Bayesian average of classical estimates for panel data: Can the puzzle of the shape of the regional Kuznets curve be solved?

🗺️ Motivation

• Regional inequality shapes social cohesion, migration & political stability
• Kuznets (1955): inverted-U link between development & inequality
• Recent evidence hints at more complex (N-shaped) patterns
• Need robust econometric tools to settle the “shape” debate

📚 Literature Snapshot

• Inverted-U support: List & Gallet (1999); Thornton (2001)
• Mixed / non-U evidence: Tam (2008); Huang (2012)
• N-shape claim: Lessmann (2014); Lessmann & Seidel (2017)
• Gap: model uncertainty rarely addressed explicitly

🎯 Research Goals

• Extend Bayesian Averaging of Classical Estimates (BACE) to panel fixed-effects
• Test the robustness of Kuznets curve shape under model uncertainty
• Identify determinants that consistently drive regional inequality

🛠️ Methodology Highlights

• Search space: 14 candidate regressors → 2¹⁴ = 16 384 models, each estimated with two-way (country + period) fixed effects.

• Robustness sweep: Allowing four fixed-effects options (none, time, country, two-way) expands the universe to 65 536 models; posterior model probabilities (PMPs) concentrate entirely on the two-way specification.

• Bayesian Averaging of Classical Estimates (BACE):

  • Retains simple FE-OLS for every model—no heavy MCMC.
  • Translates each model’s BIC into an approximate marginal likelihood.
  • Uses a uniform prior so PMPs sum to 1, then forms probability-weighted averages for all coefficients, predictions, and derivatives.

• Variable screening: Posterior Inclusion Probability (PIP) highlights robust determinants—“substantial evidence” at PIP ≥ 0.75, “strong” at PIP ≥ 0.90.

• Curve peaks: Inequality turning points come from the BACE-weighted derivative of the cubic GDP polynomial, with analytic standard errors for credible bands.

• Validation: Monte-Carlo experiments with a known data-generating process show BACE pinpoints the correct fixed-effects structure and true drivers, underscoring the method’s reliability.

📈 Data Overview

• 180 countries, five 5-year windows (1990-2013)
• Dependent variable: population-weighted Gini from satellite night-lights
• Key covariates (14): GDP pc (linear–quintic), resource rents, arable land, ethnic Gini, trade, FDI, etc.

🧪 Simulation Check

• Simulated panel with known DGP

• BACE recovered:

  • Correct two-way FE spec (PMP ≈ 100 %)
  • True drivers (GDP pc, rents, land, ethnic Gini)

🔍 Determinant Robustness (Real Data)

High PIP (> 0.75)

• Natural-resource rents ↑ inequality
• Arable land share ↓ inequality
• Ethnic Gini ↑ inequality Kuznets terms
• GDP pc (linear & quadratic) robust
• Cubic term not robust (PIP ≈ 0.48)

📐 Shape of the Curve

• Inequality rises: USD 189 → 2 189
• Stabilises: USD 2 189 → 3 935
• Falls: USD 3 935 → 71 682
• Stabilises again beyond USD 71 682

Evidence favours an inverted-U with plateau in rich economies, not a full N-shape.

🧭 Policy Takeaways

• Redistribute natural-resource rents across regions
• Invest in agricultural productivity & equitable land access
• Target ethnic inclusion to curb spatial disparities
• Growth alone won’t close gaps after the peak—active regional policy required

🏁 Conclusion

• Panel-BACE offers transparent, probabilistic insight into inequality drivers
• Robust inverted-U confirmed; inequality stabilises, not rebounds, at high incomes
• Future work: interact technology diffusion & institutions in the Kuznets framework