Identifying relationship-level effects using covariance restrictions

We propose a new model in which relationship-specific effects 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 Euro-area 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 effects of the post-2022 monetary contraction on exposed firms. We highlight novel heterogeneity in the transmission of monetary policy.