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

^{1}

^{2}

^{3}

^{*}

## 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 |

## References

- Abadie, Alberto, Alexis Diamond, and Jens Hainmueller. 2010. Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program. Journal of the American statistical Association 105: 493–505. [Google Scholar] [CrossRef] [Green Version]
- Abadie, Alberto, Alexis Diamond, and Jens Hainmueller. 2015. Comparative politics and the synthetic control method. American Journal of Political Science 59: 495–510. [Google Scholar] [CrossRef]
- Bai, Jushan, and Pierre Perron. 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66: 47–78. [Google Scholar] [CrossRef]
- Bai, Jushan, and Pierre Perron. 2003. Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18: 1–22. [Google Scholar] [CrossRef] [Green Version]
- Beran, Jan, Yuanhua Feng, Sucharita Ghosh, and Rafal Kulik. 2013. Long-Memory Processes: Probabilistic Theories and Statistical Methods. Berlin and Heidelberg: Springer. [Google Scholar] [CrossRef]
- Bolt, Jutta, Robert Inklaar, Herman de Jong, and Jan Luiten van Zanden. 2018. Rebasing Maddison: New income comparisons and the shape of long-run economic development. Maddison Project Database. Available online: https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2018 (accessed on 1 July 2020).
- Brainerd, Elizabeth, and Mark V Siegler. 2003. The Economic Effects of the 1918 Influenza Epidemic. CEPR Discussion Paper 3791. Available online: https://ssrn.com/abstract=394606 (accessed on 1 July 2020).
- Breitung, Jörg, and Uwe Hassler. 2002. Inference on the cointegration rank in fractionally integrated processes. Journal of Econometrics 110: 167–85. [Google Scholar] [CrossRef] [Green Version]
- Campbell, Bruce M. S., Alexander Klein, Mark Overton, and Bas van Leeuwen. 2015. British Economic Growth, 1270–1870. Cambridge: Cambridge University Press. [Google Scholar]
- Clark, Gregory. 2007. The long march of history: Farm wages, population, and economic growth, England 1209–1869. Economic History Review 60: 97–135. [Google Scholar] [CrossRef] [Green Version]
- Clark, Gregory. 2010. The macroeconomic aggregates for England, 1209–2008. In Research in Economic History. Bingley: Emerald Group Publishing Limited, vol. 27, pp. 51–140. [Google Scholar] [CrossRef] [Green Version]
- Colbourn, Tim. 2020. COVID-19: Extending or relaxing distancing control measures. The Lancet Public Health 5: e236-37. [Google Scholar] [CrossRef] [Green Version]
- Conference Board. 2020. Total Economic Database. Available online: https://www.conference-board.org/data/economydatabase/ (accessed on 1 July 2020).
- Ergemen, Yunus Emre, Niels Haldrup, and Carlos Vladimir Rodríguez-Caballero. 2016. Common long-range dependence in a panel of hourly Nord Pool electricity prices and loads. Energy Economics 60: 79–96. [Google Scholar] [CrossRef]
- Ferguson, Neil, Daniel Laydon, Gemma Nedjati Gilani, Natsuko Imai, Kylie Ainslie, Marc Baguelin, Sangeeta Bhatia, Adhiratha Boonyasiri, ZULMA Cucunuba Perez, Gina Cuomo-Dannenburg, and et al. 2020. Report 9: Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID19 Mortality and Healthcare Demand. Available online: https://www.imperial.ac.uk/media/imperial-college/medicine/mrc-gida/2020-03-16-COVID19-Report-9.pdf (accessed on 1 July 2020).
- Geweke, John, and Susan Porter-Hudak. 1983. The estimation and application of long memory time series models. Journal of Time Series Analysis 4: 221–38. [Google Scholar] [CrossRef]
- Gil-Alana, Luis A, and Peter M Robinson. 1997. Testing of unit root and other nonstationary hypotheses in macroeconomic time series. Journal of Econometrics 80: 241–68. [Google Scholar] [CrossRef] [Green Version]
- Granger, Clive W. J., and R Joyeux. 1980. An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis 1: 15–29. [Google Scholar] [CrossRef]
- Guerrieri, Veronica, Guido Lorenzoni, Ludwig Straub, and Iván Werning. 2020. Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages? National Bureau of Economic Research WP 26918. Available online: https://ssrn.com/abstract=3569382 (accessed on 1 July 2020).
- Harvey, Andrew, and Stephen Thiele. 2017. Co-Integration and Control: Assessing the Impact of Events Using Time Series Data. Cambrige Working Paper Economics 1731. Cambridge: Cambridge University, Available online: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1731.pdf (accessed on 1 July 2020).
- Hosking, J. R. M. 1981. Fractional differencing. Biometrika 68: 165–76. [Google Scholar] [CrossRef]
- Hurvich, Clifford M., Rohit Deo, and Julia Brodsky. 1998. The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis 19: 19–46. [Google Scholar] [CrossRef]
- Jordà, Oscar, Sanjay R. Singh, and Alan M. Taylor. 2020. Longer-Run Economic Consequences of Pandemics. Federal Reserve Bank of San Francisco Working Paper 2020-09. Available online: https://doi.org/10.24148/wp2020-09 (accessed on 1 July 2020).
- Karlsson, Martin, Therese Nilsson, and Stefan Pichler. 2014. The impact of the 1918 Spanish flu epidemic on economic performance in Sweden: An investigation into the consequences of an extraordinary mortality shock. Journal of Health Economics 36: 1–19. [Google Scholar] [CrossRef]
- Martins, Luis F., and Paulo M. M. Rodrigues. 2014. Testing for persistence change in fractionally integrated models: An application to world inflation rates. Computational Statistics and Data Analysis 76: 502–22. [Google Scholar] [CrossRef] [Green Version]
- McKibbin, Warwick J., and Roshen Fernando. 2020. The Global Macroeconomic Impacts of COVID-19: Seven Scenarios. Brookings Institution Report. Washington, DC: Brookings Institution, Available online: https://www.brookings.edu/wp-content/uploads/2020/03/20200302_COVID19.pdf (accessed on 1 July 2020).
- Meltzer, Martin I., Nancy J. Cox, and Keiji Fukuda. 1999. The economic impact of pandemic influenza in the United States: Priorities for intervention. Emerging Infectious Diseases 5: 659. [Google Scholar] [CrossRef]
- Nelson, Charles R., and Charles R. Plosser. 1982. Trends and random walks in macroeconmic time series. Some evidence and implications. Journal of Monetary Economics 10: 139–62. [Google Scholar] [CrossRef]
- Osterrieder, Daniela, Daniel Ventosa-Santaulària, and J. Eduardo Vera-Valdés. 2019. The VIX, the variance premium, and expected returns. Journal of Financial Econometrics 17: 517–58. [Google Scholar] [CrossRef] [Green Version]
- Prados de la Escosura, Leandro, Carlos Álvarez-Nogal, and Carlos Santiago-Caballero. 2020. Growth Recurring in Preindustrial Spain: Half a Millennium Perspective. Technical report. England: European Historical Economics Society (EHES). [Google Scholar]
- Prados de la Escosura, Leandro, and Carlos Vladimir Rodríguez-Caballero. 2020. Growth, War, and Pandemics: Europe in the Very Long-Run. EHES Working Paper Series 185. Available online: http://www.ehes.org/EHES_185.pdf (accessed on 1 July 2020).
- Prem, Kiesha, Yang Liu, Timothy W. Russell, Adam J. Kucharski, Rosalind M. Eggo, Nicholas Davies, Stefan Flasche, Samuel Clifford, Carl A. B. Pearson, James D. Munday, and et al. 2020. The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: A modelling study. The Lancet Public Health 5: e61–e270. [Google Scholar] [CrossRef] [Green Version]
- Robinson, Peter M. 1995. Log-periodogram regression of time series with long range dependence. The Annals of Statistics 23: 1048–72. [Google Scholar] [CrossRef]
- Shimotsu, Katsumi, and Peter C. B. Phillips. 2005. Exact local Whittle estimation of fractional integration. The Annals of Statistics 33: 1890–933. [Google Scholar] [CrossRef] [Green Version]
- The Federal Reserve. 2020. Federal Open Market Committee announces approval of updates to its Statement on Longer-Run Goals and Monetary Policy Strategy [Press Release]. Available online: https://www.federalreserve.gov/newsevents/pressreleases/monetary20200827a.htm (accessed on 27 August 2020).
- Thomas, R., and N. Dimsdale. 2017. A milllenium of UK data. Bank of England Datasets. Available online: https://www.bankofengland.co.uk/statistics/research-datasets (accessed on 1 July 2020).
- Varneskov, Rasmus T., and Pierre Perron. 2018. Combining long memory and level shifts in modelling and forecasting the volatility of asset returns. Quantitative Finance 18: 371–93. [Google Scholar] [CrossRef]
- Vera-Valdés, J. Eduardo. 2020. On long memory origins and forecast horizons. Journal of Forecasting 39: 811–26. [Google Scholar] [CrossRef] [Green Version]

**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