#!/usr/bin/env python3 """ Efficiency-Fragility Tradeoff — Empirical Tests Paper 2 (CES Potential), Section 3; Paper 3 (Dynamics), Section 4: 1. GFC crisis sequence: correlation→superadditivity→strategic independence 2. Pre-crisis calm amplifies severity (VIX interaction with K_eff) Lean backing: - crisis_sequence_ordering (EffectiveCurvature.lean): (1-x)^2 < (1-x) for 0 < x < 1 — the K^2 (correlation robustness) channel is MORE SENSITIVE than the K (superadditivity) channel. This is a sensitivity ordering; the test checks temporal ordering in the GFC. - efficiency_fragility_tradeoff (BilateralTrade.lean): more complementary goods have higher K_eff but lower T*. Data: FRED (BAA10Y, TEDRATE, INDPRO, USREC, VIXCLS) Review Notes (2026-03-12): Theory match: PARTIAL. GFC sequence: The Lean theorem proves a SENSITIVITY ordering ((1-x)^2 < (1-x)), not a TEMPORAL ordering. Temporal ordering in the GFC matches sensitivity ordering — consistent but not directly proven. Pre-crisis calm: The theory predicts low T (calm) periods allow K_eff to rise, lowering T* and increasing fragility. VIX is a reasonable proxy for market-implied information friction. I/O audit: CORRECT. BAA spread (correlation proxy), IP decline (output), TED spread (coordination). All are observable proxies for the three curvature channels. Data-signal alignment: ADEQUATE for GFC sequence, WEAK for pre-crisis calm. GFC sequence: N=1 event but all three data series (BAA, INDPRO, TED) are standard crisis indicators. The mapping to curvature channels is theoretically grounded. Pre-crisis calm: N=3 recessions (2001, GFC, COVID) with VIX data. Structurally underpowered — minimum Kendall tau p-value is 0.333. COVID is exogenous confounder. Code quality: CLEAN. Confidence in verdict: MEDIUM (GFC sequence is compelling N=1; pre-crisis calm is structurally underpowered). Subtests retired (2026-03-12): - Sectoral asymmetry (test 1): DELETED. Proxy failure — sigma_OR measures input complementarity but recession drops are driven by output demand cyclicality. The sigma → cycle amplitude relationship is tested more rigorously in test_business_cycle_predictions.py (CONSISTENT, r=-0.398). - Expansion fragility (test 5): DELETED. Proxy failure — expansion length is a weak proxy for cumulative rho-drift. Exogenous shocks (Volcker 1981, COVID 2020) dominate. The Minsky rho-shift is tested directly in test_minsky_rho_shift.py. """ import warnings warnings.filterwarnings("ignore") import numpy as np import pandas as pd from scipy import stats import sys, os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..')) from common.data import load_fred from common.stats import log_result from common.plotting import setup_figure, save_figure def _identify_recessions(usrec): """Identify recession start/end dates from USREC indicator.""" recessions = [] in_rec = False start = None for date, val in usrec.items(): if val == 1 and not in_rec: in_rec = True start = date elif val == 0 and in_rec: in_rec = False recessions.append((start, date)) if in_rec: recessions.append((start, usrec.index[-1])) return recessions def _test_crisis_sequence(data): """Test 1: GFC crisis sequence: correlation → superadditivity → strategic.""" # (a) Correlation robustness failure: BAA credit spread spike baa = data.get('BAA10Y') diversification_fail = None if baa is not None and len(baa) > 0: baa_base = baa[(baa.index >= '2004-01-01') & (baa.index <= '2006-12-31')] baa_crisis = baa[(baa.index >= '2007-01-01') & (baa.index <= '2010-06-01')] if len(baa_base) > 0: threshold = baa_base.mean() + 2 * baa_base.std() spike = baa_crisis[baa_crisis > threshold] diversification_fail = spike.index[0] if len(spike) > 0 else None # (b) Superadditivity failure: sustained 3-month IP decline indpro = data.get('INDPRO') output_decline = None if indpro is not None: ip_3m = indpro.pct_change(3) * 100 ip_crisis = ip_3m[(ip_3m.index >= '2007-01-01') & (ip_3m.index <= '2010-06-01')] for i in range(len(ip_crisis) - 2): if ip_crisis.iloc[i] < 0 and ip_crisis.iloc[i+1] < 0 and ip_crisis.iloc[i+2] < 0: output_decline = ip_crisis.index[i] break # (c) Strategic independence failure: TED > 2.0 (Lehman-level defection) ted = data.get('TEDRATE') coordination_fail = None if ted is not None and len(ted) > 0: ted_crisis = ted[(ted.index >= '2007-01-01') & (ted.index <= '2010-06-01')] ted_spike = ted_crisis[ted_crisis > 2.0] coordination_fail = ted_spike.index[0] if len(ted_spike) > 0 else None if diversification_fail and output_decline and coordination_fail: seq_ok = diversification_fail <= output_decline <= coordination_fail verd = "CONSISTENT" if seq_ok else "INCONSISTENT" elif diversification_fail and output_decline: seq_ok = diversification_fail <= output_decline verd = "CONSISTENT" if seq_ok else "AMBIGUOUS" else: seq_ok = False verd = "AMBIGUOUS" return 1.0 if seq_ok else 0.0, np.nan, verd, { "diversification_fail": str(diversification_fail) if diversification_fail else None, "output_decline": str(output_decline) if output_decline else None, "coordination_fail": str(coordination_fail) if coordination_fail else None, } def _test_precrisis_calm(data): """Test 2: Lower pre-recession VIX predicts worse outcomes.""" vix = data.get('VIX') indpro = data.get('INDPRO') usrec = data.get('USREC') if vix is None or indpro is None or usrec is None: return np.nan, np.nan, "AMBIGUOUS", {"reason": "missing data"} recessions = _identify_recessions(usrec) vix_recessions = [(s, e) for s, e in recessions if s.year >= 1990] rec_results = [] for rec_start, rec_end in vix_recessions: pre_start = rec_start - pd.DateOffset(months=12) pre_vix = vix[(vix.index >= pre_start) & (vix.index < rec_start)] rec_ip = indpro[(indpro.index >= rec_start) & (indpro.index <= rec_end + pd.DateOffset(months=6))] if len(rec_ip) < 3 or len(pre_vix) == 0: continue peak = rec_ip.max() trough = rec_ip.min() severity = (trough / peak - 1) * 100 rec_results.append({'pre_vix': float(pre_vix.mean()), 'severity': float(severity)}) if len(rec_results) < 3: return np.nan, np.nan, "AMBIGUOUS", {"reason": f"only {len(rec_results)} recessions"} vix_vals = [r['pre_vix'] for r in rec_results] sev_vals = [r['severity'] for r in rec_results] # Prediction: positive tau (higher VIX → less negative severity) tau, p = stats.kendalltau(vix_vals, sev_vals) sign_ok = tau > 0 if sign_ok and p < 0.10: verd = "CONSISTENT" elif sign_ok: verd = "AMBIGUOUS" else: verd = "AMBIGUOUS" # very few datapoints, don't call inconsistent return tau, p, verd, {"n_recessions": len(rec_results), "rec_results": rec_results} _cache = {} def main(): results = [] # Load data data = {} for sid in ['INDPRO', 'USREC']: try: data[sid] = load_fred(sid) except FileNotFoundError: results.append(log_result("efficiency_fragility", np.nan, np.nan, "AMBIGUOUS", {"reason": f"{sid} not available"}, description="Tests efficiency-fragility tradeoff predictions. Required data series not available.")) return results # VIX (daily → monthly) try: vix = load_fred('VIXCLS') data['VIX'] = vix.resample('MS').mean() except FileNotFoundError: pass # BAA10Y try: baa = load_fred('BAA10Y') data['BAA10Y'] = baa.resample('MS').mean() except FileNotFoundError: pass # TED spread try: ted = load_fred('TEDRATE') data['TEDRATE'] = ted.resample('MS').mean() except FileNotFoundError: pass # Test 1: GFC crisis sequence stat, p2, verd2, details2 = _test_crisis_sequence(data) results.append(log_result("efficiency_fragility_gfc_sequence", stat, p2, verd2, details2, description="Tests the GFC crisis sequence predicted by the sensitivity " "ordering theorem: correlation robustness (K^2 channel) fails first " "(BAA credit spread > 2-sigma above 2004-06 baseline), then " "superadditivity (K channel) fails (3 consecutive months of negative " "3-month IP growth), then strategic independence (K/J channel) fails " "(TED spread > 2.0%). Checks temporal ordering: diversification_fail " "<= output_decline <= coordination_fail. Data: FRED BAA10Y (monthly " "mean), INDPRO (3-month pct change), TEDRATE (monthly mean), " "2007-01 to 2010-06. N=1 event (GFC only). Lean: " "crisis_sequence_ordering proves (1-x)^2 < (1-x) for 0 < x < 1 " "(sensitivity ordering, not temporal).")) # Test 2: Pre-crisis calm tau3, p3, verd3, details3 = _test_precrisis_calm(data) results.append(log_result("efficiency_fragility_pre_crisis_calm", tau3, p3, verd3, details3, description="Tests whether lower pre-recession VIX (greater calm, lower " "information friction T) predicts worse recession outcomes, consistent " "with efficiency-fragility tradeoff: low T allows deeper " "complementarity (lower rho, lower T*), creating thinner stability " "margin. Method: Kendall tau between 12-month pre-recession mean VIX " "and INDPRO peak-to-trough severity across post-1990 U.S. recessions. " "H0: tau <= 0 (no calm-severity link). Data: FRED VIXCLS (daily -> " "monthly mean), INDPRO, USREC. N=3 recessions (2001, 2008, 2020). " "STRUCTURAL LIMITATION: With N=3, minimum achievable p = 0.333 -- " "test cannot reach statistical significance. COVID (2020) is exogenous " "pandemic, not endogenous information-friction shock.")) # Overall verdict: GFC sequence is the core test; pre-crisis calm is # structurally underpowered (N=3, min p=0.333) so AMBIGUOUS there does # not count against the theory. n_consistent = sum(1 for r in results if r['verdict'] == 'CONSISTENT') n_inconsistent = sum(1 for r in results if r['verdict'] == 'INCONSISTENT') if n_inconsistent >= 1: overall = "INCONSISTENT" elif n_consistent >= 1: overall = "CONSISTENT" else: overall = "AMBIGUOUS" results.append(log_result("efficiency_fragility_overall", float(n_consistent), np.nan, overall, {"n_consistent": n_consistent, "n_total": len(results)}, description="Combined verdict across efficiency-fragility sub-tests: " "GFC crisis sequence ordering and pre-crisis calm severity prediction.")) # Store data for figures _cache['results'] = results _cache['data'] = data return results def figures(): """Generate figures for each efficiency-fragility subtest.""" if not _cache: main() paths = [] data = _cache.get('data', {}) results = _cache.get('results', []) # --- Figure 1: GFC crisis sequence timeline --- gfc_result = next((r for r in results if r['name'] == 'efficiency_fragility_gfc_sequence'), None) if gfc_result and gfc_result.get('diversification_fail'): fig, ax = setup_figure(width=10, height=4) events = [] labels = [] colors_list = [] if gfc_result.get('diversification_fail'): events.append(pd.Timestamp(gfc_result['diversification_fail'])) labels.append(f'Correlation fail\n(BAA spike)\n{gfc_result["diversification_fail"][:7]}') colors_list.append('#e74c3c') if gfc_result.get('output_decline'): events.append(pd.Timestamp(gfc_result['output_decline'])) labels.append(f'Output decline\n(IP sustained drop)\n{gfc_result["output_decline"][:7]}') colors_list.append('#f39c12') if gfc_result.get('coordination_fail'): events.append(pd.Timestamp(gfc_result['coordination_fail'])) labels.append(f'Coordination fail\n(TED > 2.0)\n{gfc_result["coordination_fail"][:7]}') colors_list.append('#8e44ad') for i, (evt, lbl, col) in enumerate(zip(events, labels, colors_list)): ax.axvline(evt, color=col, linewidth=2, linestyle='--') ax.text(evt, 0.8 - i * 0.25, lbl, transform=ax.get_xaxis_transform(), fontsize=8, color=col, ha='center', va='top', bbox=dict(boxstyle='round,pad=0.3', facecolor='white', alpha=0.8)) # Plot INDPRO if available indpro = data.get('INDPRO') if indpro is not None: ip_plot = indpro[(indpro.index >= '2006-01-01') & (indpro.index <= '2010-06-01')] ax.plot(ip_plot.index, ip_plot.values, 'k-', linewidth=1.5, label='INDPRO') ax.set_ylabel('Industrial Production Index') ax.legend(loc='lower left') ax.set_title('GFC Crisis Sequence: K² → K → K/J') ax.set_xlim(pd.Timestamp('2006-01-01'), pd.Timestamp('2010-06-01')) paths.extend(save_figure(fig, 'efficiency_fragility_gfc_sequence', subfolder='dynamics')) # --- Figure 2: Pre-crisis calm scatter --- vix = data.get('VIX') indpro = data.get('INDPRO') usrec = data.get('USREC') if vix is not None and indpro is not None and usrec is not None: recessions = _identify_recessions(usrec) vix_recessions = [(s, e) for s, e in recessions if s.year >= 1990] rec_results = [] for rec_start, rec_end in vix_recessions: pre_start = rec_start - pd.DateOffset(months=12) pre_vix = vix[(vix.index >= pre_start) & (vix.index < rec_start)] rec_ip = indpro[(indpro.index >= rec_start) & (indpro.index <= rec_end + pd.DateOffset(months=6))] if len(rec_ip) >= 3 and len(pre_vix) > 0: peak = rec_ip.max() trough = rec_ip.min() severity = (trough / peak - 1) * 100 year_label = str(rec_start.year) rec_results.append({ 'pre_vix': float(pre_vix.mean()), 'severity': float(severity), 'label': year_label }) if rec_results: fig, ax = setup_figure() vix_vals = [r['pre_vix'] for r in rec_results] sev_vals = [r['severity'] for r in rec_results] ax.scatter(vix_vals, sev_vals, s=100, zorder=5, c='#2c3e50') for r in rec_results: ax.annotate(r['label'], (r['pre_vix'], r['severity']), textcoords="offset points", xytext=(8, 8), fontsize=10, fontweight='bold') tau, p = stats.kendalltau(vix_vals, sev_vals) ax.set_xlabel('Pre-Recession Mean VIX (12-month)') ax.set_ylabel('Recession Severity (% peak-to-trough)') ax.set_title(f'Pre-Crisis Calm: $\\tau$={tau:.2f}, p={p:.3f} (N={len(rec_results)})') ax.annotate('N=3: min possible p = 0.333', xy=(0.02, 0.02), xycoords='axes fraction', fontsize=8, fontstyle='italic', color='gray') paths.extend(save_figure(fig, 'efficiency_fragility_pre_crisis_calm', subfolder='dynamics')) return paths if __name__ == "__main__": res = main() for r in res: print(f"{r['name']}: {r['verdict']} (stat={r['statistic']}, p={r['p_value']})")

p value	1
statistic	0.3333
n recessions	3

Efficiency Fragility Pre Crisis Calm

Description

Figures

Statistics

Script

▸ Source Code

Reproduction Steps