#!/usr/bin/env python3 """ Low-Rate Environment -> Deeper Crises (Minsky Trap) -- Paper 3, Section 18.2 ============================================================================= Tests the Minsky trap prediction: extended easy financial conditions (low T) increase effective curvature K_eff = K*(1-T/T*), making the economy more fragile. The empirical implication: lower pre-recession NFCI (easier conditions) should predict deeper subsequent recessions. Lean theorem: `minsky_trap_margin` — if dT*/dT < 1 then stability margin shrinks (dDelta/dT = dT*/dT - 1 < 0). Proved by linarith. Three subtests: T1: OLS of recession depth on pre-recession average NFCI (12-month window), one-sided test for negative coefficient, HC1 robust SEs. T2: Spearman rank correlation (non-parametric, robust to small N). T3: Sensitivity: exclude COVID-2020 (exogenous shock, not Minsky-type). Data: NFCI (Chicago Fed, weekly from 1971, FRED) -> monthly average. GDPC1 (Real GDP, quarterly from 1947, FRED) for recession depth. Review Notes (2026-03-11): Theory match: PARTIAL — Minsky trap theorem is about endogenous rho dynamics narrowing stability margin, not directly about interest rates -> crisis depth. The test captures a reasonable empirical implication (easy conditions -> fragility) but uses NFCI as proxy for information friction T, not the core rho mechanism. I/O audit: CORRECT — NFCI is a reasonable proxy for financial conditions / information friction T (low NFCI = easy conditions = low T). GDP peak-to-trough is a direct measure of recession depth. Data-signal: WEAK — N=7 NBER recessions post-1970 is fundamentally low-power. COVID-2020 is an exogenous shock, not a Minsky-type endogenous crisis. NFCI goes back to 1971, covering all 7 recessions. Code quality: CLEAN — one-sided p-value, HC1 robust SEs, Spearman for robustness. Confidence: LOW — low power (N=7), heterogeneous recession types, and the test checks a weaker implication than the core Minsky rho-shift mechanism. """ import warnings warnings.filterwarnings("ignore") import numpy as np import pandas as pd 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, verdict from common.plotting import setup_figure, save_figure NBER_RECESSIONS = [ ('1973-11', '1975-03'), ('1980-01', '1980-07'), ('1981-07', '1982-11'), ('1990-07', '1991-03'), ('2001-03', '2001-11'), ('2007-12', '2009-06'), ('2020-02', '2020-04'), ] _cache = {} def load_data(): """Load NFCI (weekly -> monthly) and real GDP. Returns (nfci_monthly, gdp).""" nfci = load_fred('NFCI') nfci = nfci.astype(float).resample('MS').mean().dropna() nfci.name = 'nfci' gdp = load_fred('GDPC1') gdp = gdp.astype(float).dropna() gdp.name = 'gdp' return nfci, gdp def compute_recession_data(nfci, gdp, exclude_covid=False): """Compute pre-recession NFCI and recession depth for each NBER recession. Returns list of dicts with: label, peak_date, pre_nfci, depth_pct. """ records = [] recessions = NBER_RECESSIONS if exclude_covid: recessions = [r for r in recessions if r[0] != '2020-02'] for peak_str, trough_str in recessions: peak_date = pd.Timestamp(peak_str) trough_date = pd.Timestamp(trough_str) # Pre-recession average NFCI: 12 months before peak pre_start = peak_date - pd.DateOffset(months=12) pre_window = nfci[(nfci.index >= pre_start) & (nfci.index < peak_date)] if len(pre_window) < 6: continue avg_nfci = float(pre_window.mean()) # Recession depth: peak-to-trough % decline in real GDP gdp_near_peak = gdp[(gdp.index >= peak_date - pd.DateOffset(months=3)) & (gdp.index <= peak_date + pd.DateOffset(months=3))] gdp_near_trough = gdp[(gdp.index >= trough_date - pd.DateOffset(months=3)) & (gdp.index <= trough_date + pd.DateOffset(months=3))] if len(gdp_near_peak) == 0 or len(gdp_near_trough) == 0: continue peak_gdp = float(gdp_near_peak.max()) trough_gdp = float(gdp_near_trough.min()) if peak_gdp <= 0: continue depth_pct = (peak_gdp - trough_gdp) / peak_gdp * 100.0 records.append({ 'label': f'{peak_str} to {trough_str}', 'peak_date': peak_date, 'pre_nfci': avg_nfci, 'depth_pct': depth_pct, }) return records def main(): results = [] try: nfci, gdp = load_data() except FileNotFoundError as e: return [log_result( name='low_rate_deeper_crises_nfci', stat=float('nan'), p=float('nan'), verd='SKIPPED', details={'reason': str(e)}, description=( "Tests Minsky trap prediction (Paper 3, Section 18.2): easy pre-recession " "financial conditions (low NFCI = low information friction T) predict deeper " "subsequent crises. FRED data not found."), )] # Compute recession data (all 7 recessions) records = compute_recession_data(nfci, gdp, exclude_covid=False) _cache['records'] = records _cache['nfci'] = nfci if len(records) < 4: return [log_result( name='low_rate_deeper_crises_nfci', stat=float('nan'), p=float('nan'), verd='SKIPPED', details={'reason': f'Only {len(records)} recessions with data', 'n_recessions': len(records)}, description=( "Tests Minsky trap prediction: lower pre-recession NFCI -> deeper crises. " "Insufficient recession observations."), )] pre_nfci = np.array([r['pre_nfci'] for r in records]) depth = np.array([r['depth_pct'] for r in records]) # T1: OLS of recession depth on pre-recession NFCI with HC1 SEs # Prediction: negative beta (easier conditions -> deeper crises) # Low NFCI = easy = low T; deeper = larger depth_pct t1_desc = ( "Tests Minsky trap prediction (Paper 3, Thm minsky_trap_margin): easier " "pre-recession financial conditions predict deeper subsequent crises. OLS of " "recession depth (peak-to-trough % real GDP decline from FRED GDPC1) on " "pre-recession average NFCI (12-month window before NBER peak, from FRED NFCI " "weekly resampled monthly, 1971-2026). HC1 robust SEs, one-sided p-value for " "H0: beta >= 0 vs H1: beta < 0. Low NFCI = easy conditions = low information " "friction T -> higher K_eff -> more fragile. N=7 NBER recessions (1973-2020).") try: import statsmodels.api as sm X = sm.add_constant(pre_nfci) m = sm.OLS(depth, X).fit(cov_type='HC1') beta = m.params[1] # One-sided p-value: H1 is beta < 0 p_twosided = m.pvalues[1] if beta < 0: p_onesided = p_twosided / 2 else: p_onesided = 1 - p_twosided / 2 sign_ok = beta < 0 verd = verdict(p_onesided, sign_ok, threshold=0.10) _cache['t1_model'] = m _cache['t1_beta'] = beta _cache['t1_p'] = p_onesided results.append(log_result( name='low_rate_deeper_crises_nfci', stat=float(beta), p=float(p_onesided), verd=verd, details={ 'beta': round(float(beta), 4), 'intercept': round(float(m.params[0]), 4), 'p_twosided': round(float(p_twosided), 4), 'p_onesided': round(float(p_onesided), 4), 'r_squared': round(float(m.rsquared), 4), 'n_recessions': len(records), 'per_recession': [ {'label': r['label'], 'pre_nfci': round(r['pre_nfci'], 3), 'depth_pct': round(r['depth_pct'], 2)} for r in records ], }, description=t1_desc, )) except Exception as e: results.append(log_result( name='low_rate_deeper_crises_nfci', stat=float('nan'), p=float('nan'), verd='SKIPPED', details={'reason': str(e)}, description=t1_desc, )) # T2: Spearman rank correlation (non-parametric, robust to N=7) from scipy import stats as sp_stats r_sp, p_sp = sp_stats.spearmanr(pre_nfci, depth) # One-sided: H1 is negative correlation (easier conditions -> deeper) if r_sp < 0: p_sp_onesided = p_sp / 2 else: p_sp_onesided = 1 - p_sp / 2 sign_ok = r_sp < 0 verd_sp = verdict(p_sp_onesided, sign_ok, threshold=0.10) _cache['t2_r'] = r_sp _cache['t2_p'] = p_sp_onesided results.append(log_result( name='low_rate_deeper_crises_spearman', stat=float(r_sp), p=float(p_sp_onesided), verd=verd_sp, details={ 'r_spearman': round(float(r_sp), 4), 'p_twosided': round(float(p_sp), 4), 'p_onesided': round(float(p_sp_onesided), 4), 'n_recessions': len(records), }, description=( "Non-parametric test of Minsky trap prediction: Spearman rank correlation " "of pre-recession average NFCI (12-month window, FRED weekly resampled monthly) " "with recession depth (peak-to-trough % real GDP decline, FRED GDPC1). " "One-sided H0: rho >= 0 vs H1: rho < 0 (easier conditions -> deeper crises). " "N=7 NBER recessions (1973-2020). Spearman is robust to outliers and small N."), )) # T3: Sensitivity — exclude COVID-2020 (exogenous pandemic, not Minsky-type) records_no_covid = compute_recession_data(nfci, gdp, exclude_covid=True) _cache['records_no_covid'] = records_no_covid if len(records_no_covid) >= 4: pre_nfci_nc = np.array([r['pre_nfci'] for r in records_no_covid]) depth_nc = np.array([r['depth_pct'] for r in records_no_covid]) r_nc, p_nc = sp_stats.spearmanr(pre_nfci_nc, depth_nc) if r_nc < 0: p_nc_onesided = p_nc / 2 else: p_nc_onesided = 1 - p_nc / 2 sign_ok_nc = r_nc < 0 verd_nc = verdict(p_nc_onesided, sign_ok_nc, threshold=0.10) _cache['t3_r'] = r_nc _cache['t3_p'] = p_nc_onesided results.append(log_result( name='low_rate_deeper_crises_no_covid', stat=float(r_nc), p=float(p_nc_onesided), verd=verd_nc, details={ 'r_spearman': round(float(r_nc), 4), 'p_onesided': round(float(p_nc_onesided), 4), 'n_recessions': len(records_no_covid), 'excluded': '2020-02 to 2020-04 (COVID, exogenous shock)', 'per_recession': [ {'label': r['label'], 'pre_nfci': round(r['pre_nfci'], 3), 'depth_pct': round(r['depth_pct'], 2)} for r in records_no_covid ], }, description=( "Sensitivity test: Minsky trap prediction excluding COVID-2020 recession " "(exogenous pandemic shock, not endogenous Minsky-type fragility). Spearman " "rank correlation of pre-recession NFCI with recession depth across N=6 NBER " "recessions (1973-2009). One-sided H0: rho >= 0 vs H1: rho < 0."), )) _cache['results'] = results return results def figures(): """Generate figures for low-rate/deeper-crises subtests.""" if not _cache: main() paths = [] records = _cache.get('records') if not records or len(records) < 3: return paths pre_nfci = np.array([r['pre_nfci'] for r in records]) depth = np.array([r['depth_pct'] for r in records]) labels = [r['label'].split(' to ')[0] for r in records] # Figure 1: Scatter of NFCI vs recession depth with OLS line fig, ax = setup_figure(width=10, height=7) ax.scatter(pre_nfci, depth, s=80, color='steelblue', zorder=5) # Label each point with recession date for x, y, lbl in zip(pre_nfci, depth, labels): ax.annotate(lbl, (x, y), textcoords='offset points', xytext=(8, 5), fontsize=9, color='gray') # Highlight COVID for r in records: if '2020-02' in r['label']: ax.scatter(r['pre_nfci'], r['depth_pct'], s=120, color='red', zorder=6, marker='D', label='COVID-2020 (exogenous)') # OLS trend line m = _cache.get('t1_model') if m is not None: x_range = np.linspace(pre_nfci.min() - 0.1, pre_nfci.max() + 0.1, 100) y_pred = m.params[0] + m.params[1] * x_range beta = _cache.get('t1_beta', 0) p = _cache.get('t1_p', 1) ax.plot(x_range, y_pred, 'r--', linewidth=2, label=f'OLS: $\\beta$={beta:.2f}, p={p:.3f} (one-sided)') ax.set_xlabel('Pre-Recession Average NFCI (12-month window)') ax.set_ylabel('Recession Depth (peak-to-trough % GDP decline)') ax.set_title('Minsky Trap: Easy Conditions Predict Deeper Crises') ax.legend(loc='upper right', fontsize=9) paths += save_figure(fig, 'low_rate_nfci_scatter', subfolder='dynamics') # Figure 2: Ranked bar chart of recession depth colored by pre-NFCI fig, ax = setup_figure(width=12, height=6) sorted_idx = np.argsort(depth)[::-1] bar_colors = [] for i in sorted_idx: if '2020-02' in records[i]['label']: bar_colors.append('#e74c3c') # red for COVID elif pre_nfci[i] < 0: bar_colors.append('#3498db') # blue for easy conditions else: bar_colors.append('#f39c12') # orange for tight conditions sorted_labels = [labels[i] for i in sorted_idx] sorted_depths = [depth[i] for i in sorted_idx] sorted_nfci = [pre_nfci[i] for i in sorted_idx] bars = ax.bar(range(len(sorted_depths)), sorted_depths, color=bar_colors) ax.set_xticks(range(len(sorted_labels))) ax.set_xticklabels([f'{l}\nNFCI={n:.2f}' for l, n in zip(sorted_labels, sorted_nfci)], fontsize=8, rotation=45, ha='right') ax.set_ylabel('Recession Depth (% GDP decline)') ax.set_title('NBER Recessions Ranked by Depth (colored by pre-NFCI)') # Legend from matplotlib.patches import Patch legend_elements = [ Patch(facecolor='#3498db', label='Easy conditions (NFCI < 0)'), Patch(facecolor='#f39c12', label='Tight conditions (NFCI > 0)'), Patch(facecolor='#e74c3c', label='COVID-2020 (exogenous)'), ] ax.legend(handles=legend_elements, loc='upper right', fontsize=9) paths += save_figure(fig, 'low_rate_recession_bars', subfolder='dynamics') return paths if __name__ == '__main__': for r in main(): p = r['p_value'] p_str = f'{p:.4f}' if not (p is None or (isinstance(p, float) and np.isnan(p))) else 'NaN' print(f" {r['name']}: {r['verdict']} (stat={r['statistic']:.4f}, p={p_str})")

reason	fewer than 6 recession observations
n recessions	2

Low Rate Deeper Crises

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