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Model-based indicators for the identification of cyclical systemic risk


The credit-to-GDP gap, as proposed by the Basel methodology, is the reference measure for the activation of the Countercyclical Capital Buffer. However, most of the countries implementing this instrument in recent years are not following its signals due to the large downward biases that it is presenting after the last financial crisis that do not reflect properly the current macrofinancial environment. In this context, credit gap measures that incorporate economic fundamentals may provide more accurate signals of cyclical systemic risk. We propose two alternative model-based indicators that account for these factors. We assess their performance using time series data from the 1970s for six European countries and compare them to the Basel gap. We find that our proposed models provide more accurate early warning signals of the build-up of cyclical systemic risk than the Basel gap, as well as lower biases after rapid changes in fundamentals. Furthermore, we identify the model specifications that are optimal for each of the countries considered. Our flexible approach can easily accommodate national specificities, which are key to maximize the performance of the models.

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  1. EU Regulation 575/2013 and EU Directive 2013/36/EU.

  2. Recommendation ESRB/2014/1.

  3. For instance, in Spain, although bank credit to households has been much related to crises, the key trigger in the past has been mainly credit to real estate companies.

  4. In addition, adding this constraint improves the identification of the parameters in the estimation.

  5. Previous studies have identified financial cycles to follow AR(2) processes and to be a fair assumption for modelling credit gaps (Rünstler and Vlekke 2017; Lang and Welz 2018). In general, this is derived from the standard assumption in the literature on measuring output gaps where output is modelled as a local linear trend with an AR(2) component for the cycle (see Clark, 1987).

  6. A general state-space model can be specified as: \( y_{t} = \varvec{Dz}_{t} + \varvec{Ez}_{t} + \varvec{v}_{t} ; \varvec{z}_{t} = \varvec{Az}_{t} + \varvec{Bx}_{t} + \varepsilon_{t} ; \varvec{v}_{t} \sim N\left( {0,\varvec{R}} \right);\varepsilon_{t} \sim N\left( {0,\varvec{Q}} \right), \) where \( \varvec{y}_{t} \) represents the observation equations and \( \varvec{z}_{t} \) represents the state equations; \( \varvec{w}_{t} \) and \( \varvec{x}_{t} \) represent vectors of exogenous variables; \( \varvec{v}_{t} \) and \( \varepsilon_{t} \) are error terms assumed to be zero mean, normally distributed and serially uncorrelated; and \( \varvec{R} \) and \( \varvec{Q} \) represent the covariance matrixes of the error terms..

  7. This definition is similar in spirit to the leverage gap in Juselius et al. (2017), who argue that this cointegrating relation may identify a long-run equilibrium for the credit-to-GDP ratio. Nonetheless, the authors do not assess the early warning performance of this gap given that the aim of the study is to assess implications of monetary policy. Interestingly, the authors also propose a second cointegrating relation with respect to the lending rate on outstanding debt. However, this relation, which is intended to capture a debt service gap, is found to be useful to characterize the recovery phase of the financial cycle given that it is more related to contemporaneous signals of materialization of systemic risk than to the build-up of cyclical vulnerabilities.

  8. The following country abbreviations are used in tables and figures: France (FR), Germany (DE), Italy (IT), Spain (ES), the Netherlands (NL) and the UK (UK).

  9. Table A2 in Annex presents the results of the lags and the trace statistics for determining the number of cointegrating relations. It is also worth mentioning that after applying the Dickey–Fuller GLS test for the presence of unit roots, variables are identified to be integrated of order one in levels for all countries. Additionally, eigenvalues stability conditions are checked after estimations, the greatest modulus is also reported, where all values are found to be strictly lower than 1. This suggests that the number of cointegrating equations is not misspecified and that they are stationary. Finally, the table includes the likelihood ratio test of identifying restrictions. Results suggest that restrictions are valid in all the cases.

  10. Time windows from 5 to 16 and from 5 to 20 quarters ahead of systemic events are also assessed, and results are found to be robust in terms of the comparison between models.

  11. Germany presents the lowest dispersion of the credit-to-GDP ratio during the whole sample period (see Annex 1), and the same is true for the Netherlands after the launch of the monetary union.


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We thank Mikael Juselius and the colleagues of the working groups of the European Central Bank where this study has been discussed for their useful comments and suggestions. We are also grateful to the participants of the internal research seminar at Banco de España, the Joint BdP/ECB/ESRB Workshop 2018 on Advances in Systemic Risk Analysis and the International Finance and Banking Society Conference Chile 2018, for the useful comments received.

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Correspondence to Jorge E. Galán.

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See Tables 8, 9.

Table 8 Summary statistics by country
Table 9 Pre- and post-estimation tests of VEC models

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Galán, J.E., Mencía, J. Model-based indicators for the identification of cyclical systemic risk. Empir Econ 61, 3179–3211 (2021).

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  • Credit imbalances
  • Cyclical systemic risk
  • Early warning models
  • Macroprudential policy
  • Model-based indicators

JEL Classification

  • C32
  • E32
  • E58
  • G01
  • G28