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### Major findings and conclusions
- The choice of inequality measure has a first-order impact on estimated empirical effects: “the choice of data matters.”
- Three estimation methods are used and contrasted: event studies, weighted-average least squares (WALS), and Pooled-Mean Group (PMG) regressions. Each addresses neglected problems in the empirical inequality literature and together highlight sensitivity to indicator choice.
- Empirical relationships between inequality and growth transmission channels are contingent on the inequality indicator: relationships statistically significant with one indicator tend not to replicate with another.
- Variations within indicator groups matter more for empirical results than variations between indicator groups (Gini versus Top10 income share).
- The same inequality indicator compiled using different methodologies can yield substantially different empirical relationships with transmission channels.
- Estimated effects of inequality change over time and are sensitive to the inclusion of fragile countries; social conflict in fragile countries can create significant correlations between inequality and political stability (causality not asserted).

### Empirical focus and transmission channels
- The paper studies association between inequality and five transmission channels through which inequality can affect economic growth:
  - Human capital
  - Fertility
  - Capital services (investment)
  - Total factor productivity (TFP)
  - Political stability
- Approach contrasts transmission-channel analysis with reduced-form inequality–growth nexus analyses.
- Theoretical implications noted:
  - Disposable income affects ability to save and invest; market income influences incentives for innovation.
  - Most theoretical effects pertain to the long term (human capital accumulation takes years/decades), but savings-to-investment and technological change can act on shorter horizons.

### Data: inequality indicators and measurement issues
- Six inequality indicators, grouped:
  - Top10 income shares (three sources):
    - The Top10 income share, WDI
    - The Top10 income share, WID
    - The Top10 income share, LIS
  - Gini coefficients (three sources):
    - The Gini coefficient, SWIID v8.3
    - The Gini coefficient, SWIID v3.1
    - The Gini coefficient, FAD
- General coverage: indicators generally cover 1970–2017, with variation in start/end dates.
- Key measurement differences that create substantial variation across series:
  - Definition of income (pre-tax vs post-tax; inclusion/exclusion of pensions, transfers, realized capital gains, corporate retained earnings, imputed rental income, underreported income).
  - Unit of analysis (individuals, adult equivalents, adults; household, tax units).
  - Primary source data (household surveys vs administrative tax records).
- Specific measurement complications:
  - Household surveys: measurement error and selection bias.
  - Tax records: less measurement error but confidentiality limits micro detail; fail to reflect informal sector; affected by tax-legislation changes.
  - Consumption measures: issues with long-lived asset consumption and valuing publicly provided in-kind transfers; consumption tends to be less volatile over time than income.
- Conceptual caution: inequality indicators reduce complex distributions to a single number; implicit value judgments differ (Top10 focuses on top decile; Gini weighs center more than tails).

### Indicator descriptive statistics (preserved from source)
- Table 2 summary (Obs., Mean, St. Dev., Min, Max, Countries with at least one observation, Share of advanced economies (% of total)):
  - The Top10 income share, WDI: Obs. 1,459; Mean 31; St. Dev. 7; Min 19; Max 62; Countries with at least one observation 162; Share of advanced economies (%) 26
  - The Top10 income share, WID: Obs. 3,592; Mean 42; St. Dev. 12; Min 15; Max 80; Countries with at least one observation 115; Share of advanced economies (%) 37
  - The Top10 income share, LIS: Obs. 340; Mean 26; St. Dev. 7; Min 17; Max 55; Countries with at least one observation 50; Share of advanced economies (%) 71
  - The Gini coefficient, SWIID v8.3: Obs. 5,297; Mean 38; St. Dev. 9; Min 18; Max 67; Countries with at least one observation 192; Share of advanced economies (%) 29
  - The Gini coefficient, SWIID v3.1: Obs. 4,040; Mean 38; St. Dev. 10; Min 15; Max 71; Countries with at least one observation 163; Share of advanced economies (%) 31
  - The Gini coefficient, FAD: Obs. 1,667; Mean 37; St. Dev. 9; Min 19; Max 66; Countries with at least one observation 155; Share of advanced economies (%) 39
- Pairwise correlations between the six inequality indicators (Table 3; rows and columns in order: WDI Top10, WID Top10, LIS Top10, SWIID v8.3 Gini, SWIID v3.1 Gini, FAD Gini):
  - WDI Top10: with WDI 1.00; WID 0.88; LIS 0.93; SWIID v8.3 0.89; SWIID v3.1 0.91; FAD 0.98
  - WID Top10: with WDI 0.88; WID 1.00; LIS 0.80; SWIID v8.3 0.87; SWIID v3.1 0.87; FAD 0.87
  - LIS Top10: with WDI 0.93; WID 0.80; LIS 1.00; SWIID v8.3 0.97; SWIID v3.1 0.96; FAD 0.96
  - SWIID v8.3 Gini: with WDI 0.89; WID 0.87; LIS 0.97; SWIID v8.3 1.00; SWIID v3.1 0.90; FAD 0.93
  - SWIID v3.1 Gini: with WDI 0.91; WID 0.87; LIS 0.96; SWIID v8.3 0.90; SWIID v3.1 1.00; FAD 0.96
  - FAD Gini: with WDI 0.98; WID 0.87; LIS 0.96; SWIID v8.3 0.93; SWIID v3.1 0.96; FAD 1.00

### Indicator-level means correlations (advanced economies; Table 4)
- Correlations between country-year means (1980–2015) weaken relative to country-year correlations; values preserved:
  - Mean, Top10 Income Share, WDI — correlations: WDI 1.00; WID -0.07; LIS 0.06; SWIID v8.3 -0.18; SWIID v3.1 -0.02; FAD -0.05
  - Mean, Top10 Income Share, WID — correlations: WDI -0.07; WID 1.00; LIS 0.27; SWIID v8.3 0.87; SWIID v3.1 0.90; FAD 0.43
  - Mean, Top10 Income Share, LIS — correlations: WDI 0.06; WID 0.27; LIS 1.00; SWIID v8.3 0.43; SWIID v3.1 0.34; FAD 0.85
  - Mean, Gini, SWIID, v8.3 — correlations: WDI -0.18; WID 0.87; LIS 0.43; SWIID v8.3 1.00; SWIID v3.1 0.94; FAD 0.52
  - Mean, Gini, SWIID, v3.1 — correlations: WDI -0.02; WID 0.90; LIS 0.34; SWIID v8.3 0.94; SWIID v3.1 1.00; FAD 0.49
  - Mean, Gini, FAD — correlations: WDI -0.05; WID 0.43; LIS 0.85; SWIID v8.3 0.52; SWIID v3.1 0.49; FAD 1.00
- Stylized fact: stylized facts about inequality depend greatly on the underlying indicator; the median and population-weighted mean give qualitatively almost identical results (footnote in source).

### Data overview for transmission channels (Table 5)
- Human Capital (index): Obs. 6,593; Mean 2.170; Std. Dev. 0.722; Min 1.007; Max 3.974
- Physical Capital Stock (index; 2011=1): Obs. 5,728; Mean 0.611; Std. Dev. 0.349; Min 0.016; Max 3.034
- TFP (index; 2011=1): Obs. 5,039; Mean 1.011; Std. Dev. 0.311; Min 0.289; Max 7.107
- Political Stability (index; 12=most stable): Obs. 4,484; Mean 7.563; Std. Dev. 2.058; Min 0.667; Max 12.000
- Fertility (children per woman): Obs. 8,847; Mean 3.835; Std. Dev. 1.968; Min 0.860; Max 8.864

### Empirical strategy and methods
- Three methods:
  - Event studies: fixed-effect panel difference-in-difference; event defined as five-year change above 75th percentile; control group below 25th percentile; event window ten years (five years of change plus five years after).
    - Sample selection requires transmission channel observed continuously through event window and at most one large-increase/large-decrease episode per country (retain most recent).
    - Summary statistics for ‘large changes’ (Table 6: Obs., Mean, St. Dev., Min, Max, Share of advanced economies (% of total)):
      - Large increases:
        - WDI Top10: 49; 3; 3; 1; 15; 27
        - WID Top10: 74; 6; 4; 2; 24; 41
        - LIS Top10: 14; 2; 1; 1; 3; 79
        - SWIID v8.3 Gini: 95; 2; 2; 1; 11; 37
        - SWIID v3.1 Gini: 116; 7; 5; 2; 26; 29
        - FAD Gini: 54; 4; 2; 1; 11; 37
      - Large decreases:
        - WDI Top10: 49; -5; 3; -12; -2; 14
        - WID Top10: 68; -6; 4; -21; -1; 37
        - LIS Top10: 12; -3; 1; -5; -1; 67
        - SWIID v8.3 Gini: 83; -2; 1; -7; 0; 29
        - SWIID v3.1 Gini: 122; -6; 5; -25; -2; 25
        - FAD Gini: 51; -6; 3; -18; -3; 25
  - WALS: addresses model uncertainty by averaging across 2^k possible models; treats changes in inequality as an ‘auxiliary’ variable and uses t-statistic > 1 as a 'robust determinant' criterion (corresponding roughly to posterior inclusion probability > 0.5).
    - Auxiliary regressors grouped into Policy, Structural, Institutional, Shocks (list preserved in source).
    - Example table excerpt (dependent variable: Capital Stock (t-5 to t)): Inequality change (t-10 to t-5) 0.89* 0.40 1.19**; Observations 91 91 91; R-squared 0.08 0.38 0.14; Notes: *** p<0.01, ** p<0.05, * p<0.1.
  - PMG: short-run relationships vary across countries; imposes identical long-run structural β1 across countries; rolling-window estimation over 28-year windows (first: 1970-1997; last: 1990-2017); includes cross-sectional means to control unobserved common factors; uses five-year lagged Gini to mitigate reverse causality.
    - Baseline PMG symbolic form preserved in source; main coefficient of interest is long-run β1.
    - Cross-sectional dependence tested with Pesaran (2004) CD test; strong rejection of no dependence (Table 8 values preserved):
      - CD Test statistics: Gini 277.8***; Human Capital 623.4***; Capital Services 382.5***; TFP 17.9***; Political Stability 282.9***; Fertility 605.1***; P-values all (0.000).
      - Number of Countries: Gini 161; Human Capital 126; Capital Services 115; TFP 108; Political Stability 114; Fertility 136.

### Main empirical results — event study (Section IV)
- Core patterns documented:
  - (i) Estimated relationships are sensitive to inequality indicator; sensitivity greater within indicator groups than across groups.
  - (ii) For a given indicator, inequality can affect transmission channels in opposite directions.
  - (iii) Estimated relationships change over time.
  - (iv) Results for political stability sensitive to inclusion of fragile countries.
- Top10 income shares (Figure 2.1; summary):
  - Only capital services and TFP display ‘consistent’ results across indicators.
  - Capital services: three point estimates at five years positive, bounded between 0 and 10 percent, statistically insignificant.
  - TFP: WDI and WID are (just about) statistically significant and negative; LIS positive and insignificant.
  - Fertility and political stability: sign and significance flip across Top10 sources (e.g., WID suggests significantly positive impact on political stability; WDI signals marginally significantly negative relationship).
- Gini coefficients (Figure 2.2; summary):
  - Human capital, fertility, and political stability show ‘consistent results’ across Gini variants.
  - Human capital: five-year relationship negative (between zero and minus two percent) and insignificant.
  - Fertility and political stability: point estimates share sign but statistical significance differs across Ginis.
  - Capital services and TFP: effects carry different signs and are all statistically insignificant.
- Cross-indicator comparison:
  - No systematic difference between Top10 income shares and the Gini.
  - Simple averages of estimated five-year impacts for the three Top10 income shares and the three Ginis are very close.
  - ANOVA decomposition: within-group variation accounts for 98 percent of total variation when comparing five-year coefficients from Top10 shares (15 coefficients) to Gini coefficients.
- Overall event-study summary:
  - (i) Inequality exhibits no strong relationship with human capital (all coefficients negative but none statistically significant).
  - (ii) Inequality may be negatively related to TFP and political stability (each with two significant coefficients), but this depends on specific indicator and can reverse when switching indicators.
  - (iii) Capital services and fertility results inconclusive across indicators.
- Caveats: potential reverse causality, omitted variable bias, failure of common trends in some cases, and aggregation challenges in mapping channel effects to net growth.

### WALS results and interpretation
- WALS regressions broadly "paint a similar picture as the event study": neither Top10 income shares nor the Gini exhibit a robust empirical relationship with the transmission channels.
- Only three out of ten indicator–transmission channel combinations yield "consistent" results (using WALS coefficient and t-statistic > 1 rule).
- One-way ANOVA using WALS estimated coefficients attributes 95 percent of total variation to within-group variation.
- Compared to auxiliary regressors, inequality has relatively weak explanatory power; other auxiliary regressors more frequently appear as "robust determinants."
- WALS — Top10 shares (Table 9.1) highlights:
  - Point estimates for human capital, TFP, and fertility do not exceed the "robust" threshold.
  - Marginally significant event-study relationships (e.g., WDI/WID and TFP; WID and fertility; WID and political stability) become insignificant in WALS.
  - Two WALS models reach t-statistic > 1:
    - Negative link between WID Top10 and capital services.
    - Positive link between WDI Top10 and political stability (opposite sign to event study).
- WALS — Gini (Table 9.2) highlights:
  - At least one Gini variant enters significantly in four out of five channels; t-statistics generally just above one.
  - Political stability is the only channel without a significant association with the Gini in WALS (contrasting event study).
  - Human capital and capital services show consistent negative coefficients with SWIID variants moving above the "robust" threshold.
  - TFP results mixed with opposite-signed significant associations, suggesting income-level dependence.
  - Fertility: negative and significant with FAD Gini; close to zero with other Gini variants.
- Indicator heterogeneity conclusion: differences within each indicator group dominate; no systematic difference between Top10 shares and Gini; averages of coefficients across indicators are similar.
- Role of development stage and interactions:
  - Many "robust" associations include significant interaction between inequality and GDP per capita (log).
  - Reported example thresholds:
    - Negative impact of WID Top10 on TFP turns positive for countries with per capita income > $3,300 (current PPP).
    - For FAD Gini and TFP, effect turns negative when per capita income exceeds $11,000.

### PMG results, rolling-window stability, and heterogeneity
- PMG reinforces that inequality lacks a consistently robust long-term relationship with transmission channels.
- Short-run vs long-run:
  - For full sample, short-run effect positive for TFP, long-run effect never significant.
  - Significant short-run effects (when present) tend to be positive: human capital and fertility in advanced economies; capital services in EMDEs.
- A significant negative long-run association emerges between inequality and capital services in advanced economies (relative to full sample).
- Effects differ significantly across country-income groups.
- Rolling-window PMG (28-year windows) findings:
  - Structural long-run effect of inequality on human capital, physical capital, TFP, and fertility indistinguishable from zero throughout time.
  - Exception: political stability in EMDEs — estimated effect turns significantly positive in windows ending in 2006–2011.

### Overall assessment, limitations, and interpretation caveats
- WALS and PMG do not settle whether inequality is related to transmission channels; methods and data limitations leave statistical power low.
- Inequality emerges as a "robust determinant" only in a few specifications, and those are sensitive to indicator compilation methodology.
- Short-run positive effects (when present) tend to wane or reverse in the long run; effects vary by country-income group.
- Authors caution: "absence of evidence is not evidence of absence" — low statistical power and cross-country annual datasets limit the ability to detect effects.

### Conclusion and policy/data recommendations
- Inequality indicator sensitivity:
  - Significant associations found with one indicator typically fail to replicate when switching indicators.
  - Empirical relationships are more sensitive to the choice of a particular indicator variant than to the choice between Gini and Top10 sets.
  - Possible interpretation: only specific subtypes of income inequality (e.g., after-tax income between adults only, adjusted for in-kind public services and owner-occupied housing but excluding monetary unemployment benefits) may exert economic effects; evidence is consistent but not conclusive.
- Inequality and political stability:
  - Brief positive relationship between rising inequality and political stability reflects co-movement in fragile countries that experienced violent social conflict in the 2000s (examples in source: DR Congo, Haiti, Côte d’Ivoire, Zimbabwe).
  - When fragile countries are excluded, the significant relationship disappears — underscoring non-linearities and sample-sensitivity.
- Data and methodological recommendations:
  - Expand country coverage of existing inequality statistics, ensuring comparability across household surveys and administrative tax records.
  - Intensify development of comparable distributional indicators within the Systems of National Accounts (SNA) framework; update to SNA 2008 and embed distributional indicators to facilitate international comparability.
  - Advantages of SNA-based indicators: comprehensive and standardized income definitions; facilitate more robust cross-country empirical work on economic effects of inequality.
- IMF recommendation: intensify development of comparable distributional indicators within the SNA framework.

*Source: wpiea2020164-print-pdf — IMF Working Paper content unit provided.*

### REFERENCES ___________________________________________________________________________________ 36

### wpiea2020164-print-pdf - REFERENCES ___________________________________________________________________________________ 36

### Major findings and conclusions
- The choice of inequality measure has a first-order impact on estimated empirical effects: “the choice of data matters.”
- Three estimation methods are used and contrasted: event studies, weighted-average least squares (WALS), and Pooled-Mean Group (PMG) regressions. Each addresses neglected problems in the empirical inequality literature and together highlight sensitivity to indicator choice.
- Empirical relationships between inequality and growth transmission channels are contingent on the inequality indicator: relationships statistically significant with one indicator tend not to replicate with another.
- Variations within indicator groups (methodological differences that make one Gini different from another, or one Top10 income share different from another) matter more for empirical results than variations between the two indicator groups (Gini versus Top10 income share).
- The same inequality indicator compiled using different methodologies can yield substantially different empirical relationships with transmission channels.
- The estimated effects of inequality change over time and are sensitive to the inclusion of fragile countries; social conflict in fragile countries can create significant correlations between inequality and political stability, although causality is not asserted.

### Empirical focus and transmission channels
- The paper studies the empirical association between inequality and transmission channels through which inequality can affect economic growth: human capital, fertility, capital services, total factor productivity (TFP), and political stability.
- The paper contrasts this transmission-channel approach with the more common reduced-form inequality–growth nexus analyses.

### Data: inequality indicators used
- Six inequality indicators are used, grouped into two sets:
  - Top10 income shares (three sources):
    - The Top10 income share, WDI
    - The Top10 income share, WID
    - The Top10 income share, LIS
  - Gini coefficients (three sources):
    - The Gini coefficient, SWIID v8.3
    - The Gini coefficient, SWIID v3.1
    - The Gini coefficient, FAD
- General coverage: indicators generally cover the time period 1970–2017, with some variation in start and end dates across indicators.

### Measurement issues and methodological choices
- Three key methodological choices create substantial differences across inequality series:
  - The definition of income (e.g., pre-tax versus post-tax; inclusion of pensions, transfers, realized capital gains, corporate retained earnings, imputed rental income, underreported income).
  - The unit of analysis (e.g., individuals, adult equivalents, adults only; household, tax units, married couples).
  - The primary source data (household surveys versus administrative tax records).
- Specific measurement complications noted:
  - Household surveys: measurement error and selection bias (recall error; richer respondents less likely to reply).
  - Tax records: less measurement error and nonresponse bias but confidentiality and less micro detail; fail to reflect informal sector activity; affected by tax legislation changes.
  - Consumption as alternative: issues with long-lived asset consumption measurement and valuing publicly provided in-kind transfers; consumption tends to be less volatile over time than income.
- Conceptual caution: inequality indicators reduce complex income distributions to a single number and embed implicit value judgments (e.g., Top10 focuses on the top decile; Gini weighs center more than tails).

### Methodological characteristics (Table 1 summary)
- World Bank WDI — Top10 income share:
  - Income concept: Market, gross, and disposable income, and consumption expenditure
  - Unit of observation: Individuals
  - Primary source data: Household surveys
  - Comment: Available in PovcalNet; mixes different income concepts depending on national definitions.
- World Inequality Database (WID) — Top10 income share:
  - Income concept: Pre-tax national income, after pensions
  - Unit of observation: Adults
  - Primary source data: Administrative tax records and national accounts data
  - Comment: Follows Distributional National Accounts guidelines; scales taxable income to pre-tax national income with imputations for national accounts items and taxes.
- Luxemburg Income Study (LIS) — Top10 income share:
  - Income concept: Disposable income
  - Unit of observation: Adult equivalents
  - Primary source data: Household surveys
  - Comment: Uses harmonized household surveys; disposable income excludes non-monetary capital income and in-kind social transfers.
- SWIID v8.3 — Gini:
  - Income concept: Disposable income
  - Unit of observation: Adult equivalents
  - Primary source data: Household surveys
  - Comment: Predicts ‘LIS-like’ Ginis where LIS data unavailable; LIS observations serve as anchors.
- SWIID v3.1 — Gini:
  - Same income concept and unit as v8.3
  - Comment: Includes more than 600 country-year observations from non-representative surveys of employed population for 1960–1979.
- International Disposable Income Gini Database (FAD) — Gini:
  - Income concept: Disposable income, consumption
  - Unit of observation: Individuals and adult equivalents
  - Primary source data: Household surveys
  - Comment: Based on five primary source-data Ginis (LIS, Eurostat, OECD, SEDLAC, PovcalNet); mixes disposable income and consumption and per capita and adult-equivalent scales.

### Key summary statistics (Tables 2 and 3)
- Table 2: Overview of Inequality Indicators (Obs., Mean, St. Dev., Min, Max, Countries with at least one observation, Share of advanced economies (% of total)):
  - The Top10 income share, WDI: Obs. 1,459; Mean 31; St. Dev. 7; Min 19; Max 62; Countries with at least one observation 162; Share of advanced economies (%) 26
  - The Top10 income share, WID: Obs. 3,592; Mean 42; St. Dev. 12; Min 15; Max 80; Countries with at least one observation 115; Share of advanced economies (%) 37
  - The Top10 income share, LIS: Obs. 340; Mean 26; St. Dev. 7; Min 17; Max 55; Countries with at least one observation 50; Share of advanced economies (%) 71
  - The Gini coefficient, SWIID v8.3: Obs. 5,297; Mean 38; St. Dev. 9; Min 18; Max 67; Countries with at least one observation 192; Share of advanced economies (%) 29
  - The Gini coefficient, SWIID v3.1: Obs. 4,040; Mean 38; St. Dev. 10; Min 15; Max 71; Countries with at least one observation 163; Share of advanced economies (%) 31
  - The Gini coefficient, FAD: Obs. 1,667; Mean 37; St. Dev. 9; Min 19; Max 66; Countries with at least one observation 155; Share of advanced economies (%) 39
- Table 3: Pairwise correlations between the six inequality indicators:
  - Correlations (rows vs columns in order: WDI Top10, WID Top10, LIS Top10, SWIID v8.3 Gini, SWIID v3.1 Gini, FAD Gini):
    - The Top10 income share, WDI with: WDI 1.00; WID 0.88; LIS 0.93; SWIID v8.3 0.89; SWIID v3.1 0.91; FAD 0.98
    - The Top10 income share, WID with: WDI 0.88; WID 1.00; LIS 0.80; SWIID v8.3 0.87; SWIID v3.1 0.87; FAD 0.87
    - The Top10 income share, LIS with: WDI 0.93; WID 0.80; LIS 1.00; SWIID v8.3 0.97; SWIID v3.1 0.96; FAD 0.96
    - The Gini coefficient, SWIID v8.3 with: WDI 0.89; WID 0.87; LIS 0.97; SWIID v8.3 1.00; SWIID v3.1 0.90; FAD 0.93
    - The Gini coefficient, SWIID v3.1 with: WDI 0.91; WID 0.87; LIS 0.96; SWIID v8.3 0.90; SWIID v3.1 1.00; FAD 0.96
    - The Gini coefficient, FAD with: WDI 0.98; WID 0.87; LIS 0.96; SWIID v8.3 0.93; SWIID v3.1 0.96; FAD 1.00

### Research contribution and context
- The paper contributes to three strands of empirical literature:
  - Literature documenting lack of consistency in international inequality statistics and efforts to improve comparability.
  - Debate on evolution of top income shares where methodological differences produce starkly different trends and levels.
  - Empirical work on inequality’s effects on economic growth by focusing on transmission channels (human capital, fertility, capital services, TFP, political stability).

_Imf Working Paper: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020164-print-pdf.pdf_

### 20.      Imperfect correlation and systematic differences in country coverage combine to give different

### 20.      Imperfect correlation and systematic differences in country coverage combine to give different

### Summary of indicator-level findings
- As a summary measure for advanced countries, the mean of each indicator is calculated for every year from 1980 to 2015.
- The correlation between the mean of indicators weakens compared to correlations of the country-year data, especially between the three Top10 income share indicators.
- Stylized facts about inequality depend to a great extent on the underlying inequality indicator.
- Footnote: The median and population-weighted mean give qualitatively almost identical results.

### Correlations between means (advanced economies only)
- Table 4 reports the correlation matrix between the six time-series of means (values presented as in the source):
  - Mean, Top10 Income Share, WDI — correlation with:  
    - Mean, Top10 Income Share, WDI: 1.00
    - Mean, Top10 Income Share, WID: -0.07
    - Mean, Top10 Income Share, LIS: 0.06
    - Mean, Gini, SWIID, v8.3: -0.18
    - Mean, Gini, SWIID, v3.1: -0.02
    - Mean, Gini, FAD: -0.05
  - Mean, Top10 Income Share, WID — correlation with:  
    - Mean, Top10 Income Share, WDI: -0.07
    - Mean, Top10 Income Share, WID: 1.00
    - Mean, Top10 Income Share, LIS: 0.27
    - Mean, Gini, SWIID, v8.3: 0.87
    - Mean, Gini, SWIID, v3.1: 0.90
    - Mean, Gini, FAD: 0.43
  - Mean, Top10 Income Share, LIS — correlation with:  
    - Mean, Top10 Income Share, WDI: 0.06
    - Mean, Top10 Income Share, WID: 0.27
    - Mean, Top10 Income Share, LIS: 1.00
    - Mean, Gini, SWIID, v8.3: 0.43
    - Mean, Gini, SWIID, v3.1: 0.34
    - Mean, Gini, FAD: 0.85
  - Mean, Gini, SWIID, v8.3 — correlation with:  
    - Mean, Top10 Income Share, WDI: -0.18
    - Mean, Top10 Income Share, WID: 0.87
    - Mean, Top10 Income Share, LIS: 0.43
    - Mean, Gini, SWIID, v8.3: 1.00
    - Mean, Gini, SWIID, v3.1: 0.94
    - Mean, Gini, FAD: 0.52
  - Mean, Gini, SWIID, v3.1 — correlation with:  
    - Mean, Top10 Income Share, WDI: -0.02
    - Mean, Top10 Income Share, WID: 0.90
    - Mean, Top10 Income Share, LIS: 0.34
    - Mean, Gini, SWIID, v8.3: 0.94
    - Mean, Gini, SWIID, v3.1: 1.00
    - Mean, Gini, FAD: 0.49
  - Mean, Gini, FAD — correlation with:  
    - Mean, Top10 Income Share, WDI: -0.05
    - Mean, Top10 Income Share, WID: 0.43
    - Mean, Top10 Income Share, LIS: 0.85
    - Mean, Gini, SWIID, v8.3: 0.52
    - Mean, Gini, SWIID, v3.1: 0.49
    - Mean, Gini, FAD: 1.00

### Transmission channels considered
- Five variables capture transmission channels from inequality to economic growth:
  - Human capital
  - Fertility
  - Capital services (investment)
  - TFP
  - Political stability
- Theoretical and empirical background:
  - Inequality may impede liquidity-constrained households from investing in human capital, exerting optimal effort, or choosing productive occupations (Aghion and Bolton, 1997; Bénabou, 1996a; Durlauf, 1996; Galor and Zeira, 1993; Moav, 2002; Piketty, 1997).
  - Concentration of income at the top may facilitate more domestic savings and investment (Bhattacharya, 1998; Bourguignon, 1981; Galor and Moav, 2004) and spur innovation and technological progress (Galor and Tsiddon, 1997; Zweimüller, 2000).
  - Inequality may provoke political instability and social conflict (Alesina and Perotti, 1996; Bénabou, 1996b; Easterly, 2001; Keefer and Knack, 2002).
- Income concept and time horizon implications:
  - Disposable income (after redistribution) determines ability to save and invest; market income (pre-tax, pre-transfer) influences incentives for innovation.
  - Both disposable and market income inequality can affect political instability, with varying strength across channels.
  - Theoretical literature suggests most effects of inequality pertain to the long term (human capital accumulation takes years/decades); savings-to-investment and technological change can act on shorter horizons.

### Data overview for transmission channels (Table 5)
- Human Capital (index): Obs. 6,593; Mean 2.170; Std. Dev. 0.722; Min 1.007; Max 3.974
- Physical Capital Stock (index in constant prices in national currency; 2011=1): Obs. 5,728; Mean 0.611; Std. Dev. 0.349; Min 0.016; Max 3.034
- TFP (index in constant prices in national currency; 2011=1): Obs. 5,039; Mean 1.011; Std. Dev. 0.311; Min 0.289; Max 7.107
- Political Stability (index; 12=most stable): Obs. 4,484; Mean 7.563; Std. Dev. 2.058; Min 0.667; Max 12.000
- Fertility (children per woman): Obs. 8,847; Mean 3.835; Std. Dev. 1.968; Min 0.860; Max 8.864

### Empirical strategy (section III)
- Three empirical methods employed:
  - (i) Event studies
  - (ii) Weighted-Average Least Squares (WALS)
  - (iii) Pooled-Mean Group (PMG) regressions
- Rationale and limitations:
  - Event studies: less exposed to measurement error; capture complex non-linearities; not designed to capture country-specific shocks.
  - WALS: addresses model uncertainty.
  - PMG: robust to unobserved factors that affect both transmission channels and inequality; requires long time periods (at least 28 years) and sufficient country coverage.
  - No method is perfect; the paper avoids strong causal claims and focuses on sensitivities to: (i) inequality indicators; (ii) control variables; (iii) time and country samples.
- Implementation notes:
  - Event studies and WALS estimated separately for each transmission channel using six inequality indicators, yielding thirty indicator–transmission channel combinations.
  - Event studies and WALS cover ten-year time windows; PMG covers longer periods where data permit.
  - For PMG, only SWIID v8.3 Gini is consistently based on nationally representative household surveys and has sufficient coverage.

### Event study design
- Fixed-effect panel difference-in-difference model (notation preserved from source).
- Event definition:
  - A “large increase in inequality” is a five-year change in the inequality indicator above the 75th percentile of all observed changes.
  - Control group: countries with large declines (changes below the 25th percentile).
  - Event window: ten years (five years during which inequality changes and the subsequent five years).
- Identification conditions for causal interpretation:
  - (i) Common pre-event trends between treatment and control groups (testable: pre-event γj should not differ from zero for negative j).
  - (ii) Absence of country-specific shocks (not directly testable in event study).
- Sample construction and selection rules:
  - Country-year observations in the ‘large changes’ sample are specific to each inequality indicator; country compositions differ across indicator samples.
  - Two additional criteria: (i) transmission channel variable must be observed continuously throughout the event window; (ii) countries have at most one observation of large increase and large decrease (retain most recent episode if multiple).
  - The share of advanced economies in each ‘large changes’ sample generally reflects the underlying country composition of the inequality indicator; differences in country coverage remain a concern.
- Summary statistics for ‘large changes’ by inequality indicator (Table 6 values preserved):
  - Large increases (Obs., Mean, St. Dev., Min, Max, Share of advanced economies (% of total)):
    - The Top10 income share, WDI: 49; 3; 3; 1; 15; 27
    - The Top10 income share, WID: 74; 6; 4; 2; 24; 41
    - The Top10 income share, LIS: 14; 2; 1; 1; 3; 79
    - The Gini coefficient, SWIID v8.3: 95; 2; 2; 1; 11; 37
    - The Gini coefficient, SWIID v3.1: 116; 7; 5; 2; 26; 29
    - The Gini coefficient, FAD: 54; 4; 2; 1; 11; 37
  - Large decreases (Obs., Mean, St. Dev., Min, Max, Share of advanced economies (% of total)):
    - The Top10 income share, WDI: 49; -5; 3; -12; -2; 14
    - The Top10 income share, WID: 68; -6; 4; -21; -1; 37
    - The Top10 income share, LIS: 12; -3; 1; -5; -1; 67
    - The Gini coefficient, SWIID v8.3: 83; -2; 1; -7; 0; 29
    - The Gini coefficient, SWIID v3.1: 122; -6; 5; -25; -2; 25
    - The Gini coefficient, FAD: 51; -6; 3; -18; -3; 25
- Strengths of event study:
  - Flexibility and parsimony; right-hand side variables are free of measurement error (binary dummies or unobserved); accommodates complex non-linearities.

### Weighted-Average Least Squares (WALS)
- Purpose: address model uncertainty by averaging across many possible model specifications.
- Cross-sectional regression set-up (notation preserved from source).
- Identification requirement for causal interpretation:
  - Lagged five-year change in inequality and five-year lag in other explanatory variables must not be systematically related to the subsequent five-year change in the transmission channel.
- Sample construction: same selection criteria as event study (observations of countries with large changes in inequality and available subsequent five-year evolution of channels).
- Sensitivity to control variables:
  - Estimates of coefficient β crucially depend on the set of included controls X (illustrated by three OLS specifications regressing change in political stability on prior change in WDI Top10 income share; coefficient varies by a factor of three and in statistical significance).
  - Common benchmark specifications referenced: Perotti (1996) parsimonious and Barro (2000) extensive; alternative specifications include variables like financial development and trade/financial openness.
- WALS mechanics:
  - Given k possible determinants, there are 2^k possible models; WALS estimates a probability for each model based on mean-square error and computes a weighted average of model-specific estimates for β and γ.

*Source: wpiea2020164-print-pdf - 20.      Imperfect correlation and systematic differences in country coverage combine to give different*

### 41.      An explanatory variable with a WALS t-statistic larger than one is said to be a ‘robust

### wpiea2020164-print-pdf - 41.      An explanatory variable with a WALS t-statistic larger than one is said to be a ‘robust

### WALS robustness criterion and model setup
- An explanatory variable with a WALS t-statistic larger than one is said to be a ‘robust determinant.’
- At this level of statistical significance, adding the explanatory variable increases the model’s adjusted R-squared and lowers its mean-square error.
- Raftery (1995) and Masanjala and Papageorgiou (2008) show that a t-statistic greater than one in absolute value corresponds approximately to a posterior inclusion probability of greater than 0.5.
- Changes in inequality are treated as an ‘auxiliary’ rather than ‘focus’ variable; the only ‘focus’ regressor is the constant.
- The WALS methodology maximizes explanatory power of the ‘focus’ variables while determining robustness of ‘auxiliary variables.’
- The remaining ‘auxiliary regressors’ are grouped into four categories:
  - Policy: inflation and price of investment goods (as a measure of distortions).
  - Structural: GDP per capita and GDP per capita squared, financial development (financial development index from Svirydzenka, 2016), trade openness, international financial integration, share of government consumption (at current PPP exchange rates), and share of gross capital formation (at current PPP exchange rates).
  - Institutional: democracy, democracy squared, and rule of law (from V-Dem, see Coppedge et al., 2020).
  - Shocks: contemporaneous banking crisis (from Laeven and Valencia, 2018), and change in commodity terms of trade index (weighted by net exports, from Gruss and Kebhaj, 2019).
- The resulting 2^k possible versions of the specification range from the most parsimonious (no ‘auxiliary variables’) to the most extensive (all included).

- Table excerpt (preserve formatting as in source):
  - Inequality change (t-10 to t-5) 0.89* 0.40 1.19**
  - Observations 91 91 91
  - R-squared 0.08 0.38 0.14
  - Control variables (columns vary): Price level of investment goods (t-5) and GDP per capita level log (t-5); GDP per capita level log (t-5), GDP per capita level log squared (t-5), Commodity Terms of Trade Index change (t-10 to t-5), Share of government consumption PPP (t-5), Share of gross capital consumption PPP (t-5), Inflation (t-10 to t-5), Electoral democracy index (t-5), Electoral democracy index, squared, (t-5) and Rule of Law index (t-5); GDP per capita level log (t-5), Banking Crisis Dummy (t-5 to t), Trade Openness (t-5), Financial Openness (t-5) and Financial Development index (t-5).
  - Notes: *** p<0.01, ** p<0.05, * p<0.1
  - Dependent Variable: Capital Stock (t-5 to t)

### Pooled Mean-Group (PMG) estimator: specification and justification
- PMG allows short-run relationships between inequality and transmission channels to vary across countries while imposing identical long-run structural relationship across countries (Chudik and Pesaran, 2015; Pesaran, 2006; Pesaran, et al., 1999).
- PMG accounts for country-specific adjustments to long-run steady states and corrects for cross-sectional dependencies due to unobserved global factors (Pesaran, 2006).
- Baseline PMG specification (symbolic form preserved from source):
  - ∆TTt..._Ch_iii = Φi [TTt..._Ch_iii −5 − β0 − β1 Gitiii −5 ] + β2i ∆Gitiii + γi Xi_iii −5 + αi fi−5 + εiii
  - Where: ∆TT..._Ch represents change in the transmission channel between t-5 and t; Φi is speed of adjustment; β1 is long-run response of the transmission channel to inequality; β2i is short-run effect of inequality that varies across countries; Gitiii −5 is the five-year lagged level of the Gini; Xi_iii −5 is the parsimonious set of control variables (includes GDP per capita and the price level of capital formation); fi−5 contains unobservable common factors; αi are factor loadings; ε is the error term.
- Main coefficient of interest: long-run structural parameter β1.
- Rolling-window approach: estimate equation (3) 20 times over a rolling window of 28 years between 1970 and 2017:
  - First estimation window: 1970-1997
  - Last estimation window: 1990-2017
  - Rolling-window regressions run for full sample, and separately for advanced and emerging-market and low-income countries.
- To mitigate endogeneity:
  - Include cross-sectional means of dependent and independent variables (Pesaran, 2006) to control for unobserved common factors.
  - Explain change in transmission channels by the 5-year lagged level of inequality to reduce reverse causality concerns.
  - Method robust to time-invariant country-specific factors, non-stationarity, and weak/strong cross-sectionally correlated errors (Pesaran and Tosetti, 2011).

### Cross-sectional dependence evidence (Table 8)
- Pesaran (2004) CD test strongly rejects null hypothesis of no cross-sectional dependence for Gini and transmission channels.
- Table 8. Cross-Sectional Dependence Test (values preserved):
  - Variable: Gini | Human Capital | Capital Services | TFP | Political Stability | Fertility
  - CD Test: 277.8*** | 623.4*** | 382.5*** | 17.9*** | 282.9*** | 605.1***
  - P-value: (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
  - Number of Countries: 161 | 126 | 115 | 108 | 114 | 136
  - Notes: *** p<0.01, ** p<0.05, * p<0.1
- Implication: variables are related across countries via unobserved common factors; ignoring cross-sectional dependence would bias standard panel estimators such as the within-estimator.

### Main empirical results (Section IV) — event study findings and interpretation
- Key documented results:
  - (i) Estimated empirical relationships are sensitive to the choice of inequality indicator; sensitivity is greater for two indicators from the same group (two Top10 income shares or two Ginis) than for indicators from different groups (one Top10 and one Gini).
  - (ii) For a given indicator, inequality can affect transmission channels in opposite directions, making net effect difficult to determine.
  - (iii) Estimated relationships change over time.
  - (iv) Results for political stability are sensitive to inclusion of fragile countries.
- Event study design:
  - Point estimates measure differential impact of increases in inequality (relative to control group with declines in inequality) on transmission channels over a ten-year event window.
  - The point estimate at t+5 measures cumulative effect five years after a large increase in inequality.
  - Consistency rule for results at t+5: (i) all three inequality indicators carry the same sign (regardless of statistical significance); or (ii) two indicators carry the same sign and are statistically significant.
- Findings from Top10 income shares (Figure 2.1):
  - Only two of five transmission channels display ‘consistent’ results: capital services and TFP.
  - Capital services: three point estimates at five years are positive, bounded between 0 and 10 percent, and statistically insignificant.
  - TFP: two indicators (WDI and WID) are (just about) statistically significant and negative; LIS is positive and insignificant.
  - For fertility and political stability, estimated relationships after five years carry different signs when switching indicators; statistical significance differs (e.g., WID suggests significantly positive impact on political stability; WDI signals (marginally) significantly negative relationship).
- Findings from Gini coefficients (Figure 2.2):
  - Three transmission channels show ‘consistent results’: human capital, fertility, and political stability.
  - Human capital: estimated relationship at five years is negative (in the range between zero and minus two percent) and insignificant.
  - Fertility and political stability: point estimates share sign but statistical significance differs across Ginis.
  - Capital services and TFP: estimated effects carry different signs and are all statistically insignificant.
- Cross-indicator comparison and variability:
  - No systematic difference between Top10 income shares and the Gini or between indicators based on different income concepts.
  - Simple averages of estimated five-year impacts for the three Top10 income shares and the three Ginis in each transmission channel are very close.
  - ANOVA decomposition (illustrative) finds within-group variation dominates:
    - Within-group variation accounts for 98 percent of the total variation when comparing five-year coefficients from Top10 income shares (15 coefficients) to Gini coefficients.
- Overall summary of event study (as in source):
  - (i) Inequality exhibits no strong relationship with human capital (all coefficients negative but none statistically significant).
  - (ii) Inequality may be negatively related to TFP and political stability (each channel with two significant coefficients), but this depends on the specific indicator and can reverse when switching indicators.
  - (iii) Results for capital services and fertility are inconclusive (signs, magnitude, and statistical significance vary across indicators).
- Caveats and methodological concerns:
  - Interpretation challenge: inequality takes many forms (poverty, shrinking middle class, concentrated top incomes); different indicators capture different realizations with distinct economic consequences (Voitchovsky, 2005; Section II discussion).
  - Event study limitations: potential reverse causality and omitted variable bias; causality requires point estimates of γj not to differ from zero in pre-event years (common trends assumption).
  - Some significant five-year estimates in fertility and political stability may reflect pre-event developments, indicating possible violation of common trends.
  - Aggregation issues: insignificant relationship between inequality and real GDP per capita can mask offsetting significant positive and negative effects on individual transmission channels (example: WDI Top10 on real GDP ~ zero, but positive on capital services and negative on TFP).
  - Aggregating channel effects to net growth is not straightforward because importance of transmission channels varies across countries and time; a meaningful aggregation would need to be country-specific.

### Methodological robustness approaches noted
- PMG estimation with cross-sectional means to control unobserved common factors.
- Use of 5-year lagged Gini to mitigate reverse causality.
- Rolling-window PMG estimates (20 windows of 28 years each between 1970 and 2017) to test stability over time and across income groups.
- Cross-sectional dependence formally tested with Pesaran (2004) CD test; strong rejection of no dependence found.

*Italic: Source — wpiea2020164-print-pdf (content unit provided).*

### 59.      Tables 9.1 and 9.2 present the results from the WALS regressions. Overall, the WALS

### wpiea2020164-print-pdf - 59

### Key findings (summary)
- The WALS regressions broadly "paint a similar picture as the event study": neither the Top10 income shares nor the Gini exhibit a robust empirical relationship with the transmission channels.
- Only three (out of ten) indicator–transmission channel combinations yield "consistent" results (as defined in paragraph 50, using the estimated WALS coefficient instead of the five-year coefficient of the event study).
- The one-way ANOVA decomposition attributes 95 percent of the total variation to within-group variation, using the estimated coefficients of the lagged inequality indicator from the WALS regressions.
- Compared to other possible determinants (the "auxiliary regressors"), inequality has relatively weak explanatory power; other auxiliary regressors appear more frequently as "robust determinants."

### WALS results — Top10 income shares (Table 9.1)
- The point estimates of the effect of inequality do not move above the "robust" threshold in the regressions of human capital, TFP, and fertility.
- The WALS results do not replicate significant relationships found in the event study: 
  - The marginally significant event-study relationships between (i) WDI and WID and TFP; (ii) WID and fertility; and (iii) WID and political stability all become insignificant in WALS.
- Two models reach a t-statistic larger than one (the "robust" level):
  - (i) a negative link between the WID Top10 income share and capital services;
  - (ii) a positive link between the WDI Top10 income share and political stability (which was marginally negative in the event study).
- The other Top10 income shares do not mirror these statistically significant associations; at least one (capital services), if not two (political stability), of the other estimates carry the opposite sign of the "robust" estimate.

### WALS results — Gini (Table 9.2)
- At least one variant of the Gini enters significantly in four out of the five transmission channels.
- The t-statistics of the "robust associations" are generally just above one, indicating a probability of just over fifty percent that inequality (as measured by the Gini) belongs in the transmission-channel models.
- Political stability is the only transmission channel without a significant association with the Gini (contrasting with Figure 2.2, which showed two significant associations).
- Human capital and capital services show "consistent" results, with all coefficients negative. In both cases, the SWIID Gini (v3.1; v8.3 remains insignificant) moves above the "robust" threshold.
- TFP results are mixed: two significant associations carry opposite signs, suggesting effects that change with country income.
- The relationship between the Gini and fertility:
  - negative and statistically significant when using the FAD Gini;
  - close to zero with the other two Gini variants.

### Indicator heterogeneity and implications
- Differences within each group of indicators (Top10 income shares and Gini variants) are predominant: each variant can give rise to unique empirical relationships with the transmission channels.
- Given the wide dispersion in estimated coefficients within both indicator groups, WALS regressions do not suggest a systematic difference between Top10 income shares and the Gini.
- Averaging the three estimated coefficients in each transmission channel yields averages relatively close to each other.
- The capital services regressions are the only instance of a "robust" association with a variant of both the Gini and the Top10 income share, although most indicators still suggest an insignificant relationship in this channel.

### Role of stage of development and interaction terms
- Most "robust" associations between inequality and transmission channels include a significant interaction term between inequality and GDP per capita (log) (interpretation of interaction in WALS regressions is noted as not straightforward).
- Example thresholds reported:
  - The negative impact of the WID Top10 income share on TFP turns positive for richer countries—countries whose per capita income exceeds $3,300 (expressed at current PPP).
  - For the FAD Gini and TFP, increases in the Gini seem to stimulate TFP growth in poorer countries, but when per capita income exceeds $11,000, the effect turns negative.

### Pooled Mean-Group (PMG) regressions (Table 10)
- PMG results reinforce prior conclusions: inequality does not display a significantly robust long-term relationship with the transmission channels.
- Short-run and long-run effects differ markedly:
  - For the full sample, the short-run effect is positive for TFP, whereas the long-run effect is never significant.
  - Short-run effects, when significant, tend to be positive: human capital and fertility in advanced economies (AEs); capital services in emerging-market and developing economies (EMDEs).
- A new significant negative long-run association emerges between inequality and the level of capital services (investment) in advanced economies (relative to the full sample).
- The effects of inequality differ significantly across country groups, underscoring the importance of accounting for country-income levels.

### Stability over time — rolling-window PMG estimates (Figures 3–4)
- Rolling-window PMG estimates of the long-run parameter (28-year estimation windows) show:
  - The structural long-run effect of inequality on four transmission channels (human capital, physical capital, TFP, and fertility) is indistinguishable from zero throughout time.
  - An exception appears for political stability in EMDEs: the estimated effect turns significantly positive in estimation windows ending in the period of 2006–2011.

### Overall assessment and limitations
- WALS regressions do not settle whether and how strongly inequality is related to the transmission channels despite the method's claim to "let the data speak."
- Top10 income shares and the Gini generally have lower explanatory power for changes in transmission channels than many other variables commonly used in empirical growth literature.
- Inequality emerges as a "robust determinant" only in a few specifications, and these specifications are not robust to changes in compilation methodology of the underlying inequality indicator.
- Short-run positive effects of inequality (when present) tend to wane or reverse over longer horizons; effects vary by country-income group.

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020164-print-pdf.pdf*

### 70.      We dig into this brief positive relationship by identifying the responsible country

### V. CONCLUSION

### Inequality indicator sensitivity and empirical findings
- Significant associations between income inequality and growth transmission channels found with one inequality indicator typically fail to replicate when switching to another indicator.
- Empirical relationships are more sensitive to the choice of a particular inequality indicator from a given set of indicators (one particular Gini from the set of available Ginis) than the choice between different inequality indicator sets (Gini versus Top10 income share).
- One possible interpretation: only a specific subtype of income inequality (example given in text: "inequality in after-tax income between adults only, after adjusting for income from the provision of in-kind public services and owner-occupied housing but excluding monetary unemployment benefits") may exert economic effects, whereas other definitions do not. The paper presents evidence consistent with this interpretation but expresses reservations about its constructiveness.

### Inequality and political stability (fragile-country episodes)
- The observed brief positive relationship between rising inequality and political stability reflects co-movement in countries that experienced (violent) social conflict in the 2000s.
- Examples of such countries: DR Congo, Haiti, Côte d’Ivoire, and Zimbabwe.
- In these countries, inequality worsened amid the social conflict and then persisted at higher levels after the conflict ended; political stability, however, quickly improves once peace is restored, producing an apparent positive impact of rising inequality on political stability.
- When these fragile countries are excluded from the estimation sample, the significant relationship between inequality and political stability disappears.
- This finding underscores possible non-linearities in the relationship between inequality and political stability.

### Statistical power and interpretation caveats
- The paper cautions against interpreting its results to mean that inequality does not matter for economic growth: "absence of evidence is not evidence of absence."
- The study confronts limitations common in empirical economics and the inequality-growth literature, notably low statistical power (Ioannidis et al., 2017).
- Even with multiple empirical methods and data sources, the authors cannot be sure their specific estimates have sufficient power to discriminate between a non-existing effect and an effect observable only in specific circumstances.
- Cross-country datasets at annual frequencies pose a binding constraint on statistical power.

### Data and methodological recommendations
- The way forward calls for more and better data:
  - Expand the country coverage of existing inequality statistics, ensuring they are based on comparable household surveys and administrative tax records.
  - Intensify the development of comparable distributional indicators within the Systems of National Accounts (SNA) framework; ongoing research efforts to update the 2008 SNA are the natural place for these efforts.
- Advantages of SNA-based distributional indicators:
  - SNA have comprehensive and standardized income definitions compared to household surveys and tax records.
  - Embedding income inequality statistics in national accounts will facilitate international comparability and pave the way towards more robust cross-country empirical work on the economic effects of inequality.
- The IMF (2020) recommendation: intensify development of comparable distributional indicators within the SNA framework.

*Source: Excerpt from wpiea2020164-print-pdf (pages 70–74), IMF Working Paper text provided.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020164-print-pdf.pdf_