outputs/variable_dictionary.md

Variable Dictionary — every modelled variable: source, transformation, window, rationale, fitted sign

Data window: panel quarters t=1..60 ≙ 2000Q2–2015Q1 (calendar anchoring verified vs FRED UNRATE, corr 0.996). Train = t≤40 (2000Q2–2010Q1); OOT = t=41–60 (2010Q2–2015Q1, the stress aftermath). All fits on train only. Macro series are US national (state-level upgrade = Freddie rung 3). Timing convention: every macro regressor is lagged; the two deliberate current-quarter state variables are flagged ⚡ below.

Variable (model name)	Source → transformation	Lag / window	Economic rationale	Expected sign	Fitted (verified)	Consumed by
fico_s	FICO_orig_time / 100	static (origination)	Ability/willingness to pay	PD ↓	✓ negative	default hazard; LGD cure
ltv10 ⚡	updated_ltv/10 = LTV_orig × (bal_t/bal_orig) × (hpi_orig/hpi_t), winsor 300	current-quarter state (collateral indexation, documented exception)	Equity cushion / strategic-default trigger; = vendor LTV_time to 5e-9	PD ↑, severity ↑, cure ↓	✓ all three (sev +0.107/10pp, cure −0.764)	default hazard; LGD both stages; staging legs
loan_age	time − orig_time → natural cubic spline (hazard) / linear (LGD)	per-quarter	Seasoning baseline; underwriting → trouble → survivor selection	hump	✓ peak 12q fitted vs 10q empirical	both hazards; LGD
prepay_incentive ⚡	interest_rate_time − rate_time (note − market rate)	current-quarter state (option value is real-time)	Refinancing incentive (competing risk)	prepay ↑	✓ (Spearman +0.95)	prepay hazard
investor_orig_time, RE-type flags	raw origination flags	static	Strategic default propensity (no home to lose)	PD ↑ (investor)	✓	default hazard
uer_lag1	uer_time (national level, pp) via within-loan shift	lag 1q	Cash-flow channel (job loss → arrears)	net shock ↑	✓ net +1pp → HR 1.28 (level −0.367 + momentum +0.614 under 0.94 collinearity — quote the NET effect)	default hazard; LGD cure (+0.277 disclosed anomaly)
uer_chg4_lag1	4-quarter change of uer_time, lagged	lag 1q over 4q window	Labour-market momentum	↑	✓ +0.614	default hazard
hpi_growth_lag1	Δlog hpi_time (national index)	lag 1q	Collateral macro channel	PD ↓	✓	default hazard; satellite (+13.64)
gdp_lag1 / gdp_growth_lag2	gdp_time growth	lag 1q / 2q	Activity channel	PD ↓ / Z ↑	✓ (+0.730 satellite)	default hazard; satellite
dt_ltv_uer	center(ltv10) × center(uer_lag1)	mixed	Double trigger (can't pay AND negative equity)	↑	−0.006 (p=.04): in-sample substitution; main effects + momentum carry the joint stress — honest finding, see fit_stats.md	default hazard
lgd_time (target)	vendor realised workout LGD, resolved workouts only (res_time non-null): 9,496 of 11,420 train defaults	resolution window	Two-stage: cure (≤0.05) × severity; LGD>1 tail (14.2% of non-cures, max 3.17) = constant excess loading +0.0255, never clipped	—	OOT calibration +0.047 (conservative)	LGD
Z_t (recovered)	Vasicek inversion of observed vs composition-adjusted expected quarterly default rates (frozen hazard, macro at panel means)	60 quarters	Systematic credit-cycle factor; ρ via Belkin Var(Z)=1 → ρ=0.0227 (vs 0.12 notes / 0.15 Basel — regulatory ρ is conservatism, not time-series fit); mean(Z)=−1.145 level gap documented	trough in GFC	✓ trough 2008Q1 (Z=−2.74)	satellite target; PIT conditioning
Scenario paths	DFAST 2026 CSVs: UER (pp), HPI level → Δlog, GDP SAAR → quarterly, mortgage rate	2026Q1–2029Q1 (13q) rebased as deltas onto the 2015Q1 jump-off, reversion to panel long-run means by q21, hold to 40q	Coherent supervisory multivariate shapes; upside = damped mirror (×−0.35), weights 50/25/25 (SPF anchoring = named enhancement)	severe ECL > base > upside	✓ ($47.6m / $30.5m / $27.7m)	scenario ECL

Model equations live in the module docstrings (cloglog hazard; two-stage LGD; ECL sum; Vasicek PIT transform with the Gauss-Hermite anchor proof; satellite Z = −1.694 + 13.642·hpi_growth_lag1 + 0.730·gdp_growth_lag2, n=57, with ADF/KPSS/DW/AIC and the GFC-dummy sensitivity in outputs/satellite/satellite_report.md). Coefficient tables with CIs: outputs/hazard/hazard_ratios.md, outputs/lgd/lgd_report.md.