The Phase Locking Distance Index and Dual Breach Principle: A Multi-Dimensional Framework for Synchronized Crisis Risk and Policy Evaluation in Advanced Economies, with Detailed Application to Australia and Canada

Lai, Yehong (2026): The Phase Locking Distance Index and Dual Breach Principle: A Multi-Dimensional Framework for Synchronized Crisis Risk and Policy Evaluation in Advanced Economies, with Detailed Application to Australia and Canada.

Abstract

[Version note] This MPRA deposit (2026-05-13) is the v0.10.16 working-draft revision of SSRN Working Paper No. 6742863. The current SSRN-archived version is v0.12-canada-extended (revision approved 2026-05-12; initial v0.3.3 deposit 2026-05-10). The present MPRA version incorporates additional prior-art engagement completed within 24 hours of SSRN approval - specifically Section 2.2 (Kathiravelu 2026 Kuramoto-trading), Section 2.3 (ECB CISS via Holló-Kremer-Lo Duca 2012), Section 2.5.5 (Aikman et al. 2017 Journal of Banking and Finance + Lee-Posenau-Stebunovs 2017 Federal Reserve IFDP 1191), Section 3.2 (phase-locking-value disambiguation via Lachaux et al. 1999), and Section 4.4 (portfolio-variance aggregation choice note). The SSRN abstract ID 6742863 remains the canonical citation; this MPRA deposit serves as the prior-art-strengthened version pending the next major SSRN revision.

[Abstract] This paper introduces a multi-dimensional framework for measuring synchronized macroeconomic crisis risk in advanced economies. The Phase Locking Distance Index (PLDI) is defined as the geometric mean of standardised distances across four pre-committed dimensions - CPI inflation (A, two-sided), unemployment (B), federal net debt-to-GDP (C), and household debt-to-GDP (H) - derived from first principles via three independent theoretical traditions (Brunnermeier-Sannikov 2014; Reinhart-Rogoff 2009 6-type crisis taxonomy; Schularick-Taylor 2012 + Reinhart-Reinhart-Rogoff 2012). The Talon Threshold is the decision-theoretic universal cutoff PLDI_pr >= 0.80 (risk-asymmetric optimal under high false-negative / false-positive cost asymmetry). The Dual Breach Principle states that when any two of the four dimensions simultaneously breach in a crisis-conditional episode, the remaining two converge to warning zone within 6-24 months in 28 of 30 historical cases (93.3%, 95% Clopper-Pearson CI [78.0%, 99.2%]; n=30 across 20+ countries, 1929-2024). Policy-Induced Phase Locking (PIPL) captures the qualitative claim that policy bundles can synchronise the four dimensions, with the Policy Phase Locking Elasticity (PPLE) providing operational evaluation.

Empirical validation comprises (i) joint OOS rolling-window logit on a 33-country panel of 2,148 country-quarters, yielding joint PLDI + Borio-Drehmann credit-gap AUC 0.84-0.85 vs 0.79-0.81 credit-gap alone (complementary-signal pattern with LR tests rejecting either single-predictor specification at p < 0.0001 in both directions); (ii) direct causal identification via Jordà (2005) local projections on a 17-country high-frequency monetary policy shock panel (peak t-statistic = -3.08 at horizon h=13 quarters with country-clustered standard errors); (iii) cross-frequency Cox proportional-hazards validation (quarterly z = -3.32 / annual z = -4.09 on independent Jordà-Schularick-Taylor data); (iv) a 15-case ex-post PPLE track record (14/15 = 93.3% >= 2/3 hit rate across 8 countries, political-symmetry verified via N=3 within-coalition cross-validation, Abadie-Diamond-Hainmueller 2010 synthetic control 13/15 sign-agreement).

The framework is applied in detail to Australia 2026 (aggregate PPLE approximately -0.35; PLDI = 1.16 = 0.36 units above the Talon Threshold) and as a second-country detailed application to Canada 2026 (aggregate cost-share-weighted PPLE = -0.085 vs Australia -0.21, indicating Canada is approximately 60% less synchronising than Australia at the same cycle point). The paper concludes with a Sequenced Demolition counterfactual for both countries, falsifiability conditions, and generalisability discussion for New Zealand, United Kingdom, Korea, and other advanced economies.

• Item Type: MPRA Paper
• Language: English
• Keywords: Phase Locking Distance Index; Dual Breach Principle; Talon Threshold; Policy Phase Locking Elasticity; multi-dimensional crisis early warning; macroprudential policy evaluation; composite financial vulnerability indicator; household debt; federal fiscal sustainability; Australia; Canada
• Subjects: E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E44 - Financial Markets and the Macroeconomy; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E62 - Fiscal Policy; G - Financial Economics > G0 - General > G01 - Financial Crises; G - Financial Economics > G1 - General Financial Markets > G18 - Government Policy and Regulation; G - Financial Economics > G2 - Financial Institutions and Services > G28 - Government Policy and Regulation

References

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