#!/usr/bin/env python3 """ Empirical Tests for Accumulation.lean Propositions =================================================== Tests five properties against US macroeconomic data: 1. steadyState_KY_eq: K/Y in expected range for nonresidential capital 2. Depreciation rate: delta = CFC/K in expected range [8%, 18%] 3. capitalAccumulation_eq_zero_iff: |ΔK/Y| small (near steady state) 4. goldenRule_savings_eq_capitalShare: s < s_K (dynamically efficient) 5. ramsey_above_goldenRule: MPK > delta (Ramsey wedge positive) Data: us_capital_stock_timeseries.csv (FAAt101 line 4, 1997-2024), us_gdi_timeseries.csv (T11000 with GDI, CFC, NOS, Compensation) Lean: CESProofs/Macro/Accumulation.lean — 34 theorems, 0 sorry, 0 axioms. All backing theorems fully proved. Review Notes (2026-03-11) ------------------------- Theory match: CORRECT — all 5 subtests directly test Solow/Ramsey propositions formalized in Accumulation.lean. I/O audit: CORRECT — CFC, K, GDI, NOS are direct BEA measures, no proxying. Data-signal: STRONG — official BEA data, 28 years (1997-2024), adequate for calibration checks. Code quality: CLEAN — simple range/sign checks, no statistical tests needed. Confidence: HIGH — all 5 subtests CONSISTENT with wide margins. """ import numpy as np import sys, os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..')) from common.data import load_compiled from common.stats import log_result from common.plotting import setup_figure, setup_subplots, save_figure def _load_data(): """Load capital stock and GDI data, return aligned dicts by year.""" cap = load_compiled('us_capital_stock_timeseries') gdi = load_compiled('us_gdi_timeseries') k_by_year = {} for _, r in cap.iterrows(): yr = int(r['Year']) k_by_year[yr] = float(r['NonresidentialCapitalStock']) gdi_by_year = {} for _, r in gdi.iterrows(): yr = int(r['Year']) gdi_by_year[yr] = { 'GDI': float(r['GDI']), 'Compensation': float(r['Compensation']), 'CFC': float(r['CFC']), 'NOS': float(r['NetOperatingSurplus']), } years = sorted(set(k_by_year.keys()) & set(gdi_by_year.keys())) return years, k_by_year, gdi_by_year # ── Sub-tests ───────────────────────────────────────────────────── def test_capital_output_ratio(years, k_by_year, gdi_by_year): """Test 1: K/Y in expected range [0.8, 2.0] for private nonresidential capital.""" ratios = [] for yr in years: K = k_by_year[yr] Y = gdi_by_year[yr]['GDI'] if Y > 0: ratios.append(K / Y) if len(ratios) < 5: return log_result('accumulation_ky_ratio', np.nan, np.nan, 'SKIPPED', description="Checks that the mean capital-output ratio K/Y for US private nonresidential capital falls within [0.8, 2.0], consistent with the Solow steady-state prediction. Computed as the time-series average of BEA fixed-asset K divided by GDI.") mean_ky = np.mean(ratios) if 0.8 < mean_ky < 2.0: verd = 'CONSISTENT' else: verd = 'INCONSISTENT' return log_result('accumulation_ky_ratio', mean_ky, np.nan, verd, details={'mean_KY': mean_ky, 'std_KY': np.std(ratios)}, description="Checks that the mean capital-output ratio K/Y for US private nonresidential capital falls within [0.8, 2.0], consistent with the Solow steady-state prediction. Computed as the time-series average of BEA fixed-asset K divided by GDI.") def test_depreciation_rate(years, k_by_year, gdi_by_year): """Test 2: delta = CFC/K in expected range [8%, 18%].""" deltas = [] for yr in years: K = k_by_year[yr] CFC = gdi_by_year[yr]['CFC'] if K > 0: deltas.append(CFC / K) if len(deltas) < 5: return log_result('accumulation_depreciation_rate', np.nan, np.nan, 'SKIPPED', description="Tests that the aggregate depreciation rate is economically reasonable. " "Calibration check: mean(CFC/K) over 1997-2024 should fall in [8%, 18%]. " "Data: BEA Consumption of Fixed Capital (NIPA T11000) / nonresidential " "capital stock (FAAt101). Backs capitalAccumulation K_dot = sY - delta*K.") mean_delta = np.mean(deltas) if 0.08 < mean_delta < 0.18: verd = 'CONSISTENT' else: verd = 'INCONSISTENT' return log_result('accumulation_depreciation_rate', mean_delta, np.nan, verd, details={'mean_delta': mean_delta, 'pct': mean_delta * 100}, description="Tests that the aggregate depreciation rate is economically reasonable. " "Calibration check: mean(CFC/K) over 1997-2024 should fall in [8%, 18%]. " "Data: BEA Consumption of Fixed Capital (NIPA T11000) / nonresidential " "capital stock (FAAt101). Backs capitalAccumulation K_dot = sY - delta*K.") def test_near_steady_state(years, k_by_year, gdi_by_year): """Test 3: |ΔK/Y| small — net investment as fraction of GDP.""" kdot_ratios = [] for i in range(1, len(years)): yr = years[i] yr_prev = years[i - 1] K = k_by_year[yr] K_prev = k_by_year[yr_prev] Y = gdi_by_year[yr]['GDI'] if Y > 0: delta_K = K - K_prev kdot_ratios.append(delta_K / Y) if len(kdot_ratios) < 5: return log_result('accumulation_near_steady_state', np.nan, np.nan, 'SKIPPED', description="Tests the capitalAccumulation_eq_zero_iff proposition: at steady state net investment relative to output should be small. Checks that |delta_K/Y| < 10% on average, using year-over-year changes in the BEA capital stock divided by GDI.") mean_kdot = np.mean(kdot_ratios) if abs(mean_kdot) < 0.10: verd = 'CONSISTENT' else: verd = 'INCONSISTENT' return log_result('accumulation_near_steady_state', mean_kdot, np.nan, verd, details={'mean_net_inv_rate': mean_kdot, 'pct': mean_kdot * 100}, description="Tests the capitalAccumulation_eq_zero_iff proposition: at steady state net investment relative to output should be small. Checks that |delta_K/Y| < 10% on average, using year-over-year changes in the BEA capital stock divided by GDI.") def test_dynamic_efficiency(years, k_by_year, gdi_by_year): """Test 4: s_implied < s_K → economy below golden rule → dynamically efficient.""" s_Ks = [] s_implieds = [] for yr in years: K = k_by_year[yr] Y = gdi_by_year[yr]['GDI'] CFC = gdi_by_year[yr]['CFC'] NOS = gdi_by_year[yr]['NOS'] if Y > 0 and K > 0: s_K = (NOS + CFC) / Y # capital share delta = CFC / K ky = K / Y s_implied = delta * ky # s = delta*K/Y at SS s_Ks.append(s_K) s_implieds.append(s_implied) if len(s_Ks) < 5: return log_result('accumulation_dynamic_efficiency', np.nan, np.nan, 'SKIPPED', description="Tests the golden-rule savings prediction: the economy is dynamically efficient when the implied savings rate s = delta*K/Y is below the capital share s_K = (NOS+CFC)/Y. A positive gap (s_K > s) indicates the US operates below the golden rule.") mean_sK = np.mean(s_Ks) mean_s = np.mean(s_implieds) gap = mean_sK - mean_s if mean_s < mean_sK: verd = 'CONSISTENT' else: verd = 'AMBIGUOUS' return log_result('accumulation_dynamic_efficiency', gap, np.nan, verd, details={'mean_s_K': mean_sK, 'mean_s': mean_s, 'gap': gap}, description="Tests the golden-rule savings prediction: the economy is dynamically efficient when the implied savings rate s = delta*K/Y is below the capital share s_K = (NOS+CFC)/Y. A positive gap (s_K > s) indicates the US operates below the golden rule.") def test_modified_golden_rule(years, k_by_year, gdi_by_year): """Test 5: MPK > delta — Ramsey overaccumulation wedge positive.""" mpks = [] deltas = [] for yr in years: K = k_by_year[yr] Y = gdi_by_year[yr]['GDI'] CFC = gdi_by_year[yr]['CFC'] NOS = gdi_by_year[yr]['NOS'] if Y > 0 and K > 0: s_K = (NOS + CFC) / Y MPK = s_K * (Y / K) delta = CFC / K mpks.append(MPK) deltas.append(delta) if len(mpks) < 5: return log_result('accumulation_modified_golden_rule', np.nan, np.nan, 'SKIPPED', description="Tests the Ramsey overaccumulation wedge: MPK should exceed the depreciation rate delta, implying a positive real return r = MPK - delta. MPK is computed as capital_share * Y/K from BEA GDI and fixed-asset data.") mean_MPK = np.mean(mpks) mean_delta = np.mean(deltas) if mean_MPK > mean_delta: verd = 'CONSISTENT' else: verd = 'INCONSISTENT' return log_result('accumulation_modified_golden_rule', mean_MPK - mean_delta, np.nan, verd, details={'mean_MPK': mean_MPK, 'mean_delta': mean_delta, 'mean_r': mean_MPK - mean_delta}, description="Tests the Ramsey overaccumulation wedge: MPK should exceed the depreciation rate delta, implying a positive real return r = MPK - delta. MPK is computed as capital_share * Y/K from BEA GDI and fixed-asset data.") # ── Main ────────────────────────────────────────────────────────── _cache = {} def main(): """Run all accumulation tests. Returns list of result dicts.""" try: years, k_by_year, gdi_by_year = _load_data() except (FileNotFoundError, KeyError) as e: return [log_result('accumulation', np.nan, np.nan, 'SKIPPED', details={'error': str(e)}, description="Master fallback: all accumulation tests skipped due to data loading failure for US capital stock or GDI time series.")] results = [] results.append(test_capital_output_ratio(years, k_by_year, gdi_by_year)) results.append(test_depreciation_rate(years, k_by_year, gdi_by_year)) results.append(test_near_steady_state(years, k_by_year, gdi_by_year)) results.append(test_dynamic_efficiency(years, k_by_year, gdi_by_year)) results.append(test_modified_golden_rule(years, k_by_year, gdi_by_year)) _cache['results'] = results _cache['years'] = years _cache['k_by_year'] = k_by_year _cache['gdi_by_year'] = gdi_by_year return results def figures(): """Generate 3-panel accumulation tests figure: K/Y, depreciation, MPK bars.""" if not _cache: main() paths = [] years = _cache.get('years', []) k_by_year = _cache.get('k_by_year', {}) gdi_by_year = _cache.get('gdi_by_year', {}) results = _cache.get('results', []) if not years: return paths fig, axes = setup_subplots(1, 3, width=14, height=4) # Panel 1: K/Y over time ky_vals = [k_by_year[yr] / gdi_by_year[yr]['GDI'] for yr in years if gdi_by_year[yr]['GDI'] > 0] ky_years = [yr for yr in years if gdi_by_year[yr]['GDI'] > 0] axes[0].plot(ky_years, ky_vals, 'b-o', markersize=3) axes[0].set_xlabel('Year') axes[0].set_ylabel('K/Y') axes[0].set_title('Capital-Output Ratio') axes[0].grid(True, alpha=0.3) # Panel 2: Depreciation rate over time delta_vals = [gdi_by_year[yr]['CFC'] / k_by_year[yr] * 100 for yr in years if k_by_year[yr] > 0] delta_years = [yr for yr in years if k_by_year[yr] > 0] axes[1].plot(delta_years, delta_vals, 'g-o', markersize=3) axes[1].set_xlabel('Year') axes[1].set_ylabel('delta (%)') axes[1].set_title('Implied Depreciation Rate') axes[1].grid(True, alpha=0.3) # Panel 3: MPK vs delta bar chart r5 = next((r for r in results if r['name'] == 'accumulation_modified_golden_rule'), None) if r5 and r5.get('details'): d = r5['details'] labels = ['MPK', 'delta', 'r = MPK-delta'] vals = [d.get('mean_MPK', 0) * 100, d.get('mean_delta', 0) * 100, d.get('mean_r', 0) * 100] colors = ['steelblue', 'coral', 'green'] axes[2].bar(labels, vals, color=colors) axes[2].set_ylabel('Rate (%)') axes[2].set_title('Modified Golden Rule') for i, v in enumerate(vals): axes[2].text(i, v + 0.1, f'{v:.1f}%', ha='center', fontsize=9) axes[2].grid(True, alpha=0.3) fig.suptitle('Accumulation Tests', fontsize=14, y=1.02) paths.extend(save_figure(fig, 'accumulation_tests', subfolder='macro')) 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']})")

mean r	0.1981
mean MPK	0.3275
statistic	0.1981
mean delta	0.1294

Accumulation Modified Golden Rule

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