# Findings: US Insurance Rate Leading-Indicator Analysis **Generated**: 2026-05-22 **Analysis scope**: FRED monthly data 2000–2026 · n=291–303 observations per correlation pair (YoY changes) **Y variables**: CPI Tenants/Household Insurance (CUSR0000SEHG, n=315); CPI Transportation (CPITRNSL, n=315) **Note on target series**: CPI Motor Vehicle Insurance (CUSR0000SETC01) returned HTTP 400 from FRED API — series appears retired/renamed. CPI Tenants Insurance and CPI Transportation used as substitutes. All correlations residualized on month-of-year fixed effects. n<50 flagged as unreliable. --- ## Data Scope and Honest Framing This analysis relies on FRED CPI insurance series as Y, not NAIC state premium data. NAIC data available locally is a single-year cross-section (153 rows, 2023 only) — insufficient for time-series correlation. NAIC 2023 was analyzed via median polish for cross-sectional heterogeneity. **NAIC 2023 state-level heterogeneity**: - Auto: FL $166.15/mo (most expensive) vs ME $77.17/mo (cheapest) — 2.2× spread across states - Home premiums average ~8.8% above auto baseline (log-scale product effect +0.085) - Renters: ~85% cheaper than auto (log-effect −1.97) **Three data gaps blocked deeper analysis:** 1. NAIC 2018-2022 state data not cached — prevents time-series panel regression by state 2. Manheim Used Vehicle Index (private Cox Automotive) — missing best auto repair cost signal 3. NOAA state-level catastrophe event counts — weather→home premium channel untestable --- ## Finding 1: Motor Vehicle Parts Inflation Is the Dominant Rate Predictor **Mechanism**: Auto body repair is the largest single component of personal auto claims cost. When parts prices rise (supply chain disruption, tariffs, materials inflation), claims inflate within 2–3 quarters. Actuaries file rate increases with state DOIs; approval takes 3–9 months. CPI prints 1–3 months after effective dates. Total pipeline: PPI shock → CPI move ≈ 4–8 quarters. This chain is empirically anchored in Rate Authority's internal correlation-scan utilities. **This analysis**: CPI Motor Vehicle Parts/Equipment (CUSR0000SETC) vs CPI Tenants Insurance, YoY changes residualized on month-of-year, n=279–303: - Lag 12m: Spearman ρ=+0.489 (raw +0.489), Pearson r=+0.379, n=279, agree=True - Lag 18m: Spearman ρ=+0.480 (raw +0.480), Pearson r=+0.437, n=285, agree=True - Lag 24m: Spearman ρ=+0.465 (raw +0.465), Pearson r=+0.453, n=291, agree=True PPI Motor Vehicle Parts (WPU1412) also confirmed: Spearman ρ=+0.388 (lag 2m), +0.375 (lag 4m), +0.372 (lag 6m), +0.353 (lag 8m) — all residualized, all agree=True. RF permutation importance: CUSR0000SETC at 12m lag is the #1 most important feature (imp=0.0966 ±0.0098); at 18m lag is #2 (imp=0.0634 ±0.0052). These two features alone account for ~40% of total positive permutation importance across all 120 features. **Status**: REDISCOVERED AND QUANTIFIED. Novel finding: peak correlation is at 12m lag, not 6m as commonly cited, suggesting the state filing/approval pipeline adds ~6 months to commonly assumed timelines. This has practical value for rate-cycle timing models. --- ## Finding 2: Food Inflation as Household Insurance Pressure Signal (Partially Novel) **Mechanism**: CPI Food at Home is an income-stress proxy. When food inflation is elevated, household budgets compress, increasing insurance lapse risk. Separately, food-price CPI co-moves with supply-chain disruption cycles that also drive repair material costs. The signal likely has a dual nature: direct (income compression → lapses → adverse selection) and coincident (shared supply-chain inflation driver). **This analysis**: CPI Food at Home (CUSR0000SAF11) vs CPI Tenants Insurance, YoY changes residualized, n=279–303: - Lag 4m: Spearman ρ=+0.473 (raw +0.473), Pearson r=+0.442, n=291, agree=True - Lag 2m: Spearman ρ=+0.421 (raw +0.421), Pearson r=+0.365, n=297, agree=True - Lag 6m: Spearman ρ=+0.411 (raw +0.410), Pearson r=+0.378, n=285, agree=True RF: Food at Home at 6m lag ranks #3 overall (imp=0.0403 ±0.0041). Appears in best-performing triple: [Food@6m + Shelter@0m + Electricity@12m] → R²=0.4519 (n=291). Strongest interaction found: Motor Vehicle Parts × Food × Unemployment → main R²=0.2768, interaction R²=0.4508, gain +0.174 (largest interaction effect of all 120 triples). **Status**: PARTIALLY NOVEL. Food inflation as an insurance predictor is not standard in actuarial literature. The 4-month lag (not 0-month) suggests it is a leading, not coincident, indicator. Confound risk: partial out energy CPI before claiming independence. The interaction gain with Motor Vehicle Parts (+0.174 R²) is the most novel finding — when both vehicle repair AND food inflation are elevated, rate pressure compounds nonlinearly. **Medical CPI note**: CPI Medical Care (CPIMEDSL) shows ρ=+0.255 vs CPI Tenants Insurance at lag 8m (n=279, agree=True) — weaker than expected from the 1.3× BI amplifier documented in `marc_lore_models_6_13.py:414`. The BI channel is more visible in CPI Auto Insurance (retired FRED series) than in tenants/transportation composites used here. This is a data limitation, not a null finding for the mechanism. --- ## Finding 3: High-Yield Spread as Counter-Cyclical Rate Pressure Signal **Mechanism**: Insurance carriers hold investment portfolios (mostly investment-grade bonds). When credit stress rises (high-yield spreads widen), investment income falls. Combined ratio pressure forces underwriting margin recovery via rate increases — even independent of claims inflation. This channel is underappreciated by non-actuarial analysts. **This analysis**: High Yield Bond Spread (BAMLH0A0HYM2) vs CPI insurance series: - CPI Transportation (includes a lag=12m: Spearman ρ=0.527 (raw ρ=0.527), Pearson r=0.862, n=10, lag=12m [SMALL-N: effect size unreliable] - CPI Transportation (includes a lag=6m: Spearman ρ=0.521 (raw ρ=0.521), Pearson r=0.520, n=16, lag=6m [SMALL-N: effect size unreliable] - CPI Transportation (includes a lag=0m: Spearman ρ=-0.362 (raw ρ=-0.362), Pearson r=-0.356, n=22, lag=0m [SMALL-N: effect size unreliable] - CPI Tenants/Household Insuranc lag=6m: Spearman ρ=-0.209 (raw ρ=-0.209), Pearson r=-0.249, n=16, lag=6m [SMALL-N: effect size unreliable] **Status**: PARTIALLY NOVEL at this level of specificity. Investment income → underwriting cycle is standard in insurance economics textbooks but the FRED-testable lag structure is not commonly published. **Caveat**: This channel is confounded with economic cycle: recessions drive both spread widening AND claims frequency. Cannot cleanly isolate investment income channel without carrier-level data. --- ## Finding 4: Unemployment at 24-Month Lag Ranks 4th by RF Importance **Mechanism**: Two competing channels. (a) Claims channel: unemployment-driven uninsured motorist rates inflate average claim severity with multi-year lag. (b) Demand channel: unemployment-driven lapses reduce risk pool, forcing cross-subsidy on remaining policyholders. Both channels operate on 18–24 month timescales as actuaries embed multi-year trend assumptions in rate filings. **This analysis**: Unemployment Rate (UNRATE) vs CPI Transportation, YoY changes, n=279–285: - Lag 8m: Spearman ρ=+0.378 (raw +0.383), Pearson r=+0.403, n=279, agree=True - Lag 6m: Spearman ρ=+0.369 (raw +0.369), Pearson r=+0.482, n=285, agree=True RF: UNRATE at 24m lag ranks #4 (imp=0.0350 ±0.0035). **Status**: REDISCOVERED for short lag. The 24-month lag in RF is more novel — consistent with actuaries using 2-year loss development periods in their filed trend assumptions. Caution: Pearson r (+0.482) exceeds Spearman (+0.369), suggesting outlier episodes (2008–2009, 2020) drive much of the effect. The relationship is not consistently monotone across the full distribution. **Shelter CPI note**: CPI Shelter/OER at lag 0 ranks 7th by RF importance (imp=0.0129). Pairwise Spearman ρ=−0.227 to −0.257 (negative — higher shelter inflation → lower tenants insurance YoY growth). This is counterintuitive for the replacement-cost channel. Most likely explanation: shelter inflation is coincident with low-catastrophe periods when insurance rate growth is muted. Mortgage rate shows ρ=−0.376 at lag 8m vs Transportation CPI (agree=True, n=279) — documented as REDISCOVERED. --- ## Finding 5: RF Multi-Factor Model (OOB R²=0.87) and Best Triple Combinations **RF Overview**: Random Forest (300 trees, depth≤5, min_leaf=5) on 120 features (24 predictors × 5 lags: 0/6/12/18/24m) against CPI Tenants Insurance YoY changes, n=291. Permutation importance 30 repeats. **OOB R²=0.8718** — out-of-bag estimate on full 25-year window. High, but see caveat below. **Top 8 features by permutation importance:** 1. CPI Motor Vehicle Parts | lag=12m: imp=0.0966 ±0.0098 2. CPI Motor Vehicle Parts | lag=18m: imp=0.0634 ±0.0052 3. CPI Food at Home | lag=6m: imp=0.0403 ±0.0041 4. Unemployment Rate | lag=24m: imp=0.0350 ±0.0035 5. CPI Used Cars/Trucks | lag=24m: imp=0.0165 ±0.0018 6. Industrial Production Mfg | lag=12m: imp=0.0134 ±0.0020 7. CPI Shelter/OER | lag=0m: imp=0.0129 ±0.0016 8. CPI Motor Vehicle Parts | lag=24m: imp=0.0120 ±0.0011 Feature importance is "fat head / thin tail": top 2 features account for ~40% of total positive importance; items 3–8 each contribute 1–4%. **Best triple combinations** (R² with 3-way interactions, n=291): - Food@6m + Shelter@0m + Electricity@12m: R²=0.4519, AIC=−2825.9, interaction gain +0.010 - Vehicle Parts@12m + Food@6m + Unemployment@24m: R²=0.4508, gain +0.174 ← largest interaction - Food@6m + Shelter@0m + Vehicle Parts@24m: R²=0.4497, gain +0.023 The Motor Vehicle Parts × Food × Unemployment interaction gain (+0.174 R²) is the strongest nonlinear effect found: these three series have compound, non-additive effects when all elevated simultaneously. **Status**: NOVEL for this specific predictor set and lag structure over 25 years. OOB R²=0.87 should be treated with caution — 120 features on n=291 observations has overfitting risk even with RF regularization. The permutation importance rankings (not the R²) are the defensible finding. **COVID caveat**: All 2001–2026 window includes 2020–2022 supply chain shocks that amplify every cost-inflation correlation. Pre-COVID sub-sample (2001–2019) analysis is warranted before citation. --- ## Honest Caveats 1. **Primary Y series unavailable**: CPI Motor Vehicle Insurance (CUSR0000SETC01) returned HTTP 400 from FRED API. The auto-specific insurance CPI is the correct target for auto rate prediction. Substitutes (Tenants Insurance, Transportation CPI) are valid but diluted by non-insurance components (Transportation) or represent a different product line (Tenants). Findings are directional for auto; more directly applicable to renters. 2. **COVID structural break**: The 2020–2022 supply chain episode amplifies all cost-inflation correlations artificially. Full-window Spearman estimates should be treated as upper bounds. Pre-COVID subsample (2001–2019) validation is required before citation in external research. 3. **High-yield spread results are small-n**: BAMLH0A0HYM2 has only 35 monthly observations (2023–2026). All correlations with this series are flagged SMALL-N and unreliable. The investment income → underwriting cycle thesis is mechanistically sound but untestable at this sample size. 4. **Year-month median polish is trend, not signal**: CPI Tenants year effects correlate ρ=1.00 with Medical CPI, Rent CPI, M2, Electricity annual means. This is expected co-integration. Year effects here ≈ general inflation level. Documented but not a novel finding. 5. **State panel requires NAIC history**: Only 2023 cross-section available locally. State-level heterogeneity (2.2× FL/ME auto spread) is documented but cannot be connected to macro leads without multi-year state panel. NAIC 2018–2022 state data acquisition is the highest-value data gap to close for the next analysis run. 6. **What we cannot test without more data**: - State-by-state CAT event counts → home premium channel (needs NOAA NCEI state data) - Manheim Used Vehicle Index → strongest auto repair cost signal (private, Cox Automotive) - Carrier-specific competitive pricing dynamics (needs quarterly carrier-level premiums) - Tort reform event timing → BI liability severity channel