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The Real Effects of Endogenous Defaults on the Interbank Market

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Abstract

This paper explains the reaction of the interbank market to confidence shocks by means of a micro-founded general equilibrium model with heterogeneous banks. The contribution of the model is threefold: first, it micro-founds the decision problem of banks, by explicitly relating counterparty risk to the issuance of new credit on the interbank market and showing that this channel amplifies the effects of the shocks; second, the model analyses the effects of a pure confidence crisis (i.e. when banks assess that their counterparts on the interbank market are more likely to default despite the fundamentals remain sound) showing that its effects are long-lasting and severe (i.e. a 1% increase in risk generates a contracts GDP by 1.5 bp and investments by 50 bp); third, the model shows that conventional policies to offset a confidence crisis (i.e. monetary policy cannot restore trust on the interbank market and solve the liquidity crisis induced by a confidence shock induces).

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Notes

  1. See Albertazzi et al. (2009), Gorton (2009) and Affinito and Piazza (2018).

  2. See also Delli Gatti (2012) , Guillen (2011), Allen et al. (2009).

  3. See Dib (2010), Hilberg and Hollmayr (2011), Carrera and Vega (2012), Takamura (2013).

  4. In a nutshell, lending banks stop issuing credit on the interbank market when risk-weighted returns on interbank loans become lower than the opportunity cost of capital.

  5. Iyer et al. (2014), Cignano et al. (2016) and Barone et al. (2016) provide empirical evidence of this phenomenon after the GFC.

  6. See Gertler and Kiyotaki (2010), Phelan and Townsend (1991) and Meeks et al. (2017).

  7. Further proofs and derivations are reported in the Online Appendix.

  8. As there is perfect competition, profits are defined as returns on the invested capital, there are no “extra profits”.

  9. See Calvo (1983).

  10. It is assumed that bankers act in the interest of households: maximizing end of period net worth they maximize the funds that can be transferred to households in case the bank closes.

  11. This is a common way to model agency problems between lenders and borrowers, see Kiyotaki and Moore (1997), Krishnamurthy (2003) and Fostel and Geanakoplos (2009).

  12. It will be shown later that the interest rate on deposits is equal to the riskless rate.

  13. \(\Pi _{t}=\Pi _{t}^{B}+\Pi _{t}^{F}\), with \(\Pi ^{B}\) the dividends of banks and \(\Pi ^{F}\) the profits of firms.

  14. Which is \(C_{t}+D_{h,t+1}+\frac{T_{t}}{P_{t}}\le \frac{W_{t}}{P_{t}}L_{t}+\frac{\Pi _{t}}{P_{t}}+\frac{R_{t}^{D}D_{h,t}}{P_{t}}\).

  15. Notice that \(\frac{1}{X_t}\) is the real price of wholesale goods.

  16. Notice that this setting prevents the insurgence of a agency problem between bankers and entrepreneurs la Bernanke et al. (1999).

  17. Dixit and Stiglitz (1977).

  18. See Online Appendix B.1 for a complete derivation.

  19. With \(f^{\prime }\left( \bullet \right) >0\), \(f^{\prime \prime }\left( \bullet \right) <0\) and \(f\left( 0\right) =0\). This production function allows for physical adjustment costs in the production of new capital following Kiyotaki and Moore (1997).

  20. Notice that new capital is sold only on areas with new investment opportunities, therefore the superscript i. See Gertler and Kiyotaki (2010) for a detailed discussion.

  21. Banks choose ex ante the level of deposits; therefore it is rational to choose a weighted average between the optimal value in the i and n state of the world.

  22. The shock is modeled following Bernanke et al. (1999), Angeloni and Faia (2009) and Diamond and Rajan (2001).

  23. This is a common assumption in macro-finance models, as banks are financially constrained retaining earnings makes them less constrained and boosts profits. See Gertler and Karadi (2011) or Gertler and Kiyotaki (2010).

  24. This is the simplest configuration of Gertler and Kiyotaki (2010) which is preferable in this setting to maintain tractability and focus on interbank risk.

  25. Notice that interbank loans are an asset for lending banks and a liability for borrowing banks.

  26. For more details see Moody’s (2009).

  27. An alternative approach would be to use macro-priors following Lombardi and Nicoletti (2012); in this case the standard approach is used which is also consistent with the variables selected.

  28. See Online Appendix B.5 for a complete derivation.

  29. For the truncaed sample, the MCMC algorithm needs 2 million draws to converge, so each chain has 2 million iterations.

  30. Full IRFs for all variables and shocks are reported in the Online Appendix C.

  31. See Figures C.IX and C.VIII of the Online Appendix C.

  32. These IRFs are reported in in Figure C.VII in the Online Appendix C.

  33. Firms may maintain the same level of production substituting capital with labor. This, however, increases the marginal cost of production and therefore prices as the combination of inputs is less efficient.

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  1. European Central Bank, Frankfurt-am-Main, Germany

    Massimo Minesso Ferrari

  2. Catholic University of Milan, Milan, Italy

    Massimo Minesso Ferrari

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I am grateful to Domenico Delli Gatti, Gianluca Femminis, Alessandro Flamini, Giovanni Lombardo, Maria Sole Pagliari, Justine Pedrono, Patrizio Tirelli and participants at seminars at the Catholic University of Milan and the Bicocca University of Milan.

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Minesso Ferrari, M. The Real Effects of Endogenous Defaults on the Interbank Market. Ital Econ J 6, 411–439 (2020). https://doi.org/10.1007/s40797-019-00104-0

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