识别关系层级效应：使用协方差约束

Identifying relationship-level effectsusing covariance restrictions Olivier De Jonghe, Daniel Lewis Challenges for Monetary Policy Transmission in a Changing World Network (ChaMP) This paper contains research conducted within the network “Challenges for Monetary Policy Transmission in a Changing WorldNetwork” (ChaMP). It consists of economists from the European Central Bank (ECB) and the national central banks (NCBs) of theEuropean System of Central Banks (ESCB). ChaMP is coordinated by a team chaired by Philipp Hartmann (ECB), and consisting of Diana Bonfim (Banco de Portugal), MargheritaBottero (Banca d’Italia), Emmanuel Dhyne (Nationale Bank van België/Banque Nationale de Belgique) and Maria T. Valderrama(Oesterreichische Nationalbank), who are supported by Melina Papoutsi and Gonzalo Paz-Pardo (both ECB), 7 central bank advisersand 8 academic consultants. ChaMP seeks to revisit our knowledge of monetary transmission channels in the euro area in the context of unprecedented shocks,multiple ongoing structural changes and the extension of the monetary policy toolkit over the last decade and a half as well as the recentsteep inflation wave and its reversal. More information is provided on its website. Abstract We propose a new model in which relationship-specific effects or shocks are identifiedin a bipartite network under mild covariance restrictions, generalizing the influentialAbowd et al. (1999) framework. For example, separate demand shocks are identified foreach bank from which a firm borrows. We show how previous approaches break downwhen confronted with such heterogeneity, while our novel identification strategy yields asimple estimator that is consistent and asymptotically normal, under weaker networkdensity assumptions than previous approaches.The methodology performs well inempirically-calibrated simulations. We apply our approach to identify relationship-levelcredit demand and supply shocks for thousands of firms and banks across nine Euro-area countries and three distinct economic episodes. We formally reject the Abowd etal. (1999) assumptions in nearly every country-period and show that within-firm/bankshock variation is of comparable scale to between firm/bank variation. We documentconsiderable bias in Abowd et al. (1999) style estimates and associated regressions,while finding significant deleterious effects of the post-2022 monetary contraction onexposed firms. We highlight novel heterogeneity in the transmission of monetary policy. Keywords:networks, two-way fixed effects, supply shock, demand shock, corporate credit,identification, higher moments, networksJEL codes:C33, C58, E44, G21, G30 Non-Technical Summary Many important questions in economics concern how outcomes are shaped by a specificre-lationshipbetween two parties: the wage a worker earns at a particular firm, the price aconsumer pays to a particular retailer, the volume of credit a firm obtains from a particularbank. In each case, the observed outcome reflects contributions from both sides of the rela-tionship – the worker’s productivity and the firm’s pay policy, the consumer’s preferences andthe retailer’s pricing, the firm’s creditworthiness and the bank’s lending conditions.Sepa-rating these two-sided effects is central to empirical work across labour economics, industrialorganization, international trade, and finance. The dominant tool for this separation is the two-way fixed effects estimator, introducedby Abowd et al. (1999) – henceforth AKM – and since applied to a vast range of settingsinvolving bipartite networks, that is, networks in which two distinct types of agents formrelationships with one another but not with agents of their own type. AKM decomposes theobserved outcome into an effect attributed to one side and an effect attributed to the other.This approach assumes that each agent’s effect isthe same across all of its relationships. Aworker is assumed to bring identical productivity regardless of which firm employs her; a firmis assumed to have homogeneous credit demand across banks. This homogeneity assumptionis both conceptually restrictive and, as we show, empirically untenable. The contribution of this paper is twofold.First, we develop a new econometric frame-work applicable to any bipartite network setting in which two outcome variables are jointlyobserved for each relationship.The core goal is to decompose this pair of outcomes intotwo underlying structural shocks – one associated with each side of the market – at thelevel of the individual relationship, rather than at the level of the agent.We explain thismethodology in the context of corporate credit markets, where the two outcomes are loanquantities and interest rates, and the two structural objects of interest are credit demandand supply. In this setting, rather than assigning a single demand shock to each firm (as ifits demand were the same across all its lenders) or a single supply shock to each bank (asif its supply conditions were the