# The Time-Spatial Dimension of Eurozone Banking Systemic Risk

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Econometrics Spatial Model

#### “Spatial” Distance in Finance

## 3. Data

#### Covariates

## 4. Estimation Results

## 5. Spillover Effects on the Real Economy

## 6. The Monetary Policy Impact

#### 6.1. The Classical VECM

#### 6.2. Systemic Risk-Taking Channel

#### 6.2.1. The Colletaz Long-Run Measures

#### 6.2.2. Building a (One) Monetary Policy Stance

#### 6.2.3. Auxiliary Variables

#### 6.2.4. Results

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABS | Asset-Backed Securities |

CDS | Credit Default Swap |

ECB | European Central Bank |

EFSF | European Financial Stability Facility |

ESM | European Stability Mechanism |

ESRB | European Systemic Risk Board |

LTROs | Long-Term Refinancing Operations |

OMT | Outright Monetary Transactions |

SMP | Securities Markets Programme |

SSM | Single Supervisory Mechanism |

TBTF | Too Big To Fail |

TITF | Too Interconnected To Fail |

TLTRO | Targeted Longer-Term Refinancing Operations |

## Appendix A. Event Study Approach

**Figure A1.**Cross-Correlation Matrix: (

**top**) the cross-correlation matrix for raw data; and (

**bottom**) for the full model residuals. Breusch–Pagan LM test of independence: F-statistic: 0.61, p-value: 0.4348. This implies there is no cross-sectional dependence among residuals.

**Figure A4.**Each figure refers to $CAC\widehat{{\rho}_{t}}$ 10 days before and after the event estimate.

**Table A1.**Sample Banks. The table lists the larger banks in the Eurozone in 2012. Source: Bankscope.

Country | Bank Name | Ticker | Size of Bank (USD bn, 2012) | GDP (USD bn, 2012) | %GDP |
---|---|---|---|---|---|

Austria | Erste Group Bank AG | EBS | 282 | 334 | 84 |

Austria | Raiffeisen Zentralbank | RBI | 179 | 334 | 54 |

Belgium | KBC Group | KBC | 339 | 406 | 83 |

France | BNP Paribas | BNP | 2516 | 2189 | 115 |

France | Crédit Agricole | ACA | 2134 | 2189 | 98 |

France | Natixis | KN | 697 | 2189 | 32 |

Germany | Deutsche Bank AG | DBK | 2668 | 2894 | 92 |

Germany | Commerzbank AG | CBK | 839 | 2894 | 29 |

Greece | National Bank of Greece | NBGIF | 138 | 201 | 69 |

Greece | EFG Eurobank Ergasias | EGFEY | 89 | 201 | 45 |

Greece | Alpha Bank | ALPHA | 76 | 201 | 38 |

Ireland | Allied Irish Banks Plc | AIBG | 161 | 184 | 88 |

Ireland | Bank of Ireland Plc | BIRG | 148 | 184 | 80 |

Italy | Unicredit | UCG | 1223 | 1692 | 72 |

Italy | Intesa Sanpaolo | ISP | 888 | 1692 | 53 |

Italy | BPM | BPM | 616 | 1692 | 36 |

Italy | Monte dei paschi di Siena | BMPS | 288 | 1692 | 17 |

Netherlands | ING Group NV | ING | 1538 | 676 | 227 |

Portugal | Banco Commercial Portugues | BCP | 118 | 177 | 67 |

Spain | Banco Santander | SAN | 1675 | 1090 | 154 |

Spain | Banco Bilbao Vizcaya Argentaria | BBVA | 841 | 1090 | 77 |

Spain | CaixaBank | CABK | 459 | 1090 | 42 |

**Table A2.**Panel unit-root test: Levin–Lin–Chu. t-statistics are reported; t* stands for t-statistics significant; *** stands for statistical signiﬁcance at 1%.

Panel Unit-Root Test: Levin–Lin–Chu | Statistics | |
---|---|---|

CDS Spread | Unadjusted t | −1.3 × 10${}^{2}$ |

Adjusted t* | −1.8 × 10${}^{2}$ *** | |

VStoxx | Unadjusted t | − 1.2 × 10${}^{2}$ |

Adjusted t* | −1.5 × 10${}^{2}$ *** | |

Eonia-Euribor | Unadjusted t | −18.91 |

Adjusted t* | −9.203 *** | |

Stock Return | Unadjusted t | −99.66 |

Adjusted t* | −44.61 *** | |

Term Structure | Unadjusted t | −29.36 |

Adjusted t* | −18.63 *** |

**Table A3.**The spatial model results. Estimated parameters and their robust (sandwich) standard errors in parentheses, for the static spatial lag model and the time-varying spatial model, based on Student’s t distributed errors. $\mathbf{W}$ matrix = Spearman correlation matrix of stock return.

Static Model | Time-Varying | |
---|---|---|

$\rho $ | 0.7129 (0.000) | |

$\omega $ | 0.030 (0.009) | |

a | 0.029 (0.107) | |

b | 0.966 (0.021) | |

$log{\sigma}^{2}$ | 1.036 (0.000) | 1.037 (0.000) |

logLik | −51.99 | −51.98 |

**Table A4.**Augmented Dickey–Fuller (ADF) test. T-statistics are reported; *** stands for statistical significance at 1%; the appropriate lag length () for ADF test is selected using Schwarz Bayesian criterion (SC).

Variables | Level | Differences |
---|---|---|

$\widehat{{\rho}_{t}}$ | −2.71 (0) | −12.4 (0) *** |

M2 | −1.98 (0) | −7.33 (0) *** |

MRO | −1.37 (0) | −8.69 (0) *** |

HICP | −1.13 (0) | −9.16 (0) *** |

Null Hypothesis | F-Statistic | Prob. |
---|---|---|

${s}_{r}$ does not Granger Cause $\widehat{{\rho}_{t}}$ | 7.626 | 0.000 |

$\widehat{{\rho}_{t}}$ does not Granger Cause ${s}_{r}$ | 0.686 | 0.506 |

**Table A6.**Significant Event: (−10, +10) days around the event, in which the event is centred. Significance is assessed with a two-sided t-test where the observed changes on announcements days are compared with the corresponding means on non-announcements days; ** denotes statistical significance at 5%, *** denotes statistical significance at 1%.

Events | t-test | |
---|---|---|

5 July 2009 | CBPP I | 6.94 *** |

25 March 2010 | Support to Greece | −3.58 *** |

10 May 2010 | SMP | 6.89 *** |

6 October 2011 | CBPP II | −0.37 |

22 December 2011 | LTRO I | 7.41 *** |

1 March 2012 | LTRO II | −7.11 *** |

27 July 2012 | “Whatever it takes” | 6.98 *** |

2 August 2012 | OMT | −1.67 |

15 October 2014 | CBPP III | −5.43 *** |

19 October 2014 | ABSPP | −2.27 ** |

9 March 2015 | PSPP | −2.11 |

10 March 2016 | TLTRO II and APP | −4.18 *** |

2 June 2016 | New-TLTRO | −0.73 |

TOTAL Effect | 4.76 *** |

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1 | We are well aware that the parameter is not the “right definition” measure of systemic risk because we do not consider important variables such as balance sheet data. Nevertheless, in our framework, the systemic risk arises from the systematic risk component and the contagion risk component that is modelled. As in the work by Blasques et al. (2016), we interpret the spatial parameter as a measure of a change in systemic risk that associates to the interconnectedness of the system as the unconditional correlation measures in the spirit of Forbes and Rigobon (2002). In the remainder of this study, for simplicity, we use the terms contagion and systemic risk as synonymous, although the two definitions are quite different. |

2 | In addition, we use an event study approach to examine the impact of significant monetary policy events as reflected in a change in CDS spreads (see Appendix A). |

3 | See Kireyev and Leonidov (2015) for a review of the financial network. |

4 | For an exhaustive and complete exposition of the CDS market see Angelini (2012) and its determinants Ericsson et al. (2009). |

5 | The spatial autocorrelation coefficient is bound to $\rho <1$ for standardised weighting matrices. |

6 | ${p}_{e}$ represents the Student’s t distribution where $\lambda $ is the degrees of freedom parameter. |

7 | For details, visit www.gasmodel.com, which provides a general framework for modelling time variation in parametric models. |

8 | Following Blasques et al. (2016), we adopt unit scaling, i.e., ${S}_{t}=1$ such that ${s}_{t}={\nabla}_{t}$. In addition, we assume that the inverse matrix $Z={({I}_{n}-\rho W)}^{-1}$ exists with ${I}_{n}$ as the $n\times n$ identity matrix. We consider the multivariate Student’s t distribution as pertinent to assign the disturbance density ${p}_{e}$. |

9 | We use relative changes (log differences multiplied by 100) of CDS spreads for each bank. We select the CDS spread contract based on five-year senior bond since these obligations are the most liquid (Meng and Gwilym (2008)). |

10 | See Appendix A Table A2. |

11 | Table A3 in Appendix A reports the results with a stock correlation weighted matrix. |

12 | To validate this result, we have applied the Vuong test following Engle (2016). The Voung test (=3.28) suggests significant improvement using time-varying $\rho $. The results from residual diagnostic are shown in Appendix A (see Figure A1). |

13 | In addition, in 2009, Greece reached its highest (negative) deficit level. In addition, in 2011, Greece self-proclaimed a much larger than expected fiscal deficit. This event spread to a series of downgrades, financial market turbulence, affecting the other countries members, as well as other financial systems. |

14 | For more details of ECB monetary policy during the Eurozone crisis, please see “The crisis response in the euro area”, a speech by Peter Praet, Member of the Executive Board of the ECB, at the afternoon session “The Challenges Ahead” at Pioneer Investments’ Colloquia Series “Redrawing the Map: New Risk, New Reward” organised by Unicredit S.p.A., Beijing, 17 April 2013. |

15 | Clare Distinguished Lecture in Economics and Public Policy by Jean-Claude Trichet, President of the ECB organised by the Clare College, University of Cambridge, 10 December 2009. Defining and Measuring Systemic Risk, Charles Wyplosz, ECB Supervision. |

16 | We apply interpolation methodology following Litterman and Weiss (1983). |

17 | The lag is chosen using three criteria information: AIC, BIC and HQC. According to these, the appropriate number of lags is 1. |

18 | See Dufour and Taamouti (2010) for mathematical derivation of the model. |

19 | To ensure the robustness of the analysis, we applied the classic Granger test between the shadow measure of monetary policy (${s}_{r}$) and $\widehat{{\rho}_{t}}$. The results (Table A5 in Appendix A) show how monetary policy has an effect on systemic risk and not the other way around, supporting the results from the model of Dufour and Taamouti (2010). |

**Figure 1.**Banks CDS Spread. Plot of the median (red line) CDS spread; blue line indicates the 0.75, while the light blue line indicates 0.25 percentiles.

**Figure 5.**Impulse response. The figure reports 90% bootstrap coverage areas. Bootstrapped confidence intervals are based on 1000 replications.

**Figure 6.**Dashed lines represent the 90% confidence intervals; the values of our measures are between 0 (not significant) and 1. z = GRAI.

**Figure 7.**Dashed lines represent the 90% confidence intervals; the values of our measures are between 0 (not significant) and 1. z = COE.

**Figure 8.**Dashed lines represent the 90% confidence intervals; the values of our measures are between 0 (not significant) and 1. z = ROE.

**Figure 9.**Dashed lines represent the 90% confidence intervals; the values of our measures are between 0 (not significant) and 1. z = LIQ.

**Table 1.**The spatial model results. Estimated parameters and their robust (sandwich) standard errors in parentheses, for the static spatial lag model and the time-varying spatial model, based on Student’s t distributed errors.

Static Model | Time-Varying | |
---|---|---|

$\rho $ | 0.52 (0.003) | |

$\omega $ | 0.0048 (0.000) | |

a | 0.004 (0.000) | |

b | 0.9918 (0.000) | |

${\sigma}^{2}$ | 1.0434 (0.017) | 1.046 (0.014) |

VStoxx | −0.037 (0.004) | −0.04 (0.014) |

E-E | 0.098 (0.011) | 0.01 (0.044) |

Local | ||

Stock Return | −0.05 (0.001) | −0.035 (0.000) |

Term structure | −0.001 (0.000) | −0.005 (0.000) |

const | −0.0002 (0.0004) | −0.0002 (0.0003) |

$\lambda $ | 1.735 (0.016) | 1.738 (0.034) |

logLik/T | −52.00 | −51.88 |

AICc | 120 | 123.76 |

**Table 2.**The table reports the results of the Granger causality; ${\chi}^{2}$ statistics of lagged first differenced term; in parentheses, the p-value.

$\Delta \widehat{{\mathit{\rho}}_{\mathit{t}}}$ | $\Delta \mathit{U}\mathit{R}$ | $\Delta \mathit{G}\mathit{D}\mathit{P}$ | |
---|---|---|---|

$\Delta \widehat{{\rho}_{t}}$ | 0.711 (0.700) | 1.223 (0.542) | |

$\Delta UR$ | 2.369 (0.306) | 5.528 (0.063) | |

$\Delta GDP$ | 9.897 (0.007) | 11.63 (0.003) |

**Table 3.**Johansen and Juselius test. Trace and Max eigenvalue indicate two cointegration equation at 1%; *** indicates the rejection of null hypothesis at 1%.

Hypothesised | Critical Value (5%) | ||
---|---|---|---|

No. of CE(s) | Eigenvalue | Trace | Max |

$r=0$ | 0.334 | 76.06 *** | 37.87 *** |

$r\le 1$ | 0.294 | 38.19 *** | 32.33 *** |

$r\le 2$ | 0.059 | 5.865 | 5.702 |

$r\le 3$ | 0.001 | 0.164 | 0.164 |

**Table 4.**The table reports the results of the Granger causality; ${\chi}^{2}$, statistics of lagged first differenced term; in parentheses, the p-value.

$\Delta \widehat{{\mathit{\rho}}_{\mathit{t}}}$ | $\Delta \mathit{M}2$ | $\Delta \mathit{M}\mathit{R}\mathit{O}$ | $\Delta \mathit{H}\mathit{I}\mathit{C}\mathit{P}$ | ECT (1) | ECT (2) | |
---|---|---|---|---|---|---|

$\Delta \widehat{{\rho}_{t}}$ | 0.083 (0.773) | 3.099 (0.078) | 2.699 (0.101) | −0.464 (0.000) | −0.018 (0.000) | |

$\Delta M2$ | 0.454 (0.500) | 1.584 (0.208) | 3.229 (0.072) | −0.166 (0.784) | −0.071 (0.008) | |

$\Delta MRO$ | 0.8323 (0.3604) | 0.215 (0.645) | 4.536 (0.033) | 0.148 (0.321) | 0.001 (0.924) | |

$\Delta HICP$ | 4.355 (0.036) | 0.283 (0.594) | 0.049 (0.824) | −1.526 (0.001) | −0.051 (0.015) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Foglia, M.; Angelini, E.
The Time-Spatial Dimension of Eurozone Banking Systemic Risk. *Risks* **2019**, *7*, 75.
https://doi.org/10.3390/risks7030075

**AMA Style**

Foglia M, Angelini E.
The Time-Spatial Dimension of Eurozone Banking Systemic Risk. *Risks*. 2019; 7(3):75.
https://doi.org/10.3390/risks7030075

**Chicago/Turabian Style**

Foglia, Matteo, and Eliana Angelini.
2019. "The Time-Spatial Dimension of Eurozone Banking Systemic Risk" *Risks* 7, no. 3: 75.
https://doi.org/10.3390/risks7030075