欧洲部门企业违约的分位数概率模型

A quantile probability model forsectoral corporate defaults in Europe Paul Konietschke, Julian Metzler,Aurea Ponte Marques Abstract Conventional credit risk models understate tail risk by centering on mean default prob-abilities and neglecting distributional and sectoral heterogeneity.We propose a QuantileProbability of Default (QPD) framework based on unconditional quantile regressions es-timated on flow default rates from five million non-financial firms across nine countries,conditioned on macro- and sectoral scenario covariates standard in stress testing. The tailexhibits three- to five-fold stronger sensitivity than at the median, revealing non-linearitiesand asymmetric sectoral propagation of credit risk.We validate the performance of ourmodel across crisis periods and benchmark models to confirm the framework’s robustnessand prudential efficiency. Under the European Central Banks’s 2025 increasing geopoliticaland trade tensions scenario, the QPD identifies higher tail vulnerabilities in construction,trade, hospitality, and real estate.The framework embeds distributional estimation intostress testing, advancing scenario-based assessment of sectoral credit risk for policy andprudential applications. JEL codes:C21, C54, D22, G21, G32Keywords:Firm dynamics, Non-linearity, Probability of default, Stress testing, Trade tension Non-Technical Summary This paper introduces a new framework to measure sector-level corporate credit risk in theeuro area and to improve its integration into banking stress-testing.It proposes a “quantileprobability of default” (QPD) model that uses quantile regression techniques to estimate thefull distribution of sectoral default rates, rather than a single conditional mean. This distribu-tional perspective allows the authors to characterise not only average default risk but also tailbehaviour and sector-specific vulnerabilities under adverse macro-financial scenarios, includingthose driven by geopolitical and trade tensions. Empirically, the paper assembles a new panel of sectoral flow default rates using firm-levelbalance sheet information from the Orbis database for roughly five million non-financial firmsin nine euro area countries over 1999–2023. Defaults are identified using a balance-sheet-basedcriterion `a la Gourinchas et al. (2020), whereby a firm is classified as defaulted once internalcash flow fails to cover financial expenses in two consecutive years, so that the measure cap-tures persistent rather than transitory liquidity stress. Firm-level indicators are aggregated tocountry–sector “flow” default rates, interpreted as empirical hazard rates for new defaults. De-scriptive evidence reveals strong cyclical variation and pronounced cross-sector heterogeneity:construction, tourism, real estate and other cyclical sectors display higher and more volatiledefault rates than utilities or some business and professional services, and high energy-intensivemanufacturing is systematically riskier than low energy-intensive manufacturing. The QPD model relates these sectoral default rates to a set of macro-financial variables thatare chosen to coincide with those used in euro-area stress-testing scenarios: real sectoral GrossValue Added (GVA), unemployment, short- and long-term interest rates, the term spread, eq-uity prices and property prices. Methodologically, the paper adopts an unconditional quantileregression framework with sector–country fixed effects, implemented via recentered influencefunctions. This allows the authors to estimate how macro-financial shocks affect different quan-tiles (e.g., the median, 70th or 90th percentile) of the sectoral default-rate distribution, whilecontrolling for time-invariant heterogeneity across sector–country pairs.The results point toeconomically meaningful non-linearities: the response of default rates to adverse movements inunemployment, long-term interest rates or GVA is significantly larger in the upper tail of thedistribution than around the median, implying that macro-financial shocks have disproportion-ately severe effects in already stressed states. A series of validation exercises demonstrates that the QPD model satisfies key criteria forstress-testing use.In-sample, euro-area aggregate PDs, obtained by GVA-weighting sectoralQPD estimates, track realised default rates closely and reproduce the spikes associated withthe global financial crisis and the euro area sovereign debt crisis. Realised defaults tend to liebetween the model’s 50th and 70th percentiles in tranquil periods and move closer to higherquantiles during crises, consistent with the intended interpretation of the quantile dimension.Out-of-sample projection exercises, in which the model is estimated only on data available up toa given year and then conditioned on realised macro-financial paths over a three-year horizon,indicate that QPD-based forecasts match both the direction and approximate magnitude ofsubsequent default episodes and outperform simple benchma