Identifying relationship-level effects using covariance restrictions

We propose a new model in which relationship-specific e!ects or shocks are identified in a bipartite network under mild covariance restrictions, generalizing the influential Abowd et al. (1999) framework. For example, separate demand shocks are identified for each bank from which a firm borrows. We show how previous approaches break down when confronted with such heterogeneity, while our novel identification strategy yields a simple estimator that is consistent and asymptotically normal, under weaker network density assumptions than previous approaches. The methodology performs well in empirically-calibrated simulations. We apply our approach to identify relationship-level credit demand and supply shocks for thousands of firms and banks across nine Euroarea countries and three distinct economic episodes. We formally reject the Abowd et al. (1999) assumptions in nearly every country-period and show that within-firm/bank shock variation is of comparable scale to between firm/bank variation. We document considerable bias in Abowd et al. (1999) style estimates and associated regressions, while finding significant deleterious e!ects of the post-2022 monetary contraction on exposed firms. We highlight novel heterogeneity in the transmission of monetary policy