企业应对总体波动的非线性和异质性：我们能从机器学习中学到什么？

Nonlinearities and heterogeneity infirms response to aggregatefluctuations: what can we learn frommachine learning? Marco Errico, Simone Pesce, Luigi Pollio Disclaimer:Thispaper should not be reported as representing the views of the European Central Bank(ECB). The views expressed are those of the authors and do notnecessarily reflect those of the ECB. Abstract Firms respond heterogeneously to aggregate fluctuations, yet standard linear modelsimpose restrictive assumptions on firm sensitivities.Applying the Generalized RandomForest to U.S. firm-level data, we document strong nonlinearities in how firm characteristicsshaperesponses to macroeconomic shocks.Weshow that nonlinearities significantlylower aggregate responses, leading linear models to overestimate the economy’s sensitivityto shocks by up to 1.7 percentage points.We also find that larger firms, which carrydisproportionate economic weight, exhibit lower sensitivities, leading to a median reductionin aggregate economic sensitivity of 52%. Our results highlight the importance of accountingfor nonlinearities and firm heterogeneity when analyzing macroeconomic fluctuations andthe transmission of aggregate shocks. JEL Codes:D22, E32, C14, E5 Keywords:Firm Sensitivity, Monetary Policy, Business Cycle, Uncertainty, Oil Shock. Non-technical Summary This paper investigates the heterogeneity in firm-level responses to aggregate economic shocks, de-parting from traditional models that impose linear constraints on the effects of firm characteristics. Usingan advanced machine learning methodology - specifically, the Generalized Random Forest (GRF) devel-oped by Athey et al. (2019) - the study analyzes a comprehensive dataset of U.S. firms spanning from1990 to 2019. In contrast to conventional linear panel models, which assume a direct, proportional rela-tionship between firm attributes (such as size, leverage, liquidity, and industry scope) and their sensitivityto macroeconomic fluctuations, the GRF framework enables the detection of complex, nonlinear interac-tions among these characteristics. This methodological innovation permits a more flexible estimation ofhow firms respond to various sources of aggregate shocks, including business cycle fluctuations, monetarypolicy shocks, uncertainty shocks, and oil price shocks. The empirical findings indicate that the relationship between firm characteristics and sensitivity toaggregate fluctuations exhibits pronounced nonlinearities. Although average responses estimated by theGRF are broadly similar to those derived from linear models, the distribution of firm sensitivities is con-siderably more moderated under the GRF approach. Specifically, the GRF estimates reveal substantiallylower dispersion and kurtosis, suggesting that traditional linear models may overstate the heterogeneityamong firms. Moreover, the analysis identifies firm size as a dominant determinant of economic weight,with larger firms exhibiting more muted responses to shocks relative to their smaller counterparts.Tobridge firm-level responses with aggregate outcomes, the study develops an aggregation framework thatweights individual firm sensitivities by their economic significance.The results demonstrate that theoverall impact of aggregate shocks is significantly influenced not only by the average firm response butalso by the covariance between firm sensitivities and their respective economic weights.In particular,the presence of large, less-sensitive firms is shown to dampen the aggregate effects of economic shocks,leading to more stable macroeconomic outcomes than those predicted by linear models. In sum, this paper contributes to the literature by highlighting the importance of accounting fornonlinearities and complex interactions in firm behavior. The findings underscore that an accurate un-derstanding of aggregate economic dynamics requires a comprehensive analysis of firm heterogeneity.The insights provided by the GRF methodology have important implications for both policymakers andpractitioners, suggesting that policies designed to stabilize the economy should consider the diverse andnonlinear responses of firms to economic disturbances. By advancing the empirical framework for ana-lyzing firm-level sensitivity, the paper offers a more nuanced perspective on the transmission mechanismsof aggregate shocks, thereby enriching our understanding of macroeconomic dynamics. 1Introduction Firms do not respond uniformly to aggregate fluctuations and shocks. Some adjust sharply to changesin GDP growth and interest rates, while others remain largely unaffected. Studying the cross-sectionalheterogeneity in firm sensitivity to aggregate fluctuations and its underlying drivers provides insights intothe dynamics of aggregate outcomes across different phases of the economic cycle (Cooley and Quadrini,2006; Buera and Moll, 2015).Prior research suggests that firm responses to aggregate shocks dependlinearly on their underlying characteristics, such as