## wp17127

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### I. Introduction — purpose and contribution
- Macro-critical structural issues (poverty, equality, inclusiveness, gender, employment, migration, governance, corruption, natural disasters, climate change) affect economic performance and stability and should be addressed holistically.
- The paper outlines an Inclusive Growth Framework (IGF) to embed poverty and inequality measures into a macroeconomic framework for policy analysis under the IMF mandate.
- Builds on prior research and tools including Loungani (2017); Berg and Ostry (2011); Berg, Buffie and Zanna (2016); Datt and Ravallion (1992); Ravallion and Chen (2003); Kraay (2004); Acemoglu and Robinson (2012); Rodrik (2014); Araar and Duclos (2013).
- Main contributions:
  - Proposes the IGF concept and quantifies key effects to assess growth inclusiveness.
  - Offers economic interpretation of standard statistical outputs and interconnections.
  - Provides a tool for policymakers to identify targeted measures to improve growth inclusiveness.
- Scope limits:
  - Focuses on diagnostics, not on exhaustive policy prescriptions; policies must be country-specific.
  - Illustrative country cases mentioned: Senegal and Djibouti.

### II. Inclusive Growth Framework — Diagnostics roadmap
- Definitions:
  - Narrow: growth that improves equality (distributional focus).
  - Broad (used here): growth that is high, sustained, extensive across sectors in per capita terms and also: (i) reduces poverty, (ii) reduces inequality, (iii) creates jobs, (iv) reduces the gender gap, (v) improves governance, (vi) responds to climate change.
- Focus: interaction between growth and poverty, and growth and inequality.
- Core inputs required for IGF:
  - Real per capita growth.
  - Static poverty indicators: poverty rate, poverty gap.
  - Static inequality indicators: Gini coefficient, mean log deviation (MLD), Lorenz curve.
- Derived dynamic indicators:
  - Changes in poverty.
  - Changes in consumption or expenditure (by decile and aggregate).
- Two estimated effects central to the IGF:
  - Growth and distribution effects in the poverty change measure.
  - Decile growth effect in the inequality change measure (including Growth Incidence Curves).

### III. Metrics and data requirements
- Poverty and inequality metrics highlighted:
  - Squared poverty gap.
  - Watts index.
  - Gini coefficient.
  - Mean log deviation (MLD).
  - Decile ratio (average income of richest 10 percent divided by average income of poorest 10 percent).
  - Dynamic comparison: income increase of bottom deciles versus average income increase or income increase in highest deciles.
- Data requirements and limitations:
  - At least two household surveys covering consumption or expenditure, comparable in methodology and variables (household and socio-demographic variables: head of household, education, marital status, employment, residence).
  - Challenges: missing informal sector data, outliers, changing definitions/coverage (rural/urban), national versus World Bank international poverty lines (national data preferred for country policy advice).
  - Using only two sample periods may limit representativeness over longer intervals.
  - Focus here on consumption/expenditure inequality (data-driven): consumption inequality may fall even if income inequality rises.

### IV. Decomposing change in poverty: growth and distribution effects
- Representation and intuition:
  - Poverty rate at time t: P_t = P(z, L_t, μ_t), where z is the poverty line, μ is mean income, and L_t is the Lorenz curve at time t.
  - Changes in poverty arise from changes in mean income (growth) or changes in relative inequality (Lorenz curve shifts).
- Decomposition:
  - P_{t+n} − P_t = G + D + R
    - G: growth effect — change in poverty due to change in mean income, holding the Lorenz curve constant.
      - G ≡ P(z, L_{t}, μ_{t+n}) − P(z, L_{t}, μ_{t}).
    - D: distribution effect — change in poverty due to change in the Lorenz curve, holding mean income constant.
      - D ≡ P(z, L_{t+n}, μ_{t}) − P(z, L_{t}, μ_{t}).
    - R: residual due to nonlinearity.
- Practical calculation using sample surveys (Datt and Ravallion approach):
  - Generic poverty index:
    - P_α = (1/n) Σ_i ((z − y_i)/z)^α (censored).
    - α = 0 yields headcount index; α = 1 yields poverty gap index.
  - Growth and redistribution components computed using two reference-period variants (period 1 reference and period 2 reference).
  - Residual expressions given for each reference; residual can be eliminated by averaging the components obtained using period 1 and period 2 as references (Shapley-style average):
    - P_2 − P_1 = C_1 + C_2, where C_1 and C_2 are averages across the two reference decompositions.

### V. Analytical outputs and interpretation (diagnostic use)
- Key analytic outputs from IGF diagnostics:
  - Growth Incidence Curves (GIC) to visualize decile-level growth incidence across the distribution.
  - Decile growth effects to assess inequality changes (compare bottom decile growth to average).
  - Growth and distribution effects quantify contributions to poverty change.
- Use in policy:
  - Diagnostic outputs allow policymakers to:
    - Assess whether growth is poverty- and inequality-reducing.
    - Identify which deciles or groups are benefiting from growth.
    - Infer the extent to which poverty reduction is driven by mean income growth versus distributional shifts.
  - Policy recommendations must be country-specific and follow from diagnostics.

### DASP (Distributive Analysis STATA package) and operational tools
- DASP functionality:
  - Calculates poverty and inequality indices, conducts decomposition procedures, and builds growth incidence curves.
  - Menus and dialog boxes available as alternatives to writing code.
  - Supports distributive analysis on more than one database.
- Footnote in source:
  - "The latest DASP 2.3 version can be downloaded from http://dasp.ecn.ulaval.ca/modules.htm.  A user manual is available from http://dasp.ecn.ulaval.ca/manuals.htm."

### Growth Incidence Curves (GIC): definition, algebra, and interpretation
- Definition:
  - Vertical axis: growth rate of consumption expenditure.
  - Horizontal axis: consumption expenditure percentiles.
- Formal expression (preserved notation from source):
  - (2.3) g_t(p) = [L_{t+n}(p)/L_t(p)]^{(s_t+1)} − 1  (text defines L̇_{t}(p) as rate of change of the Lorenz curve, p as deciles, s_t as growth rate of mean).
- Key interpretations:
  - Parts of the curve above the X-axis: deciles that benefit from growth.
  - Parts below the X-axis: deciles that lost because of growth.
  - If GIC entirely above X-axis: growth leads to poverty reduction.
  - If GIC crosses X-axis: impact of growth on poverty is ambiguous.
  - Segments above the overall mean: deciles benefiting relatively more than an average household.
  - Segments below the mean but above zero: deciles benefiting less than an average household.
- Stylized cases (six schematic outcomes preserved from source):
  1. Mean growth zero, GIC overlaps X-axis (no per capita growth).
  2. Positive mean growth, GIC above X-axis.
  3. Mean zero and non-inclusive: GIC positively sloped (negative growth at lower deciles offset by higher growth at higher deciles) → increased inequality.
  4. Mean zero but inclusive: GIC negatively sloped with lower deciles growing and higher deciles declining.
  5. Positive and non-inclusive: mean consumption increases and GIC positively sloped.
  6. Positive and inclusive: mean consumption increases and GIC negatively sloped.
- Four change patterns for GIC shape:
  1. Increase in growth with unchanged inclusiveness → GIC shifts up.
  2. Increase in inclusiveness, not growth → GIC tilts, slope more negative.
  3. Increase in inclusive growth → GIC shifts up and slope more negative.
  4. Increase in growth with worsened inclusiveness → GIC shifts up while slope becomes less negative or positive.
- Slope implications:
  - Horizontal GIC: growth neutral from distributive perspective.
  - Negatively sloping GIC: inclusive growth (poorer deciles grow faster than richer).
  - Positively sloping GIC: growth not inclusive.
- Linear assumption (preserved formulas):
  - (2.5) assume linear ratio for rate of change of Lorenz curve leading to:
    - (2.6) g_t(p) = (α p + β)(s_t + 1) − 1
    - (2.7) g_t(p|α) = (s_t + 1) − 1 + β (s_t + 1) p
  - Consequences (verbatim summaries preserved) about equality of decile growth to average growth when slope of Lorenz curve does not change, and directional comparisons when slope increases or decreases.

### Operational steps to assess inclusiveness of growth (verbatim)
- Recommended actions for a country:
  - (i) establish the slope of the incidence curve based on the information of at least two sequential household surveys;
  - (ii) if the slope is positive, suggesting that growth has not been inclusive, identify measures that could increase the income and spending of the lowest deciles, while increasing the mean growth rate, that is, not at the expense of higher deciles;
  - (iii) if the slope of the incidence curve is negative, suggesting growth has been inclusive, identify measures to increase the absolute value of the slope by making the growth of consumption of lower deciles even faster, without hampering any other deciles; and, alternatively or in addition,
  - (iv) find a measure to reduce inequality in the Lorenz curve coefficient in the next period that would shift the entire incidence curve up.
- Caveat: "The linear form of the growth incidence curve is a simplification assumption taken to illustrate its key properties better. Growth incidence curves usually have complex shapes... analysis for the purposes of public policies should be performed on carefully constructed growth incidence curves based on the two most recent household surveys."

### Applications — Senegal (empirical summary)
- Time periods analyzed: 2001–2005, 2005–2011, and 2001–2011.
- Findings by period:
  - 2001–2005:
    - "consumption increased on average because the mean of the growth incidence curve is above zero, driven by the middle of the distribution (from the 3rd to the 8th deciles)."
    - "The growth incidence curve is positively sloped, suggesting some increase in inequality during this period."
  - 2005–2011:
    - "the mean of the growth incidence curve is above zero, but the curve is broadly flat, suggesting no clear trend in changes in inequality."
  - 2001–2011 (overall):
    - "a clear increase in mean consumption confirms the decline in poverty, as the middle class improved their relative position."
    - "for 2001–11 the growth incidence curve has a slightly positive slope, which may point to some worsening of inclusiveness. This trend may not be statistically significant, indicating no substantial distributional changes during this period other than the improvement in the relative position of the middle class."
- Urban vs. rural:
  - Urban: middle of distribution benefitted most; 2001–05 incidence curve substantially above mean except top decile; 2005–2011 curve hovers around zero and is upward sloping.
  - Rural: median growth rates closer to mean growth than in urban areas; rural distribution skewed to the right (most households relatively poorer than mean).
- Overall conclusions for Senegal:
  - (i) "poverty in this country has fallen in the last two decades, although poverty reduction has slowed in recent years;"
  - (ii) "although available indicators sometimes give conflicting signals on distributional shifts, growth seems to have benefitted most people in the middle of the income distribution;"
  - (iii) "the middle class has benefitted from growth, mainly in urban areas, while both the poorest and the richest have lost ground."

### Growth inclusiveness analysis — Djibouti (2002–2013)
- Data and methods:
  - Based on household surveys in 2002 and 2012, and updated in 2013 (EDAM2-2002, EDAM3-2012 et EBC-2013).
  - Decomposition separates growth and distribution effects using Datt & Ravallion approaches and the Shapley approach (average of both years).
  - Growth inclusiveness assessed via Growth Incidence Curves (GICs) with 95 percent confidence bounds.
  - Confidence intervals indicate relatively low statistical significance for many estimates.
- Key poverty and distribution outcomes:
  - Extreme poverty: reduced from 24.1 percent in 2002 to 23 percent in 2013 (based on new poverty thresholds calculated in 2013).
  - Overall poverty: dropped from 46.7 percent to 40.8 percent between 2002 and 2013.
  - Urban/rural disparity (2013): capital (urban) extreme and overall poverty rates at 16.5 and 34.2 percent, respectively; rest of the country at 44.5 and 62.5 percent, respectively.
- Change decomposition (2012 → 2013, overall poverty rate):
  - Overall poverty rate dropped by 5.9 percentage points.
  - Growth effect contributed 8.8 ppts.
  - Distribution effect subtracted 2.9 ppts.
- Extreme poverty change (2012 → 2013):
  - Improvement marginal, only 1 ppt, as most gains from growth were offset by losses from the distribution effect.
- Poverty gaps:
  - Overall poverty gap improvement marginal, at about one percentage point, with growth effect nearly offset by negative distribution effect.
  - Extreme poverty gap increased by about 0.5 percentage points due to a strongly negative distribution effect that could not be offset by growth.
- Growth incidence and distributional patterns (2002–13):
  - Mean household consumption increased on average (mean of the GIC is above zero), driven by the middle of the distribution (from the 2nd to the 10th deciles).
  - The GIC is positively sloped, suggesting an increase in inequality during this period.
  - For low percentiles, the GIC is below the horizontal axis: at least 10 percent of the poorest groups experienced a negative growth rate of their living standards.
  - The 95 percent confidence interval around the GIC touches or crosses the X-axis several times (notably in the 5th to the 8th percentiles), indicating a substantial margin of error and marginal statistical significance for some changes.
  - After shifting the GIC to align its mean with the X-axis (displaced GIC):
    - Up to the 8th decile the curve is below the X-axis — for 80 percent of the poorest population, consumption grew slower relative to the wealthiest 20 percent.
    - The two poorest deciles clearly experienced lower growth of consumption even relative to an average; their 95 percent confidence interval is squarely below the horizontal axis.
    - Consumption of the high-income deciles (above the 8th decile) clearly increased.
- Main findings and interpretation:
  - (i) Overall poverty declined in 2002-13, although there has been no significant change in extreme poverty.
  - (ii) Inequality remains high and there are indications that inequality may have worsened.
  - (iii) Growth was not inclusive in 2002-13: it mainly benefited people on the upper side of the income distribution, while the poorest groups became even poorer in relative terms.
  - (iv) Based on comparator experiences, growth in rural areas most likely was less inclusive than in urban areas, and gender disparity might have increased; existing statistics do not permit direct assessment of these two effects for Djibouti.
  - (v) Underlying data are marginally sufficient and not entirely comparable between surveys; statistical significance of most estimates is low and margins of error are high, so results are indicative pending better data.

### Policy implications and selected recommendations (Box 1 — policies to increase growth inclusiveness)
- Overarching:
  - Sustained economic growth and well-designed public policies are the preconditions.
- Structural policies (pre-distribution):
  - Improve access to education and healthcare
  - Build inclusive institutions
  - Promote gender inclusiveness
  - Accelerate infrastructure reforms (energy, irrigation)
  - Introduce flexible labor market policies
- Fiscal policies (redistribution):
  - Cut (progressive) direct taxes
  - Increase (regressive) indirect taxes
  - Increase the tax base – reduce informality
  - Increase public investment
- Financial sector policies:
  - Improve access to financial services
  - Align financial reforms with capacity
- Agricultural policies:
  - Improve productivity, reduce productivity gap
  - Eliminate unproductive subsidies
- Operational lesson: decomposing changes in poverty into growth and distribution effects is essential to identify policies that ensure both effects work toward poverty reduction; GICs and decomposition analyses help target households that need the most help and to replace generalized incentives with well-targeted support measures.

*Source: IMF working paper "Inclusive Growth Diagnostics Framework" (excerpt from wp17127).*

### 1. Inclusive Growth Diagnostics Framework .......................................................................... 7

### 1. Inclusive Growth Diagnostics Framework

### I. Introduction — purpose and contribution
- Macro-critical structural issues (poverty, equality, inclusiveness, gender, employment, migration, governance, corruption, natural disasters, climate change) affect economic performance and stability and should be addressed holistically.
- The paper outlines an Inclusive Growth Framework (IGF) to embed poverty and inequality measures into a macroeconomic framework for policy analysis under the IMF mandate.
- Builds on prior research and tools:
  - Loungani (2017); Berg and Ostry (2011); Berg, Buffie and Zanna (2016); Datt and Ravallion (1992); Ravallion and Chen (2003); Kraay (2004); Acemoglu and Robinson (2012); Rodrik (2014); Araar and Duclos (2013).
- Main contributions:
  - Proposes the IGF concept and quantifies key effects to assess growth inclusiveness.
  - Offers economic interpretation of standard statistical outputs and interconnections.
  - Provides a tool for policymakers to identify targeted measures to improve growth inclusiveness.
- Scope limits:
  - Focuses on diagnostics, not on exhaustive policy prescriptions; policies must be country-specific.
  - Illustrative country cases mentioned: Senegal and Djibouti (policy origins not analyzed in this paper).

### II. Inclusive Growth Framework — Diagnostics roadmap
- Definition(s):
  - Narrow definition: growth that improves equality (distributional focus).
  - Broad definition used here: growth that is high, sustained, extensive across sectors in per capita terms and also:
    - (i) reduces poverty,
    - (ii) reduces inequality,
    - (iii) creates jobs,
    - (iv) reduces the gender gap,
    - (v) improves governance,
    - (vi) responds to climate change.
- Focus of the paper: interaction between growth and poverty, and growth and inequality.
- Core inputs required for IGF:
  - Real per capita growth.
  - Static indicators related to poverty: poverty rate, poverty gap.
  - Static indicators related to inequality: Gini coefficient, mean log deviation (MLD), Lorenz curve.
- Derived dynamic indicators:
  - Changes in poverty.
  - Changes in consumption or expenditure (by decile and aggregate).
- Two estimated effects central to the IGF:
  - Growth and distribution effects in the poverty change measure.
  - Decile growth effect in the inequality change measure (including Growth Incidence Curves).
- Conclusion: Quantifying these effects is sufficient for a broad assessment of growth inclusiveness and to inform policy recommendations.

### III. Metrics and data requirements
- Poverty and inequality metrics highlighted:
  - Squared poverty gap: captures severity of poverty among the poor (weights households further from the poverty line more heavily).
  - Watts index: distribution-sensitive poverty measure (logarithm of the quotient of the poverty line and a geometric mean of a censored distribution).
  - Gini coefficient: measures deviation from perfect equality.
  - Mean log deviation (MLD): more sensitive to changes at the lower end of the distribution.
  - Decile ratio: average income of the richest 10 percent divided by the average income of the poorest 10 percent.
  - Dynamic comparison: income increase of bottom deciles versus average income increase or income increase in highest deciles (if bottom decile income rises proportionately or faster than average, growth is inclusive).
- Data requirements and limitations:
  - At least two household surveys covering consumption or expenditure, comparable in methodology and variables (household and socio-demographic variables: head of household, education, marital status, employment, residence).
  - Challenges: missing informal sector data, outliers, changing definitions/coverage (rural/urban), national versus World Bank international poverty lines (national data preferred for country policy advice).
  - Using only two sample periods may limit representativeness over longer intervals.
  - Focus here on consumption/expenditure inequality (data-driven): consumption inequality may fall even if income inequality rises.

### IV. Decomposing change in poverty: growth and distribution effects
- Representation:
  - Poverty rate at time t: P_t = P(z, L_t, μ_t) — expressed as P(z, L_t, μ_t) (equation labeled (1.1) in source).
    - where z is the poverty line, μ is mean income, and L_t is the Lorenz curve at time t.
  - Intuition: changes in poverty arise from changes in mean income (growth) or changes in relative inequality (Lorenz curve shifts).
- Decomposition:
  - The change in the poverty rate between two times can be decomposed into:
    - Growth effect G: change in poverty due to change in mean income, holding the Lorenz curve constant.
    - Distribution effect D: change in poverty due to change in the Lorenz curve, holding mean income constant at reference level.
    - Residual R.
  - Formal decomposition expression (as in source, equation (1.2)):
    - P_t+n – P_t = G + D + R  (notation following source: (,; )(,; )(,; ) tnt P P Gttnr Dttnr Rttnr ﹢ ﹭ ﹺ — presented in source text as the decomposition).
  - Growth effect definition (source equation (1.3)):
    - G ≡ P(z, L_{t}, μ_{t+n}) − P(z, L_{t}, μ_{t})  (expressed in the source as (,;) (/, ) (/ , )tnrtr Gtt nrPzLPzLμμ ﹫﹩﹢ ).
  - Distribution effect definition (source equation (1.4)):
    - D ≡ P(z, L_{t+n}, μ_{t}) − P(z, L_{t}, μ_{t})  (expressed in source as (,;) (/ , ) (/ , )rtnrt Dtt nrP zLP zLμμ ﹫ ).
  - Residual arises because of nonlinearity; can be specified and interpreted as difference between growth/redistribution components evaluated at terminal and initial Lorenz curves and mean incomes (source gives expressions (1.8), (1.9), (2.0), (2.1) for residual forms).
- Practical calculation using sample surveys (Datt and Ravallion approach):
  - Generic poverty index (source equation (1.5)):
    - P_α = (1/n) Σ_i ((z − y_i)/z)^α for censored terms (notation as in source: ܲ ఈ = ∑ ...).
    - α = 0 yields headcount index; α = 1 yields poverty gap index.
  - Growth and redistribution components computed using two reference-period variants:
    - Using period 1 as reference: decomposition form given (source equation labeled 1.6).
    - Using period 2 as reference: decomposition form given (source equation labeled 1.7).
  - Residual expressions:
    - Residual when using period 1 reference: expression given in source (equation (1.8) and (1.9)).
    - Residual when using period 2 reference: expression given in source (equations (2.0) and (2.1)).
  - Eliminating residual: average the components obtained using period 1 and period 2 as references (source equation (2.2)):
    - P_2 − P_1 = C_1 + C_2, where C_1 and C_2 are averages across the two reference decompositions (source defines C_1 and C_2 via averaging specific P(·) differences).

### V. Analytical outputs and interpretation (diagnostic use)
- Key analytic outputs from IGF diagnostics:
  - Growth Incidence Curves (GIC) to visualize decile-level growth incidence across the distribution.
  - Decile growth effects to assess inequality changes (compare bottom decile growth to average).
  - Growth and distribution effects quantify contributions to poverty change.
- Use in policy:
  - These diagnostic outputs allow policymakers to:
    - Assess whether growth is poverty- and inequality-reducing.
    - Identify which deciles or groups are benefiting from growth.
    - Infer the extent to which poverty reduction is driven by mean income growth versus distributional shifts.
  - Policy recommendations must be country-specific and follow from diagnostics (paper provides only summary policy directions; detailed country analyses required to identify specific reforms).

*Source: IMF working paper "Inclusive Growth Diagnostics Framework" (chapter text provided).*

### 16.      The growth and distribution effects can be estimated using the Distributive

### wp17127 - 16.      The growth and distribution effects can be estimated using the Distributive

### DASP (Distributive Analysis STATA package)
- DASP allows for calculating poverty and inequality indices, conducting decomposition procedures, and building growth incidence curves.
- DASP menus and dialog boxes can be used instead of writing codes.
- DASP supports distributive analysis on more than one database.
- Footnote references in the source:
  - "The latest DASP 2.3 version can be downloaded from http://dasp.ecn.ulaval.ca/modules.htm.  A user manual is available from http://dasp.ecn.ulaval.ca/manuals.htm." (as presented in the source)

### Growth Incidence Curves (GIC): definition and interpretation
- GIC definition (from Ravallion and Chen, 2003; Foster and others, 2013):
  - Vertical axis: growth rate of consumption expenditure.
  - Horizontal axis: consumption expenditure percentiles.
- Formal expression (equation numbering preserved):
  - (2.3) ݃௧ሺ݌ሻ = ܮ௧ᇱሺ݌ሻ ܮ௧ିଵᇱሺ݌ሻ (ߛ௧ ൅1) േ1
  - Explanation in text: ܮ௧ᇱሺ݌ሻ is the rate of change (slope) of the Lorenz curve, ݌ is the deciles of the population, and ߛ௧ is the growth rate of its mean.
- Key GIC interpretations:
  - Parts of the curve above the X-axis: deciles that benefit from growth.
  - Parts below the X-axis: deciles that lost because of growth.
  - If GIC is entirely above the X-axis: growth leads to poverty reduction.
  - If GIC crosses the X-axis: impact of growth on poverty is ambiguous.
  - Segments above the overall mean: deciles benefiting relatively more than an average household.
  - Segments below the mean but above zero: deciles benefiting less than an average household.

### Growth averaging measures and pro-poor vs. inclusive distinctions
- Definitions:
  - Median income growth: change in income of the household at the midpoint of a frequency distribution.
  - Growth in mean income: change in the income of an average household in the whole distribution.
  - Mean growth rate: average income growth of the poor (only of those households that are below the poverty line).
- Relationship and interpretation:
  - "Therefore, the quotient of mean growth income to growth in mean measures shifts in the distribution."
  - "When mean growth is higher than growth in mean, growth can be considered pro-poor, but not yet inclusive as the comparisons of means say nothing about growth at different deciles."

### Stylized cases, slope implications, and algebraic representation
- Six schematic outcomes (as described):
  1. Mean growth zero, GIC overlaps X-axis (no per capita growth).
  2. Positive mean growth, GIC above X-axis.
  3. Mean zero and non-inclusive: GIC with zero mean is positively sloped (negative growth at lower deciles offset by higher growth at higher deciles) → increased inequality.
  4. Mean zero but inclusive: GIC negatively sloped with lower deciles growing and higher deciles declining.
  5. Positive and non-inclusive: mean consumption increases and GIC positively sloped.
  6. Positive and inclusive: mean consumption increases and GIC negatively sloped.
- Shifts in GIC due to growth and inclusiveness (four cases described):
  1. Increase in growth with unchanged inclusiveness → GIC shifts up.
  2. Increase in inclusiveness, not growth → GIC tilts, slope more negative.
  3. Increase in inclusive growth → GIC shifts up and slope more negative.
  4. Increase in growth with worsened inclusiveness → GIC shifts up while slope becomes less negative or positive.
- Slope interpretation:
  - Completely horizontal GIC: growth neutral from distributive perspective.
  - Negatively sloping GIC: inclusive growth (poorer deciles grow faster than richer).
  - Positively sloping GIC: growth not inclusive.
- Formal linear assumption and derived expressions:
  - Assume linear ratio of rate of change of the Lorenz curve:
    - (2.5) ௅೟ᇲሺ௣ሻ ௅೟షభᇲሺ௣ሻ ݌ߚ൅ߙ = 
  - Then:
    - (2.6) ݃௧ሺ݌ሻ = (݌ߚ൅ߙ)(ߛ௧ ൅1) േ1
    - (2.7) ݃௧ሺ݌ሻߙ = (ߛ௧ ൅1) േ1 ൅ߚ(ߛ௧ ൅1)݌
  - Consequences from equation (2.3) (verbatim formulations preserved):
    - ݃௧ሺ݌ሻߛ = ௧, if ܮ௧ᇱሺ݌ሻ ܮ	ൌ ௧ିଵᇱሺ݌ሻ: growth at each decile of incidence curve will be equal to the average growth of the distribution at each decile of the population, if the slope of the Lorenz curve does not change over time.
    - ݃௧ሺ݌ሻߛ൐௧, if ܮ௧ᇱሺ݌ሻ ܮ	൐ ௧ିଵᇱሺ݌ሻ: growth at each decile of the incidence curve will be higher than the average growth of the distribution at each decile of the population, if the slope of the Lorenz curve increases over time.
    - ݃௧ሺ݌ሻߛ൏௧, if ܮ௧ᇱሺ݌ሻ ܮ	൏ ௧ିଵᇱሺ݌ሻ: growth at each decile of the incidence curve will be lower than the average growth of the distribution at each decile of the population, if the slope of the Lorenz curve decreases over time.
    - The slope of the incidence curve is positive if:
      - ݃௧ᇱሺ݌ሻ = ௅೟ᇲᇲ௅೟షభᇲି௅೟ᇲ௅೟షభᇲᇲ (ሺ௅೟షభᇲሻ మ ൐1)
    - The slope of the incidence curve is negative if:
      - ݃௧ᇱሺ݌ሻ = ௅೟ᇲᇲ௅೟షభᇲି௅೟ᇲ௅೟షభᇲᇲ (ሺ௅೟షభᇲሻ మ ൏1)

### Operational steps to assess inclusiveness of growth
- Recommended actions for a country (verbatim operational perspective):
  - (i) establish the slope of the incidence curve based on the information of at least two sequential household surveys;
  - (ii) if the slope is positive, suggesting that growth has not been inclusive, identify measures that could increase the income and spending of the lowest deciles, while increasing the mean growth rate, that is, not at the expense of higher deciles;
  - (iii) if the slope of the incidence curve is negative, suggesting growth has been inclusive, identify measures to increase the absolute value of the slope by making the growth of consumption of lower deciles even faster, without hampering any other deciles; and, alternatively or in addition,
  - (iv) find a measure to reduce inequality in the Lorenz curve coefficient in the next period that would shift the entire incidence curve up.
- Caveat: "The linear form of the growth incidence curve is a simplification assumption taken to illustrate its key properties better. Growth incidence curves usually have complex shapes... analysis for the purposes of public policies should be performed on carefully constructed growth incidence curves based on the two most recent household surveys."

### Applications — Senegal (summary of empirical findings)
- Time periods analyzed: 2001–2005, 2005–2011, and 2001–2011 (figures referenced).
- Main empirical points:
  - Between 2001 and 2005:
    - "consumption increased on average because the mean of the growth incidence curve is above zero, driven by the middle of the distribution (from the 3rd to the 8th deciles)."
    - "The growth incidence curve is positively sloped, suggesting some increase in inequality during this period."
  - Between 2005 and 2011:
    - "the mean of the growth incidence curve is above zero, but the curve is broadly flat, suggesting no clear trend in changes in inequality."
  - For 2001–2011 (overall):
    - "a clear increase in mean consumption confirms the decline in poverty, as the middle class improved their relative position."
    - "for 2001–11 the growth incidence curve has a slightly positive slope, which may point to some worsening of inclusiveness. This trend may not be statistically significant, indicating no substantial distributional changes during this period other than the improvement in the relative position of the middle class."
  - Two-period GIC caveat:
    - "The fact that only two sample periods may raise concern whether these two periods are representative of the 2001‒2011 period."
  - Urban vs. rural differences:
    - Urban areas: "people in the middle of the distribution seem to have benefitted the most from growth." 2001–05 incidence curve substantially above the mean for the whole distribution other than the top decile; 2005–2011 curve hovers around zero and is upward sloping.
    - Rural areas: "The difference between the median growth rates of spending by households in rural areas is closer to the mean growth rate than in urban areas." Overall distributional change heavily influenced by rural changes; rural distribution skewed to the right (most households relatively poorer than mean).
- Overall statistical analysis conclusions for Senegal:
  - (i) "poverty in this country has fallen in the last two decades, although poverty reduction has slowed in recent years;"
  - (ii) "although available indicators sometimes give conflicting signals on distributional shifts, growth seems to have benefitted most people in the middle of the income distribution;"
  - (iii) "the middle class has benefitted from growth, mainly in urban areas, while both the poorest and the richest have lost ground."

*wp17127 - 16.      The growth and distribution effects can be estimated using the Distributive*

### 31.      In this case of Djibouti (for details see Kireyev, 2017), the growth inclusiveness

### Growth inclusiveness analysis — Djibouti (2002–2013)

### Data and methods
- Analysis is based on two household surveys conducted in 2002 and 2012, and updated in 2013 (Enquête d’Auprès des Ménages pour les Indicateurs Sociaux–Budget et Consommation, EDAM2-2002, EDAM3-2012 et EBC-2013).
- Decomposition of poverty changes separates growth and distribution effects using Datt & Ravallion approaches (reference period t1 or t2) and the Shapley approach (average of both years).
- Growth inclusiveness is assessed via Growth Incidence Curves (GICs) with 95 percent confidence bounds.
- Confidence intervals indicate relatively low statistical significance for many estimates.

### Key poverty and distribution outcomes
- Extreme poverty: reduced from 24.1 percent in 2002 to 23 percent in 2013 (based on new poverty thresholds calculated in 2013).
- Overall poverty: dropped from 46.7 percent to 40.8 percent between 2002 and 2013.
- Urban/rural disparity (2013): capital (urban) extreme and overall poverty rates at 16.5 and 34.2 percent, respectively; rest of the country at 44.5 and 62.5 percent, respectively.
- Change decomposition (2012 → 2013, overall poverty rate):
  - Overall poverty rate dropped by 5.9 percentage points.
  - Growth effect contributed 8.8 ppts.
  - Distribution effect subtracted 2.9 ppts.
- Extreme poverty change (2012 → 2013):
  - Improvement marginal, only 1 ppt, as most gains from growth were offset by losses from the distribution effect.
- Poverty gaps:
  - Overall poverty gap improvement marginal, at about one percentage point, with growth effect nearly offset by negative distribution effect.
  - Extreme poverty gap increased by about 0.5 percentage points due to a strongly negative distribution effect that could not be offset by growth.

### Growth incidence and distributional patterns (2002–13)
- Mean household consumption increased on average (mean of the GIC is above zero), driven by the middle of the distribution (from the 2nd to the 10th deciles).
- The GIC is positively sloped, suggesting an increase in inequality during this period.
- For low percentiles, the GIC is below the horizontal axis: at least 10 percent of the poorest groups experienced a negative growth rate of their living standards.
- The 95 percent confidence interval around the GIC touches or crosses the X-axis several times (notably in the 5th to the 8th percentiles), indicating a substantial margin of error and marginal statistical significance for some changes.
- After shifting the GIC to align its mean with the X-axis (displaced GIC):
  - Up to the 8th decile the curve is below the X-axis — for 80 percent of the poorest population, consumption grew slower relative to the wealthiest 20 percent.
  - The two poorest deciles clearly experienced lower growth of consumption even relative to an average; their 95 percent confidence interval is squarely below the horizontal axis.
  - Consumption of the high-income deciles (above the 8th decile) clearly increased.

### Main findings and interpretation
- (i) Overall poverty declined in 2002-13, although there has been no significant change in extreme poverty.
- (ii) Inequality remains high and there are indications that inequality may have worsened.
- (iii) Growth was not inclusive in 2002-13: it mainly benefited people on the upper side of the income distribution, while the poorest groups became even poorer in relative terms.
- (iv) Based on comparator experiences, growth in rural areas most likely was less inclusive than in urban areas, and gender disparity might have increased; existing statistics do not permit direct assessment of these two effects for Djibouti.
- (v) Underlying data are marginally sufficient and not entirely comparable between surveys; statistical significance of most estimates is low and margins of error are high, so results are indicative pending better data.

### Policy implications and recommendations
- The distribution effect worked against the growth effect; poverty reduction could have been substantially higher if the distribution effect had been at least neutral or positive.
- Decomposing changes in poverty into growth and distribution effects is essential to identify policies that ensure both effects work toward poverty reduction.
- Growth inclusiveness diagnostics (GICs and decomposition) provide actionable guidance to target households that need the most help and to replace generalized incentives with well-targeted support measures.

- Box 1 — Policies to Increase Growth Inclusiveness (selected recommendations reproduced from the source)
  - Sustained economic growth and well-designed public policies are the preconditions.
  - Structural policies (pre-distribution policies)
    - Improve access to education and healthcare
    - Build inclusive institutions
    - Promote gender inclusiveness
    - Accelerate infrastructure reforms (energy, irrigation)
    - Introduce flexible labor market policies
  - Fiscal policies (redistribution policies)
    - Cut (progressive) direct taxes
    - Increase (regressive) indirect taxes
    - Increase the tax base – reduce informality
    - Increase public investment
  - Financial sector policies
    - Improve access to financial services
    - Align financial reforms with capacity
  - Agricultural policies
    - Improve productivity, reduce productivity gap
    - Eliminate unproductive subsidies

### Concluding note
- The inclusive growth framework allows coherent quantification of growth, poverty, and inequality effects; GICs and decomposition analyses help identify households and policies to improve growth inclusiveness, but better data are needed to increase statistical confidence and to design targeted reforms.

*Source: IMF staff analysis (excerpt from wp17127: Growth Inclusiveness in Djibouti, 2002–2013).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17127.pdf_