The Compound Trap: No Combination of Monetary, Fiscal, or Regulatory Policy Can Offset the Basel Credit Instability

Abstract

Basel III's countercyclical capital buffer is steered by the credit-to-GDP gap: credit relative to a one-sided Hodrick-Prescott trend that, at the codified smoothing parameter, behaves like an 80-quarter moving average. A companion paper, "The Measurement Trap," showed that a feedback rule built on so long a memory destabilizes the credit loop it regulates whenever credit persistence is high. This paper asks the question that determines whether that result matters: can any other arm of policy — monetary, fiscal, or financial — offset the instability that the regulatory filter creates? We embed the Basel credit loop in a four-loop compound system with monetary, fiscal, and financial-conditions feedback, each parameterized from primary sources and estimated couplings, for the United States, the United Kingdom, Japan, the Euro Area, and South Korea. The compound spectral radius exceeds one in all five countries (1.00998 for the US), and the dominant eigenvector loads almost entirely on the credit loop (credit weight US 0.997654; UK 0.997673; JP 0.997716; EA 0.997755; KR 0.997663); the instability is robust to the operative form of the codified kernel — under the literal gap-form trigger the compound radius remains above one in all five countries as well (US 1.000985; UK 1.000864; JP 1.000634; EA 1.000385; KR 1.000956; verdict FORM-ROBUST). No counter-cyclical monetary pass-through within eleven times the observed coupling envelope stabilizes the system (c* = none on [−5, 0] against envelope 0.431042), crisis-time coupling shifts do not rescue it (T = +0.205202, left-tail p = 0.8617), and every disaggregated credit component is individually unstable under the codified window (bg·S: C&I loans 10.8759; consumer credit 11.8673; CRE loans 8.9308; household mortgages 11.8502; nonfinancial corporate debt 11.725, against the threshold π²/2 = 4.9348) — the window, not the credit mix, binds. A zero-DC two-window divergence element stabilizes the credit loop in isolation yet still fails at the system level (best passing point: none — 0 of the corridor passes), and we prove that no such element can ever remove a pure unit root (Theorem 1: p(1) = 1 − φ, machine-verified symbolically and numerically over 735 cells, both PASS). What works is quantified: shortening the window stabilizes all five countries (normal-coupling compound radius US 0.98364; UK 0.98334; JP 0.98284; EA 0.982269; KR 0.983626), and a five-percent level-anchor dose closes the reform menu (λ* = 0.05 in all 12 cells, max ρ 0.999853; 0 cells stable at 0.02). A crisis-prediction horse race on 150 years of data confirms the BIS's own defense of the gap as a sensor (gap AUROC 0.684457 vs divergence 0.573777) — which sharpens, rather than softens, the conclusion: the codified gap is the better warning signal and the destabilizing controller; no tested filter wins both roles. Measure with the best sensor; act through a stable control law.Verified rebuild under the Research-to-Publication Standard v1.9.4: every load-bearing number is registered in a machine-checked ledger (claims.lock) and regenerated on demand by verify.py on hash-pinned inputs, then independently reproduced from a clean checkout; a capped single-round adversarial review under a fix-or-rebut protocol and a public corrections log are committed in the repository. Two dated, reader-runnable forward predictions are registered publicly as prospective out-of-sample falsifiers — that at the next NBER-dated US recession, the BIS US credit-to-GDP ratio will be higher two quarters after the recession peak than at the peak, and that total US bank credit (FRED series TOTBKCR) will not decline by more than 3 percent from its pre-recession peak regardless of the monetary, fiscal, or financial policy response — to be resolved on finalized BIS and FRED data at the stated horizons, and carried forward if no NBER-dated recession occurs before April 2031. The paper is licensed CC BY-NC-ND 4.0; the accompanying plain-English companion is CC BY-NC 4.0, and the reconstruction and verification code is MIT-licensed.