#!/usr/bin/env python3 """ Two-Sided Pricing Test — Proposition prop:two_sided of Paper 1 ============================================================== Tests CES predictions about platform pricing: Test 1: Spearman of comp_index vs deep_subsidy (active below-cost pricing) Test 2: Fisher exact — among free-side platforms, high comp → deeper subsidy Test 3: 3-tier active subsidy incidence (matching Paper 5 Result res:subsidy) Test 4: Anti-network restriction — Mann-Whitney on comp_index Test 5: Durbin Amendment cross-side pass-through calibration Test 6: EU Interchange Fee Regulation (2015) pass-through calibration Data: Compiled cross-section of 33 two-sided platforms (embedded). Sources: SEC filings, Epoch AI, company disclosures, academic case studies. Theory: Paper 1, Proposition prop:two_sided. V(n_B, n_S) = (a_B n_B^rho + a_S n_S^rho)^{1/rho}, rho < 1. Cross-group externality d^2V/dn_B dn_S = (1-rho) a_B a_S ... > 0. Effective marginal cost c_j^eff = c_j - n_k d^2V/dn_j dn_k. Predictions: (i) below-cost pricing when (1-rho) large, (ii) price structure non-neutrality, (iii) anti-network reversal for rho < 0 (restrict abundant side). Lean: platformValue, below_cost_pricing (CESProofs/CurvatureRoles/NetworkCES.lean), platform_cross_externality_positive (CESProofs/EntryExit/NetworkEntry.lean). Review Notes (2026-03-12): Theory match: CORRECT. Three predictions from Prop. two_sided. I/O audit: CORRECT. deep_subsidy (fee_a < 0) tests active below-cost pricing. Durbin/EU IFR use policy shocks for clean identification. Data-signal alignment: ADEQUATE for calibrations, WEAK-ADEQUATE for cross-section. comp_index is hand-coded but scored blind to pricing. N=33 platforms. deep_subsidy has only 5 events (Visa, AmEx, PS, Xbox, Epic), limiting power. Code quality: CLEAN. Confidence in verdict: MEDIUM. Improvements (2026-03-12): - Added 6 platforms: DoorDash, Stripe, Booking.com, TikTok, Fiverr, Epic Games - Replaced broken subsidy_direction (wrong sign, free_side confound) with Spearman on comp_index vs deep_subsidy - Added 3-tier breakdown matching Paper 5 Result res:subsidy - Formalized anti-network with Mann-Whitney (real p-value) Paper-code note: Paper 5 res:subsidy tier numbers (0%/18%/25%) don't match current data (0%/0%/15%) due to comp_index scoring revision. Paper needs update. """ import warnings warnings.filterwarnings('ignore') import numpy as np import pandas as pd from scipy import stats from common.stats import verdict, log_result from common.plotting import setup_figure, setup_subplots, save_figure def build_platform_dataset(): """Cross-section of two-sided platforms with pricing and structural data. comp_index scoring (each 0-2, total /5): cross_dep: 2 = neither side functions without the other (payments, rides, ads) 1 = value enhanced but side can function alone (e-commerce, jobs) 0 = minimal cross-side value (classifieds, encyclopedia) specificity: 2 = transactions highly specific (payments, rides — real-time match) 1 = moderate specificity (e-commerce, software — browse and choose) 0 = no transaction specificity (ads — impressions, not bilateral match) simultaneity: 1 = real-time simultaneity required (payments, rides) 0 = asynchronous (most platforms) Ad platform scoring rationale: Google, Meta, YouTube, Twitter, TikTok, Snap all have cross_dep=2 because advertisers cannot reach users without the platform and users' experience is funded by advertising (strong indirect externality). specificity=1 because ad targeting is moderately specific (not bilateral match like payments, but not zero either — targeted by demographics/interest). """ records = [] def add(platform, industry, side_a, side_b, fee_a, fee_b, cross_dep, specificity, simultaneity, restricts=False, **kw): comp_idx = (cross_dep + specificity + simultaneity) / 5.0 free_side = 1 if fee_a <= 0 else 0 deep_subsidy = 1 if fee_a < 0 else 0 # net transfer to side A records.append({ "platform": platform, "industry": industry, "fee_a_pct": fee_a, "fee_b_pct": fee_b, "cross_dep": cross_dep, "specificity": specificity, "simultaneity": simultaneity, "comp_index": comp_idx, "free_side": free_side, "deep_subsidy": deep_subsidy, "restricts": int(restricts), }) # Payment networks (comp: cross_dep=2, specificity=2, simultaneity=1 → 1.0) add("Visa/Mastercard", "Payments", "Cardholders", "Merchants", -1.0, 2.3, 2, 2, 1) add("American Express", "Payments", "Cardholders", "Merchants", -2.0, 3.2, 2, 2, 1) add("PayPal", "Payments", "Buyers", "Sellers", 0.0, 2.9, 2, 2, 1) add("Stripe", "Payments", "Buyers", "Merchants", 0.0, 2.9, 2, 2, 1) # Ride-sharing / delivery (comp: 2,2,1 → 1.0 for rides; 2,1,1 → 0.8 for delivery) add("Uber (rides)", "Transport", "Riders", "Drivers", 0.0, 25.0, 2, 2, 1) add("Lyft", "Transport", "Riders", "Drivers", 0.0, 25.0, 2, 2, 1) add("Uber Eats", "Delivery", "Diners", "Restaurants", 5.0, 30.0, 2, 1, 1) add("DoorDash", "Delivery", "Diners", "Restaurants", 12.0, 25.0, 2, 1, 1) add("Airbnb", "Lodging", "Guests", "Hosts", 3.0, 14.0, 2, 2, 0) add("Booking.com", "Lodging", "Guests", "Hotels", 0.0, 15.0, 2, 2, 0) # E-commerce (comp: 1,1,0 → 0.4) add("Amazon Marketplace", "E-commerce", "Buyers", "Sellers", 0.0, 15.0, 1, 1, 0) add("eBay", "E-commerce", "Buyers", "Sellers", 0.0, 13.0, 1, 1, 0) add("Etsy", "E-commerce", "Buyers", "Sellers", 0.0, 11.5, 1, 1, 0) # Advertising / social (comp: 2,1,0 → 0.6) add("Google Search", "Search/Ad", "Users", "Advertisers", 0.0, 32.0, 2, 1, 0) add("Meta (Facebook)", "Social/Ad", "Users", "Advertisers", 0.0, 28.0, 2, 1, 0) add("YouTube", "Media/Ad", "Viewers", "Creators", 0.0, 45.0, 2, 1, 0) add("TikTok", "Social/Ad", "Users", "Advertisers", 0.0, 30.0, 2, 1, 0) add("Twitter/X", "Social/Ad", "Users", "Advertisers", 0.0, 25.0, 2, 1, 0, restricts=True) # Software platforms (comp: 2,1,0 → 0.6) add("Apple App Store", "Software", "Users", "Developers", 0.0, 30.0, 2, 1, 0) add("Google Play", "Software", "Users", "Developers", 0.0, 30.0, 2, 1, 0) add("Steam", "Gaming", "Gamers", "Publishers", 0.0, 30.0, 2, 1, 0) # Console gaming / gaming storefronts (comp: 2,1,0 → 0.6) add("PlayStation", "Console", "Gamers", "Publishers", -5.0, 30.0, 2, 1, 0) add("Xbox", "Console", "Gamers", "Publishers", -5.0, 30.0, 2, 1, 0) # Epic: 12% dev commission (vs 30% industry), free weekly AAA games to users # fee_a ~ -3%: estimated user-side value of free games relative to spending add("Epic Games Store", "Gaming", "Gamers", "Publishers", -3.0, 12.0, 2, 1, 0) # Job / professional (comp: 1,1,0 → 0.4) add("LinkedIn", "Professional", "Seekers", "Recruiters", 0.0, 15.0, 1, 1, 0) add("Indeed", "Jobs", "Seekers", "Employers", 0.0, 12.0, 1, 1, 0) # Gig marketplace (comp: 1,1,0 → 0.4) add("Fiverr", "Gig", "Buyers", "Sellers", 5.5, 20.0, 1, 1, 0) # Real estate (comp: 1,1,0 → 0.4) add("Zillow", "Real estate", "Buyers", "Agents", 0.0, 8.0, 1, 1, 0) # Traditional (comp varies) add("Newspaper (trad.)", "Media", "Readers", "Advertisers", 3.0, 7.0, 1, 0, 0) add("Telephone (trad.)", "Telecom", "Callers", "Receivers", 5.0, 5.0, 1, 2, 1) add("Craigslist", "Classifieds", "Buyers", "Sellers", 0.0, 1.0, 0, 1, 0) # Anti-network / quality-restricted add("Stack Overflow", "Q&A", "Readers", "Contributors", 0.0, 0.0, 1, 0, 0, restricts=True) add("Wikipedia", "Encyclopedia", "Readers", "Editors", 0.0, 0.0, 0, 0, 0, restricts=True) return pd.DataFrame(records) _cache = {} def main(): results = [] df = build_platform_dataset() # ── Test 1: Active subsidy vs complementarity (Spearman) ── # Theory: higher comp_index → more likely to actively subsidize (fee_a < 0). # Spearman uses continuous comp_index (avoids lossy median split). # deep_subsidy = 1 if fee_a < 0 (active net transfer: cashback, hardware loss, # free games). This filters the zero-marginal-cost confound that afflicts free_side. r_s, p_s = stats.spearmanr(df['comp_index'], df['deep_subsidy']) # One-tailed: theory predicts positive correlation p_one = p_s / 2 if r_s > 0 else 1 - p_s / 2 sign_ok = r_s > 0 verd_spear = verdict(p_one, sign_ok) n_deep = int(df['deep_subsidy'].sum()) deep_platforms = df[df['deep_subsidy'] == 1]['platform'].tolist() results.append(log_result( 'two_sided_pricing_active_subsidy', round(r_s, 4), round(p_one, 4), verd_spear, details={ 'N': len(df), 'n_deep_subsidy': n_deep, 'deep_subsidy_platforms': deep_platforms, 'spearman_r': round(r_s, 4), 'p_two_tailed': round(p_s, 4), }, description=( "Tests whether CES complementarity predicts active below-cost pricing " "(Paper 1, Prop. two_sided, part i). Spearman rank correlation of " "comp_index (hand-coded: cross-dependence + specificity + simultaneity, " "normalized [0,1]) vs deep_subsidy (fee_A < 0, i.e. net transfer to " "subsidized side: cashback rewards, hardware loss, free games). " f"N={len(df)} platforms, {n_deep} with active subsidies. " "One-tailed: theory predicts positive r (more complementary → more " "likely to subsidize). Avoids the free_side confound (85% universal)." ), )) # ── Test 2: Subsidy depth among free-side platforms (Fisher exact) ── median_comp = df["comp_index"].median() df["high_comp"] = (df["comp_index"] >= median_comp).astype(int) df_free = df[df["free_side"] == 1].copy() if len(df_free) >= 4: ct_depth = pd.crosstab(df_free["high_comp"], df_free["deep_subsidy"]) odds_depth, p_depth = stats.fisher_exact(ct_depth, alternative='greater') n_free_high = (df_free["high_comp"] == 1).sum() n_free_low = (df_free["high_comp"] == 0).sum() n_deep_high = ((df_free["high_comp"] == 1) & (df_free["deep_subsidy"] == 1)).sum() n_deep_low = ((df_free["high_comp"] == 0) & (df_free["deep_subsidy"] == 1)).sum() pct_deep_high = n_deep_high / n_free_high if n_free_high > 0 else 0 pct_deep_low = n_deep_low / n_free_low if n_free_low > 0 else 0 sign_ok_depth = pct_deep_high >= pct_deep_low verd_depth = verdict(p_depth, sign_ok_depth, threshold=0.10) else: odds_depth, p_depth = np.nan, np.nan pct_deep_high, pct_deep_low = np.nan, np.nan n_deep_high, n_deep_low, n_free_high, n_free_low = 0, 0, 0, 0 verd_depth = 'AMBIGUOUS' results.append(log_result( 'two_sided_pricing_subsidy_depth', odds_depth, round(p_depth, 4) if not np.isnan(p_depth) else p_depth, verd_depth, details={ 'N_free_side': len(df_free), 'n_free_high_comp': int(n_free_high), 'n_free_low_comp': int(n_free_low), 'pct_deep_high_comp': round(pct_deep_high, 3) if not np.isnan(pct_deep_high) else None, 'pct_deep_low_comp': round(pct_deep_low, 3) if not np.isnan(pct_deep_low) else None, 'n_deep_high': int(n_deep_high), 'n_deep_low': int(n_deep_low), }, description=( "Among platforms that subsidize one side (free_side=1), tests whether high " "complementarity predicts DEEPER subsidy (fee_A < 0, i.e. net transfer like " "cashback rewards or hardware subsidies). Fisher exact test on 2x2: " "high_comp (above median) x deep_subsidy. One-tailed (greater). " "Theory: stronger cross-group externality (1-rho)*a*n^rho > c justifies " "below-cost pricing; platforms with rho closer to -inf subsidize more aggressively." ), )) # ── Test 3: 3-tier active subsidy incidence ── # Matching Paper 5 Result res:subsidy. Cochran-Armitage trend test. tier_labels = ['Low (<0.3)', 'Medium (0.3-0.6)', 'High (>=0.6)'] low_t = df[df['comp_index'] < 0.3] mid_t = df[(df['comp_index'] >= 0.3) & (df['comp_index'] < 0.6)] high_t = df[df['comp_index'] >= 0.6] tiers = [low_t, mid_t, high_t] tier_n = [len(t) for t in tiers] tier_deep = [int(t['deep_subsidy'].sum()) for t in tiers] tier_pct = [d / n * 100 if n > 0 else 0 for d, n in zip(tier_deep, tier_n)] # Cochran-Armitage trend test: test for linear trend in proportions # Score tiers as 0, 1, 2. Compute Z statistic. scores = np.array([0, 1, 2]) n_arr = np.array(tier_n) x_arr = np.array(tier_deep) N = n_arr.sum() p_bar = x_arr.sum() / N if N > 0 else 0 # T = sum(score_i * x_i) - p_bar * sum(score_i * n_i) numerator = np.sum(scores * x_arr) - p_bar * np.sum(scores * n_arr) denominator = np.sqrt(p_bar * (1 - p_bar) * ( np.sum(scores**2 * n_arr) - (np.sum(scores * n_arr))**2 / N )) if p_bar > 0 and p_bar < 1 else 1e-10 z_trend = numerator / denominator if denominator > 1e-10 else 0.0 # One-tailed: theory predicts increasing trend (positive Z) p_trend = 1 - stats.norm.cdf(z_trend) if z_trend > 0 else 1.0 sign_ok_trend = z_trend > 0 verd_trend = verdict(p_trend, sign_ok_trend, threshold=0.10) results.append(log_result( 'two_sided_pricing_tier_incidence', round(z_trend, 3), round(p_trend, 4), verd_trend, details={ 'tier_labels': tier_labels, 'tier_n': tier_n, 'tier_deep_subsidy': tier_deep, 'tier_pct': [round(p, 1) for p in tier_pct], 'z_trend': round(z_trend, 3), }, description=( "Tests monotonic trend in active subsidy incidence across 3 complementarity " "tiers (Paper 5, Result res:subsidy). Cochran-Armitage trend test: scores " "tiers 0/1/2, tests whether proportion with fee_A < 0 increases linearly. " f"Low (<0.3): {tier_deep[0]}/{tier_n[0]}={tier_pct[0]:.0f}%, " f"Medium (0.3-0.6): {tier_deep[1]}/{tier_n[1]}={tier_pct[1]:.0f}%, " f"High (>=0.6): {tier_deep[2]}/{tier_n[2]}={tier_pct[2]:.0f}%. " "One-tailed: theory predicts increasing incidence with complementarity." ), )) # ── Test 4: Anti-network restriction (Mann-Whitney) ── # Theory part (iii): platforms with anti-network behavior should have lower # comp_index (they restrict because additional participants dilute value — # broadcast/community model where bilateral match specificity is low). restrict = df[df["restricts"] == 1] no_restrict = df[df["restricts"] == 0] r_comp = restrict["comp_index"].values nr_comp = no_restrict["comp_index"].values if len(r_comp) >= 2 and len(nr_comp) >= 2: u_stat, p_mw_two = stats.mannwhitneyu(r_comp, nr_comp, alternative='less') sign_ok_anti = r_comp.mean() < nr_comp.mean() verd_anti = verdict(p_mw_two, sign_ok_anti, threshold=0.10) else: u_stat, p_mw_two = np.nan, np.nan sign_ok_anti = restrict["comp_index"].mean() < no_restrict["comp_index"].mean() verd_anti = 'CONSISTENT' if sign_ok_anti else 'AMBIGUOUS' results.append(log_result( 'two_sided_pricing_anti_network', round(u_stat, 1) if not np.isnan(u_stat) else np.nan, round(p_mw_two, 4) if not np.isnan(p_mw_two) else np.nan, verd_anti, details={ 'restrict_comp_mean': round(restrict["comp_index"].mean(), 3), 'nonrestrict_comp_mean': round(no_restrict["comp_index"].mean(), 3), 'restrict_spec_mean': round(restrict["specificity"].mean(), 3), 'nonrestrict_spec_mean': round(no_restrict["specificity"].mean(), 3), 'n_restricting': len(restrict), 'n_nonrestricting': len(no_restrict), 'restricting_platforms': restrict['platform'].tolist(), }, description=( "Tests anti-network prediction (Paper 1, Prop. two_sided, part iii): " "platforms that restrict participation should have lower complementarity " "(broadcast/community model where bilateral match specificity is low). " "Mann-Whitney U test: comp_index of restricting vs non-restricting platforms. " f"N={len(restrict)} restricting ({', '.join(restrict['platform'].tolist())}) " f"vs N={len(no_restrict)} non-restricting. One-tailed (less). " "Restricting platforms have mean comp={:.3f} vs non-restricting {:.3f}.".format( restrict["comp_index"].mean(), no_restrict["comp_index"].mean()) ), )) # ── Test 5: Durbin Amendment calibration ── interchange_pre, interchange_post = 0.44, 0.21 consumer_low = 3.0 / 25 # $3/mo on $25/mo avg debit spend consumer_high = 5.0 / 25 # $5/mo interchange_drop = interchange_pre - interchange_post pt_low = consumer_low / interchange_drop pt_high = consumer_high / interchange_drop rho_low = 1 - 2 * pt_high rho_high = 1 - 2 * pt_low verd_durbin = 'CONSISTENT' if rho_high < 1 else 'AMBIGUOUS' results.append(log_result( 'two_sided_pricing_durbin_passthrough', round((pt_low + pt_high) / 2, 4), np.nan, verd_durbin, details={ 'passthrough_range': (round(pt_low, 3), round(pt_high, 3)), 'rho_symmetric': (round(rho_low, 3), round(rho_high, 3)), }, description=( "Durbin Amendment calibration: computes cross-side pass-through from the observed " "interchange fee drop (0.44% to 0.21%) and consumer fee increase ($3-$5/month on " "$25/month average debit spend). Pass-through PT = consumer_fee_increase / interchange_drop. " "Implied rho = 1 - 2*PT (from symmetric CES: PT approx (1-rho)/2). " "CONSISTENT if rho < 1 (complementary). " "Real policy shock (2010 Dodd-Frank Section 1075) provides clean identification. " "Source: Mukharlyamov and Sarin (2019)." ), )) # ── Test 6: EU IFR calibration ── ifr_pre = 0.75 ifr_post = 0.22 ifr_drop = ifr_pre - ifr_post consumer_pct_low = 5.0 / 8000 * 100 consumer_pct_high = 15.0 / 5000 * 100 eu_pt_low = consumer_pct_low / ifr_drop eu_pt_high = consumer_pct_high / ifr_drop eu_rho_low = 1 - 2 * eu_pt_high eu_rho_high = 1 - 2 * eu_pt_low verd_eu = 'CONSISTENT' if eu_rho_high < 1 else 'AMBIGUOUS' results.append(log_result( 'two_sided_pricing_eu_ifr_passthrough', round((eu_pt_low + eu_pt_high) / 2, 4), np.nan, verd_eu, details={ 'ifr_interchange_drop_pp': round(ifr_drop, 3), 'passthrough_range': (round(eu_pt_low, 3), round(eu_pt_high, 3)), 'rho_symmetric': (round(eu_rho_low, 3), round(eu_rho_high, 3)), }, description=( "EU Interchange Fee Regulation (2015) calibration: interchange capped at 0.20% debit / " "0.30% credit. Pre-IFR weighted average ~0.75%, post ~0.22% (drop = 0.53pp). " "Consumer fee increases EUR 5-15/year on EUR 5000-8000 annual card spend. " "Pass-through PT = consumer_fee_pct / interchange_drop. Implied rho = 1 - 2*PT. " "CONSISTENT if rho < 1. Independent replication of Durbin test using EU policy shock. " "Sources: EC Impact Assessment (2013), Frontier Economics (2018)." ), )) _cache['df'] = df _cache['results'] = results _cache['df_free'] = df_free _cache['median_comp'] = median_comp _cache['tier_data'] = { 'labels': tier_labels, 'n': tier_n, 'deep': tier_deep, 'pct': tier_pct, } _cache['durbin'] = { 'pt_low': pt_low, 'pt_high': pt_high, 'rho_low': rho_low, 'rho_high': rho_high, } _cache['eu_ifr'] = { 'pt_low': eu_pt_low, 'pt_high': eu_pt_high, 'rho_low': eu_rho_low, 'rho_high': eu_rho_high, } return results def figures(): """Generate figures for each subtest.""" if not _cache: main() paths = [] df = _cache.get('df') if df is None: return paths import matplotlib.pyplot as plt median_comp = _cache.get('median_comp', df['comp_index'].median()) # --- Figure 1: Active subsidy Spearman (scatter) --- fig, ax = setup_figure(width=9, height=6) colors = ['#e74c3c' if ds == 1 else '#95a5a6' for ds in df['deep_subsidy']] ax.scatter(df['comp_index'], df['deep_subsidy'] + np.random.uniform(-0.03, 0.03, len(df)), c=colors, s=100, edgecolors='white', lw=0.8, alpha=0.8, zorder=3) for _, row in df.iterrows(): offset_y = 0.05 if row['deep_subsidy'] == 1 else -0.05 ax.annotate(row['platform'], (row['comp_index'], row['deep_subsidy'] + offset_y), fontsize=5.5, alpha=0.7, ha='center') # Show the Spearman result r_s = _cache.get('results', [{}])[0].get('spearman_r', 0) p_val = _cache.get('results', [{}])[0].get('p_two_tailed', 1) ax.set_xlabel('Complementarity Index', fontsize=11) ax.set_ylabel('Active Subsidy (fee_A < 0)', fontsize=11) ax.set_yticks([0, 1]) ax.set_yticklabels(['No (fee_A >= 0)', 'Yes (fee_A < 0)']) ax.set_title(f'Active Subsidies by Complementarity (Spearman r={r_s:.3f})') ax.set_xlim(-0.05, 1.1) ax.set_ylim(-0.15, 1.25) ax.grid(True, alpha=0.2) fig.tight_layout() paths += save_figure(fig, 'active_subsidy_spearman', subfolder='potential') plt.close(fig) # --- Figure 2: Subsidy depth (Fisher exact, bar chart) --- df_free = _cache.get('df_free', df[df['free_side'] == 1]) high_free = df_free[df_free["comp_index"] >= median_comp] low_free = df_free[df_free["comp_index"] < median_comp] pct_deep_h = high_free["deep_subsidy"].mean() * 100 if len(high_free) > 0 else 0 pct_deep_l = low_free["deep_subsidy"].mean() * 100 if len(low_free) > 0 else 0 fig2, ax2 = setup_figure(width=7, height=5) bars = ax2.bar(['Low Comp\n(free-side only)', 'High Comp\n(free-side only)'], [pct_deep_l, pct_deep_h], color=['#f39c12', '#3498db'], edgecolor='white', width=0.5) for bar, pct, n in zip(bars, [pct_deep_l, pct_deep_h], [len(low_free), len(high_free)]): ax2.text(bar.get_x() + bar.get_width() / 2, bar.get_height() + 2, f'{pct:.0f}%\n(n={n})', ha='center', fontsize=10) ax2.set_ylabel('% with Deep Subsidy (fee_A < 0)') ax2.set_title('Subsidy Depth: Net Transfers by Complementarity\n(among platforms with free side)') ax2.set_ylim(0, max(pct_deep_h, pct_deep_l, 10) + 25) ax2.grid(True, alpha=0.25, axis='y') fig2.tight_layout() paths += save_figure(fig2, 'subsidy_depth', subfolder='potential') plt.close(fig2) # --- Figure 3: 3-tier incidence --- tier_data = _cache.get('tier_data', {}) if tier_data: fig3, ax3 = setup_figure(width=8, height=5) tier_colors = ['#e74c3c', '#f39c12', '#2ecc71'] bars = ax3.bar(tier_data['labels'], tier_data['pct'], color=tier_colors, edgecolor='white', width=0.6) for bar, pct, n, d in zip(bars, tier_data['pct'], tier_data['n'], tier_data['deep']): ax3.text(bar.get_x() + bar.get_width() / 2, bar.get_height() + 1, f'{pct:.0f}%\n({d}/{n})', ha='center', fontsize=10) ax3.set_ylabel('Active Subsidy Incidence (%)') ax3.set_title('Active Subsidy by Complementarity Tier\n(Cochran-Armitage Trend Test)') ax3.set_ylim(0, max(tier_data['pct']) + 15) ax3.grid(True, alpha=0.25, axis='y') fig3.tight_layout() paths += save_figure(fig3, 'tier_incidence', subfolder='potential') plt.close(fig3) # --- Figure 4: Anti-network comparison --- fig4, ax4 = setup_figure(width=7, height=5) restrict_df = df[df['restricts'] == 1] no_restrict_df = df[df['restricts'] == 0] components = ['cross_dep', 'specificity', 'simultaneity'] labels = ['Cross-Side\nDependence', 'Transaction\nSpecificity', 'Simultaneity'] x = np.arange(len(components)) width = 0.35 r_means = [restrict_df[c].mean() for c in components] nr_means = [no_restrict_df[c].mean() for c in components] ax4.bar(x - width / 2, nr_means, width, label=f'Non-restricting (n={len(no_restrict_df)})', color='#1f77b4', edgecolor='white') ax4.bar(x + width / 2, r_means, width, label=f'Restricting (n={len(restrict_df)})', color='#d62728', edgecolor='white') ax4.set_xticks(x) ax4.set_xticklabels(labels, fontsize=9) ax4.set_ylabel('Mean Score') ax4.set_title('Anti-Network Platforms: Lower Complementarity Components') ax4.legend(fontsize=9) ax4.grid(True, alpha=0.25) fig4.tight_layout() paths += save_figure(fig4, 'anti_network_comparison', subfolder='potential') plt.close(fig4) # --- Figure 5: Durbin + EU IFR calibration comparison --- fig5, ax5 = setup_figure(width=8, height=5) durbin = _cache.get('durbin', {}) eu = _cache.get('eu_ifr', {}) if durbin and eu: labels_cal = ['Durbin Amendment\n(US 2010)', 'EU IFR\n(EU 2015)'] rho_mids = [ (durbin['rho_low'] + durbin['rho_high']) / 2, (eu['rho_low'] + eu['rho_high']) / 2, ] rho_errs = [ [(durbin['rho_high'] - durbin['rho_low']) / 2], [(eu['rho_high'] - eu['rho_low']) / 2], ] y_pos = [0, 1] ax5.barh(y_pos, rho_mids, xerr=np.array(rho_errs).T, height=0.4, color=['#2ecc71', '#3498db'], edgecolor='white', capsize=8) ax5.axvline(1.0, color='red', ls='--', lw=2, alpha=0.7, label='rho=1 (Cobb-Douglas)') ax5.axvline(0.0, color='gray', ls=':', alpha=0.5) for i, (mid, lo, hi) in enumerate(zip(rho_mids, [durbin['rho_low'], eu['rho_low']], [durbin['rho_high'], eu['rho_high']])): ax5.text(hi + 0.05, i, f'[{lo:.2f}, {hi:.2f}]', va='center', fontsize=9) ax5.set_yticks(y_pos) ax5.set_yticklabels(labels_cal, fontsize=10) ax5.set_xlabel('Implied rho') ax5.set_title('Cross-Side Pass-Through Calibration: Implied rho') ax5.legend(fontsize=9) ax5.grid(True, alpha=0.25, axis='x') fig5.tight_layout() paths += save_figure(fig5, 'passthrough_calibration', subfolder='potential') plt.close(fig5) 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']})")

statistic	0.6957
rho symmetric	[-0.7391, -0.0435]
passthrough range	[0.5217, 0.8696]

Two Sided Pricing Durbin Passthrough

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