# Breakpoint Analysis for the COVID-19 Pandemic and Its Effect on the Stock Markets

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## Abstract

**:**

## 1. Introduction

## 2. Modeling and Methodology

_{1}related to the health security of country i measured by the global health security (GHS) index for 2019 [37]; ${x}_{2i}={f}_{2}\left({\mathrm{Risk}}_{i}\right)$ is the value of X

_{2;}and ${x}_{3i}={f}_{3}\left({\mathrm{StdRisk}}_{i}\right)$ is the value of X

_{3}, both of them associated with the average risk value and its standard deviation for country i, respectively; and two control variables ${x}_{4i}={f}_{4}\left({\mathrm{OECD}}_{i}\right)$ is the value of X

_{4}, an indicator of whether or not country i belongs to the OECD group; as well as ${x}_{5i}={f}_{5}\left({\mathrm{GDP}}_{i}\right)$ is the value of X

_{5}, which is linked to the gross domestic product (GDP) of country i [35]. Note that the response variable Y is measured as a percentage of the variation in the index between the average of the last three months (Diff3M), or six months (Diff6M), before the structural change and the value of the index as an average after two month of this change—which represents a loss of wealth of the countries present in this study; whereas $\mathrm{Health}$ represents a benchmarking of the health security of 195 countries [37].

## 3. Results of the Study and Model Specification

## 4. Discussions, Conclusions, Limitations, and Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**S&P500 price evolution from 1 June 2019 to 30 May 2020. The vertical line in red corresponds to the estimated date of structural breakdown (9 March 2020).

Country | Index | Country | Index | Country | Index | Country | Index |
---|---|---|---|---|---|---|---|

Australia | Asx 200 | France | * EN 100 | Nigeria | Nse 30 | Serbia | Belex 15 |

Belgium | Bel 20 | Germany | Dax | Norway | Oseax | Slovakia | Sax |

Brazil | Ibov | Hungary | Bux | NZ | Nzx 50 | SK | Kospi 50 |

Bulgaria | Sofix | Italy | Ftse Mib | Pakistan | Kse 100 | Spain | Ibex |

Canada | Tsx | India | Nifty 50 | Peru | Igbvl | SL | Cse |

Chile | Ipsa | IN | Jci | Philippines | Psei | Sweden | Omx 30 |

China | Shanghai | Irak | Isx | Poland | Wig 30 | SW | Smi |

Colombia | Colcap | Iceland | Icexi | Portugal | Psi 20 | Thailand | Set |

Croatia | Crobex | Israel | Ta 100 | Qatar | Qe | Turkey | Xu 100 |

Cyprus | Cymain | Japan | Nikkei 225 | Romania | Bet | Ukraine | Pfts |

Egypt | Egx 70 | Malaysia | Fbm Klci | Russia | Moex | UK | Ftse 100 |

Finland | Hex 25 | Mexico | Mexbol | SA | ** MT 30 | US | S&P500 |

Country | Date | Country | Date | Country | Date | Country | Date |
---|---|---|---|---|---|---|---|

Australia | 03/09/20 | France | 03/09/20 | Nigeria | 03/11/20 | Serbia | 03/12/20 |

Belgium | 03/09/20 | Germany | 03/09/20 | Norway | 03/09/20 | Slovakia | 03/17/20 |

Brazil | 03/04/20 | Hungary | 03/09/20 | NZ | 03/12/20 | SK | 03/12/20 |

Bulgaria | 03/09/20 | Italy | 03/09/20 | Pakistan | 03/16/20 | Spain | 03/09/20 |

Canada | 03/09/20 | India | 03/12/20 | Peru | 03/12/20 | SL | 01/31/20 |

Chile | 03/13/20 | IN | 03/09/20 | Philippines | 03/09/20 | Sweden | 03/09/20 |

China | 03/16/20 | Iraq | 12/18/19 | Poland | 03/09/20 | SW | 03/06/20 |

Colombia | 03/09/20 | Iceland | 03/06/20 | Portugal | 03/09/20 | Thailand | 03/09/20 |

Cyprus | 03/09/20 | Israel | 03/09/20 | Qatar | 03/02/20 | Turkey | 03/09/20 |

Croatia | 03/09/20 | Japan | 03/06/20 | Romania | 03/09/20 | Ukraine | 02/10/20 |

Egypt | 03/16/20 | Malaysia | 03/06/20 | Russia | 03/10/20 | UK | 03/09/20 |

Finland | 03/09/20 | Mexico | 03/09/20 | SA | 03/09/20 | US | 03/09/20 |

Variable | Minimum | Maximum | Mean | Standard Deviation |
---|---|---|---|---|

Health | 25.80 | 83.50 | 54.87 | 13.22 |

Risk | 11,037.89 | 462,453.50 | 106,106.13 | 130,742.35 |

StdRisk | 505.46 | 54,134.31 | 10,521.88 | 12,775.89 |

Diff3M | 1.87 | 34.23 | 16.67 | 7.69 |

Diff6M | 0.47 | 33.96 | 18.34 | 7.44 |

**Table 4.**Parameter estimate and the corresponding standard error (in parenthesis) of the indicated model, as well as statistical indicators of goodness-of-fit (${R}^{2})$ and significance.

Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
---|---|---|---|---|---|---|

Variable | (Diff3M) | (Diff6M) | (Diff3M) | (Diff6M) | (Diff3M) | (Diff6M) |

Health | 0.0618 | 0.0199 | 0.0312 | 0.0125 | 0.0243 | 0.0064 |

(0.141) | (0.145) | (0.149) | (0.154) | (0.150) | (0.155) | |

Log(Risk) | −1.631 | −2.574 | −1.477 | −2.537 | −0.61 | −1.773 |

(3.026) | (3.111) | (3.056) | (3.156) | (3.239) | (3.353) | |

Log(StdRisk) | 1.712 | 2.146 | 1.719 | 2.148 | 0.923 | 1.447 |

(2.215) | (2.276) | (2.23) | (2.303) | (2.433) | (2.519) | |

OECD | 1.806 | 0.437 | 1.36 | 0.0449 | ||

(2.766) | (2.857) | (2.827) | (2.927) | |||

Log(GDP) | 0.463 | 0.408 | ||||

(0.556) | (0.576) | |||||

Constant | 18.37 | 25.6 | 17.36 | 25.35 | 12.49 | 21.06 |

(27.09) | (27.85) | (27.32) | (28.22) | (28.04) | (29.03) | |

${R}^{2}$ | 0.026 | 0.028 | 0.035 | 0.029 | 0.051 | 0.040 |

F-statistic | 0.376 | 0.415 | 0.385 | 0.31 | 0.444 | 0.345 |

Breusch–Pagan test | ||||||

${\chi}^{2}$(1) | 4.10 | 3.92 | 7.10 | 4.60 | 5.29 | 3.68 |

Prob $>{\chi}^{2}$ | 0.0428 | 0.0476 | 0.0077 | 0.0320 | 0.0214 | 0.0551 |

**Table 5.**Parameter estimate and standard error of the indicated model considering heteroscedasticity, as well as statistical indicators of goodness-of-fit (${R}^{2})$ and significance.

Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
---|---|---|---|---|---|---|

Variable | (Diff3M) | (Diff6M) | (Diff3M) | (Diff6M) | (Diff3M) | (Diff6M) |

Health | 0.038 | 0.0203 | −0.00258 | 0.00543 | −0.130 *** | −0.130 *** |

(0.113) | (0.118) | (0.104) | (0.116) | (0.0190) | (0.0275) | |

Log(Risk) | −1.545 | −2.903 | −1.811 | −3.105 | −3.628 *** | −5.336 *** |

(2.744) | (2.946) | (2.588) | (2.900) | (0.403) | (0.584) | |

Log(StdRisk) | 2.481 | 3.535 * | 3.114 * | 3.900 ** | 4.718 *** | 6.035 *** |

(1.877) | (2.010) | (1.718) | (1.897) | (0.266) | (0.386) | |

OECD | 3.367 | 1.924 | 8.157 ** | 7.115 * | ||

(2.325) | (2.47) | (3.44) | (3.796) | |||

Constant | 12.33 | 17.32 | 9.765 | 16.69 | 21.20 *** | 26.65 *** |

(22.9) | (24.7) | (21.14) | (24.30) | (4.992) | (6.518) | |

$\mathbf{Log}\left({\mathit{\sigma}}^{\mathbf{2}}\right)$ | ||||||

Health | −0.018 | −0.0244 | −0.0133 | −0.0165 | 0.00280 | 0.000176 |

(0.0261) | (0.0256) | (0.0261) | (0.0261) | (0.0401) | (0.0441) | |

Log(Risk) | 0.761 | 0.723 | 0.915 | 0.833 | −1.905 * | −1.545 |

(0.586) | (0.575) | (0.624) | (0.608) | (1.055) | (1.083) | |

Log(StdRisk) | −0.342 | −0.439 | −0.608 | −0.566 | 1.549 ** | 1.291 |

(0.472) | (0.445) | (0.493) | (0.462) | (0.780) | (0.786) | |

OECD | −0.847 * | −0.627 | −1.532 ** | −1.235 * | ||

(0.467) | (0.454) | (0.714) | (0.716) | |||

Log(GDP) | −2.253 *** | −2.136 *** | ||||

(0.568) | (0.550) | |||||

Constant | −0.598 | 1.117 | 0.103 | 0.851 | 25.78 *** | 23.13 ** |

(4.978) | (4.997) | (4.918) | (4.958) | (8.948) | (9.030) | |

Likelihood Ratio Test for${Log}\left({\mathit{\sigma}}^{\mathbf{2}}\right)\mathsf{=}\mathsf{0}$ | ||||||

$\mathrm{Prob}>{\chi}^{2}$ | 0.0570 | 0.1180 | 0.0144 | 0.0824 | 0.0000 | 0.0001 |

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**MDPI and ACS Style**

Chahuán-Jiménez, K.; Rubilar, R.; de la Fuente-Mella, H.; Leiva, V.
Breakpoint Analysis for the COVID-19 Pandemic and Its Effect on the Stock Markets. *Entropy* **2021**, *23*, 100.
https://doi.org/10.3390/e23010100

**AMA Style**

Chahuán-Jiménez K, Rubilar R, de la Fuente-Mella H, Leiva V.
Breakpoint Analysis for the COVID-19 Pandemic and Its Effect on the Stock Markets. *Entropy*. 2021; 23(1):100.
https://doi.org/10.3390/e23010100

**Chicago/Turabian Style**

Chahuán-Jiménez, Karime, Rolando Rubilar, Hanns de la Fuente-Mella, and Víctor Leiva.
2021. "Breakpoint Analysis for the COVID-19 Pandemic and Its Effect on the Stock Markets" *Entropy* 23, no. 1: 100.
https://doi.org/10.3390/e23010100