# The Incidence of Spillover Effects during the Unconventional Monetary Policies Era

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. A Brief Overview of the ECB’s Unconventional Monetary Policy

## 3. The Multiplicative Error Model

#### 3.1. The MS-AMEMX

## 4. Empirical Application

#### 4.1. The Dataset

#### 4.2. Estimation Results

#### 4.3. Out-of-Sample Analysis

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | |

2 | The program—consisting of outright transactions of government bond with a maturity up to 3 years in the secondary market—was never implemented because of the tight conditions it required. In particular, according to the “conditionality condition”, a Eurozone country could have requested for entry in the program if it had been in serious and blatant macroeconomic distress. |

3 | It concerned corporate bonds issued by companies different from credit institutions with a minimum BBB rating and a remaining maturity between 6 months and 30 years. |

4 | Including both central and local government bonds. |

5 | In any case, the program will last up to the end of March 2022. |

6 | Given this assumption, the error term has a unit conditional mean, whereas its variance is equal to $\frac{1}{\theta}$. |

7 | Actually, this condition for stationarity could be considered too strong. Indeed, Gallo and Otranto (2018) show how—given the properties of stationarity and ergodicity of the MS GARCH model (Francq et al. (2001))—the necessary condition for the MS-AMEM to be stationary and ergodic is $\sum _{{s}_{t}=1}^{n}{\pi}_{{s}_{t}}E[log({\alpha}_{{s}_{t}}+{\gamma}_{{s}_{t}}{D}_{t}){\u03f5}_{t}+{\beta}_{{s}_{t}}]<0$, where ${\pi}_{{s}_{t}}({s}_{t}=1\dots n)$ represents the ergodic probability of each regime. |

8 | Given that in the MEM framework one does not need to resort to logs, the GJR–GARCH model should be preferred to other GARCH specifications such as the EGARCH. As regards other specifications, the GJR-GARCH coincides with the TGARCH (Zakoian 1994) when the squared variables are considered. |

9 | All the data are provided by the Oxford Man’s Institute: https://realized.oxford-man.ox.ac.uk/data/download. |

10 | Quantitative data are available at: https://www.ecb.europa.eu/stats/policy_and_exchange_rates/minimum_reserves/html/index.en.html. |

11 | Information on monetary policy announcements is available at: https://www.ecb.europa.eu/press/pr/activities/mopo/html/index.en.html. |

12 | In particular, on these days, the value of the $R{V}^{S\&P500}$ belongs to the last percentile of the series. |

13 | As given by $\alpha +\beta +\gamma /2$. |

14 | The smoothed probabilities are defined as an ex post measure of how likely the volatility process is in a certain state at time t, given the full information set (Hamilton 1994, chp. 22). |

15 | Estimation results obtained from the two sub-samples are available upon request. In general, results do not change significantly, with coefficients (${\rho}_{{s}_{t}}$ and $\delta $, in particular) that are still significant and enter the model with the expected sign. We interpret this result as a robustness check about the sensitivity of the estimated coefficients. |

16 | This conclusion is supported by the fact that, by estimating our model through the ECB’s total asset growth as a proxy for the balance sheet size, we obtain a non-significant coefficient. Estimation results are available upon request. |

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**Figure 1.**CAC40, DAX30, FTSEMIB and IBEX35 Realized Volatility. Sample period: 1 June 2009 to 31 December 2020. The vertical lines represent relevant events (see the text) causing spikes in the $R{V}^{S\&P500}$ (red dashed lines) and ECB monetary policy announcement days (blue dashed lines).

**Figure 2.**ECB’s Balance Sheet composition (millions of Euro). Sample period: 1 June 2009–31 December 2020. Source: European Central Bank.

**Figure 3.**CAC40, DAX30, FTSEMIB and IBEX35 Realized Volatility (black line); red points represents the high volatility regime probability (in blue, high-volatility regime in correspondence with some important events, see text). Sample period: 1 June 2009 to 31 December 2019.

**Figure 4.**CAC40, DAX30, FTSEMIB and IBEX35 realized (black line) and fitted (gray line) volatility. Sample period: 1 June 2009 to 31 December 2019.

**Figure 5.**CAC40, DAX30, FTSEMIB and IBEX35 realized (black line), forecasted (red line) volatility and high regime forecasted probability. Estimation period: 1 June 2009 to 31 December 2019. Forecasting period: 1 January 2020 to 31 December 2020.

**Table 1.**Descriptive statistics for CAC40, DAX30, FTSEMIB, IBEX35 Realized Volatility. Sample period: 1 June 2009 to 31 December 2020.

CAC40 | DAX30 | FTSEMIB | IBEX35 | |
---|---|---|---|---|

Mean | 14.16 | 14.369 | 15.569 | 17.024 |

Min | 1.102 | 2.141 | 1.578 | 2.974 |

Max | 106.37 | 89.92 | 97.699 | 148.61 |

St.Dev. | 8.616 | 8.031 | 8.243 | 9.768 |

Skewness | 3.106 | 2.761 | 2.458 | 3.379 |

Kurtosis | 18.797 | 14.823 | 11.432 | 24.285 |

N. observations | 2882 | 2853 | 2857 | 2877 |

**Table 2.**Model Estimation results from the AMEM (robust s.e. in parenthesis) and p-values for the Ljung–Box statistics. Estimation period: 1 June 2009–31 December 2019. Dependent Variable: Realized Volatility.

CAC40 | DAX30 | FTSEMIB | IBEX35 | |
---|---|---|---|---|

$\omega $ | 0.920 | 0.957 | 1.224 | 1.092 |

(0.198) | (0.249) | (0.291) | (0.243) | |

$\alpha $ | 0.188 | 0.119 | 0.286 | 0.236 |

(0.026) | (0.225) | (0.028) | (0.028) | |

$\beta $ | 0.69 | 0.693 | 0.594 | 0.662 |

(0.032) | (0.024) | (0.035) | (0.034) | |

$\gamma $ | 0.104 | 0.092 | 0.074 | 0.066 |

(0.013) | (0.011) | (0.011) | (0.012) | |

$\theta $ | 7.474 | 9.795 | 10.807 | 9.113 |

(0.256) | (0.542) | (0.509) | (0.342) | |

p-values for Ljung-Box statistics | ||||

Ljung–Box 1 | 0.019 | 0.053 | 0.105 | 0.002 |

Ljung–Box 5 | 0.08 | 0.023 | 0.723 | 0.017 |

Ljung–Box 10 | 0.118 | 0.008 | 0.871 | 0.102 |

**Table 3.**Model Estimation results from the AMEMX (robust s.e. in parenthesis) and p-values for the Ljung–Box statistics. Estimation period: 1 June 2009–31 December 2019. Dependent Variable: Realized Volatility.

CAC40 | DAX30 | FTSEMIB | IBEX35 | |
---|---|---|---|---|

$\omega $ | 1.358 | 1.136 | 1.876 | 1.739 |

(0.264) | (0.294) | (0.37) | (0.232) | |

$\alpha $ | 0.156 | 0.178 | 0.286 | 0.215 |

(0.024) | (0.022) | (0.025) | (0.028) | |

$\beta $ | 0.633 | 0.666 | 0.517 | 0.611 |

(0.041) | (0.029) | (0.041) | (0.043) | |

$\gamma $ | 0.112 | 0.091 | 0.074 | 0.072 |

(0.013) | (0.011) | (0.012) | (0.012) | |

$\rho $ | 0.069 | 0.036 | 0.052 | 0.047 |

(0.018) | (0.013) | (0.014) | (0.014) | |

$\delta $ | −0.853 | −0.448 | −1.337 | −1.305 |

(0.21) | (0.183) | (0.316) | (0.282) | |

$\phi $ | 1.48 | 1.104 | 2.228 | 2.042 |

(0.453) | (0.373) | (0.493) | (0.494) | |

$\theta $ | 7.74 | 9.991 | 11.371 | 9.513 |

(0.252) | (0.524) | (0.492) | (0.351) | |

p-values for Ljung-Box statistics | ||||

Ljung–Box 1 | 0.335 | 0.188 | 0.813 | 0.052 |

Ljung–Box 5 | 0.324 | 0.087 | 0.899 | 0.073 |

Ljung–Box 10 | 0.086 | 0.006 | 0.517 | 0.232 |

**Table 4.**Model Estimation results from the MS-AMEMX (robust s.e. in parenthesis) and p-values for the Ljung–Box statistics. Estimation period: 1 June 2009–31 December 2019. Dependent Variable: realized volatility.

CAC40 | DAX30 | FTSEMIB | IBEX35 | |
---|---|---|---|---|

$\omega $ | 1.103 | 0.705 | 1.436 | 1.396 |

(0.184) | (0.109) | (0.239) | (0.242) | |

$\alpha $ | 0.139 | 0.172 | 0.279 | 0.155 |

(0.02) | (0.018) | (0.025) | (0.029) | |

$\beta $ | 0.677 | 0.701 | 0.551 | 0.689 |

(0.037) | (0.027) | (0.04) | (0.041) | |

$\gamma $ | 0.113 | 0.088 | 0.069 | 0.073 |

(0.011) | (0.008) | (0.01) | (0.009) | |

${\rho}_{0}$ | 0.047 | 0.038 | 0.043 | 0.01 |

(0.016) | (0.011) | (0.014) | (0.019) | |

${\rho}_{1}$ | 0.182 | 0.278 | 0.214 | 0.241 |

(0.11) | (0.119) | (0.081) | (0.069) | |

$\delta $ | −0.737 | −0.251 | −0.948 | −1.047 |

(0.158) | (0.102) | (0.206) | (0.209) | |

$\phi $ | 1.061 | 0.641 | 1.717 | 1.342 |

(0.387) | (0.305) | (0.398) | (0.374) | |

${\theta}_{0}$ | 9.14 | 11.288 | 14.406 | 13.228 |

(0.513) | (0.429) | (1.338) | (1.105) | |

${\theta}_{1}$ | 2.879 | 0.769 | 3.124 | 8.403 |

(0.909) | (0.785) | (1.888) | (1.259) | |

${p}_{00}$ | 0.969 | 0.994 | 0.955 | 0.844 |

(0.032) | (0.005) | (0.038) | (0.086) | |

${p}_{11}$ | 0.583 | 0.286 | 0.33 | 0.252 |

(0.381) | (0.238) | (0.201) | (0.154) | |

p-values for Ljung-Box statistics | ||||

Ljung–Box 1 | 0.417 | 0.529 | 0.875 | 0.004 |

Ljung–Box 5 | 0.369 | 0.977 | 0.855 | 0.015 |

Ljung–Box 10 | 0.424 | 0.994 | 0.977 | 0.127 |

**Table 5.**(

**a**) Spillover effect $({\rho}_{{s}_{t}}\xb7R{V}_{t}^{S\&P500})$, (

**b**) unconventional policy effect $(\delta \xb7{\frac{UMP}{TA}}_{t})$ and (

**c**) net effect (

**a**,

**b**) from the MS-AMEMX.

(a) | Spillover Effect | ||
---|---|---|---|

Full Sample | Sub-Sample | Sub-Sample | |

2009–2014 | 2015–2019 | ||

CAC40 | 0.542 | 1.105 | 0.452 |

DAX30 | 0.412 | 0.574 | 0.469 |

FTSEMIB | 0.5 | 0.844 | 0.507 |

IBEX35 | 0.268 | 0.46 | 0.475 |

(b) | Unconventional Policy Effect | ||

Full Sample | Sub-Sample | Sub-Sample | |

2009–2014 | 2015–2019 | ||

CAC40 | −0.212 | −0.12 | −1.248 |

DAX30 | −0.072 | −0.002 | −0.852 |

FTSEMIB | −0.273 | 0.003 | −0.934 |

IBEX35 | −0.301 | −0.121 | −1.53 |

(c) | Net Effect | ||

Full Sample | Sub-Sample | Sub-Sample | |

2009–2014 | 2015–2019 | ||

CAC40 | 0.33 | 0.985 | −0.795 |

DAX30 | 0.34 | 0.572 | −0.383 |

FTSEMIB | 0.227 | 0.841 | −0.428 |

IBEX35 | −0.033 | 0.339 | −1.055 |

**Table 6.**Models comparison (best model in bold) through the Information Criteria (AIC and BIC) and forecasting capability (MSE and QLike loss functions). Sample period: 1 June 2009–31 December 2019.

CAC40 | DAX30 | |||||
---|---|---|---|---|---|---|

AMEM | AMEMX | MS-AMEMX | AMEM | AMEMX | MS-AMEMX | |

LogLik | −7712.012 | −7663.943 | −7627.295 | −7365.365 | −7338.932 | −7254.689 |

AIC | 5.853 | 5.819 | 5.794 | 5.643 | 5.626 | 5.564 |

BIC | 5.864 | 5.837 | 5.821 | 5.655 | 5.643 | 5.591 |

MSE | 30.357 | 29.222 | 29.481 | 23.847 | 23.352 | 23.17 |

QLIKe | 0.068 | 0.066 | 0.066 | 0.052 | 0.051 | 0.052 |

FTSEMIB | IBEX35 | |||||

AMEM | AMEMX | MS-AMEMX | AMEM | AMEMX | MS-AMEMX | |

LogLik | −7514.834 | −7446.347 | −7373.76 | −7970.565 | −7911.763 | −7860.52 |

AIC | 5.749 | 5.699 | 5.647 | 6.065 | 6.023 | 5.987 |

BIC | 5.76 | 5.717 | 5.674 | 6.076 | 6.041 | 6.014 |

MSE | 28.327 | 27.47 | 27.817 | 42.957 | 41.452 | 41.859 |

QLIKe | 0.047 | 0.045 | 0.045 | 0.056 | 0.053 | 0.054 |

**Table 7.**t-statistics and p-value of the Diebold–Mariano test. ${H}_{0}:$ MSE (model 1) = MSE (model 2); ${H}_{a}:$ MSE (model 1) < MSE (model 2). In bold, p-values < 0.1. Sample period: 1 June 2009–31 December 2019. Forecasting period: 1 January 2020 to 31 December 2020.

CAC40 | DAX30 | |||
---|---|---|---|---|

Model 1/Model 2 | t-Statistics | p-Value | t-Statistics | p-Value |

AMEM/AMEMX | 1.999 | 0.023 | 1.792 | 0.037 |

AMEM/MS-AMEMX | 1.349 | 0.089 | 0.846 | 0.199 |

AMEMX/MS-AMEMX | 0.307 | 0.379 | -0.035 | 0.514 |

FTSEMIB | IBEX35 | |||

Model 1/Model 2 | t-Statistics | p-Value | t-Statistics | p-Value |

AMEM/AMEMX | 1.548 | 0.062 | 2.233 | 0.013 |

AMEM/MS-AMEMX | 1.355 | 0.088 | 1.328 | 0.093 |

AMEMX/MS-AMEMX | 0.967 | 0.167 | 0.752 | 0.226 |

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**MDPI and ACS Style**

Lacava, D.; Scaffidi Domianello, L.
The Incidence of Spillover Effects during the Unconventional Monetary Policies Era. *J. Risk Financial Manag.* **2021**, *14*, 242.
https://doi.org/10.3390/jrfm14060242

**AMA Style**

Lacava D, Scaffidi Domianello L.
The Incidence of Spillover Effects during the Unconventional Monetary Policies Era. *Journal of Risk and Financial Management*. 2021; 14(6):242.
https://doi.org/10.3390/jrfm14060242

**Chicago/Turabian Style**

Lacava, Demetrio, and Luca Scaffidi Domianello.
2021. "The Incidence of Spillover Effects during the Unconventional Monetary Policies Era" *Journal of Risk and Financial Management* 14, no. 6: 242.
https://doi.org/10.3390/jrfm14060242