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Identifying Relationship-level Effects Using Covariance Restrictions

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  • De Jonghe, Olivier
  • Lewis, Daniel

Abstract

We propose a novel decomposition to identify relationship-specific effects or shocks in a bipartite network under covariance restrictions. We show existing two-way fixed effects decompositions are ill-suited to correlations consistent with realistic heterogeneity. Our strategy yields a simple consistent estimator. We estimate relationship-level credit demand and supply shocks across nine euro-area countries and three episodes. We find evidence demand and supply each have both firm and bank components, and within-firm/bank shock variation is of comparable scale to between-firm/bank variation. Regressions using firm fixed effects as demand controls are at odds with economic theory, while our method uncovers significant deleterious effects of the post-2022 monetary contraction on exposed firms.

Suggested Citation

  • De Jonghe, Olivier & Lewis, Daniel, 2026. "Identifying Relationship-level Effects Using Covariance Restrictions," CEPR Discussion Papers 21400, Centre for Economic Policy Research.
    • Handle: RePEc:cpr:ceprdp:21400
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    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G30 - Financial Economics - - Corporate Finance and Governance - - - General

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