https://carlos-mendez.org/tag/bayesian-model-averaging/Bayesian model averagingWowchemy (https://wowchemy.com)en-us© 2018–2026 Carlos Mendez. All rights reserved.Thu, 05 Jun 2025 00:00:00 +0000https://carlos-mendez.org/media/icon_huedfae549300b4ca5d201a9bd09a3ecd5_79625_512x512_fill_lanczos_center_3.pnghttps://carlos-mendez.org/tag/bayesian-model-averaging/https://carlos-mendez.org/publication/20250605-ee/Thu, 05 Jun 2025 00:00:00 +0000https://carlos-mendez.org/publication/20250605-ee/<div style="position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden;"> <iframe style="position: absolute; top: 0; left: 0; width: 100%; height: 100%;" src="https://www.youtube.com/embed/K1yj-Aw2Vlg?si=iMlgTPuVHk9twxPQ" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> </div> <h2 id="-motivation">🗺️ Motivation</h2> <ul> <li>Regional inequality shapes social cohesion, migration &amp; political stability</li> <li>Kuznets (1955): inverted-U link between development &amp; inequality</li> <li>Recent evidence hints at more complex (N-shaped) patterns</li> <li>Need robust econometric tools to settle the “shape” debate</li> </ul> <hr> <h2 id="-literature-snapshot">📚 Literature Snapshot</h2> <ul> <li>Inverted-U support: List &amp; Gallet (1999); Thornton (2001)</li> <li>Mixed / non-U evidence: Tam (2008); Huang (2012)</li> <li>N-shape claim: Lessmann (2014); Lessmann &amp; Seidel (2017)</li> <li>Gap: model uncertainty rarely addressed explicitly</li> </ul> <hr> <h2 id="-research-goals">🎯 Research Goals</h2> <ul> <li>Extend Bayesian Averaging of Classical Estimates (BACE) to panel fixed-effects</li> <li>Test the robustness of Kuznets curve shape under model uncertainty</li> <li>Identify determinants that consistently drive regional inequality</li> </ul> <hr> <h2 id="-methodology-highlights">🛠️ Methodology Highlights</h2> <ul> <li> <p><strong>Search space:</strong> 14 candidate regressors → 2¹⁴ = <strong>16 384</strong> models, each estimated with two-way (country + period) fixed effects.</p> </li> <li> <p><strong>Robustness sweep:</strong> Allowing four fixed-effects options (none, time, country, two-way) expands the universe to <strong>65 536</strong> models; posterior model probabilities (PMPs) concentrate entirely on the two-way specification.</p> </li> <li> <p><strong>Bayesian Averaging of Classical Estimates (BACE):</strong></p> <ul> <li>Retains simple FE-OLS for every model—no heavy MCMC.</li> <li>Translates each model’s BIC into an approximate marginal likelihood.</li> <li>Uses a uniform prior so PMPs sum to 1, then forms <strong>probability-weighted averages</strong> for all coefficients, predictions, and derivatives.</li> </ul> </li> <li> <p><strong>Variable screening:</strong> Posterior Inclusion Probability (PIP) highlights robust determinants—“substantial evidence” at PIP ≥ 0.75, “strong” at PIP ≥ 0.90.</p> </li> <li> <p><strong>Curve peaks:</strong> Inequality turning points come from the BACE-weighted derivative of the cubic GDP polynomial, with analytic standard errors for credible bands.</p> </li> <li> <p><strong>Validation:</strong> 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.</p> </li> </ul> <hr> <h2 id="-data-overview">📈 Data Overview</h2> <ul> <li>180 countries, five 5-year windows (1990-2013)</li> <li>Dependent variable: population-weighted Gini from satellite night-lights</li> <li>Key covariates (14): GDP pc (linear–quintic), resource rents, arable land, ethnic Gini, trade, FDI, etc.</li> </ul> <hr> <h2 id="-simulation-check">🧪 Simulation Check</h2> <ul> <li> <p>Simulated panel with known DGP</p> </li> <li> <p>BACE recovered:</p> <ul> <li>Correct two-way FE spec (PMP ≈ 100 %)</li> <li>True drivers (GDP pc, rents, land, ethnic Gini)</li> </ul> </li> </ul> <hr> <h2 id="-determinant-robustness-real-data">🔍 Determinant Robustness (Real Data)</h2> <p><strong>High PIP (&gt; 0.75)</strong></p> <ul> <li>Natural-resource rents ↑ inequality</li> <li>Arable land share ↓ inequality</li> <li>Ethnic Gini ↑ inequality <strong>Kuznets terms</strong></li> <li>GDP pc (linear &amp; quadratic) robust</li> <li>Cubic term not robust (PIP ≈ 0.48)</li> </ul> <hr> <h2 id="-shape-of-the-curve">📐 Shape of the Curve</h2> <ul> <li>Inequality <strong>rises</strong>: USD 189 → 2 189</li> <li><strong>Stabilises</strong>: USD 2 189 → 3 935</li> <li><strong>Falls</strong>: USD 3 935 → 71 682</li> <li><strong>Stabilises</strong> again beyond USD 71 682</li> </ul> <blockquote> <p>Evidence favours an inverted-U with plateau in rich economies, <strong>not</strong> a full N-shape.</p> </blockquote> <hr> <h2 id="-policy-takeaways">🧭 Policy Takeaways</h2> <ul> <li>Redistribute natural-resource rents across regions</li> <li>Invest in agricultural productivity &amp; equitable land access</li> <li>Target ethnic inclusion to curb spatial disparities</li> <li>Growth alone won’t close gaps after the peak—active regional policy required</li> </ul> <hr> <h2 id="-conclusion">🏁 Conclusion</h2> <ul> <li>Panel-BACE offers transparent, probabilistic insight into inequality drivers</li> <li>Robust inverted-U confirmed; inequality stabilises, not rebounds, at high incomes</li> <li>Future work: interact technology diffusion &amp; institutions in the Kuznets framework</li> </ul>