Sectoral Default Rates under Stress: The Importance of Non-Linearities.” Bank of Canada Financial System Review
Bibliographic record
Abstract
he purpose of aggregate-level stress testing is to identify the circumstances that could impair the functioning of the financial system and have economy-wide (systemic) implications. In models typi-cally used for stress tests of aggregate credit risk, macroeconomic shocks are assumed to affect financial institutions via their impact on either individual or industry-level default probabili-ties.1 Therefore, sound modelling of the rela-tionship between macroeconomic variables and defaults is of considerable importance. In this report, we examine how the functional form used in the specification of default regres-sions affects the nature of the responses of de-fault probabilities under stress. In particular, we argue that the assumption of a linear relation-ship imposes severe restrictions on the respons-es of default probabilities to macroeconomic shocks. These restrictions are particularly unde-sirable in stress-testing exercises. To remedy this problem, we introduce non-linearities in a sim-ple, but effective, way and illustrate their impact on responses with a series of examples. We begin with a general discussion of the nature of the restrictions that linearity implies and their undesirability in the context of stress test-ing. This is followed by an empirical exercise in which we compare the performance of linear and non-linear models by varying the severity of a recession and the initial state of the econo-my. In the concluding section, we draw broader implications of our results for stress testing.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".