# Long-Lasting Economic Effects of Pandemics:Evidence on Growth and Unemployment

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## Abstract

**:**

## 1. Introduction

## 2. Structural Changes and Long Memory

#### 2.1. Tests for Structural Breaks

#### 2.2. The Fractional Difference Operator

- A process with $d=0$ displays short memory and implies that any shock that affects the series only has repercussions in the short term. Thus, its impact will completely vanish in the long run.
- The process will display long memory for $0<d<1$, and implies that any shock that affects the series has long-lasting repercussions.
- The process will be stationary as long as $d<1/2$.
- The process will revert to its mean as long as $d<1$, but the speed to which it converges could be quite slow.
- Processes with $d>1$ are such that past innovations have permanent effects.

#### 2.3. Semiparametric Estimators of Long Memory

#### 2.4. Tests for Change in Persistence

## 3. Evidence from the United Kingdom

#### 3.1. Data

#### 3.2. Real GDP Per Capita in the UK

#### 3.3. Unemployment in the UK

## 4. International Evidence

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

UK | United Kingdom |

USA | United States of America |

GPH | Geweke and Porter-Hudak log-periodogram regression |

ELW | exact local Whittle estimator |

MR | Martins and Rodrigues methodology |

BP | Bai and Perron methodology |

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**Figure 1.**Real GDP per capita for the UK, 1270–2019 (in logs). Breaks are represented by the vertical black dashed lines, while their confidence intervals at 95% are displayed by blue small intervals in the bottom of the figure. BP methodology with a trimming parameter of $h=0.08$ is executed.

**Figure 2.**Real GDP per capita for the UK, 1645–1800 (in logs). The break is represented by the vertical black dashed line. The counterfactual values are computed by forecasting the linear trend with long memory disturbances estimated in the period associated with the Great Plague of London.

**Figure 3.**UK monthly unemployment rates. Breaks are represented by the vertical black dashed lines, while their confidence intervals at 95% are displayed by blue small intervals in the bottom of the figure. BP methodology with a trimming parameter of $h=0.12$ is executed.

**Figure 4.**Real GDP per capita for Spain, Italy, the Netherlands, and the USA (in logs). Breaks are represented by the vertical black dashed lines, while their confidence intervals at 95% are displayed by blue small intervals in the bottom of the figure.

**Table 1.**Main outbreaks and pandemics in terms of death toll in the UK the respective period. Source: https://en.wikipedia.org/wiki/List_of_epidemics and references therein. ${}^{*}$ The death toll in London alone is estimated to have been of up to 20%.

Period | Outbreaks or Pandemics | Death Toll in the UK | Death Rate in the UK |
---|---|---|---|

1270–1350 | Black Death | Between 112,000 and 270,000 | Between 25% and 60% |

1427–1580 | Small London plagues | ≈40,000 | ≈2% |

1581–1644 | Small London plagues | ≈50,000 | ≈1.5% |

1645–1705 | Great Plague of London ${}^{*}$ | >100,000 | >2% |

1834–1920 | Different cholera outbreaks, | ≈160,000 | ≈1.5% |

Great Pandemic of 1870–1875, | ≈80,000 | ≈0.5% | |

and Russian flu | >100,000 | >0.5% | |

1921–2019 | Spanish flu and remaining | ≈228,000 | ≈1% |

pandemics of the 20th century |

Memory | Autocorrelation Threshold | |||
---|---|---|---|---|

$\mathbf{d}$ | ${\mathbf{10}}^{-\mathbf{1}}$ | ${\mathbf{10}}^{-\mathbf{2}}$ | ${\mathbf{10}}^{-\mathbf{3}}$ | ${\mathbf{10}}^{-\mathbf{4}}$ |

0.1 | 3 | 22 | 367 | >500 |

0.2 | 6 | 220 | >500 | >500 |

0.3 | 41 | >500 | >500 | >500 |

>0.4 | >500 | >500 | >500 | >500 |

**Table 3.**Dates for structural changes detected by the BP methodology in yearly UK real GDP per capita. The confidence intervals are shown below each date.

Estimated date | 1350 | 1426 | 1580 | 1644 | |
---|---|---|---|---|---|

Confidence interval | [1349–1353] | [1425–1444] | [1572–1584] | [1642–1645] | |

Estimated date cont. | 1705 | 1834 | 1920 | ||

Confidence interval cont. | [1704–1709] | [1833–1835] | [1919–1921] |

**Table 4.**Long memory estimates and change of persistence tests for yearly real GDP per capita for the UK. The table presents the estimates by both GPH and ELW methods together with their standard errors. Moreover, it presents the critical values for the MR test for the 90%, 95%, and 99% confidence levels, and the associated MR statistic for the test for change in persistence on either direction from the regime in the row above to the current row.

Period | GPH est. | GPH s.e. | ELW est. | ELW s.e. | MR Test | |||
---|---|---|---|---|---|---|---|---|

90% | 95% | 99% | Stat. | |||||

1270–1350 | 0.466 | 0.144 | 0.507 | 0.086 | ||||

1351–1426 | 0.597 | 0.147 | 0.583 | 0.087 | 5.324 | 6.440 | 8.878 | 3.122 |

1427–1580 | 0.498 | 0.102 | 0.494 | 0.066 | 5.294 | 6.519 | 9.426 | 2.107 |

1581–1644 | 0.589 | 0.161 | 0.606 | 0.093 | 5.288 | 6.497 | 9.335 | 5.155 |

1645–1705 | 0.865 | 0.166 | 0.867 | 0.094 | 5.340 | 6.411 | 8.654 | 5.318 |

1706–1834 | 0.877 | 0.112 | 0.813 | 0.071 | 5.331 | 6.495 | 9.139 | 5.653 |

1834–1920 | 1.084 | 0.138 | 1.080 | 0.083 | 5.248 | 6.460 | 9.305 | 11.116 |

1921–2019 | 1.041 | 0.129 | 1.186 | 0.079 | 5.690 | 7.022 | 10.853 | 7.846 |

**Table 5.**Dates for structural changes detected by the BP methodology in monthly UK unemployment rates. The confidence intervals are shown below each date.

Estimated date | 1888:2 | 1920:11 | 1940:5 |
---|---|---|---|

Confidence interval | [1887:12–1889:04] | [1920:08–1920:12] | [1940:04–1940:07] |

Estimated date cont. | 1977:6 | 1996:12 | |

Confidence interval cont. | [1977:04–1977:07] | [1996:10–1997:06] |

**Table 6.**Long memory estimates and change of persistence tests for monthly UK unemployment. The table presents the estimates by both GPH and ELW methods together with their standard errors. Moreover, it presents the critical values for the MR test for the 90%, 95%, and 99% confidence levels, and the associated MR statistic for the test for change in persistence on either direction from the regime in the row above to the current row.

Period | GPH est. | GPH s.e. | ELW est. | ELW s.e. | MR Test | |||
---|---|---|---|---|---|---|---|---|

90% | 95% | 99% | Stat. | |||||

1854:07–1888:02 | 0.963 | 0.065 | 1.137 | 0.045 | ||||

1888:03–1920:09 | 0.825 | 0.066 | 0.910 | 0.046 | 5.434 | 6.562 | 9.553 | 39.541 |

1920:10–1940:12 | 1.018 | 0.084 | 1.116 | 0.056 | 5.251 | 6.344 | 8.966 | 44.837 |

1941:01–1976:06 | 0.518 | 0.062 | 0.607 | 0.044 | 5.355 | 6.440 | 9.084 | 174.608 |

1976:07–1996:09 | 0.682 | 0.084 | 0.949 | 0.056 | 5.404 | 6.521 | 9.200 | 336.402 |

1996:10–2016:12 | 1.109 | 0.083 | 1.042 | 0.056 | 5.049 | 6.195 | 8.901 | 39.233 |

**Table 7.**Dates for structural changes detected by the BP methodology in yearly real GDP per capita for Spain, Italy, the Netherlands, and the USA. Column ELW indicates long memory estimates by ELW method, while column MR test shows the MR statistic for the test for change in persistence on either direction from the regime in the row above to the current row. Symbols ${}^{*},{\phantom{\rule{0.166667em}{0ex}}}^{**},$ and ${}^{***}$ denote rejection of the null hypothesis at 10%, 5%, and 1% levels, respectively.

Spain | Italy | ||||
---|---|---|---|---|---|

Period | ELW | MR Test | Period | ELW | MR Test |

1277–1369 | 1.180 | - | - | - | |

1370–1559 | 0.455 | 33.397 ${}^{***}$ | 1310–1412 | 0.823 | |

1560–1648 | 0.337 | 11.669 ${}^{***}$ | 1413–1609 | 0.701 | 7.423 ${}^{**}$ |

1649–1838 | 0.628 | 10.537 ${}^{***}$ | 1610–1849 | 0.573 | 31.583 ${}^{***}$ |

1839–1930 | 0.863 | 7.611 ${}^{**}$ | 1850–1934 | 0.922 | 3.461 |

1931–2019 | 1.377 | 30.884 ${}^{***}$ | 1935–2019 | 1.625 | 23.212 ${}^{***}$ |

Netherlands | USA | ||||

Period | ELW | MR Test | Period | ELW | MR Test |

1348–1511 | 0.608 | - | - | - | |

1512–1651 | 0.585 | 17.134 ${}^{***}$ | - | - | - |

1652–1791 | 0.538 | 6.520 ${}^{**}$ | 1800–1843 | 1.090 | |

1792–1905 | 0.904 | 9.181 ${}^{**}$ | 1844–1897 | 0.920 | 7.365 ${}^{**}$ |

- | - | - | 1898–1940 | 1.323 | 10.477 ${}^{**}$ |

1906–2019 | 1.098 | 38.989 ${}^{***}$ | 1941–2019 | 0.999 | 7.583 ${}^{*}$ |

© 2020 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**

Rodríguez-Caballero, C.V.; Vera-Valdés, J.E. Long-Lasting Economic Effects of Pandemics:Evidence on Growth and Unemployment. *Econometrics* **2020**, *8*, 37.
https://doi.org/10.3390/econometrics8030037

**AMA Style**

Rodríguez-Caballero CV, Vera-Valdés JE. Long-Lasting Economic Effects of Pandemics:Evidence on Growth and Unemployment. *Econometrics*. 2020; 8(3):37.
https://doi.org/10.3390/econometrics8030037

**Chicago/Turabian Style**

Rodríguez-Caballero, C. Vladimir, and J. Eduardo Vera-Valdés. 2020. "Long-Lasting Economic Effects of Pandemics:Evidence on Growth and Unemployment" *Econometrics* 8, no. 3: 37.
https://doi.org/10.3390/econometrics8030037