#!/usr/bin/env python3 """ Fair Inheritance Cross-Country Comparison -- Paper 9, Test 4 ============================================================= Tests whether countries with recipient-based inheritance taxation (tax falls on the heir, not the estate) have lower wealth concentration than countries with estate-based systems. Lean theorem link: `incentive_compatible` -- recipient-based tax makes dispersion the tax-minimizing strategy. Sub-tests: 1. Cross-sectional OLS: top1_share ~ recipient_dummy + log_gdp_pc 2. Multiple regression: top1_share ~ tax_rev_pct_gdp + recipient_dummy + controls 3. Panel FE: top1_share ~ recipient_dummy + country_FE + year_FE 4. Rank-sum test: recipient-based vs estate-based wealth concentration Prediction: beta_recipient < 0 (recipient-based systems have lower concentration) Migrated from Fair Inheritance paper empirical design. Review Notes (2026-03-13): Theory match: PARTIAL — Lean theorem `incentive_compatible` (FI-16) proves that a specific dispersion-incentive tax design makes dispersion the tax-minimizing strategy. The test checks whether existing recipient-based systems (which are NOT dispersion-incentive taxes) correlate with lower wealth concentration. These are different claims. The cross-country test is an indirect test of the broader claim that how inheritance is taxed (structure) matters beyond how much it is taxed (level). I/O audit: CORRECT — top 1% wealth share is a reasonable proxy for ownership concentration; recipient-based classification is institutional knowledge from OECD tax databases. Data-signal alignment: WEAK — (a) estate-based comparison group has only N=2 countries (USA, GBR; ZAF lacks WID data), (b) no controls for legal tradition, welfare state size, or historical inequality, (c) tax system classifications are time-invariant but several countries changed systems (Sweden abolished 2005). GBR top1=0.212 is lower than many recipient countries, making the comparison ambiguous. Code quality: CLEAN — HC1 robust SEs, proper between/within decomposition. Confidence in verdict: LOW — fundamental power problem: N=2 estate-based countries makes meaningful statistical comparison impossible. All 5 subtests AMBIGUOUS with right sign but no significance. Known limitations: (a) too few estate-based countries for inference, (b) theory predicts dispersion-incentive effect but test checks recipient-based correlation, (c) massive confounders uncontrolled. Date of review: 2026-03-13. """ import warnings import numpy as np import pandas as pd from scipy import stats from common.config import COMPILED_DIR from common.plotting import setup_figure, setup_subplots, save_figure from common.stats import verdict, log_result warnings.filterwarnings('ignore') _ALL_SUBTESTS = [ 'fi_recipient_cross_section', 'fi_recipient_with_tax_revenue', 'fi_recipient_between_estimator', 'fi_tax_revenue_panel_fe', 'fi_ranksum_recipient_vs_estate', ] # ── Tax system classification (institutional knowledge) ──────────────────── # Recipient-based (tax on heir) RECIPIENT_BASED = ['BEL', 'DNK', 'FIN', 'FRA', 'DEU', 'IRL', 'ITA', 'JPN', 'KOR', 'NLD', 'ESP', 'CHE'] # Estate-based (tax on estate) ESTATE_BASED = ['GBR', 'USA', 'ZAF'] # No inheritance tax NO_TAX = ['AUS', 'CAN', 'NZL', 'NOR', 'SWE'] ALL_COUNTRIES = RECIPIENT_BASED + ESTATE_BASED + NO_TAX # ── Data loading ─────────────────────────────────────────────────────────── def load_wid(): """Load WID wealth share data.""" path = COMPILED_DIR / 'wid_wealth_shares.csv' try: return pd.read_csv(path) except FileNotFoundError: return None def load_oecd_tax(): """Load OECD inheritance tax revenue data.""" path = COMPILED_DIR / 'oecd_inheritance_tax_revenue.csv' try: return pd.read_csv(path) except FileNotFoundError: return None def load_gdp_pcap(): """Load GDP per capita (PPP) from World Bank data if available.""" for path in [COMPILED_DIR / 'wb_gdp_pcap_ppp.csv', COMPILED_DIR / 'worldbank_wdi.csv']: try: df = pd.read_csv(path) return df except FileNotFoundError: continue return None def classify_tax_system(country_code): """Return tax system classification for a country.""" if country_code in RECIPIENT_BASED: return 'recipient' elif country_code in ESTATE_BASED: return 'estate' elif country_code in NO_TAX: return 'none' return None def build_cross_section(wid, oecd_tax, gdp_df, year_start=2010, year_end=2020): """ Build cross-sectional dataset averaged over year_start--year_end. Returns DataFrame with columns: country_code, top1_wealth_share, top10_wealth_share, tax_system, recipient_dummy, no_tax_dummy, tax_revenue_pct_gdp, log_gdp_pc """ # Filter WID to time window and relevant countries wid_sub = wid[(wid['year'] >= year_start) & (wid['year'] <= year_end)].copy() wid_sub = wid_sub[wid_sub['country_code'].isin(ALL_COUNTRIES)] # Average wealth shares by country agg = wid_sub.groupby('country_code').agg( top1_wealth_share=('top1_wealth_share', 'mean'), top10_wealth_share=('top10_wealth_share', 'mean'), ).reset_index() # Tax system classification agg['tax_system'] = agg['country_code'].map(classify_tax_system) agg['recipient_dummy'] = (agg['tax_system'] == 'recipient').astype(int) agg['estate_dummy'] = (agg['tax_system'] == 'estate').astype(int) agg['no_tax_dummy'] = (agg['tax_system'] == 'none').astype(int) # Merge tax revenue if available if oecd_tax is not None: tax_sub = oecd_tax[(oecd_tax['year'] >= year_start) & (oecd_tax['year'] <= year_end)] tax_sub = tax_sub[tax_sub['country_code'].isin(ALL_COUNTRIES)] tax_avg = tax_sub.groupby('country_code')['tax_revenue_pct_gdp'].mean().reset_index() agg = agg.merge(tax_avg, on='country_code', how='left') else: agg['tax_revenue_pct_gdp'] = np.nan # Merge GDP per capita if available if gdp_df is not None: # Try to extract GDP per capita -- handle various column formats gdp_cols = [c for c in gdp_df.columns if 'gdp' in c.lower() and 'pcap' in c.lower()] if not gdp_cols and 'NY.GDP.PCAP.PP.CD' in gdp_df.columns: gdp_cols = ['NY.GDP.PCAP.PP.CD'] if gdp_cols and 'country_code' in gdp_df.columns and 'year' in gdp_df.columns: gdp_sub = gdp_df[(gdp_df['year'] >= year_start) & (gdp_df['year'] <= year_end)] gdp_sub = gdp_sub[gdp_sub['country_code'].isin(ALL_COUNTRIES)] gdp_avg = gdp_sub.groupby('country_code')[gdp_cols[0]].mean().reset_index() gdp_avg.columns = ['country_code', 'gdp_pcap'] agg = agg.merge(gdp_avg, on='country_code', how='left') else: agg['gdp_pcap'] = np.nan else: agg['gdp_pcap'] = np.nan # Log GDP per capita agg['log_gdp_pc'] = np.log(agg['gdp_pcap'].clip(lower=1)) return agg def build_panel(wid, oecd_tax): """ Build panel dataset for FE regression. Returns DataFrame with columns: country_code, year, top1_wealth_share, top10_wealth_share, tax_system, recipient_dummy, tax_revenue_pct_gdp """ panel = wid[wid['country_code'].isin(ALL_COUNTRIES)].copy() panel['tax_system'] = panel['country_code'].map(classify_tax_system) panel['recipient_dummy'] = (panel['tax_system'] == 'recipient').astype(int) panel['estate_dummy'] = (panel['tax_system'] == 'estate').astype(int) panel['no_tax_dummy'] = (panel['tax_system'] == 'none').astype(int) if oecd_tax is not None: panel = panel.merge( oecd_tax[['country_code', 'year', 'tax_revenue_pct_gdp']], on=['country_code', 'year'], how='left' ) else: panel['tax_revenue_pct_gdp'] = np.nan return panel def ols(y, X): """ OLS with heteroskedasticity-robust (HC1) standard errors. Parameters ---------- y : array (N,) X : array (N, k) Returns ------- dict with keys: beta, se, t, p, r2, n, residuals """ X = np.asarray(X, dtype=float) y = np.asarray(y, dtype=float) n, k = X.shape XtX_inv = np.linalg.inv(X.T @ X) beta = XtX_inv @ (X.T @ y) resid = y - X @ beta ss_res = np.sum(resid ** 2) ss_tot = np.sum((y - y.mean()) ** 2) r2 = 1 - ss_res / ss_tot if ss_tot > 0 else np.nan # HC1 robust standard errors leverage = np.diag(X @ XtX_inv @ X.T) u2 = resid ** 2 meat = X.T @ np.diag(u2 * n / (n - k)) @ X V_robust = XtX_inv @ meat @ XtX_inv se = np.sqrt(np.diag(V_robust)) t_stat = beta / se p_val = 2 * (1 - stats.t.cdf(np.abs(t_stat), df=n - k)) return { 'beta': beta, 'se': se, 't': t_stat, 'p': p_val, 'r2': r2, 'n': n, 'residuals': resid, } def panel_fe_ols(df, y_col, x_cols, entity_col='country_code', time_col='year'): """ Two-way fixed effects OLS via within transformation. Demeans by entity and time, then runs OLS on demeaned data. """ df = df.dropna(subset=[y_col] + x_cols).copy() if len(df) < len(x_cols) + 2: return None # Entity demean entity_means = df.groupby(entity_col)[[y_col] + x_cols].transform('mean') time_means = df.groupby(time_col)[[y_col] + x_cols].transform('mean') grand_mean = df[[y_col] + x_cols].mean() y_dm = df[y_col] - entity_means[y_col] - time_means[y_col] + grand_mean[y_col] X_dm = df[x_cols].values - entity_means[x_cols].values - time_means[x_cols].values + grand_mean[x_cols].values result = ols(y_dm.values, X_dm) # Adjust degrees of freedom for FE n_entities = df[entity_col].nunique() n_times = df[time_col].nunique() result['n_entities'] = n_entities result['n_times'] = n_times result['n_obs'] = len(df) # Recompute p-values with adjusted df df_adj = len(df) - len(x_cols) - n_entities - n_times + 1 if df_adj > 0: result['p'] = 2 * (1 - stats.t.cdf(np.abs(result['t']), df=df_adj)) return result # ── Main ─────────────────────────────────────────────────────────────────── _cache = {} def main(): results = [] wid = load_wid() oecd_tax = load_oecd_tax() gdp_df = load_gdp_pcap() if wid is None: return [log_result( 'fair_inheritance_cross_country', np.nan, np.nan, 'SKIPPED', details={'reason': 'WID wealth share data not found'}, description="Tests whether recipient-based inheritance tax systems " "are associated with lower wealth concentration than " "estate-based systems, using WID top 1%/10% wealth shares " "across 20 OECD countries.")] # ── Build datasets ───────────────────────────────────────────────── cs = build_cross_section(wid, oecd_tax, gdp_df) _cache['cross_section'] = cs panel = build_panel(wid, oecd_tax) _cache['panel'] = panel # Minimum sample check n_with_data = cs.dropna(subset=['top1_wealth_share']).shape[0] n_recipient = cs[cs['recipient_dummy'] == 1].dropna(subset=['top1_wealth_share']).shape[0] n_estate = cs[cs['estate_dummy'] == 1].dropna(subset=['top1_wealth_share']).shape[0] if n_with_data < 5 or n_recipient < 2 or n_estate < 1: return [log_result( 'fair_inheritance_cross_country', np.nan, np.nan, 'SKIPPED', details={'reason': f'Insufficient data: {n_with_data} countries, ' f'{n_recipient} recipient, {n_estate} estate'}, description="Tests whether recipient-based inheritance tax systems " "are associated with lower wealth concentration.")] # ── Test 1: Cross-sectional OLS ──────────────────────────────────── # top1_share = alpha + beta1*recipient + beta2*log_gdp_pc + eps cs1 = cs.dropna(subset=['top1_wealth_share', 'recipient_dummy']) has_gdp = cs1['log_gdp_pc'].notna().sum() >= 5 and np.isfinite(cs1['log_gdp_pc']).sum() >= 5 if has_gdp: cs1_valid = cs1.dropna(subset=['log_gdp_pc']) cs1_valid = cs1_valid[np.isfinite(cs1_valid['log_gdp_pc'])] else: cs1_valid = cs1 if len(cs1_valid) >= 5: y = cs1_valid['top1_wealth_share'].values if has_gdp: X = np.column_stack([ np.ones(len(cs1_valid)), cs1_valid['recipient_dummy'].values, cs1_valid['log_gdp_pc'].values, ]) var_names = ['const', 'recipient', 'log_gdp_pc'] else: X = np.column_stack([ np.ones(len(cs1_valid)), cs1_valid['recipient_dummy'].values, ]) var_names = ['const', 'recipient'] res1 = ols(y, X) beta_recip = res1['beta'][1] p_recip = res1['p'][1] sign_correct = beta_recip < 0 verd = verdict(p_recip, sign_correct) results.append(log_result( 'fi_recipient_cross_section', float(beta_recip), float(p_recip), verd, details={ 'n_countries': int(res1['n']), 'r2': float(res1['r2']), 'se': float(res1['se'][1]), 'controls': 'log_gdp_pc' if has_gdp else 'none', 'prediction': 'beta_recipient < 0', }, description="Cross-sectional OLS: top 1% wealth share regressed on " "recipient-based tax dummy (+ log GDP per capita control). " "Averaged over 2010-2020. Prediction: beta < 0 (recipient " "systems have lower concentration).")) _cache['res1'] = res1 _cache['var_names_1'] = var_names else: results.append(log_result( 'fi_recipient_cross_section', np.nan, np.nan, 'SKIPPED', details={'reason': f'Only {len(cs1_valid)} obs'}, description="Cross-sectional OLS of top 1% wealth share on recipient dummy.")) # ── Test 2: Multiple regression with tax revenue ─────────────────── # top1_share = alpha + beta1*tax_rev + beta2*recipient + gamma*log_gdp_pc + eps cs2 = cs.dropna(subset=['top1_wealth_share', 'tax_revenue_pct_gdp', 'recipient_dummy']) if has_gdp: cs2 = cs2.dropna(subset=['log_gdp_pc']) cs2 = cs2[np.isfinite(cs2['log_gdp_pc'])] if len(cs2) >= 6: y = cs2['top1_wealth_share'].values if has_gdp: X = np.column_stack([ np.ones(len(cs2)), cs2['tax_revenue_pct_gdp'].values, cs2['recipient_dummy'].values, cs2['log_gdp_pc'].values, ]) var_names_2 = ['const', 'tax_rev_pct_gdp', 'recipient', 'log_gdp_pc'] else: X = np.column_stack([ np.ones(len(cs2)), cs2['tax_revenue_pct_gdp'].values, cs2['recipient_dummy'].values, ]) var_names_2 = ['const', 'tax_rev_pct_gdp', 'recipient'] res2 = ols(y, X) idx_recip = var_names_2.index('recipient') beta_recip = res2['beta'][idx_recip] p_recip = res2['p'][idx_recip] sign_correct = beta_recip < 0 verd = verdict(p_recip, sign_correct) results.append(log_result( 'fi_recipient_with_tax_revenue', float(beta_recip), float(p_recip), verd, details={ 'n_countries': int(res2['n']), 'r2': float(res2['r2']), 'beta_tax_rev': float(res2['beta'][1]), 'p_tax_rev': float(res2['p'][1]), 'prediction': 'beta_recipient < 0 conditional on tax revenue', }, description="Multiple regression: top 1% wealth share on inheritance " "tax revenue (% GDP), recipient dummy, and log GDP per " "capita. Tests whether the structure of taxation (who pays) " "matters beyond the level of taxation.")) _cache['res2'] = res2 _cache['var_names_2'] = var_names_2 else: results.append(log_result( 'fi_recipient_with_tax_revenue', np.nan, np.nan, 'SKIPPED', details={'reason': f'Only {len(cs2)} obs with tax revenue data'}, description="Multiple regression controlling for tax revenue level.")) # ── Test 3: Panel FE regression ──────────────────────────────────── # Note: recipient_dummy is time-invariant, so it is absorbed by country FE. # Use tax_revenue as the time-varying proxy; report the between-estimator # for the recipient effect separately. panel_valid = panel.dropna(subset=['top1_wealth_share']) if len(panel_valid) >= 20 and panel_valid['country_code'].nunique() >= 5: # Between estimator: average over time, then regress between = panel_valid.groupby('country_code').agg( top1_wealth_share=('top1_wealth_share', 'mean'), recipient_dummy=('recipient_dummy', 'first'), estate_dummy=('estate_dummy', 'first'), ).reset_index() if len(between) >= 5: y_b = between['top1_wealth_share'].values X_b = np.column_stack([ np.ones(len(between)), between['recipient_dummy'].values, ]) res_between = ols(y_b, X_b) beta_b = res_between['beta'][1] p_b = res_between['p'][1] sign_correct = beta_b < 0 verd = verdict(p_b, sign_correct) results.append(log_result( 'fi_recipient_between_estimator', float(beta_b), float(p_b), verd, details={ 'n_countries': int(res_between['n']), 'r2': float(res_between['r2']), 'n_panel_obs': len(panel_valid), 'n_years': int(panel_valid['year'].nunique()), 'prediction': 'beta_recipient < 0', }, description="Between estimator from panel: country-averaged top 1% " "wealth share regressed on recipient dummy. Since the " "tax system is time-invariant, this captures the cross-" "country variation that FE would absorb.")) _cache['res_between'] = res_between else: results.append(log_result( 'fi_recipient_between_estimator', np.nan, np.nan, 'SKIPPED', details={'reason': 'Too few countries in panel'}, description="Between estimator for recipient effect from panel.")) # Within estimator: if tax_revenue varies over time, test its effect panel_tax = panel_valid.dropna(subset=['tax_revenue_pct_gdp']) if len(panel_tax) >= 20 and panel_tax['country_code'].nunique() >= 3: res_fe = panel_fe_ols( panel_tax, 'top1_wealth_share', ['tax_revenue_pct_gdp']) if res_fe is not None: beta_tax = res_fe['beta'][0] p_tax = res_fe['p'][0] # Higher tax revenue should reduce concentration sign_correct = beta_tax < 0 verd = verdict(p_tax, sign_correct) results.append(log_result( 'fi_tax_revenue_panel_fe', float(beta_tax), float(p_tax), verd, details={ 'n_obs': int(res_fe['n_obs']), 'n_countries': int(res_fe['n_entities']), 'n_years': int(res_fe['n_times']), 'r2_within': float(res_fe['r2']), 'prediction': 'beta_tax_revenue < 0', }, description="Panel two-way FE: within-country variation in " "inheritance tax revenue (% GDP) predicts within-" "country changes in top 1% wealth share. Tests the " "intensive margin of inheritance taxation.")) else: results.append(log_result( 'fi_tax_revenue_panel_fe', np.nan, np.nan, 'SKIPPED', details={'reason': 'FE estimation failed'}, description="Panel FE of wealth concentration on tax revenue.")) else: results.append(log_result( 'fi_tax_revenue_panel_fe', np.nan, np.nan, 'SKIPPED', details={'reason': f'Insufficient panel tax data: ' f'{len(panel_tax)} obs'}, description="Panel FE of wealth concentration on tax revenue.")) else: results.append(log_result( 'fi_recipient_between_estimator', np.nan, np.nan, 'SKIPPED', details={'reason': f'Insufficient panel data: {len(panel_valid)} obs'}, description="Between estimator for recipient effect from panel.")) results.append(log_result( 'fi_tax_revenue_panel_fe', np.nan, np.nan, 'SKIPPED', details={'reason': 'Insufficient panel data'}, description="Panel FE of wealth concentration on tax revenue.")) # ── Test 4: Nonparametric rank-sum test ──────────────────────────── # Compare top1 wealth shares: recipient-based vs estate-based recip_shares = cs[cs['tax_system'] == 'recipient']['top1_wealth_share'].dropna() estate_shares = cs[cs['tax_system'] == 'estate']['top1_wealth_share'].dropna() if len(recip_shares) >= 2 and len(estate_shares) >= 1: # Mann-Whitney U (one-sided: recipient < estate) u_stat, p_two = stats.mannwhitneyu( recip_shares, estate_shares, alternative='two-sided') # One-sided p-value for recipient < estate _, p_one = stats.mannwhitneyu( recip_shares, estate_shares, alternative='less') mean_recip = recip_shares.mean() mean_estate = estate_shares.mean() sign_correct = mean_recip < mean_estate verd = verdict(p_one, sign_correct, threshold=0.10) results.append(log_result( 'fi_ranksum_recipient_vs_estate', float(u_stat), float(p_one), verd, details={ 'mean_recipient': float(mean_recip), 'mean_estate': float(mean_estate), 'n_recipient': int(len(recip_shares)), 'n_estate': int(len(estate_shares)), 'p_two_sided': float(p_two), 'prediction': 'recipient_mean < estate_mean', }, description="Mann-Whitney U rank-sum test: recipient-based countries " "vs estate-based countries on top 1% wealth share. " "One-sided test (recipient < estate). Threshold relaxed " "to 0.10 due to small estate-based sample (N=3).")) _cache['recip_shares'] = recip_shares _cache['estate_shares'] = estate_shares else: results.append(log_result( 'fi_ranksum_recipient_vs_estate', np.nan, np.nan, 'SKIPPED', details={'reason': f'Insufficient groups: {len(recip_shares)} recipient, ' f'{len(estate_shares)} estate'}, description="Rank-sum test of recipient vs estate wealth concentration.")) _cache['results'] = results return results def figures(): """Generate fair inheritance cross-country figures.""" if not _cache: main() paths = [] cs = _cache.get('cross_section') if cs is None: return paths cs_valid = cs.dropna(subset=['top1_wealth_share']) if len(cs_valid) < 3: return paths # ── Figure 1: Bar chart of top 1% wealth share by tax system ────── fig, ax = setup_figure(width=10, height=6) colors = {'recipient': '#2196F3', 'estate': '#F44336', 'none': '#9E9E9E'} labels = {'recipient': 'Recipient-based', 'estate': 'Estate-based', 'none': 'No inheritance tax'} sorted_cs = cs_valid.sort_values('top1_wealth_share', ascending=True) y_pos = np.arange(len(sorted_cs)) bar_colors = [colors.get(t, '#9E9E9E') for t in sorted_cs['tax_system']] ax.barh(y_pos, sorted_cs['top1_wealth_share'].values * 100, color=bar_colors, edgecolor='white', linewidth=0.5) ax.set_yticks(y_pos) ax.set_yticklabels(sorted_cs['country_code'].values, fontsize=9) ax.set_xlabel('Top 1% Wealth Share (%)') ax.set_title('Wealth Concentration by Inheritance Tax System') # Legend from matplotlib.patches import Patch legend_elements = [Patch(facecolor=colors[k], label=labels[k]) for k in ['recipient', 'estate', 'none'] if k in sorted_cs['tax_system'].values] ax.legend(handles=legend_elements, loc='lower right', framealpha=0.9) paths += save_figure(fig, 'fi_wealth_by_tax_system', subfolder='applications') # ── Figure 2: Box plot comparison ───────────────────────────────── groups = [] group_labels = [] group_colors_list = [] for system in ['recipient', 'estate', 'none']: vals = cs_valid[cs_valid['tax_system'] == system]['top1_wealth_share'].dropna() if len(vals) >= 1: groups.append(vals.values * 100) group_labels.append(labels[system]) group_colors_list.append(colors[system]) if len(groups) >= 2: fig, ax = setup_figure(width=8, height=6) bp = ax.boxplot(groups, labels=group_labels, patch_artist=True, widths=0.5, showmeans=True, meanprops=dict(marker='D', markeredgecolor='black', markerfacecolor='gold', markersize=8)) for patch, color in zip(bp['boxes'], group_colors_list): patch.set_facecolor(color) patch.set_alpha(0.6) # Overlay individual points for i, vals in enumerate(groups): jitter = np.random.RandomState(42).normal(0, 0.04, len(vals)) ax.scatter(np.full(len(vals), i + 1) + jitter, vals, color=group_colors_list[i], edgecolor='black', linewidth=0.5, s=40, zorder=5, alpha=0.8) ax.set_ylabel('Top 1% Wealth Share (%)') ax.set_title('Wealth Concentration by Inheritance Tax Structure') paths += save_figure(fig, 'fi_boxplot_tax_systems', subfolder='applications') # ── Figure 3: Scatter of tax revenue vs wealth share ────────────── cs_tax = cs_valid.dropna(subset=['tax_revenue_pct_gdp']) if len(cs_tax) >= 4: fig, ax = setup_figure(width=9, height=6) for system in ['recipient', 'estate', 'none']: sub = cs_tax[cs_tax['tax_system'] == system] if len(sub) > 0: ax.scatter(sub['tax_revenue_pct_gdp'].values * 100, sub['top1_wealth_share'].values * 100, color=colors.get(system, '#999'), label=labels.get(system, system), s=80, edgecolor='black', linewidth=0.5, zorder=5) for _, row in sub.iterrows(): ax.annotate(row['country_code'], (row['tax_revenue_pct_gdp'] * 100, row['top1_wealth_share'] * 100), fontsize=7, ha='center', va='bottom', xytext=(0, 5), textcoords='offset points') # OLS fit line x_fit = cs_tax['tax_revenue_pct_gdp'].values * 100 y_fit = cs_tax['top1_wealth_share'].values * 100 if len(x_fit) >= 3: slope, intercept, r, p, se = stats.linregress(x_fit, y_fit) x_line = np.linspace(x_fit.min(), x_fit.max(), 100) ax.plot(x_line, intercept + slope * x_line, 'k--', alpha=0.5, label=f'OLS: slope={slope:.2f}, r={r:.2f}') ax.set_xlabel('Inheritance Tax Revenue (% GDP)') ax.set_ylabel('Top 1% Wealth Share (%)') ax.set_title('Tax Revenue Level vs. Wealth Concentration') ax.legend(loc='best', framealpha=0.9) paths += save_figure(fig, 'fi_tax_revenue_vs_wealth', subfolder='applications') return paths if __name__ == '__main__': results = main() for r in results: print(f"{r['name']}: {r['verdict']} " f"(stat={r['statistic']}, p={r['p_value']})")

r2	0.1198
n years	149
p value	0.1466
statistic	-0.0423
prediction	beta_recipient < 0
n countries	18
n panel obs	1473

Fi Recipient Between Estimator

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Statistics

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