数据丰富模型中的风险

International Finance Discussion Papers ISSN 1073-2500 (Print)ISSN 2767-4509 (Online) Number 1435 March 2026 Risk in a Data-Rich Model Dario Caldara; Harun Mumtaz; Molin Zhong NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimu-late discussion and critical comment.The analysis and conclusions set forth are those of the authors anddo not indicate concurrence by other members of the research staff or the Board of Governors. Referencesin publications to the International Finance Discussion Papers Series (other than acknowledgement) shouldbe cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are availableon the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from theSocial Science Research Network electronic library at www.ssrn.com. Risk in a Data-Rich Model∗ Dario Caldara1, Haroon Mumtaz2, and Molin Zhong1 1Federal Reserve Board 2Queen Mary University of London March 9, 2026 Abstract We characterize asymmetric tail risk across over one hundred U.S. macroeco-nomic and financial variables using a dynamic factor model with stochastic volatil-ity.The model unifies growth-at-risk, inflation-at-risk, and sectoral heterogeneitythrough common factors whose volatility responds endogenously to shocks, com-bined with heterogeneous factor loadings.We find that asymmetric tail risk ispervasive and heterogeneous: some sectors exhibit severe asymmetry while othersshow minimal asymmetry, with variation across activity, price, and financial vari-ables. The framework disentangles supply- and demand-driven tail risk dynamics,revealing how the balance of risks shifts across episodes, and identifies where vul-nerabilities concentrate across the economy. JEL Classification: C11; C32; C38; E32; E44.Keywords: Dynamic Factor Model; Tail Risk; Stochastic Volatility; Leverage Ef-fect; Growth-at-Risk; Sectoral Heterogeneity. 1Introduction Some sectors of the economy contract sharply during recessions while others remain stable.During the 2008 financial crisis, for instance, motor vehicle production plummeted 40percent and durable goods consumption declined severely, while electricity generationdropped by less than 5 percent and food consumption remained relatively steady.Allsectors experienced the same macroeconomic environment: the same aggregate shocks,the same monetary policy response, the same measures of financial stress.Yet theirtail risk profiles differed dramatically.This heterogeneity is not isolated to the globalfinancial crisis (GFC), nor to activity. Across episodes, some sectoral activity, price, andfinancial variables consistently exhibit extreme risks while others remain relatively stable,with some sectors shifting from symmetric to highly asymmetric risk depending on thenature of shocks. Standard measures of aggregate uncertainty rise uniformly during crises,offering no explanation for this variation. Where does this heterogeneity come from? Isit idiosyncratic noise, or does it reflect systematic propagation of common shocks? Using a dynamic factor model with endogenous stochastic volatility applied to overone hundred U.S. variables, we show that the heterogeneous tail risk is systematic, aris-ing from common macroeconomic dynamics that propagate asymmetrically across theeconomy. The core mechanism is an extension of the leverage effect documented in assetmarkets (Black, 1976; Christie, 1982) and aggregate volatility (Ludvigson et al., 2021):shocks affect factor levels, and factor volatility responds endogenously.For real activ-ity, adverse shocks depress levels while elevating volatility, amplifying downside risk. Forprices and financial conditions, shocks can increase both levels and volatility—rising infla-tion or spreads accompanied by rising uncertainty—generating upside risk. Heterogeneityacross sectors reflects differential sensitivity to these dynamics. Cyclical sectors sensitiveto financial conditions face severe downside risk amplification. Price-sensitive goods ex-hibit inflation-at-risk during supply disruptions. Stable sectors remain relatively insulatedacross episodes. These dynamics unify three empirical phenomena previously studied in isolation. First,the growth-at-risk behavior documented by Adrian et al. (2019), where GDP growth’slower tail is more volatile than its upper tail, reflects these dynamics operating in real ac-tivity variables. Second, inflation-at-risk and financial-stress-at-risk observed across pricesand financial variables reflect the same mechanism with opposite sign: rising inflation orspreads accompanied by rising uncertainty generate upside rather than downside risk.Third, the substantial heterogeneity across sectors, from extreme asymmetry in cyclicalindustries to near-symmetry in stable sectors, reflects how different variables respond to common underlying shocks.Rather than requiring separate models for growth-at-risk,inflation-at-risk, a