52 to 51 years over same period.
  - Selected numeric indicators from Table 1 (preserve exact values):
    - School enrollment, primary (% gross): 74.7 (1996), 87.5 (2000), 109.1 (2005), 109.4 (2006), 112.8 (2007), 119.8 (2010).
    - School enrollment, primary (% net): n.a. (1996–2007), 92.4 (2010).
    - School enrollment, secondary (% gross): n.a. (1996), 27.7 (2000), 27.8 (2005), 24.3 (2006), n.a. (2007), 42.2 (2010).
    - Literacy rate, adult total (% ages 15+): n.a. (1996), 68.4 (2000), n.a., n.a., 70.7 (2007), n.a. (2010).
    - Primary completion rate, total (% relevant age group): n.a. (1996), 51.0 (2000), 52.9 (2005), 52.9 (2006), 57.1 (2007), 78.7 (2010).
    - Pupil-teacher ratio, primary: n.a. (1996), 51.9 (2000), 47.8 (2005), 44.7 (2006), 44.4 (2007), 45.5 (2010).
    - Mortality rate, under-5 (per 1,000): 148.1 (1996), 147.5 (2000), 142.1 (2005), 141.0 (2006), 139.9 (2007), 136.2 (2010).
    - Life expectancy at birth, total (years): 51.6 (1996), 50.1 (2000), 49.4 (2005), 49.6 (2006), 49.8 (2007), 51.1 (2010).

- B. Ghana (selected indicator highlights from Table 2)
  - Policy and trends:
    - Government strategies towards universal primary education by 2015: capitation grant (removal of school fees), expansion of early childhood development, nutrition/school feeding.
    - Education strategy plan (ESP) 2003–2015 adopted May 2003.
    - Secondary education requires payment (tuition, boarding, feeding).
    - Nationwide adoption of “capitation grant system” since early 2005: every public kindergarten, primary, junior secondary school receives about $3.30 per pupil per year; schools not allowed to charge fees.
  - Outcomes:
    - Gross primary enrollment moved from about 81 percent in 1999 to about 107 percent in 2011.
    - Net primary enrollment increased from 61 percent to 84 percent in same period.
    - Secondary gross enrollment increased from 40 percent in 1999 to 58 percent in 2011; net enrollment increased to about 49 percent.
    - Pupil-teacher ratio (primary) increased; secondary ratio broadly unchanged at about 19.
    - Literacy rate about 67 percent in 2009.
    - Primary completion rate increased from 64 percent in 1991 to 94 percent in 2011.
  - Health:
    - Health sector reform of 1985 decentralized health administration; user charges introduced as cost-recovery measures.
    - Central government remains main financier; 2003 enactment of health insurance introduced district mutual, private health insurance schemes.
    - Mortality rate (under 5) decreased from 119 per 1,000 in 1991 to 77 in 2009.
    - Life expectancy increased from 57 to 63 years (1991–2009).
  - Selected numeric indicators from Table 2:
    - School enrollment, primary (% gross): 77.6 (1991), 80.6 (1997), 80.5 (1999), 90.3 (2005), 106.3 (2009), 107.3 (2011).
    - School enrollment, primary (% net): n.a. (1991–1999), 60.7 (1999), 66.5 (2005), 76.7 (2009), 84.0 (2011).
    - School enrollment, secondary (% gross): n.a. (1991), 27.7 (1997), 40.2 (1999), 47.2 (2005), 59.1 (2009), 58.1 (2011).
    - Primary completion rate, total (% relevant age group): 63.7 (1991), n.a. (1997), 68.0 (1999), 74.6 (2005), 86.7 (2009), 94.0 (2011).
    - Pupil-teacher ratio, primary: 29.1 (1991), n.a., 29.6 (1999), 32.8 (2005), 33.1 (2009), 31.0 (2011).
    - Mortality rate, under-5 (per 1,000): 118.5 (1991), 107.0 (1997), 101.8 (1999), 86.0 (2005), 76.6 (2009), n.a. (2011).
    - Life expectancy at birth, total (years): 57.3 (1991), 58.0 (1997), 58.1 (1999), 61.0 (2005), 63.4 (2009), n.a. (2011).

- C. Mozambique (selected indicator highlights from Table 3)
  - Policy and trends:
    - Strategic plan for education implemented 1999–2005; second strategic plan 2006–2010/11 aiming at universal primary education by 2015.
    - Rapid expansion of access to primary schooling, free and compulsory primary education; responsibility division between central (design/monitoring) and local (implementation) authorities.
  - Outcomes and quality:
    - Gross primary enrollment increased from about 66 percent in 1995 to about 114 percent in 2009.
    - Net primary enrollment ratio increased to 90 percent in 2009 from 44 percent in 1995.
    - Secondary gross enrollment increased from 5 percent in 1999 to 23 percent in 2009; net enrollment from 3 percent to 15 percent.
    - High pupil-to-teacher ratios: primary increased from 58 percent in 1999 to 61 percent in 2009; secondary from 33 to 38 percent.
    - Many schools operate multiple shifts due to rapid primary expansion.
    - Literacy rate 55 percent in 2009.
    - Primary completion rate increased from 26 percent in 1995 to 56 percent in 2009.
  - Health:
    - National health system and national public health financing model; health sector strategy plan 2007–12; health sector recovery program 1994–99.
    - Mortality rate (under 5) decreased from 195 per 1,000 in 1995 to 139 in 2009.
    - Life expectancy increased from 45 to 49 years in 2009.
  - Selected numeric indicators from Table 3:
    - School enrollment, primary (% gross): 66.2 (1995), n.a. (1996), 69.1 (1999), 84.1 (2002), 114.1 (2008), 114.2 (2009).
    - School enrollment, primary (% net): 43.8 (1995), n.a., 52.0 (1999), 56.4 (2002), 89.2 (2008), 90.4 (2009).
    - School enrollment, secondary (% gross): 7.3 (1995), n.a., 5.2 (1999), 8.4 (2002), 20.5 (2008), 23.3 (2009).
    - Literacy rate, adult total (% ages 15+): n.a. (1995–2008), 55.0 (2009).
    - Primary completion rate, total (% relevant age group): 25.9 (1995), n.a., 14.0 (1999), 31.8 (2002), 25.8 (2008), 95.6? (2009) — note: table shows a sequence "25.9 n.a. 14.0 31.8 25.8 95.6 40" (original table formatting ambiguous); source text states primary completion rate increased from 26 percent in 1995 to 56 percent in 2009.
    - Pupil-teacher ratio, primary: 57.6 (1995), n.a., 61.5 (1999), 67.2 (2002), 64.0 (2008), 61.3 (2009).
    - Mortality rate, under-5 (per 1,000): 195.0 (1995), 191.0 (1996), 180.0 (1999), 169.0 (2002), 144.8 (2008), 139.6 (2009).
    - Life expectancy at birth, total (years): 45.4 (1995), 45.9 (1996), 47.0 (1999), 47.0 (2002), 48.9 (2008), 49.3 (2009).

- D. Tanzania (selected indicator highlights from Table 4)
  - Policy and trends:
    - Basic education master plan 1998–2002; education sector development program (ESDP) process began 1998; primary education development plan (PEDP) abolished fees and mandatory contributions.
    - PEDP (2002–2006) and secondary education development plan (SEDP, from 2004) focused on access, equity, quality.
  - Outcomes and quality:
    - Gross primary enrollment increased from about 68 percent in 1995 to about 102 percent in 2009.
    - Net primary enrollment ratio increased from 49 percent in 1995 to 98 percent in 2008.
    - Challenges: large classes, teacher shortages; reported classes of 60–100 pupils in some studies.
    - Pupil-to-teacher ratio high: increased from 37 percent in 1995 to 51 percent in 2010 for primary.
    - Literacy rate 73 percent in 2009.
    - Primary completion rate increased from 55 percent in 2005 to 90 percent in 2009 (table shows varied figures).
  - Health:
    - Health care reform beginning in 1994 focused on access, quality, efficiency; decentralization by devolution enacted through 1998 local government reform; cost sharing, user fees, insurance mechanisms introduced.
    - Mortality rate (under 5) decreased from 155 per 1,000 in 1995 to 92 in 2010.
    - Life expectancy increased from 50 to 57 years (1995–2010).
  - Selected numeric indicators from Table 4:
    - School enrollment, primary (% gross): 68.2 (1995), 68.3 (2000), 105.4 (2005), 111.4 (2008), 105.8 (2009), 102.3 (2010).
    - School enrollment, primary (% net): 48.7 (1995), 53.1 (2000), 90.8 (2005), 98.0 (2008), n.a. (2009–2010).
    - School enrollment, secondary (% gross): 5.4 (1995), n.a., n.a., n.a., n.a., n.a.
    - Primary completion rate, total (% relevant age group): n.a. (1995), n.a., 55.3 (1999), n.a., 102.9 (2008), 98.9 (2009).
    - Pupil-teacher ratio, primary: 36.8 (1995), 41.4 (2000), 55.9 (2005), 52.4 (2008), 53.7 (2009), 50.8 (2010).
    - Mortality rate, under-5 (per 1,000): 154.6 (1995), 130.2 (2000), 102.8 (2005), 85.4 (2008), 80.4 (2009), 92.4 (2010).
    - Life expectancy at birth, total (years): 49.6 (1995), 50.4 (2000), 53.3 (2005), 55.8 (2008), 56.6 (2009), 57.4 (2010).

- E. Zambia (selected indicator highlights from Table 5)
  - Policy and trends:
    - Education policies: “Focus on Learning” (1992), “Educating our Future” (1996).
    - Eliminated school fees for grades 1–7 and provided critical infrastructure (progress 2002–2009).
  - Outcomes:
    - Gross primary enrollment increased from 97 percent in 1990 to 115 percent in 2010.
    - Net primary enrollment increased from 77 percent in 1994 to 91 percent in 2010 (decline compared to 98 percent in 2008).
    - Pupil-teacher ratio for primary rose from 44 percent in 1990 to 58 percent in 2010.
    - Literacy rate 68 percent in 1999.
    - Primary completion rate increased from 65 percent in 1995 to 103 percent in 2010.
  - Health:
    - Health sector decentralization mid-1990s; new health management era from 1991 focusing on affordable care, essential package of cost-effective services, district-level decentralization; user fees introduced in 1993 with exemption guidelines.
    - Mortality rate (under 5) fell from 183 per 1,000 in 1990 to 111 in 2010.
    - Life expectancy increased marginally from 48 to 49 years.
  - Selected numeric indicators from Table 5:
    - School enrollment, primary (% gross): 96.6 (1990), 90.8 (1994), 83.7 (1999), 107.1 (2004), 122.0 (2008), 115.3 (2010).
    - School enrollment, primary (% net): n.a. (1990), 76.9 (1994), 70.5 (1999), 86.5 (2004), 97.6 (2008), 91.4 (2010).
    - School enrollment, secondary (% gross): 21.3 (1990), 20.7 (1994), n.a. (1999–2010).
    - Literacy rate, adult total (% ages 15+): 65.0 (1990), n.a., 68.0 (1999), n.a., n.a., n.a.
    - Primary completion rate, total (% relevant age group): 65.2 (1990), 74.5 (1994), 99.6 (1999), 96.5 (2004), 103.2 (2008), 103.2? (2010) — table lists values culminating in 103.25 (source text states increase to 103 percent in 2010).
    - Pupil-teacher ratio, primary: 44.0 (1990), n.a., 60.9 (1999), 62.4 (2004), 60.5 (2008), 58.0 (2010).
    - Mortality rate, under-5 (per 1,000): 182.8 (1990), 180.7 (1994), 161.3 (1999), 142.4 (2004), 121.8 (2008), 111.0 (2010).
    - Life expectancy at birth, total (years): 47.5 (1990), 44.1 (1994), 42.0 (1999), 43.6 (2004), 47.1 (2008), 48.5 (2010).

### IV. APPLICATION OF SOCIAL OPPORTUNITY FUNCTION TO SELECTED AFRICAN COUNTRIES
- A. Household surveys and data
  - Countries: Cameroon, Ghana, Mozambique, Tanzania, Zambia — chosen for data availability and coinciding with growth acceleration periods.
  - Survey years used:
    - Cameroon: 1996, 2001, 2007.
    - Ghana: 1991, 1998, 2005.
    - Mozambique: 1996, 2002, 2008.
    - Tanzania: 2000, 2008.
    - Zambia: 1998, 2004, 2010.
  - Variables extracted: demographic, economic, health care, educational information for individual household members; focus on access to primary and secondary education and access to health services.
  - Definition of access:
    - Education access measured by current enrollment status consistent with ISCED 97 methodology; population restricted to official primary and secondary school age; dummy variable yi = 1 if access/enrolled, 0 otherwise.
    - Health access measured as access to health "consultation" among the "sick" population — among those sick in the past several weeks, identify those able to get access to health services; dummy variable takes 0/1 values.
  - Acknowledged limitation: household survey data do not contain information on quality of primary/secondary education or health services — analysis focuses on access not quality.

- B. Empirical results — Access to primary school education (detailed country-level results)
  - General:
    - Opportunity curves for primary enrollment are upward sloping (not pro-poor) across selected countries.
    - Within-country dynamics show outward shifts in opportunity curves — improved access to primary education.
    - Opportunity indices increased for all countries due to increased average opportunities and improvements in distribution.
  - Country-specific numerical outcomes (preserve exact reported values):
    - Cameroon:
      - Average opportunity for primary-school-age population virtually unchanged at 84 percent between 1996 and 2001; increased to 87 percent in 2007.
      - Equity index of opportunity (EI) increased from 0.91 in 1996 to 0.95 in 2007 — indicates improvement in equity of access to primary education.
    - Ghana:
      - Average opportunity increased from 62.5 percent in 1991 to 73.4 percent in 1998 and to 87 percent in 2005.
      - EI increased from 0.88 in 1991 to 0.91 in 1998 and to 0.98 in 2005 — consistent improvement in distribution of opportunities.
    - Mozambique:
      - Average opportunity increased from 59 percent in 1996 to 80 percent in 2002 and to 95 percent in 2008.
      - (The source text begins to state "The equity index of opportunities improved from" but the provided excerpt ends before numeric completion.)

*Italic source attribution: Content based solely on _wp13139 - References .............................................................................................................*

### 0.84 in 1996 to 0.90 in 2002 and further to 0.99 in 2008.

### _wp13139 - 0.84 in 1996 to 0.90 in 2002 and further to 0.99 in 2008.

### Primary school enrollment — findings by country
- Tanzania
  - Average opportunity increased from 75 percent in 2000 to about 86 percent in 2008.
  - Equity Index (EI) increased from 0.88 in 2000 to 0.97 in 2008.
- Zambia
  - Average opportunity increased from 70 percent in 1998 to 83 percent in 2010.
  - EI increased from 0.83 in 1998 to 0.94 in 2007, but fell to 0.91 in 2010.
- Mozambique, Ghana, Cameroon (figures presented in figures and text; primary results indicate improvements in averages and distributions across surveyed years as shown in Figures 3 and 4).

### Secondary school enrollment — findings by country
- General point
  - Averages for secondary education are lower than for primary education; on average for the five countries access is around 50 percent.
  - Opportunity curves for secondary education are upward sloping (distribution of access considered non-pro-poor).
  - General improvement in equality of access to secondary education across countries analyzed.
- Cameroon
  - Average opportunity increased from 39 percent in 1996 to 52 percent in 2007.
  - EI increased from 0.67 in 1996 to 0.71 in 2001 and to 0.77 in 2007.
- Ghana
  - Average opportunity increased from 32 percent in 1991 to 51 percent in 2005.
  - EI increased from 0.80 in 1991 to 0.89 in 2004, but fell to 0.77 in 2005.
- Mozambique
  - Average opportunity increased from about 7 percent in 1996 to 46 percent in 2008.
  - EI improved from 0.42 in 1996 to 1.13 in 2008.
- Tanzania
  - Average opportunity increased from 17 percent in 2000 to 37 percent in 2008.
  - EI increased from 0.45 in 2000 to 0.74 in 2008.
- Zambia
  - Average opportunity increased from 32 percent in 1998 to 56 percent in 2008.
  - EI increased from 0.59 in 1998 to 0.67 in 2008.

### Access to health services — findings by country
- General point
  - Overall improvement in access to health care services driven by increases in average opportunity and improved distribution.
- Cameroon
  - Average opportunity increased from 60 percent in 1996 to 88 percent in 2001, then fell to 77 percent in 2007.
  - EI increased from 0.81 in 1996 to 0.94 in 2001, then fell to 0.92 in 2007.
- Ghana
  - Average opportunity fell from 55 percent in 1991 to 49 percent in 1998, then recovered to about 57 percent in 2005.
  - EI fell from 0.85 in 1991 to 0.81 in 1998 and improved to 0.89 in 2005.
- Mozambique
  - Average opportunity increased from 65 percent in 1996 to 74 percent in 2002 and to 77 percent in 2008.
  - EI fell from 0.96 in 1996 to 0.85 in 2002, then increased to 0.95 in 2008.
- Tanzania
  - Average opportunity increased from 86 percent in 2000 to 93 percent in 2008.
  - EI increased from 0.92 in 2000 to 0.93 in 2008.
- Zambia
  - Average opportunity increased from 59 percent in 1998 to 77 percent in 2004 and to 82 percent in 2010.
  - EI increased from 0.84 in 1998 to 0.94 in 2004 and to 0.98 in 2010.

### Methodology highlights
- Introduces the social opportunity function framework, analogous to a social welfare function, combining average opportunities and distribution of opportunities.
- Uses opportunity curves (one-to-one relationship with the social opportunity function) to analyze inclusiveness of growth quantitatively.
- Develops an equity index of opportunity to measure equity in access to education and health services.
- Dynamic assessment achieved by examining shifts in opportunity curves between periods; inclusiveness depends on upward shifts and where along the income distribution shifts occur.

### Key conclusions and policy implications
- Periods of overall growth coincided with periods of increased access (opportunities) for education and health in the countries analyzed.
- Average access and distribution have increased across countries, but equity in distribution varied across countries and over time.
- Significant progress has been made in primary school enrollment; secondary enrollment remains low.
- Improvements in health sector access and distribution have been marginal in the last decade across analyzed countries.
- Achieving overall growth is necessary but not sufficient for inclusive growth; targeted government efforts are required to create opportunities for the poor.
- Policy recommendations highlighted:
  - Target resources toward sectors that impact the poor most (health and education).
  - Implement better-targeted subsidies and active labor market policies that promote employment.
  - Invest early in human capital for the poor to reduce income inequalities at the source.
  - Design education and health services effectively to meet the needs of the poor segment of the population, supporting sustained reforms and growth momentum.

*Source: Calculated by the authors; conclusions and policy recommendations as presented in the source document.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13139.pdf_