## _wp0447

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---

### I. Scope, definitions, and empirical strategy
- Adopts broader definition of pro-poor growth: "growth is pro-poor if the poverty measure of interest falls" (Ravallion and Chen (2003)).
- Decomposes changes in poverty into three potential sources of pro-poor growth:
  - (a) a high rate of growth of average incomes;
  - (b) a high sensitivity of poverty to growth in average incomes;
  - (c) a poverty-reducing pattern of growth in relative incomes.
- Uses household-survey data and variance decompositions to summarize relative importance of the three sources and to investigate correlates of these sources in a large panel of spells (short and long).

### II. Data, samples, and construction of measures
- Data source and poverty line:
  - Household survey data (Ravallion–Chen), ten-point Lorenz information, averages in 1993 dollars PPP.
  - Dollar-a-day poverty line: $1.08 per day, or $393 per year (1993 dollars).
- Sample construction:
  - Start: 285 surveys; constructed spells produce:
    - Dataset 1 (all possible spells, discard income↔expenditure switches): 205 spells (trimmed to 128 spells covering 58 countries; average length 3.5 years).
    - Dataset 2 (one longest spell per country): 80 spells (trimmed to 42 spells; average length 9.6 years).
  - Trimming rules: drop spells with headcount < 2 percent in either period; drop spells with |average annual growth rate in survey mean| > 15 percent.
- Lorenz-curve estimation:
  - Assumes specified functional form and estimates parameters α, β, γ using combinations of three Lorenz points with averaging across valid estimates.
  - Quantile function obtained analytically; η_t(p) constructed for each poverty measure.
- Poverty measures constructed: headcount (P0), poverty gap (P1), squared poverty gap (P2), Watts index, EDEI (Atkinson) variants.

### III. Empirical framework and decomposition
- Continuous-time identity:
  - dP_t/dt = ∫_0^1 η_t(p) ⋅ g_t(p) dp,
    - η_t(p) ≡ ∂f_t/∂y evaluated at y_t(p);
    - g_t(p) ≡ (1/y_t(p)) ⋅ dy_t(p)/dt (growth incidence curve).
- Decomposition separating average-income growth:
  - dP_t/dt = (dμ_t/dt / μ_t) ⋅ ∫_0^1 η_t(p) dp + ∫_0^1 η_t(p) ⋅ (g_t(p) - dμ_t/dt / μ_t) dp.
  - First term: captures average-income growth and average sensitivity of poverty to average-income growth.
  - Second term: captures changes in relative incomes (pattern of relative growth).
- Discrete-time decomposition (Datt and Ravallion (1992) analog):
  - Decomposes proportional change in poverty into Growth component (G), Distribution component (D), and a small Residual (R); proportional changes measured as log differences and normalized by spell length for annual rates.

### IV. Illustrative examples and sensitivity of poverty measures
- China 1990–1998:
  - Survey average incomes grew at 14 percent per year.
  - Dollar-a-day headcount fell from 51 percent to 33 percent.
  - Gini rose from 34 to 40.
  - Relative growth: poorest 80 percentiles grew below average; richest 20 percent grew above average.
- Indonesia 1996–1999:
  - Survey mean income fell at nearly 9 percent per year.
  - Gini fell from 36.5 to 31.5.
  - Relative growth: downward sloping; richer percentiles fell faster than poorer percentiles; only richest 20 percent recorded below-average growth.
  - Dollar-a-day headcount rose from 8 percent to 13 percent (large negative average-growth effect dominated).
- Sensitivity patterns (example China 1990 distribution):
  - Headcount: sensitivity zero except just below poverty line where it spikes to minus infinity.
  - Poverty gap: most sensitive near the poverty line; non-zero for all poor.
  - Squared poverty gap: U-shaped sensitivity across poor percentiles.
  - Watts index: equally sensitive to growth for all percentiles below the poverty line.
  - EDEI (θ<1): most sensitive to the poorest; non-zero for all percentiles (no discontinuity at poverty line).
- Implication: whether relative growth is pro-poor depends crucially on the poverty measure used.

### V. Main empirical findings (variance decomposition and magnitudes)
- Key summary:
  - Roughly half of the variation in short-run changes in poverty is explained by growth in average incomes.
  - In medium- to long-run, between 66 and 90 percent of variation in changes in poverty can be accounted for by growth in average incomes; virtually all remainder due to changes in relative incomes.
  - Cross-country differences in sensitivity of poverty to average-income growth account for very little of the variation in changes in poverty.
- Correlations (Table 1):
  - All spells (128 observations) — Correlations of poverty measures with survey mean:
    - Head count: -0.842 (Levels), -0.590 (Growth Rates)
    - Poverty Gap: -0.727, -0.519
    - Squared poverty gap: -0.615, -0.472
    - Watts: -0.647, -0.489
  - Long spells (42 observations):
    - Headcount: -0.935 (Levels), -0.717 (Growth Rates)
    - Poverty gap: -0.722, -0.672
    - Squared poverty gap: -0.630, -0.635
    - Watts: -0.651, -0.640
- Decomposition variance shares (selected entries from Tables 2 and 3):
  - All spells — Share of variance of changes in poverty due to (G+D) vs Residual:
    - Head count: Share = 0.9859
    - Poverty gap: Share = 0.9877
    - Squared poverty gap: Share = 0.9914
    - Watts: Share = 0.9917
  - All spells — Share of variance due to Growth (G) vs Distribution (D):
    - Head count: Share of Variance Due to G = 0.4912
    - Poverty gap: 0.3781
    - Squared poverty gap: 0.3134
    - Watts: 0.3300
  - Long spells — Share of variance due to Growth (G):
    - Head count: 0.9077
    - Poverty gap: 0.7500
    - Squared poverty gap: 0.6538
    - Watts: 0.6779
  - Disentangling Growth component (log decomposition ln|G| = ln|dln μ| + ln|η|) — Share of variance of growth component due to |dln μ|:
    - All spells, Head count: Share = 0.8086
    - Long spells, Head count: Share = 0.8278
    - Comparable shares for other measures range from 0.8259 to 0.8491 (see Tables 2–3 for exact entries).
- Visual fits (Figure 3, long spells):
  - Headcount: y = -1.16x  - 0.01, R^2 = 0.51
  - Poverty Gap: y = -1.44x  - 0.01, R^2 = 0.45
  - Squared poverty gap: y = -1.63x  - 0.01, R^2 = 0.40
  - Watts: y = -1.52x  - 0.01, R^2 = 0.41

### VI. Interpretation, measurement error, and horizons
- EDEI example (log decomposition, Equation (6) in source):
  - EDEI(1) = average income; sensitivity of EDEI to average-income growth is one; distributional change corresponds to proportional change in one minus the Atkinson inequality measure.
- Under lognormal income assumption, ln EDEI(θ) converges to 2
  σ^2 θ μ⋅+ (as number of households large), implying:
  - The further θ is from one (more bottom-sensitive), the smaller the share of variance due to growth and larger the share due to distributional change.
- Measurement error hypothesis:
  - Additive zero-mean measurement error inflates measured variance by 22
  ξσ+ (notation as in source); measurement-error variance that fluctuates randomly implies average annual change in distribution component smaller the longer the interval k. Measurement error can help explain lower growth-share in short horizons.

### VII. Correlates of growth in survey mean and distributional change (regression evidence)
- Dependent variables:
  - Growth in average household incomes (annual percent).
  - Five measures of changes in relative incomes: average annual change in Gini; distribution components for P0, P1, P2, Watts.
- Right-hand-side variables (Dollar and Kraay (2002) set and additions):
  - Institutional quality: KK rule of law, CPIA, voice and accountability.
  - Openness: Trade/GDP.
  - Inflation: ln(1+CPI inflation rate).
  - Government size: Government-Consumption/GDP.
  - Financial development: M2/GDP.
  - Relative productivity in agriculture; average years of primary education.
- Overall statistical significance:
  - Across 108 regressions (Tables 4 and 5), only one coefficient significant at the 5 percent level and three at the 10 percent level.
  - Small sample sizes and measurement error noted as limitations; multiple spells per country induce negative error correlation inflating standard errors in some specifications.
- Qualitative patterns (partial correlations and multivariate Table 6):
  - Institutional quality (rule of law):
    - Positively correlated with growth.
    - Positively correlated with some measures of distributional change (i.e., distributional change tends to raise poverty in better-rule-of-law countries in sample).
    - Growth t-stat ≈ 2× average t-stat for distributional-change regressions.
  - Openness to trade:
    - Correlation with growth generally stronger than with distributional change.
    - Correlations with distributional-change measures are negative → distributional change tends to be poverty-reducing in more open countries.
  - Inflation: extremely weak correlation with growth; weakly positive with distributional change.
  - Government consumption:
    - Negatively correlated with growth.
    - Negatively correlated with distributional change → distributional change tends to be pro-poor in countries with larger governments.
  - Financial development: very weak correlations.
  - Relative productivity in agriculture: essentially uncorrelated with growth; tends to be positively correlated with distributional-change measures in this sample.
  - Primary education: virtually uncorrelated with growth and most distributional-change measures (exception: Gini in long-spells regressions).
- Selected multivariate coefficients (Table 6, long-spells regressions, 42 observations; heteroskedasticity-consistent t-statistics reported in source):
  - Initial income:
    - Headcount growth component: -0.017 (t=1.978)
    - Headcount distribution component: -0.008 (t=1.470)
  - KK rule of law:
    - Headcount growth: 0.022 (t=2.050)
    - Headcount distribution: 0.009 (t=0.919)
  - Trade/GDP:
    - Headcount growth: 0.045 (t=1.978)
    - Headcount distribution: -0.011 (t=0.911)
  - Government consumption:
    - Headcount growth: -0.280 (t=2.229)
    - Headcount distribution: -0.048 (t=0.425)
  - Regression fit examples:
    - R-squared: Headcount growth 0.239; Headcount distribution 0.095; Watts growth 0.263; Watts distribution 0.182.

### VIII. Policy implications and conclusions emphasized in the paper
- Primary conclusion:
  - In medium-to-long run, cross-country differences in growth in average incomes (source (a)) are the dominant explanation for changes in poverty; start pro-poor growth strategy by focusing on determinants of average-income growth.
- Policy guidance drawn from correlates and net effects (illustrated in Figure 5):
  - Institutional quality (rule of law): promotes growth (poverty-reducing via growth) but may coincide with distributional shifts that raise poverty; net effect in sample tends to be poverty-reducing because growth effect dominates.
  - Trade openness: associated with higher growth and with distributional shifts that reduce poverty in sample; both effects tend to lower poverty.
  - Government size: associated with slower growth but with distributional shifts that reduce poverty; net effect often dominated by adverse growth impact.
  - Recommended core policy package for pro-poor growth emphasizes known determinants of average-income growth, e.g.:
    - protection of property rights;
    - stable macroeconomic policies;
    - openness to international trade.
- Limits and further research:
  - Correlates of distributional change are weak and inconsistent; cross-country analysis is unlikely to identify robust policy levers for poverty-reducing distributional change.
  - Advocates for more micro-level and case-study research to understand determinants of poverty-reducing shifts in relative incomes.

*Source: _wp0447 (PDF)*

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

### _wp0447 - References....................................................................................................................

### Tables
- 1. Correlations of Poverty Measures and Survey Mean Income or Consumption......... 22
- 2. Decomposing Changes in Poverty: All Spells ........................................................... 23
- 3. Decomposing Changes in Poverty: Long Spells........................................................ 24
- 4. Correlates of Pro-Poor Growth: All Spells ................................................................ 25
- 5. Correlates of Pro-Poor Growth: Long Spells............................................................. 26
- 6. Multivariate Growth and Distributional Change Regressions ................................... 27

### Figures
- 1. Relative Growth Incidence Curves ............................................................................ 28
- 2. Sensitivity of Poverty to Growth in Percentile p ....................................................... 29
- 3. Growth and Poverty Reduction: Long Spells ............................................................ 30
- 4. Decomposing Changes in the Headcount .................................................................. 31

*Source: _wp0447 - References (PDF)*

### 5. Policies and Growth and Distribution Components of Changes in Policy ................ 32

### 5. Policies and Growth and Distribution Components of Changes in Policy ................ 32

### I. Introduction — scope and definitions
- Adopts the broader definition of pro-poor growth: "growth is pro-poor if the poverty measure of interest falls" (Ravallion and Chen (2003)).
- Decomposes changes in poverty into three potential sources of pro-poor growth:
  - (a) a high rate of growth of average incomes;
  - (b) a high sensitivity of poverty to growth in average incomes;
  - (c) a poverty-reducing pattern of growth in relative incomes.
- Implements decomposition for several poverty measures using household-survey data for a large sample of countries in the 1980s and the 1990s.
- Uses variance decompositions to summarize relative importance of the three sources and investigates correlates of these sources in a large panel of observations on changes in poverty.

### Main empirical findings (summary from the paper)
- Relative importance of sources:
  - Roughly half of the variation in short-run changes in poverty can be explained by growth in average incomes.
  - In the medium- to-long run, between 66 and 90 percent of the variation in changes in poverty can be accounted for by growth in average incomes.
  - Virtually all of the remainder is due to changes in relative incomes.
  - Cross-country differences in the sensitivity of poverty to growth in average incomes account for very little of the variation in changes in poverty.
- Correlates of growth in household-survey incomes:
  - Some evidence that growth in household-survey incomes is correlated with institutional quality, openness to international trade, and size of government (traditional empirical growth determinants).
  - The evidence is not especially compelling, likely reflecting limited country coverage and measurement error in household-survey data.
- Correlates of poverty-reducing patterns of growth in relative incomes:
  - Relatively little evidence that poverty-reducing patterns of distributional change are significantly correlated with variables identified in the empirical growth literature as determinants of growth in per capita GDP.
  - The same lack of robust correlation holds for a number of other variables suggested in the literature as potentially reducing inequality.

### II. Empirical framework — decomposition and interpretation
- Notation and generic additive poverty measure:
  - y_t(p) = income of the pth percentile at time t, written as y_t(p) = μ_t ⋅ dL_t(p)/dp.
  - Generic additive poverty measure: P_t = ∫_0^1 f_t(p, y_t(p)) dp.
- Differentiation yields (rate of change in poverty):
  - dP_t/dt = ∫_0^1 η_t(p) ⋅ g_t(p) dp,
    - where η_t(p) ≡ ∂f_t/∂y evaluated at y_t(p) is the semi-elasticity of the poverty measure to income at percentile p,
    - and g_t(p) ≡ (1/y_t(p)) ⋅ dy_t(p)/dt is the growth rate of income at percentile p (the growth incidence curve).
- Decomposition separating average income growth:
  - dP_t/dt = (dμ_t/dt / μ_t) ⋅ ∫_0^1 η_t(p) dp  +  ∫_0^1 η_t(p) ⋅ (g_t(p) - dμ_t/dt / μ_t) dp.
  - First term captures: (a) growth in average incomes and (b) sensitivity of poverty to average income growth (average of η_t(p)).
  - Second term captures: changes in relative incomes (pattern of growth across percentiles relative to average), weighted by η_t(p).
- Interpretations of pro-poor growth:
  - Kakwani and Pernia (2000) definition: growth is pro-poor iff the second term is negative (pattern of relative growth reduces poverty).
  - Ravallion and Chen (2003) broader definition: growth is pro-poor if the poverty measure falls; under this, three potential sources are as listed above.

### Illustrative examples and sensitivity of poverty measures
- China 1990–1998 (example from paper):
  - Survey average incomes grew at 14 percent per year.
  - Dollar-a-day headcount fell from 51 percent to 33 percent of the population.
  - Gini coefficient rose from 34 to 40.
  - Relative growth incidence: poorest 80 percentiles grew below average; richest 20 percent grew above average.
- Indonesia 1996–1999 (example from paper):
  - Survey mean income fell at nearly 9 percent per year (East Asian financial crisis).
  - Gini fell from 36.5 to 31.5.
  - Relative growth incidence: downward sloping; richer percentiles fell faster than poorer percentiles; below-average growth recorded only for the richest 20 percent.
  - Despite pro-poor relative pattern, dollar-a-day headcount increased from 8 percent to 13 percent due to large negative average-growth effect.
- Sensitivity patterns by poverty measure (using China 1990 distribution as example):
  - Headcount: sensitivity zero everywhere except just below the poverty line where it spikes to minus infinity (headcount responds only to those crossing the poverty line).
  - Poverty gap: most sensitive to those at the poverty line, non-zero for all poor people.
  - Squared poverty gap: U-shaped sensitivity across poor percentiles; most sensitive to intermediate poor percentiles.
  - Watts index: equally sensitive to growth in all percentiles below the poverty line.
  - EDEI (Atkinson’s equally distributed equivalent income) with inequality aversion (θ<1): most sensitive to the poorest, non-zero for all percentiles (no discontinuity at the poverty line).
- Implication: whether a pattern of relative income growth is pro-poor depends crucially on the chosen poverty measure; pro-poor strategies must be aligned to the poverty measure target (e.g., headcount vs. EDEI).

### III. Data — surveys, spells, and sample construction
- Data source:
  - Household survey data on average incomes and ten points on the Lorenz curve compiled by Martin Ravallion and Shaohua Chen at the World Bank.
  - Surveys measure either income or consumption depending on country; averages measured in 1993 dollars and adjusted for PPP.
  - World Bank “dollar-a-day” poverty line used: $1.08 per day, or $393 per year (1993 dollars).
- Sample construction:
  - Start: 285 surveys covering 80 developing countries (most survey dates in the 1990s; some in the 1980s).
  - Dataset 1 (all possible spells per country, discarding income↔expenditure survey switches): 205 spells; average length 3.5 years; range 1 to 13 years.
  - Dataset 2 (one spell per country maximizing spell length): 80 spells; average length 8.2 years; range 2 to 19 years.
  - Trimming:
    - Eliminate spells where headcount < 2 percent in either period.
    - Drop spells where average annual growth rate in survey mean is implausibly large: more than 15 percent in absolute value.
  - After trimming:
    - First dataset reduced to 128 spells covering 58 countries with an average length of 3.5 years.
    - Second dataset reduced to 42 spells with an average length of [text truncated in source].

### IV. Policy implications emphasized in the paper
- Central role of average-income growth:
  - Cross-country evidence underscores the importance of growth in average incomes for poverty reduction.
  - Suggests policy package focusing on known determinants of growth in average incomes should be core to pro-poor growth strategies, for example:
    - protection of property rights;
    - stable macroeconomic policies;
    - openness to international trade.
- On trade-offs between growth and distribution:
  - Absence of compelling evidence that growth-promoting policies are systematically correlated with adverse distributional changes that matter most for poverty reduction suggests no obvious trade-offs at the cross-country level.
- Limits and further research:
  - Growth in average incomes is not sufficient for poverty reduction in all cases.
  - Cross-country evidence is unlikely to be very informative about policies/institutions that lead to poverty-reducing patterns of relative-income growth.
  - Recommends more micro-level and case-study research to shed light on determinants of poverty-reducing distributional change.

*Source: _wp0447 - 5. Policies and Growth and Distribution Components of Changes in Policy ................ 32*

### 9.6 years.

### _wp0447 - 9.6 years.

### Lorenz curve estimation and construction of poverty measures
- Uses Ravallion–Chen data 10-point Lorenz information; requires full Lorenz curve to construct poverty measures and decompositions.
- Assumes Lorenz curve functional form: ()1,10,0,)1(1)(≥≤<≥−−⋅=γβα
γ
βα
pppL (Equation (4) in source).
- Parameter estimation:
  - Follows Sarabia, Castillo, and Slottje (1999) algorithm: select all combinations of three Lorenz points, solve for α, β, γ so the curve passes through the three points.
  - Final α, β, γ are averages across valid estimates, discarding those violating Equation (4) parameter restrictions (required for positive first and second derivatives).
- Quantile function obtained by analytically differentiating the Lorenz curve and multiplying by average income.
- Constructs η_t(p) for each poverty measure and computes growth incidence over the observed discrete interval: 1
)(
)(
)(
1
−=
−
py
py
pg
t
t
t
.

### Poverty measures, correlations with mean income growth, and visual evidence
- Poverty measures constructed: headcount, poverty gap, squared poverty gap, Watts index for initial and final years of each spell.
- Computes average annual changes normalized by initial value to obtain proportionate changes.
- Table 1: simple correlations of levels and average annual growth rates of poverty measures with corresponding log-levels and growth rates of survey mean income:
  - All simple correlations are negative and large in absolute value, especially those in levels and for long spells.
- Figure 3 (long spells sample): strong and highly significant negative relationship between changes in poverty and change in average incomes.
  - More dispersion for bottom-sensitive measures (poverty gap, squared poverty gap) than for headcount, potentially reflecting measurement error sensitivity in individual incomes.

### Decomposition method for sources of pro-poor growth
- Decomposes change in poverty into a “growth component” and a “distribution component” using Datt and Ravallion (1992) discrete-time analog (Equation (5) in source).
  - Growth component: proportional difference between initial poverty measure and hypothetical poverty using second period mean with first period Lorenz curve.
  - Distribution component: proportional difference between initial poverty measure and hypothetical poverty using first period mean with second period Lorenz curve.
  - Residual term arises because decomposition is discrete rather than infinitesimal.
- Measures proportional changes as log differences and normalizes by spell length to get average annual percent changes for each spell.

### Variance decomposition and relative importance of components
- Uses variance-share formula for X and Y: share of variance of X+Y due to X = ),(2)()(
),()(
YXCOVYVARXVAR
YXCOVXVAR
⋅++
+
. (As in source.)
- Top-panel findings (Tables 2 and 3):
  - Variance of residual is tiny relative to variance in measured changes in poverty.
  - Share of variance of changes in poverty due to sum of growth and distribution components is virtually one for all poverty measures.
- Middle-panel findings (growth vs distribution component):
  - Sample of all spells: between one-third and one-half of variation in changes in poverty is due to the growth component; remainder due to distributional change.
  - Long spells: growth component dominates, accounting for between 65 and 90 percent of changes in poverty.
  - Growth component relatively less important for bottom-sensitive poverty measures (poverty gap, squared poverty gap).
  - Visual evidence (Figure 4) supports that large poverty reduction is mostly due to large growth-component reductions.
- Bottom-panel findings (disentangling growth component):
  - Decomposes growth component into growth in average incomes and sensitivity of poverty to income growth.
  - Over 80 percent of cross-country variation in the growth component of poverty change is due to cross-country differences in average income growth; very little due to differences in sensitivity of poverty to growth.
  - Visual evidence: when growth component of poverty reduction is large, it is typically because growth itself was large, not because sensitivity was large.

### Interpretation using EDEI example and role of measurement error
- For EDEI measure, discrete proportional change written as: ())1(ln)(ln)1(ln)(ln
tttt
EDEIEDEIEDEIEDEI∆−∆+∆=∆θθ (Equation (6) in source).
  - EDEI(1) = average income; sensitivity of EDEI to average-income growth is one.
  - Distributional change corresponds to proportional change in one minus the Atkinson inequality measure.
- Under lognormal income assumption, ln EDEI(θ) converges to 2
2
σ
θ
μ⋅+ (as number of households large), yielding decomposition (Equation (7) in source).
- Implications:
  - The further θ is from one (more bottom- or top-sensitive), the smaller the share of variance due to growth and larger the share due to distributional change.
  - Explains why growth share declines as poverty measures become more bottom-sensitive.
- Measurement error hypothesis for shorter horizons:
  - If log household income measured with additive zero-mean measurement error i.i.d. normal across households, average income unaffected but measured variance inflated by 22
tt
ξσ+, where 2
t
ξ is measurement-error variance.
  - If measurement-error variance fluctuates randomly, average annual change in distribution component will be smaller the longer the interval k, suggesting measurement error could explain smaller growth-share in short horizons.

### Empirical summary of decomposition results
- Over longer horizons, between 65 and 90 percent of cross-country differences in poverty changes can be accounted for by growth in average incomes.
- Over shorter horizons, share due to growth is smaller and distributional changes relatively more important (potentially due in part to measurement error).
- Cross-country differences in sensitivity of poverty to growth exist but are empirically less important than differences in growth rates themselves.
- Residuals from discrete-time decomposition are small and do not undermine main conclusions.

### Correlates of growth in average incomes and distributional change (partial correlations)
- Focuses on first and third sources of pro-poor growth: growth in average incomes and changes in relative incomes.
- Dependent variables:
  - Growth in average incomes (average annual growth rate of household mean income or consumption).
  - Five measures of changes in relative incomes: average annual change in Gini; distribution components for headcount, poverty gap, squared poverty gap, Watts index.
- Right-hand-side variables (as in Dollar and Kraay (2002) set):
  - Institutional quality: “rule of law” (Kaufmann, Kraay, and Mastruzzi (2003)) and CPIA.
  - Openness: exports plus imports to GDP (constant-price local currency).
  - Inflation: log(1 + CPI inflation rate).
  - Government size: government consumption share in GDP.
  - Financial development: M2 to GDP.
  - Additional: voice and accountability, relative productivity in agriculture (value added per worker in agriculture relative to overall), primary educational attainment.
- Limitations noted:
  - Small sample, especially long spells (one spell per country), substantial measurement error in survey mean growth and distributional change measures.
  - Few spells per country prevent meaningful within-country identification; possible unobserved country-specific confounders.
  - Lagged dependent-variable regressions problematic for consistency with unobserved effects.

### Regression evidence (Tables 4–6) — patterns and magnitudes
- Overall statistical significance:
  - Across 108 regressions (Tables 4 and 5), only one coefficient significant at the 5 percent level and three at the 10 percent level.
  - Measurement error may inflate standard errors; some upward bias in standard errors in Table 4 due to negative error correlation across multiple spells per country.
- Qualitative patterns:
  - Institutional quality (rule of law):
    - Positively correlated with growth.
    - Positively correlated with measures of distributional change (i.e., distributional change tends to raise poverty in countries with good institutional quality).
    - Correlation with growth is much stronger than with distributional change (growth t-stat ≈ 2× average t-stat for distributional-change regressions).
    - Voice and accountability shows similar pattern (highly correlated with rule of law in sample).
  - Openness to trade:
    - Correlation with growth generally stronger than with distributional change.
    - Correlations with distributional change measures are negative → distributional change tends to be poverty-reducing in more open countries.
  - Inflation:
    - Extremely weak correlation with growth.
    - Weakly positive correlation with distributional change.
  - Government consumption:
    - Negatively correlated with growth.
    - Negatively correlated with distributional change → distributional change tends to be pro-poor in countries with larger governments.
  - Financial development:
    - Very weak correlation with either growth or distributional change.
  - Relative productivity in agriculture:
    - Essentially uncorrelated with growth.
    - Tends to be positively correlated with distributional change measures (suggesting higher relative agricultural productivity associated with poverty-increasing shifts in relative incomes in this sample).
  - Primary education:
    - Virtually uncorrelated with growth and most distributional-change measures (exception: Gini in long-spells regression).

- Table 6 (long spells, multivariate specification):
  - Growth regression including initial income, institutional quality, trade openness, and government consumption:
    - Initial income negative (convergence); institutional quality and trade positive; government size negative (consistent with growth literature).
  - Change in Gini: none of these correlates are significantly correlated.
  - Regressions for growth components of headcount and Watts index resemble growth regression results (institutional quality, trade, government size significant), while distribution components show very little evidence of significant correlation.
  - Exception: institutional quality significant at 10 percent in headcount distribution component regression; sign indicates poverty-increasing distributional change more likely in countries with better institutional quality.
  - Net effects (illustrated in Figure 5 for headcount):
    - Rule of law: growth effect lowers poverty; distribution effect raises poverty; net effect negative because growth effect larger.
    - Trade: both growth and distribution effects reduce poverty; growth effect much larger.
    - Government size: growth and distribution effects work in opposite directions; adverse growth effect dominates smaller poverty-reducing distribution effect.

### Conclusions and policy implications
- Identified three potential sources of pro-poor growth: (a) high rate of growth of average incomes, (b) high sensitivity of poverty to average-income growth, (c) poverty-reducing pattern of growth in relative incomes.
- Empirical findings:
  - Only (a) and (c) are empirically relevant in these decompositions.
  - In medium-to-long run, cross-country differences in growth in average incomes are the dominant explanation for poverty changes.
  - Therefore, search for pro-poor growth should begin by focusing on determinants of growth in average incomes.
- Caveats and open issues:
  - Correlates of growth in survey means are noisy; translating per capita GDP growth determinants into growth in survey means remains imperfectly understood.
  - Significant correlates of distributional change are hard to find; cross-country partial correlations are often insignificant or inconsistent across studies.
  - Some tradeoffs suggested by partial correlations:
    - Rule of law: promotes growth but may coincide with poverty-increasing relative-income shifts (net effect in sample tends to be poverty-reducing).
    - Government size: associated with slower growth but with distributional shifts that reduce poverty (net effect often dominated by growth cost).
    - Trade: associated with higher growth and poverty-reducing distributional shifts in this sample.
- Overall: prioritize policies and institutions that raise average income growth to achieve pro-poor outcomes, while recognizing the complexity and weak statistical regularities in determinants of distributional change.

*Source: IMF working paper content from _wp0447 - 9.6 years.*

### conclusions about the determinants of pro-poor changes in relative incomes from any one

### _wp0447 - conclusions about the determinants of pro-poor changes in relative incomes from any one

### Correlations of Poverty Measures and Survey Mean Income or Consumption (Table 1)
- Sample: All spells (128 observations)
  - Head count: -0.842 (Levels), -0.590 (Growth Rates)
  - Poverty Gap: -0.727, -0.519
  - Squared poverty gap: -0.615, -0.472
  - Watts: -0.647, -0.489
- Sample: Long spells (42 observations)
  - Headcount: -0.935 (Levels), -0.717 (Growth Rates)
  - Poverty gap: -0.722, -0.672
  - Squared poverty gap: -0.630, -0.635
  - Watts: -0.651, -0.640
- Source: Author's calculations.

### Decomposing Changes in Poverty: Growth, Distribution, and Residual Components (Tables 2 and 3)
- Decomposition formula: dP = G + D + R
- All spells (Table 2)
  - Growth and Distribution Components vs Residual (G+D vs R)
    - Head count: V(G+D)=0.0284, V(R)=0.0008, COV(G+D,R)=-0.0004, Share of Variance Due to G+D=0.9859
    - Poverty gap: V(G+D)=0.0485, V(R)=0.0010, COV(G+D,R)=-0.0004, Share=0.9877
    - Squared poverty gap: V(G+D)=0.0702, V(R)=0.0013, COV(G+D,R)=-0.0007, Share=0.9914
    - Watts: V(G+D)=0.0599, V(R)=0.0010, COV(G+D,R)=-0.0005, Share=0.9917
  - Growth vs Distribution Components (G vs D)
    - Head count: V(G)=0.0168, V(D)=0.0173, COV(G,D)=-0.0029, Share of Variance Due to G=0.4912
    - Poverty gap: V(G)=0.0216, V(D)=0.0334, COV(G,D)=-0.0033, Share=0.3781
    - Squared poverty gap: V(G)=0.0255, V(D)=0.0517, COV(G,D)=-0.0035, Share=0.3134
    - Watts: V(G)=0.0231, V(D)=0.0435, COV(G,D)=-0.0033, Share=0.3300
  - Average Growth and Sensitivity to Average Growth in Growth Component: ln|G| = ln|dln μ| + ln|η|
    - Head count: V(|dlnμ|)=1.12900, V(|η|)=0.15770, COV(|dlnμ|,|η|)=0.14360, Share of Variance Due to |dlnμ|=0.8086
    - Poverty gap: 1.10890, 0.13110, 0.12020, 0.8302
    - Squared poverty gap: 1.10730, 0.13690, 0.12240, 0.8259
    - Watts: 1.10210, 0.12430, 0.11350, 0.8364
- Long spells (Table 3)
  - Growth and Distribution Components vs Residual (G+D vs R)
    - Head count: V(G+D)=0.0064, V(R)=0.0005, COV(G+D,R)=-0.0004, Share=0.9836
    - Poverty gap: V(G+D)=0.0120, V(R)=0.0008, COV(G+D,R)=-0.0010, Share=1.0185
    - Squared poverty gap: V(G+D)=0.0181, V(R)=0.0011, COV(G+D,R)=-0.0017, Share=1.0380
    - Watts: V(G+D)=0.0148, V(R)=0.0009, COV(G+D,R)=-0.0011, Share=1.0148
  - Growth vs Distribution Components (G vs D)
    - Head count: V(G)=0.0077, V(D)=0.0024, COV(G,D)=-0.0018, Share of Variance Due to G=0.9077
    - Poverty gap: V(G)=0.0106, V(D)=0.0046, COV(G,D)=-0.0016, Share=0.7500
    - Squared poverty gap: V(G)=0.0129, V(D)=0.0073, COV(G,D)=-0.0010, Share=0.6538
    - Watts: V(G)=0.0116, V(D)=0.0063, COV(G,D)=-0.0015, Share=0.6779
  - Average Growth and Sensitivity to Average Growth in Growth Component
    - Headcount: V(|dlnμ|)=1.32280, V(|η|)=0.16420, COV(|dlnμ|,|η|)=0.14020, Share=0.8278
    - Poverty gap: 1.28360, 0.14920, 0.11310, 0.8419
    - Squared poverty gap: 1.27650, 0.15270, 0.11140, 0.8401
    - Watts: 1.27020, 0.14140, 0.10250, 0.8491
- Source: Author's calculations.

### Correlates of Pro-Poor Growth: Cross-Sectional Coefficient Estimates (Tables 4 and 5)
- Table 4: Distribution component of change (All spells)
  - Right-hand side variables with coefficient and heteroskedasticity-consistent t-statistic (reported below coefficient)
  - Examples (coefficient then t-statistic):
    - CPIA: 0.006, 0.920
    - KK rule of law: 0.012, 1.339
    - Trade/GDP: 0.017, 1.120
    - ln(1+Inflation): 0.001, 0.059
    - Government-Consumption/GDP: -0.154, 1.206
    - M2/GDP: 0.015, 0.638
    - KK voice and accountability: 0.002, 0.294
    - Relative productivity in agriculture: -0.005, 0.271
    - Average years of primary education: 0.003, 0.538
  - Dependent variables reported across columns: Growth, Change in Gini, P0, P1, P2, Watts; sample sizes indicated (e.g., 121–128 observations depending on variable).
- Table 5: Distribution component of change (Long spells)
  - Examples (coefficient then t-statistic):
    - CPIA: 0.005, 0.555
    - KK rule of law: 0.024, 1.726
    - Trade/GDP: 0.035, 1.656
    - ln(1+Inflation): -0.002, 0.073
    - Government-Consumption/GDP: -0.110, 0.742
    - M2/GDP: -0.028, 0.663
    - KK voice and accountability: 0.021, 1.659
    - Relative productivity in agriculture: 0.013, 0.543
    - Average years of primary education: -0.001, 0.063
  - Sample sizes: typically 32–42 observations depending on variable and dependent measure.
- Note: Heteroskedasticity-consistent t-statistics reported below coefficient estimates. CPIA is country policy and institutional asset; KK is Kaufmann and Kraay. Source: Author's calculations.

### Multivariate Growth and Distributional Change Regressions (Table 6)
- Dependent variables: Annual percent change in Headcount and Annual percent change in Watts index; Growth and Distribution components reported separately.
- Reported coefficients (example entries) with heteroskedasticity-consistent t-statistics below:
  - Initial income
    - Headcount growth component: -0.017 (t=1.978)
    - Headcount distribution component: -0.008 (t=1.470)
    - Watts growth component: 0.037 (t=1.769)
    - Watts distribution component: -0.018 (t=1.409)
  - KK rule of law
    - Headcount growth: 0.022 (t=2.050)
    - Headcount distribution: 0.009 (t=0.919)
    - Watts growth: -0.046 (t=2.188)
    - Watts distribution: 0.029 (t=1.785)
  - Trade/GDP
    - Headcount growth: 0.045 (t=1.978)
    - Headcount distribution: -0.011 (t=0.911)
    - Watts growth: -0.060 (t=1.659)
    - Watts distribution: -0.007 (t=0.361)
  - Government consumption
    - Headcount growth: -0.280 (t=2.229)
    - Headcount distribution: -0.048 (t=0.425)
    - Watts growth: 0.600 (t=2.114)
    - Watts distribution: -0.244 (t=1.010)
- Regression fit and sample:
  - R-squared values: Headcount growth 0.239, Headcount distribution 0.095, Watts growth 0.263, Watts distribution 0.182 (additional columns report other R-squared values up to 0.222 and 0.103)
  - Number of observations: 42 (per reported regressions)
- Note: Heteroskedasticity-consistent t-statistics reported below coefficient estimates. CPIA is country policy and institutional asset; KK is Kaufmann and Kraay. Source: Author's calculation.

### Empirical Figures and Visual Findings (Figures 1–5)
- Figure 1: Relative Growth Incidence Curves (examples shown for China 1990-1998 and Indonesia 1996-1999). Axes: Percentile of Income Distribution, p; Growth Rate of Percentile Relative to Average.
- Figure 2: Sensitivity of Poverty to Growth in Percentile p. Curves shown for P(1), EDEI(-1), P(2), Watts, P(0). Vertical axis values range from -2 to 0.2; horizontal axis percentiles 0 to 1.
- Figure 3: Growth and Poverty Reduction: Long Spells. Scatterplots of Average Annual Growth in Survey Mean versus Average Annual Growth in Poverty for multiple poverty measures (Headcount, Poverty Gap, Squared Poverty Gap, Watts). Reported fitted lines:
  - Headcount: y = -1.16x  - 0.01, R^2 = 0.51
  - Poverty Gap: y = -1.44x  - 0.01, R^2 = 0.45
  - Squared Poverty Gap: y = -1.63x  - 0.01, R^2 = 0.40
  - Watts: y = -1.52x  - 0.01, R^2 = 0.41
- Figure 4: Decomposing Changes in the Headcount. Panels show:
  - Growth and Distribution Components vs Residual: y = 0.97x - 0.00, R^2 = 0.92
  - Growth Component vs Distribution Component: y = 0.92x + 0.00, R^2 = 0.70
  - Growth in Mean vs Sensitivity of Poverty to Growth: y = -0.52x + 0.00, R^2 = 0.88
- Figure 5: Policies and the Growth and Distribution Components of Changes in Poverty. Bar-chart style presentation of average annual percent change in headcount by policy variables: Trade/GDP, Rule of Law, Gov/GDP; bars labeled Growth, Distribution, Net.

### References (selected items cited in the source)
- Deaton, Angus, 2003, “Measuring Poverty in a Growing World, or Measuring Growth in a Poor World,” NBER Working Paper No. 9822.
- Dollar, David, and Aart Kraay, 2002, “Growth is Good for the Poor,” Journal of Economic Growth, Vol. 7, pp. 195–225.
- Ravallion, Martin, and Shaohua Chen, 2003, “Measuring Pro-Poor Growth,” Economics Letters, Vol. 78, pp. 93–99.
- Kakwani, Nanak, 2000, “What Is Pro-Poor Growth?” Asian Development Review, Vol. 18(1), pp. 1–16.
- (Full list of references provided in the source.)

*Source: Author's calculations and figures from the document _wp0447 - conclusions about the determinants of pro-poor changes in relative incomes from any one.*

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