Income Inequality, Capitalism, and Diversity: A Goodness-of-fit Decomposition Perspective

Author: Anastasiia Rekovets · github.com/ana-rekovets
Contact: ana.rekovets@gmail.com
Year: 2023
Software: Stata 15+

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Abstract

This research explores the dynamics of income redistribution in the context of economic freedom, genetic diversity, and various socio-economic factors. Through the lens of goodness-of-fit decomposition, it quantifies the individual contributions of economic freedom, predicted genetic diversity, religious composition, economic indicators, continent-specific factors, and legal origins in explaining cross-country income inequality.

The analysis extends the merged dataset of Ashraf & Galor (2013) and Sturm & De Haan (2015), applying the rego method (Huettner & Sunder, University of Leipzig) to decompose the R-squared goodness-of-fit of OLS regression models into individual regressor contributions via Shapley values. The dataset spans 108 countries over 1971–2010 (8 five-year intervals).

Key findings: the interaction between economic freedom and genetic diversity consistently accounts for ~50% of explained variation in redistribution. Scandinavian legal origin, Protestant religious composition, and European geographic location emerge as substantial explanatory factors, while the KOF globalisation index and Catholic religious composition contribute comparatively little.

Keywords: income redistribution · economic freedom · predicted genetic diversity · Shapley decomposition · R-squared · legal origins · religious composition · panel data

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Repository Structure

income-inequality-decomposition/
│
├── README.md
│
├── code/
│   └── replication_income_inequality_decomposition.do   # Main Stata replication script
│
├── paper/
│   └── income_inequality_capitalism_diversity.docx      # Full research paper
│
├── presentation/
│   └── income_inequality_capitalism_diversity_presentation.pptx
│
└── output/
    └── output_replication_log.txt                       # Full Stata output log

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Data

The analysis draws on two publicly available datasets merged for this project:

Dataset	Variables provided	Access
Sturm & De Haan (2015)	Redistribution measure (SWIID), Economic Freedom Index (Fraser Institute), fractionalization, legal origins, religious composition, continent dummies	AEA
Ashraf & Galor (2013)	Predicted genetic heterozygosity (migratory distance from East Africa, Out-of-Africa hypothesis)	AEA

Note: Dataset files (.dta) are not included in this repository due to redistribution restrictions. Download the original supplementary files from the AEA links above, place them in a local data/ folder, and update the global root path at the top of the do-file.

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Variables

Variable	Description	Source
redistribution	Market Gini / Net Gini — ratio measuring degree of redistribution	Sturm & De Haan (2015), SWIID
ecfree	Economic Freedom Index, 5-year lag (proxy for capitalism)	Fraser Institute via Sturm & De Haan
pdiv	Predicted heterozygosity using migratory distance to East Africa	Ashraf & Galor (2013)
ecfree_pdiv	Economic Freedom × Predicted Diversity (interaction term)	Constructed
lrgdpepop	Log real GDP per capita, 5-year average	World Bank
kofgi_ecoflows	KOF Economic Globalisation Index — Flows, 5-year average	KOF via Sturm & De Haan
europe, asia, africa, wb_nam, oceania	Continent dummies	Sturm & De Haan
legor_so, legor_ge, legor_sc	Legal origin dummies: Socialist, German, Scandinavian	Sturm & De Haan
pmuslim, pprotest, pcatholic, pother	Share of religious groups in population (1980)	Sturm & De Haan

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Methodology

OLS Regression

Ten OLS regression models are estimated with income redistribution as the dependent variable. A "basic" specification (Economic Freedom, Predicted Diversity, and their interaction) is extended sequentially with additional control groups:

Model	Specification
1	Basic model — all years
2	Basic model — year 2005 only (comparison with Sturm & De Haan 2015)
3	Basic + Log GDP per capita
4	Basic + KOF Globalisation Index
5	Basic + Continent dummies
6	Basic + Legal origin dummies
7	Basic + Share of Muslims
8	Basic + Share of Protestants
9	Basic + Share of Catholics
10	Basic + Share of other religions

Three combination models (Tables 13–15) add economic indicators alongside each group of structural controls simultaneously.

Goodness-of-fit Decomposition (rego)

The rego method decomposes the overall R² of each OLS model into the individual contribution of each regressor using the Shapley value from cooperative game theory. The Shapley value calculates each variable's average marginal contribution to R² across all possible orderings of regressors, satisfying efficiency, symmetry, additivity, and null-player axioms. This provides a unique, fair attribution of explanatory power that standard regression output alone cannot supply.

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Key Results

Factor	Shapley %R²	Direction
EF × Predicted Diversity (interaction)	~49–51%	Positive
Economic Freedom Index	~22–40%	Negative
Predicted Diversity	~7–14%	Negative
Log GDP per capita (when included)	~36%	Positive
Europe dummy (when included)	~37–38%	Positive
Legal origin — Scandinavia (when included)	~31–38%	Positive
Share of Protestants (when included)	~29%	Positive
Share of Muslims (when included)	~11%	Negative
KOF Globalisation Index (when included)	~9%	Negligible
Share of Catholics (when included)	~1%	Negligible

R² across all models ranges from 0.465 to 0.701.

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Replication

Requirements

• Stata 15 or later
• The following packages are auto-installed by the do-file if not already present:

Package	Purpose
egenmore	Five-year moving averages via egen filter()
estout	Formatted regression tables via esttab
rego	Shapley R² decomposition

Steps

1. Download both datasets from the AEA links in the Data section above
2. Organise them as follows:

data/
├── data_DeHaanSturm/
│   └── Sturm_DeHaan_IncIneq_Cap_Frac_AER_P&P_data.dta
└── data_AshrafGalor/
    └── data/country.dta

3. Open code/replication_income_inequality_decomposition.do
4. Update global root on line 34 to point to your local data/ folder
5. Run the script — it installs missing packages, merges the data, runs all 13 regression and decomposition models, exports all tables, and saves a log automatically

The output/output_replication_log.txt file in this repository shows the expected output for all 16 tables, and can be used to verify your replication.

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File Descriptions

File	Description
code/replication_income_inequality_decomposition.do	Full Stata replication script. Sections: housekeeping, data prep, merge, OLS regressions, rego decompositions, combination models, descriptive statistics
paper/income_inequality_capitalism_diversity.docx	Research paper with full methodology, results, and discussion
presentation/income_inequality_capitalism_diversity_presentation.pptx	Slide deck summarising the research
output/output_replication_log.txt	Cleaned Stata output log containing all regression and rego decomposition results (Tables 3–15) and descriptive statistics (Table A2)

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References

1. Ashraf, Q., & Galor, O. (2013). The "Out of Africa" Hypothesis, Human Genetic Diversity, and Comparative Economic Development. American Economic Review, 103(1), 1–46. https://doi.org/10.1257/aer.103.1.1

2. Cann, H. M. (2002). A Human Genome Diversity Cell Line Panel. Science, 296(5566), 261–262. https://doi.org/10.1126/science.296.5566.261b

3. Desmet, K., Ortuño-Ortín, I., & Weber, S. (2009). Linguistic Diversity and Redistribution. Journal of the European Economic Association, 7(6), 1291–1318. https://doi.org/10.1162/jeea.2009.7.6.1291

4. Huettner, F., & Sunder, M. (2011). rego: R-Squared Decomposition. University of Leipzig. http://www.marco-sunder.de/stata/rego.html

5. Lawson, R., Hall, J., Murphy, R., & Gwartney, J. (2015). Economic Freedom of the World — 2015 Annual Report. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3924422

6. Solt, F. (2016). The Standardized World Income Inequality Database. Social Science Quarterly, 97(5), 1267–1281. https://doi.org/10.1111/ssqu.12295

7. Sturm, J.-E., & De Haan, J. (2015). Income Inequality, Capitalism, and Ethno-Linguistic Fractionalization. American Economic Review, 105(5), 593–597. https://doi.org/10.1257/aer.p20151112

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License

Code released under the MIT License.
The underlying datasets are subject to their own redistribution terms — please consult the original sources.