## 1. Summary Statistics for the Gini Index: 1981-2014

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### I. Introduction — research questions and approach
- Research questions:
  - Does inequality worsen during growth slowdowns and/or improve during growth upswings?
  - What are the main channels through which short-term growth and inequality dynamics are intertwined?
- Data and measures:
  - Inequality: Gini index (principal measure), income (consumption) share of the bottom 50 percent, income (consumption) share of the top 10 percent.
  - Growth fluctuations: polytomous variable based on the deviation between a country’s growth rate in a given year and its mean growth rate.
  - Sample period: 1981-2014 (inequality data from World Bank’s PovcalNet; additional macro variables from IMF WEO and World Bank WDI).
- Empirical approach:
  - Causal mediation analysis to (i) identify systematic relationships between growth conditions and subsequent-year inequality, and (ii) quantify transmission channels (e.g., unemployment, youth unemployment, fiscal stance, financial wealth/assets, inflation).
- High-level findings:
  - For developing economies, growth upswings tend to be associated with lower inequality, while growth downturns tend to be associated with higher inequality.
  - Reductions in inequality during upswings are largely undone by slowdowns.
  - Unemployment, especially youth unemployment, is a key transmission channel. Quantified effects for the developing-country sample:
    - During periods of positive growth (good times), 41.3 percent of the effect of growth fluctuations on inequality occurs through the unemployment channel.
    - During periods of negative growth (bad times), 28.4 percent of the effects of growth fluctuations on inequality is transmitted through the unemployment channel.
  - Policy implication: the quality of jobs created and labor market policies, including those targeted to younger workers, are important to ensure growth outcomes translate into reductions in inequality.

### II. Related literature (short-term vs. long-term perspectives)
- Two broad strands:
  - How growth affects inequality (e.g., Kuznets curve literature).
  - How inequality affects growth (long-run and medium-run panel studies).
- Recent short-horizon focus identifies three main transmission channels:
  - Labor markets (via unemployment affecting income).
  - Financial markets (via wealth effects).
  - Fiscal policy (automatic stabilizers, countercyclical policy).
- Noted gap: most short-term literature focuses on advanced economies; Calderón and Levy-Yeyati (2009) covers developing countries and finds regressive, asymmetric, non-linear relationships mitigated by personal wealth, public expenditure, and labor protection.

### III. Data and sample
- Primary inequality source:
  - World Bank’s PovcalNet database (July 2017 vintage used).
  - PovcalNet reports inequality for 111 advanced and developing countries based on household survey microdata.
  - For developing countries, estimates primarily based on household consumption data; Latin America & Caribbean and Europe largely based on household income data; occasional switches between consumption and income noted.
  - Database does not specify whether income-based inequality is before or after taxes and transfers.
- Sample construction:
  - Restricted to developing countries with at least 5 rounds of household surveys during 1980-2014.
  - Resulting unbalanced panel: 71 developing countries.
  - Sub-sample of 28 Emerging Market Economies (EMEs) identified using IMF categorizations.
- Controls and explanatory variables:
  - From IMF WEO and World Bank WDI: GDP per capita, population size, age structure, proxies for fiscal stance, unemployment, financial wealth/assets, inflation.
- Rationale:
  - PovcalNet chosen over SWIID to avoid imputed data points.
  - Heterogeneity addressed via dummy variables and/or country fixed effects.

### IV. Stylized facts from the data (developing countries sample)
- Aggregate and variability facts:
  - The average Gini coefficient declined by about 20 percent in the sample of developing countries over 1981-2014.
  - In about 30 percent of country cases, the change in the Gini index from one comparable survey to another exceeded ± 2 points.
  - Large declines were more prevalent than large increases.
  - The standard deviation of the Gini coefficient in the developing countries’ sample is about twice that of advanced economies — indicating more within-country volatility.
  - Box-and-whisker comparisons suggest inequality may be more sensitive to growth conditions in developing countries than in advanced economies in the sample.

### V. Summary statistics for the Gini index: 1981-2014 (observations, mean, S.D., Min, Max)
- Advanced Economies
  - Obs e rvations: 288
  - Mean: 31.6
  - S.D: 4.3
  - Min: 19.4
  - Max: 42.8
- Developing Countries — All
  - Obs e rvations: 879
  - Mean: 41.6
  - S.D: 10.2
  - Min: 16.2
  - Max: 64.8
- By Region
  - East Asia & Pacific (EAP)
    - Obs e rvations: 104
    - Mean: 37.8
    - S.D: 6.1
    - Min: 17.8
    - Max: 49.2
  - Europe and Central Asia (ECA)
    - Obs e rvations: 292
    - Mean: 32.0
    - S.D: 5.5
    - Min: 16.2
    - Max: 53.7
  - Latin America and Caribbean (LAC)
    - Obs e rvations: 333
    - Mean: 51.6
    - S.D: 5.1
    - Min: 34.4
    - Max: 63.3
  - Middle East and Northern Africa (MENA)
    - Obs e rvations: 37
    - Mean: 39.9
    - S.D: 3.0
    - Min: 34.0
    - Max: 47.4
  - South Asia (SOA)
    - Obs e rvations: 32
    - Mean: 33.3
    - S.D: 3.8
    - Min: 25.9
    - Max: 41.0
  - Sub-Saharan Africa (SSA)
    - Obs e rvations: 81
    - Mean: 44.1
    - S.D: 7.7
    - Min: 28.9
    - Max: 64.8
- By measure of inequality
  - Income (I)
    - Obs e rvations: 378
    - Mean: 48.8
    - S.D: 9.2
    - Min: 17.8
    - Max: 63.3
  - Consumption (C)
    - Obs e rvations: 501
    - Mean: 36.2
    - S.D: 7.1
    - Min: 16.2
    - Max: 64.8
- Notes:
  - Summary statistics reported for all countries in PovcalNet as of July, 2017.
  - Sub-national (rural) observations for China, India, Indonesia and Uruguay are excluded.
  - Countries with less than 5 rounds of survey results are excluded.

### VI. Empirical strategy — causal mediation analysis (methodology overview)
- Motivation:
  - Traditional IV approaches rely on exclusion restrictions and often rule out additional causal mechanisms.
  - Causal mediation analysis decomposes total effects into direct and indirect components, and can quantify multiple mediated effects for the same treatment variable.
- Conceptual framework:
  - Linear structural equations model with Y and mediator M and treatment X; residuals e1, e2, e3.
  - Four-step causal steps approach (Baron and Kenny, 1986; Kenny et al., 1998):
    1. Establish X → Y.
    2. Establish X → M.
    3. Establish M → Y controlling for X.
    4. Decompose total effect into direct (ADE) and indirect (ACME) components.
- Application:
  - Mediation analysis used to quantify how much of growth-inequality effects are transmitted through unemployment and youth unemployment.

### VII. Mediation methodology and identifying assumptions
- Decomposition:
  - ACME — effect transmitted through mediator M.
  - ADE — remaining (unmediated) effects (includes other channels).
- Framework used: Imai, Keele and Yamamoto (2010) (IKY) relying on "sequential ignorability".
  - Sequential ignorability: no omitted covariate affecting (i) variable of interest and outcome; and/or (ii) outcome and mediator.
  - If sequential ignorability holds and the system is linear, IKY is numerically equivalent to traditional linear structural equations.
- Sensitivity parameter:
  - IKY introduces correlation parameter 휌 to capture correlation between mediator error (e3) and outcome error (e2).
    - If sequential ignorability holds, 휌 = 0.
    - Non-zero 휌 suggests unobserved confounding of ACME.
  - IKY sensitivity analysis finds values of 휌 for which the confidence interval of ACME contains 0.
- Implementation detail:
  - Model parameter simulation step used 1000 iterations.

### VIII. Empirical implementation (equations, treatment, mediators)
- Primary panel regression (Eq.4):
  - 푌푖푡 = 훼 + 휷 퐺퐶푖푡−1 + 휸2 풄풄′푖푡 + 휃푖 + 휗푡 + 휀푖푡
  - 푌푖푡 is Gini index (unweighted PovcalNet); 퐺퐶푖푡−1 is lagged polytomous growth-conditions variable.
  - 푋푖푡 includes log GDP per capita, log GDP per capita squared, log population, population structure, and potential mediators.
  - Country and time fixed effects (휃푖 and 휗푡).
- Definition of "good times" and "bad times":
  - Good times: growth rate of GDP per capita strictly positive.
  - Bad times: growth rate of GDP per capita zero or negative.
  - Each classified into three regimes by country-specific standard-deviation thresholds:
    - 퐺퐶푖푡−1 = 1 if real GDP per capita growth > 0 (≤ 0 for bad times) and deviation ≤ 1.5;
    - 퐺퐶푖푡−1 = 2 if growth > 0 (≤ 0 for bad times) and deviation > 1.5 and ≤ 2.0;
    - 퐺퐶푖푡−1 = 3 if growth > 0 (≤ 0 for bad times) and deviation > 2.0.
- Candidate mediators:
  - Employment / Unemployment.
  - Access to finance.
  - Government spending.
- Mediation model equations (Eqs.5 and 6):
  - Mediation equation: 푀푖푡 = 훼1 + 휷1 퐺퐶푖푡−1 + 흉1 풄풄′푖푡 + 휇푖 + 휎푡 + 휖푖푡
  - Outcome equation: 푌푖푡 = 훼2 + 휑 푀푖푡 + 휷2 퐺퐶푖푡−1 + 휸2 풄풄′푖푡 + 휃푖 + 휗푡 + 휀푖푡
- IKY algorithm summary:
  - Specify structural equations; simulate model parameters via iterative estimation on random sub-samples; model mediator values conditional on treatment and covariates; compute ACME statistics and perform sensitivity analysis.

### IX. Key regression findings (linking growth conditions and inequality)
- Table 3 (Developing countries) — selected estimates (Dependent variable: GINI Index):
  - Good times (lag 1 year): -0.690** (column 1), -0.576* (column 2), -0.627* (column 3)
    - Robust standard errors: (0.313), (0.317), (0.322).
  - Bad times (lag 1 year): 0.676*** (column 1), 0.388 (column 2), 0.419 (column 3)
    - Robust standard errors: (0.246), (0.265), (0.265).
  - Unemployment: 0.219*** with standard error (0.059).
  - Youth Unemployment: 0.084*** with standard error (0.032).
  - Observations: 854 in columns (1)-(2); 771 in columns (3)-(6).
  - Adjusted R-squared: 0.897 (columns (1)-(2)); 0.913 (columns (3)-(4)); 0.912 (columns (5)-(6)).
- Interpretation:
  - Good times associated with lower subsequent Gini coefficients.
  - Bad times associated with higher subsequent Gini coefficients.
  - Inclusion of unemployment reduces statistical significance of good/bad times coefficients, indicating unemployment as a promising mediator.
- Table 4 (Emerging Market Economies) — selected estimates:
  - Good times (lag 1 year): -0.766* (column 1), -0.658 (column 2), -0.679 (column 3) with standard errors (0.390), (0.420), (0.423).
  - Bad times (lag 1 year): 0.652** (column 1), 0.538** (column 2), 0.539** (column 3) with standard errors (0.267), (0.273), (0.271).
  - Unemployment: 0.192** with standard error (0.075).
  - Youth Unemployment: 0.086** with standard error (0.039).
  - Observations: 425 in columns (1)-(2); 370 in columns (3)-(6).
  - Adjusted R-squared: 0.936–0.943 across columns.

### X. Mediator analysis results — unemployment as a key transmission channel
- Estimation details:
  - Unweighted GINI data from PovcalNet; standard errors clustered at country level. Full covariates and country/year fixed effects included.
- Developing countries (71 countries, labor market effects):
  - Good time (lag 1yr.) total GINI coefficient effect: -0.285 (column (1) of mediation table).
  - ACME (through unemployment): -0.206.
  - Absolute percentage mediated by unemployment: 41.299%.
  - Confidence interval for ACME: [ -0.631, -0.034 ].
- Emerging market economies (28 countries, labor market effects):
  - Good time (lag 1yr.) total GINI coefficient effect: -0.400.
  - ACME (through unemployment): -0.264.
  - Absolute percentage mediated by unemployment: 51.101%.
  - Confidence interval for ACME: [ -1.109, 0.035 ].
  - Note: coefficient on unemployment during bad times for EMEs is not statistically significant.
- Bad times (developing countries):
  - Reported absolute percentage mediated by unemployment: 28.359% (Table 5, bottom panel) and other table lines report 22.290% / 22.8% for different entries.
- Youth unemployment as mediator (Table 6):
  - Developing countries:
    - Good time (lag 1yr.) total GINI coefficient effect: -0.264.
    - ACME (through youth unemployment): -0.191.
    - Absolute percentage mediated: 38.264%.
    - Confidence interval for ACME: [ -0.613, -0.013 ].
  - Emerging market economies:
    - Good time (lag 1yr.) total effect: -0.365.
    - ACME (through youth unemployment): -0.252.
    - Absolute percentage mediated: 47.068%.
    - Confidence interval for ACME: [ -1.026, 0.037 ].
  - For bad times using youth unemployment, reported mediated percentages include 27.0 percent and 26.957 percent in different table entries.
- Summary mediated shares (Figure 6 values):
  - Developing countries — Unemployment: 41.3
  - Developing countries — Youth Unemployment: 38.3
  - EMEs — Unemployment: 51.1
  - EMEs — Youth Unemployment: 47.1
  - Developing countries — Bad times via Unemployment: 28.4
  - Developing countries — Bad times via Youth Unemployment: 27.0
  - Additional entries in figure: 22.3 and 22.8 (bad-times mediated shares reported in table lines).

### XI. Robustness and sensitivity
- Alternative inequality measures:
  - Share of income (consumption) of bottom 50 percent:
    - Good times: coefficient 0.398** (0.183); 0.334* (0.186); 0.366* (0.190) in models (1)–(3) (Developing Countries Table 1).
    - Bad times: coefficient -0.406*** (0.149); -0.227 (0.158); -0.246 (0.159).
  - Share of income (consumption) of top 10 percent:
    - Good times: -0.557** (0.256); -0.458* (0.258); -0.495* (0.260) in models (1)–(3) (Developing Countries Table 3).
    - Bad times: 0.499*** (0.188); 0.303 (0.204); 0.326 (0.202).
- Robustness of growth-condition definition:
  - Alternative definition using absolute deviation from mean growth rate yields robust results.
- Sensitivity to sequential ignorability (IKY):
  - IKY sensitivity analysis computes values of 휌 for which ACME confidence interval contains 0 (column (4) in Tables 5 and 6).
  - Example: if ρ = 0.206, the average causal effect of unemployment in good times would be zero (Table 5 example).
  - Reported values indicate violations of sequential ignorability would have to be strong to reverse conclusions about ACME.
- Figure 1 notes (sensitivity figure):
  - Vertical axis: Average mediation effect.
  - Horizontal axis: Sensitivity parameter: ρ with tick markers -1 -.5 0 .5 1.
  - Solid black lines show ACME for different ρ; shaded grey areas are 95% confidence intervals.
  - Legend entries preserved: 95% Conf. Interval; Unemployment and Good times: ACME; Unemployment and Bad times: ACME; Youth unemployment and Good times: ACME; Youth Unemployment and Bad times: ACME.

### XII. Conclusions about average causal mediation effects of unemployment and youth unemployment
- Scope and methodology:
  - Sample: 71 developing countries.
  - Period: 1981-2014.
  - Inequality source: World Bank’s PovcalNet.
  - Growth-condition variable: polytomous indicator based on real GDP per capita growth deviations.
  - Empirical technique: mediation analysis with sensitivity checks for sequential ignorability.
- Main empirical findings:
  - ‘Good’ times result in lower inequality (Gini falls); ‘Bad’ times tend to increase inequality (Gini rises).
  - Income/consumption shares:
    - Good times: share of bottom 50 percent rises; share of top 10 percent falls.
    - Bad times: share of bottom 50 percent falls; share of top 10 percent rises.
    - Net effect: reductions in inequality during good times are largely undone in bad times.
- Quantified mediation through unemployment (including youth):
  - Good times:
    - Unemployment channel explains 41.3 percent of the effect in the full sample of developing countries.
    - Unemployment channel explains 51.1 percent of the effect in the sub-sample of 28 EMEs.
  - Bad times:
    - Unemployment channel explains around 28.4 percent of the effect in developing countries.
    - For EMEs, a robust statistical causal relationship from bad times to inequality through unemployment could not be established.
  - Youth unemployment:
    - The bulk of the unemployment-mediated effect comes from youth unemployment (e.g., 38.3 percent for developing countries; 47.1 percent for EMEs for good times).
- Policy implications:
  - Labor market quality and policies are important levers to reduce inequality in developing countries.
  - Structural reforms to address labor-market features that exacerbate income disparities are recommended, including:
    - Addressing high importance of informal or self-employment.
    - Establishing social safety nets relating to employment protection or unemployment benefits.
    - Improving labor mobility.
  - Targeted policies for youth:
    - Policies aimed at increasing employability of younger workers and reducing their vulnerability to downturns are important to mitigate inequality dynamics driven by growth conditions.
- Research note:
  - Further work with more granular data is needed to inform policy design; current results provide a useful starting point.

*Source: Authors' calculations using the World Bank's PovcalNet database and supporting text from the IMF working paper section "1. Summary Statistics for the Gini Index: 1981-2014" and related sections (wp1920).*

### 1. Summary Statistics for the Gini Index: 1981-2014 .................................................9

### 1. Summary Statistics for the Gini Index: 1981-2014

### I. Introduction — research questions and approach
- Research questions:
  - Does inequality worsen during growth slowdowns and/or improve during growth upswings?
  - What are the main channels through which short-term growth and inequality dynamics are intertwined?
- Data and measures:
  - Inequality: Gini index (principal measure), income (consumption) share of the bottom 50 percent, income (consumption) share of the top 10 percent.
  - Growth fluctuations: polytomous variable based on the deviation between a country’s growth rate in a given year and its mean growth rate.
  - Sample period: 1981-2014 (inequality data from World Bank’s PovcalNet; additional macro variables from IMF WEO and World Bank WDI).
- Main empirical approach: causal mediation analysis to (i) identify whether systematic relationships exist between growth conditions and subsequent-year inequality, and (ii) quantify transmission channels (e.g., unemployment, youth unemployment, fiscal stance, financial wealth/assets, inflation).
- High-level findings summarized in the introduction:
  - For developing economies, growth upswings tend to be associated with lower inequality, while growth downturns tend to be associated with higher inequality.
  - Reductions in inequality during upswings are largely undone by slowdowns.
  - Unemployment, especially youth unemployment, is a key transmission channel. Quantified effects in the developing-country sample:
    - During periods of positive growth (good times), 41.3 percent of the effect of growth fluctuations on inequality occurs through the unemployment channel.
    - During periods of negative growth (bad times), 28.4 percent of the effects of growth fluctuations on inequality is transmitted through the unemployment channel.
  - Policy implication highlighted: the quality of jobs created and labor market policies, including those targeted to younger workers, are important to ensure growth outcomes translate into reductions in inequality.

### II. Related literature (short-term vs. long-term perspectives)
- Two broad strands historically:
  - How growth affects inequality (e.g., Kuznets curve literature).
  - How inequality affects growth (long-run and medium-run panel studies).
- Recent focus: short-horizon impacts (business-cycle frequencies) and crises on inequality; three main transmission channels identified in recent literature:
  - Labor markets (via unemployment affecting income).
  - Financial markets (via wealth effects).
  - Fiscal policy (automatic stabilizers, countercyclical policy).
- Noted gap: most short-term literature focuses on advanced economies; Calderón and Levy-Yeyati (2009) is a notable study covering developing countries and finding regressive, asymmetric, non-linear relationships mitigated by personal wealth, public expenditure, and labor protection.

### III. Data and sample
- Primary inequality source: World Bank’s PovcalNet database (July 2017 vintage used in the analysis).
  - PovcalNet reports inequality for 111 advanced and developing countries based on household survey microdata.
  - For developing countries in PovcalNet, estimates are primarily based on household consumption data, with Latin America & Caribbean and Europe largely based on household income data; occasional switches between consumption and income for some countries are noted.
  - The database does not specify whether income-based inequality is before or after taxes and transfers.
- Sample construction:
  - Restricted to developing countries with at least 5 rounds of household surveys during 1980-2014.
  - Resulting unbalanced panel: 71 developing countries.
  - Sub-sample of 28 Emerging Market Economies (EMEs) identified using IMF categorizations (Appendix IV referenced).
- Control and explanatory variables:
  - Explanatory/control variables from IMF WEO and World Bank WDI.
  - Controls include GDP per capita, population size, age structure, proxies for fiscal stance, unemployment, financial wealth/assets, inflation.
- Rationale for data choices:
  - PovcalNet chosen over SWIID to avoid imputed data points that might distort results.
  - To address heterogeneity (consumption vs income measures, methodological breaks), empirical analysis includes dummy variables and/or country fixed effects.

### IV. Stylized facts from the data (developing countries sample)
- Aggregate and variability facts:
  - The average Gini coefficient declined by about 20 percent in the sample of developing countries over 1981-2014.
  - In about 30 percent of country cases, the change in the Gini index from one comparable survey to another exceeded ± 2 points.
  - Large declines were more prevalent than large increases.
  - The standard deviation of the Gini coefficient in the developing countries’ sample is about twice that of advanced economies — indicating more within-country volatility.
  - Box-and-whisker comparisons suggest inequality may be more sensitive to growth conditions in developing countries than in advanced economies in the sample.

### V. Summary statistics for the Gini index: 1981-2014 (observations, mean, S.D., Min, Max)
- Advanced Economies
  - Obs e rvations: 288
  - Mean: 31.6
  - S.D: 4.3
  - Min: 19.4
  - Max: 42.8
- Developing Countries — All
  - Obs e rvations: 879
  - Mean: 41.6
  - S.D: 10.2
  - Min: 16.2
  - Max: 64.8
- By Region
  - East Asia & Pacific (EAP)
    - Obs e rvations: 104
    - Mean: 37.8
    - S.D: 6.1
    - Min: 17.8
    - Max: 49.2
  - Europe and Central Asia (ECA)
    - Obs e rvations: 292
    - Mean: 32.0
    - S.D: 5.5
    - Min: 16.2
    - Max: 53.7
  - Latin America and Caribbean (LAC)
    - Obs e rvations: 333
    - Mean: 51.6
    - S.D: 5.1
    - Min: 34.4
    - Max: 63.3
  - Middle East and Northern Africa (MENA)
    - Obs e rvations: 37
    - Mean: 39.9
    - S.D: 3.0
    - Min: 34.0
    - Max: 47.4
  - South Asia (SOA)
    - Obs e rvations: 32
    - Mean: 33.3
    - S.D: 3.8
    - Min: 25.9
    - Max: 41.0
  - Sub-Saharan Africa (SSA)
    - Obs e rvations: 81
    - Mean: 44.1
    - S.D: 7.7
    - Min: 28.9
    - Max: 64.8
- By measure of inequality
  - Income (I)
    - Obs e rvations: 378
    - Mean: 48.8
    - S.D: 9.2
    - Min: 17.8
    - Max: 63.3
  - Consumption (C)
    - Obs e rvations: 501
    - Mean: 36.2
    - S.D: 7.1
    - Min: 16.2
    - Max: 64.8
- Notes from table caption:
  - Summary statistics reported for all countries in PovcalNet as of July, 2017.
  - Sub-national (rural) observations for China, India, Indonesia and Uruguay are excluded.
  - Countries with less than 5 rounds of survey results are excluded.

### VI. Empirical strategy — causal mediation analysis (methodology overview)
- Motivation for mediation analysis:
  - Traditional IV approaches rely on exclusion restrictions (instrument correlated with treatment but not with outcome) and often rule out existence of causal mechanisms other than the hypothesized one.
  - Causal mediation analysis allows decomposition into direct effects and indirect (mediated) effects and can quantify multiple mediated effects for the same treatment variable.
  - This enables assessment of the relative importance of potential transmission channels and highlights where policy interventions may be needed.
- Conceptual framework:
  - Linear structural equations model specification (notation as in the source):
    - Y equations and mediator M with X as independent variable; residuals e1, e2, e3.
  - Four-step causal steps approach (Baron and Kenny, 1986; Kenny et al., 1998):
    1. Establish X → Y (significant relation).
    2. Establish X → M (significant relation).
    3. Establish M → Y when both X and M are predictors of Y.
    4. (Implicit step) Decompose total effect into direct and indirect components (ACME and ADE referenced in figures).
- Application:
  - The paper applies mediation analysis to identify how much of the effect of growth conditions on inequality is transmitted through channels such as unemployment and youth unemployment (figures illustrate ACME and ADE and implementation steps).

### VII. Key empirical quantifications and policy-relevant insights
- Quantified mediation results reported in the introduction for developing countries:
  - Good times (positive growth): 41.3 percent of the effect of growth fluctuations on inequality occurs through the unemployment channel.
  - Bad times (negative growth): 28.4 percent of the effect of growth fluctuations on inequality is transmitted through the unemployment channel.
  - The bulk of these unemployment-mediated effects comes from youth unemployment.
- Policy-relevant implication:
  - The quality of jobs created and labor market policies, including those targeted to younger workers, are important to ensure that growth reduces inequality and that gains during upswings are not undone by downturns.

*Source: Authors' calculations using the World Bank's PovcalNet database and supporting text from the IMF working paper section "1. Summary Statistics for the Gini Index: 1981-2014".*

### 4. Verifying that the absolute value of the coefficient 풄풄 in Eq 1 is larger than 풄풄’

### 4. Verifying that the absolute value of the coefficient 풄풄 in Eq 1 is larger than 풄풄’ in Eq.2

### Mediation methodology and identifying assumptions
- Mediation decomposes the total effect of a treatment into:
  - Average causal mediation effects (ACME) — effect transmitted through mediator M.
  - Average direct effects (ADE) — remaining (unmediated) effects; ADE includes effects transmitted through all other channels.
- Framework used: Imai, Keele and Yamamoto (2010) (IKY), which assumes "sequential ignorability".
  - Sequential ignorability implies no omitted covariate affecting: (i) variable of interest and outcome; and/or (ii) outcome and mediator.
  - If sequential ignorability holds and the system is linear, IKY is numerically equivalent to traditional linear structural equations.
- IKY transparency: introduces a correlation parameter 휌 (rho) that captures correlation between the error term for the mediation equation (e3 in Eq.3) and the error term for the outcome equation (e2 in Eq.2).
  - If sequential ignorability holds, 휌 equals zero.
  - Non-zero 휌 suggests unobserved confounding of the ACME estimate.
  - IKY allows sensitivity analysis by calculating values of 휌 for which the confidence interval of the ACME contains 0.
- Implementation detail: model parameter simulation step used 1000 iterations.

### Empirical implementation (equations, treatment, mediators)
- Primary panel regression (Eq.4):
  - 푌푖푡 = 훼 + 휷 퐺퐶푖푡−1 + 휸2 풄풄′푖푡 + 휃푖 + 휗푡 + 휀푖푡
  - 푌푖푡 is inequality measured by the Gini index (unweighted PovcalNet).
  - 퐺퐶푖푡−1 is a lagged polytomous variable capturing growth conditions (good/bad times).
  - 푋푖푡 is a vector of standard control variables (including log GDP per capita, log GDP per capita squared, log population, population structure) and, in some specifications, potential mediators.
  - 휃푖 and 휗푡 are country and time fixed effects.
- Definition of "good times" and "bad times":
  - Good times: year in which growth rate of GDP per capita is strictly positive.
  - Bad times: year in which growth rate of GDP per capita is zero or negative.
  - Each (good/bad) is classified into three regimes by country-specific standard-deviation thresholds (deviation from period mean):
    - 퐺퐶푖푡−1 = 1 if real GDP per capita growth > 0 (≤ 0 for bad times) and deviation ≤ 1.5;
    - 퐺퐶푖푡−1 = 2 if growth > 0 (≤ 0 for bad times) and deviation > 1.5 and ≤ 2.0;
    - 퐺퐶푖푡−1 = 3 if growth > 0 (≤ 0 for bad times) and deviation > 2.0.
- Candidate mediators (based on literature and data availability):
  - Employment / Unemployment.
  - Access to finance.
  - Government spending.
- Mediation model equations (Eqs.5 and 6):
  - Mediation equation: 푀푖푡 = 훼1 + 휷1 퐺퐶푖푡−1 + 흉1 풄풄′푖푡 + 휇푖 + 휎푡 + 휖푖푡
  - Outcome equation: 푌푖푡 = 훼2 + 휑 푀푖푡 + 휷2 퐺퐶푖푡−1 + 휸2 풄풄′푖푡 + 휃푖 + 휗푡 + 휀푖푡
- Four-step IKY algorithm summary:
  - Specify structural equations for mediator and outcome.
  - Simulate model parameters from sampling distribution by iteratively estimating regressions on random sub-samples.
  - Model all potential values of mediator conditional on treatment and covariates using parameter distributions.
  - Compute summary statistics, point estimates, confidence intervals for ACME; perform sensitivity analysis for sequential ignorability.

### Key regression findings (linking growth conditions and inequality)
- Table 3 (Developing countries) — selected estimates (Dependent variable: GINI Index):
  - Good times (lag 1 year): -0.690** (column 1), -0.576* (column 2), -0.627* (column 3)
    - Robust standard errors shown in parentheses: (0.313), (0.317), (0.322) respectively.
  - Bad times (lag 1 year): 0.676*** (column 1), 0.388 (column 2), 0.419 (column 3)
    - Robust standard errors in parentheses: (0.246), (0.265), (0.265).
  - Unemployment: 0.219*** (columns with unemployment) with standard error (0.059).
  - Youth Unemployment: 0.084*** with standard error (0.032).
  - Observations: 854 in columns (1)-(2); 771 in columns (3)-(6).
  - Adjusted R-squared: 0.897 (columns (1)-(2)); 0.913 (columns (3)-(4)); 0.912 (columns (5)-(6)).
- Interpretation:
  - Good times are associated with lower subsequent Gini coefficients (less inequality).
  - Bad times are associated with higher subsequent Gini coefficients (more inequality).
  - Inclusion of unemployment reduces statistical significance of good/bad times coefficients, indicating unemployment as a promising mediator.
- Table 4 (Emerging Market Economies) — selected estimates:
  - Good times (lag 1 year): -0.766* (column 1), -0.658 (column 2), -0.679 (column 3) with standard errors (0.390), (0.420), (0.423).
  - Bad times (lag 1 year): 0.652** (column 1), 0.538** (column 2), 0.539** (column 3) with standard errors (0.267), (0.273), (0.271).
  - Unemployment: 0.192** with standard error (0.075).
  - Youth Unemployment: 0.086** with standard error (0.039).
  - Observations: 425 in columns (1)-(2); 370 in columns (3)-(6).
  - Adjusted R-squared: 0.936–0.943 across columns.

### Mediator analysis results — unemployment as a key transmission channel
- Unweighted GINI data from PovcalNet; standard errors clustered at country level. Full covariates and country/year fixed effects included.
- Developing countries (71 countries, labor market effects):
  - Good time (lag 1yr.) total GINI coefficient effect: -0.285 (column (1) of mediation table).
  - ACME (through unemployment): -0.206.
  - Absolute percentage mediated by unemployment: 41.299%.
  - Confidence interval for ACME: [ -0.631, -0.034 ].
- Emerging market economies (28 countries, labor market effects):
  - Good time (lag 1yr.) total GINI coefficient effect: -0.400.
  - ACME (through unemployment): -0.264.
  - Absolute percentage mediated by unemployment: 51.101%.
  - Confidence interval for ACME: [ -1.109, 0.035 ].
  - Note: coefficient on unemployment during bad times for EMEs is not statistically significant.
- For bad times:
  - Developing countries: ACME transmitted through unemployment equals 0.206? (table reports Bad time (lag 1yr.) 0.141 / 0.261 22.290% — see table notes).
  - Reported absolute percentage mediated by unemployment for bad times (developing countries): 28.359% (Table 5, bottom panel) and 22.290% (Table 5 top panel line; table formatting shows multiple entries).
- Youth unemployment as mediator (Table 6):
  - Developing countries:
    - Good time (lag 1yr.) total GINI coefficient effect: -0.264.
    - ACME (through youth unemployment): -0.191.
    - Absolute percentage mediated: 38.264%.
    - Confidence interval for ACME: [ -0.613, -0.013 ].
  - Emerging market economies:
    - Good time (lag 1yr.) total effect: -0.365.
    - ACME (through youth unemployment): -0.252.
    - Absolute percentage mediated: 47.068%.
    - Confidence interval for ACME: [ -1.026, 0.037 ].
  - For bad times using youth unemployment, reported mediated percentages include 27.0 percent and 26.957 percent in table entries for different subsamples.
- Summary of mediated percentages (Figure 6 values):
  - Developing countries — Unemployment: 41.3
  - Developing countries — Youth Unemployment: 38.3
  - EMEs — Unemployment: 51.1
  - EMEs — Youth Unemployment: 47.1
  - Developing countries — Bad times via Unemployment: 28.4
  - Developing countries — Bad times via Youth Unemployment: 27.0
  - Additional entries in figure: 22.3 and 22.8 (bad-times mediated shares reported in table lines).

### Robustness and sensitivity
- Results robust to alternative inequality measures:
  - Using the share of income (or consumption) of bottom 50 percent as dependent variable:
    - Good times: positive and statistically significant coefficient (good times associated with increase in share of income/consumption of poorest 50 percent in following year).
    - Bad times: negative and statistically significant coefficient.
  - Using share of income (or consumption) of top 10 percent:
    - Good times: negative and statistically significant (redistribution away from top 10 percent following high growth).
    - Bad times: positive and statistically significant.
- Robustness of growth-condition definition:
  - Alternative definition using absolute deviation from mean growth rate instead of number of standard deviations yields robust results.
- Sensitivity to sequential ignorability:
  - IKY sensitivity analysis computes values of 휌 for which ACME confidence interval contains 0 (column (4) in Tables 5 and 6).
  - Values reported suggest violations of sequential ignorability would have to be strong to reverse analytical conclusions about ACME.

*Source: Authors’ calculations (excerpted from the IMF working paper section titled "4. Verifying that the absolute value of the coefficient 풄풄 in Eq 1 is larger than 풄풄’ in Eq.2").*

### conclusions about the average causal mediation effects of unemployment and youth

### conclusions about the average causal mediation effects of unemployment and youth unemployment

### Scope and methodology
- Sample: 71 developing countries.
- Period: 1981-2014.
- Inequality data source: World Bank’s PovcalNet database.
- Growth-condition variable: polytomous indicator assigning years as ‘good’, ‘bad’, or average based on real GDP per capita growth being exceptionally high, low, or average.
- Empirical technique: mediation analysis to identify causal effects of growth conditions on inequality through unemployment, with special focus on youth unemployment.
- Sensitivity analysis: example in Table 5 indicates that if ρ = 0.206, the average causal effect of unemployment in good times would be zero; Appendix V reports further sensitivity analysis confirming robustness of estimated mediated effects.

### Main empirical findings on inequality dynamics
- Relationship between growth conditions and inequality:
  - ‘Good’ times result in lower inequality as measured by the Gini index.
  - ‘Bad’ times tend to result in higher inequality.
- Income/consumption shares:
  - During ‘good’ times: the share of income (consumption) of the bottom 50 percent rises while the share of the top 10 percent falls.
  - During ‘bad’ times: the share of income (consumption) of the bottom 50 percent falls while the share of the top 10 percent rises.
  - Net effect: reductions in inequality during ‘good times’ are largely undone in ‘bad times’.

### Quantified mediation through unemployment (including youth)
- Contribution of unemployment channel to the effect of ‘good’ times on inequality:
  - Explains 41.3 percent of the effect of ‘good’ times in the full sample of developing countries.
  - Explains 51.1 percent of the effect of ‘good’ times in a sub-sample of 28 emerging market economies.
- Contribution of unemployment channel to the effect of ‘bad’ times on inequality:
  - Explains around 28.4 percent of the effect of ‘bad’ times in developing countries.
  - A robust statistical causal relationship from ‘bad’ times to inequality through the unemployment channel could not be established for the sub-sample of emerging market economies.
- Role of youth unemployment:
  - The bulk of the effect of growth conditions on inequality transmitted through the unemployment channel comes from youth unemployment.

### Policy implications and recommendations
- Labor market quality and policies are important levers to reduce inequality in developing countries.
- Structural reforms recommended to address labor-market features that exacerbate income disparities, including:
  - High importance of informal or self-employment.
  - Lack of established social safety nets relating to employment protection or unemployment benefits.
  - Limited labor mobility.
- Targeted policies for youth:
  - Policies aimed at increasing employability of younger workers and reducing their vulnerability to economic downturns would be important to mitigate inequality dynamics driven by growth conditions.

### Research and data notes
- The paper adds evidence on short-term growth–inequality interactions and identifies unemployment (and youth unemployment in particular) as a quantitatively important causal channel.
- Further work with more granular data is needed to inform policy design; current results provide a useful starting point.

*Source: conclusions about the average causal mediation effects of unemployment and youth unemployment (IMF working paper, based on PovcalNet data, 1981–2014).*

### APPENDIX IV.  COUNTRIES SAMPLES USED IN EMPIRICAL ANALYSIS

### APPENDIX IV.  COUNTRIES SAMPLES USED IN EMPIRICAL ANALYSIS

### Country samples
- All countries (101) * Developing countries (71) Emerging countries (28)
- All countries list (order preserved):
  Albania Latvia Albania Moldova Argentina  
  Argentina Lithuania Argentina Mongolia Belarus  
  Armenia Luxembourg Armenia Montenegro Brazil  
  Australia Macedonia Azerbaijan Morocco Chile  
  Austria Madagascar Bangladesh Nicaragua China  
  Azerbaijan Malaysia Belarus Niger Colombia  
  Bangladesh Mauritania Belize Nigeria Croatia  
  Belarus Mexico Bolivia Pakistan Dominican Republic  
  Belgium Moldova Brazil Panama Ecuador  
  Belize Mongolia Bulgaria Paraguay Hungary  
  Bolivia Montenegro Burkina Faso Peru India  
  Brazil Morocco Cambodia Philippines Indonesia  
  Bulgaria Netherlands Chile Poland Malaysia  
  Burkina Faso Nicaragua China Romania Mexico  
  Cambodia Niger Colombia Russia Morocco  
  Canada Nigeria Costa Rica Rwanda Pakistan  
  Chile Norway Cote d'Ivoire Senegal Peru  
  China Pakistan Croatia Serbia Philippines  
  Colombia Panama Dominican Republic South Africa Poland  
  Costa Rica Paraguay Ecuador Sri Lanka Romania  
  Cote d'Ivoire Peru El Salvador Tajikistan Russia  
  Croatia Philippines Georgia Thailand South Africa  
  Cyprus Poland Ghana Tunisia Sri Lanka  
  Czech Republic Portugal Guatemala Turkey Thailand  
  Denmark Romania Guinea Uganda Turkey  
  Dominican Republic Russia Honduras Ukraine Ukraine  
  Ecuador Rwanda Hungary Uruguay Uruguay  
  El Salvador Senegal India Uzbekistan Venezuela  
  Estonia Serbia Indonesia Venezuela   
  Finland Slovak Republic Iran Vietnam   
  France Slovenia Jamaica West Bank and Gaza   
  Georgia South Africa Kazakhstan Zambia   
  Germany Spain Kyrgyzstan   
  Ghana Sri Lanka Lao     
  Greece Sweden Macedonia     
  Guatemala Switzerland Madagascar     
  Guinea Tajikistan Malaysia     
  Honduras Thailand Mauritania     
  Hungary Tunisia Mexico     
  Iceland Turkey       
  India Uganda       
  Indonesia Ukraine       
  Iran United Kingdom       
  Ireland United States       
  Israel Uruguay       
  Italy Uzbekistan       
  Jamaica Venezuela       
  Kazakhstan Vietnam       
  Kosovo West Bank and Gaza       
  Kyrgyzstan Zambia       
  Lao         
- Sources: World Bank List of Economies June 2017 and IMF, Fiscal Monitor databases
- Note: The "All countries" sample only includes countries with at least 5 rounds of survey data.

### Empirical analysis samples counts
- All countries: 101
- Developing countries: 71
- Emerging countries: 28

*Source: wp1920 - APPENDIX IV.  COUNTRIES SAMPLES USED IN EMPIRICAL ANALYSIS*

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### APPENDIX V. ROBUSTNESS CHECKS

### Table 1. Developing Countries: Relationship between the Income (Consumption) Share of the Bottom 50 percent and Growth Conditions
- Dependent Variable: Share of Bottom 50 percent
- Coefficients and statistics (models (1)–(6)):
  - Good times (lag 1 year): 0.398** (0.183); 0.334* (0.186); 0.366* (0.190)
  - Bad times (lag 1 year): -0.406*** (0.149); -0.227 (0.158); -0.246 (0.159)
  - Log of GDP per capita: -1.921 (3.217); -1.687 (3.223); 5.929* (3.113); 5.980* (3.129); 5.100 (3.118); 5.146 (3.138)
  - Log of GDP per capita squared: 0.086 (0.192); 0.072 (0.192); -0.409** (0.196); -0.409** (0.196); -0.358* (0.196); -0.357* (0.196)
  - Log of population: 3.894*** (1.330); 4.049*** (1.304); 0.254 (1.557); 0.466 (1.536); 0.293 (1.559); 0.528 (1.544)
  - Population structure: 0.124** (0.057); 0.129** (0.057); 0.056 (0.060); 0.057 (0.060); 0.047 (0.059); 0.047 (0.060)
  - Unemployment: -0.136*** (0.036); -0.137*** (0.036) [models including]
  - Youth Unemployment: -0.052*** (0.019); -0.052*** (0.020) [models including]
  - Constant: -9.352 (16.893); -12.121 (16.888); 11.996 (18.301); 9.299 (18.370); 14.602 (18.383); 11.646 (18.505)
  - Observations: 854; 854; 771; 771; 771; 771
  - Adjusted R-squared: 0.898; 0.899; 0.914; 0.914; 0.913; 0.913
  - rmse: 1.906; 1.899; 1.716; 1.717; 1.725; 1.726
- Notes: Robust standard errors in parentheses. Standard errors are robust to autocorrelation and heteroskedasticity. *** p<0.01, ** p<0.05, * p<0.1

### Table 2. Emerging Market Economies: Relationship between the Income (Consumption) Share of the Bottom 50 percent and Growth Conditions
- Dependent Variable: Share of Bottom 50 percent
- Coefficients and statistics (models (1)–(6)):
  - Good times (lag 1 year): 0.414* (0.225); 0.349 (0.240); 0.363 (0.242)
  - Bad times (lag 1 year): -0.369** (0.154); -0.294* (0.157); -0.296* (0.156)
  - Log of GDP per capita: -29.285*** (6.482); -28.908*** (6.487); -15.453* (8.348); -15.904* (8.263); -16.507* (8.412); -16.960** (8.329)
  - Log of GDP per capita squared: 1.458*** (0.364); 1.436*** (0.363); 0.646 (0.468); 0.673 (0.461); 0.703 (0.472); 0.730 (0.464)
  - Log of population: 5.061** (2.474); 5.037** (2.425); -2.207 (3.233); -1.966 (3.114); -1.892 (3.238); -1.633 (3.116)
  - Population structure: 0.194* (0.108); 0.197* (0.110); 0.198 (0.141); 0.196 (0.139); 0.173 (0.140); 0.172 (0.139)
  - Unemployment: -0.114*** (0.042); -0.113*** (0.042) [models including]
  - Youth Unemployment: -0.050** (0.022); -0.049** (0.022) [models including]
  - Constant: 51.537 (38.287); 50.732 (38.208); 124.850*** (47.537); 122.870*** (47.150); 125.116*** (47.938); 122.751** (47.577)
  - Observations: 425; 425; 370; 370; 370; 370
  - Adjusted R-squared: 0.938; 0.939; 0.946; 0.946; 0.945; 0.946
  - rmse: 1.536; 1.526; 1.382; 1.375; 1.387; 1.381
- Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

### Table 3. Developing Countries: Relationship between the Income (Consumption) Share of the Top 10 percent and Growth Conditions
- Dependent Variable: Share of top 10 percent
- Coefficients and statistics (models (1)–(6)):
  - Good times (lag 1 year): -0.557** (0.256); -0.458* (0.258); -0.495* (0.260)
  - Bad times (lag 1 year): 0.499*** (0.188); 0.303 (0.204); 0.326 (0.202)
  - Log of GDP per capita: 2.599 (4.787); 2.298 (4.870); -7.669 (4.915); -7.749 (5.000); -6.726 (4.893); -6.796 (4.983)
  - Log of GDP per capita squared: -0.106 (0.276); -0.089 (0.280); 0.550* (0.289); 0.551* (0.292); 0.492* (0.288); 0.492* (0.292)
  - Log of population: -3.792** (1.717); -4.013** (1.695); -0.065 (2.117); -0.350 (2.103); -0.116 (2.132); -0.429 (2.124)
  - Population structure: -0.163** (0.079); -0.168** (0.080); -0.050 (0.084); -0.051 (0.085); -0.040 (0.084); -0.040 (0.085)
  - Unemployment: 0.152*** (0.048); 0.154*** (0.049) [models including]
  - Youth Unemployment: 0.058** (0.025); 0.058** (0.026) [models including]
  - Constant: 59.564** (24.750); 63.217** (25.124); 42.087 (28.720); 45.731 (29.183); 39.226 (28.817); 43.164 (29.345)
  - Observations: 854; 854; 771; 771; 771; 771
  - Adjusted R-squared: 0.882; 0.882; 0.900; 0.899; 0.899; 0.899
  - rmse: 2.642; 2.637; 2.387; 2.389; 2.396; 2.397
- Notes: Robust standard errors in parentheses. Standard errors are robust to autocorrelation and heteroskedasticity. *** p<0.01, ** p<0.05, * p<0.1

### Table 4. Emerging Market Economies: Relationship between the Income (Consumption) Share of the Top 10 percent and Growth Conditions
- Dependent Variable: Share of top 10 percent
- Coefficients and statistics (models (1)–(6)):
  - Good times (lag 1 year): -0.658** (0.321); -0.576* (0.348); -0.591* (0.349)
  - Bad times (lag 1 year): 0.507** (0.221); 0.443* (0.228); 0.444* (0.226)
  - Log of GDP per capita: 38.020*** (7.475); 37.474*** (7.479); 21.731** (10.635); 22.331** (10.483); 22.989** (10.653); 23.606** (10.502)
  - Log of GDP per capita squared: -1.912*** (0.425); -1.881*** (0.423); -0.932 (0.605); -0.969 (0.593); -0.999 (0.607); -1.037* (0.594)
  - Log of population: -8.399*** (3.165); -8.404*** (3.108); -1.319 (4.303); -1.671 (4.172); -1.683 (4.310); -2.062 (4.174)
  - Population structure: -0.170 (0.152); -0.175 (0.153); -0.131 (0.211); -0.129 (0.209); -0.100 (0.212); -0.099 (0.210)
  - Unemployment: 0.139** (0.064); 0.138** (0.064) [models including]
  - Youth Unemployment: 0.062* (0.034); 0.061* (0.034) [models including]
  - Constant: 28.969 (49.242); 30.702 (48.854); -33.858 (64.601); -30.775 (63.493); -34.484 (65.110); -30.878 (64.002)
  - Observations: 425; 425; 370; 370; 370; 370
  - Adjusted R-squared: 0.926; 0.926; 0.929; 0.930; 0.929; 0.929
  - rmse: 2.190; 2.182; 2.077; 2.070; 2.082; 2.075
- Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

### Sensitivity analysis: Figure 1. Sensitivity of the Average Causal Mediated Effect (ACME) to violations of the Sequential Ignorability Assumption
- Notes describing figure:
  - The figure shows the estimated ACME for different values of ρ for unemployment and youth unemployment during good and bad times, respectively.
  - The solid black lines show the value of the ACME for different values of the parameter ρ, which measures potential violations of the sequential ignorability assumption, and the shaded grey areas correspond to the 95% confidence intervals for the estimates.
- Visual axes and labels present in the figure (preserved text):
  - Vertical axis label: Average mediation effect
  - Horizontal axis label: Sensitivity parameter: ρ
  - Legend: 95% Conf. Interval; Unemployment and Good times: ACME; Unemployment and Bad times: ACME; Youth unemployment and Good times: ACME; Youth Unemployment and Bad times: ACME
  - Tick/scale markers shown in figure: -6 -4 -2 0 2 4 (Average mediation effect); -1 -.5 0 .5 1 (Sensitivity parameter: ρ) (variants appear across panels)

*Source: wp1920 - APPENDIX V. ROBUSTNESS CHECKS (tables and figure notes reproduced verbatim)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wp1920.pdf_