Political Calculations | Posted: Sep 17, 2020 12:18 PM
Can you
trust the numbers the U.S. government reports daily for the number of confirmed
COVID-19 cases? Can you trust China's or Italy's figures? How about the case
counts reported by Russia or other nations?
2020 has
been a bad year for many people around the world, mainly because of the
coronavirus pandemic and many governments' response to it, which has almost
made COVID-19 as much a political condition as a viral infection. Among the
factors that make it a political condition is the apparent motives of political
leaders to justify their policies in responding to the pandemic, which raises
questions of whether they are honestly reporting the number of cases their
nations are experiencing.
Telling
whether they are or not is where Benford's Law might be used. Benford's
Law describes the frequency by which leading digits appear in sets of data
where exponential growth is observed, as shown in the chart above. The expected
pattern that emerges in data showing exponential growth over time according to
Benford's Law is strong enough that significant deviations from it can be taken
as evidence that non-natural forces, such
as fraud or
manipulation for political purposes are at play.
Economists
Christoffer Koch and Ken Okamura wondered if the data being reported by
China, Italy and the United States for their respective numbers of reported
cases was trustworthy and turned to Benford's Law to find out. We won't keep
you in suspense, they found that the growth of each nation's daily COVID-19
case counts prior to their imposing 'lockdown' restrictions were consistent
with the expectations of Benford's Law, leading them to reject the potential
for the data having been manipulated to benefit the interests of their
political leaders. Here's the chart illustrating their findings from their
recently published report:
To see the
chart, click here.
But that's
only three countries. Are there any nations whose leaders have significantly
manipulated their data?
A preprint
study by Anran Wei and Andre Eccle Vellwock also found no evidence of
manipulation in COVID-19 case data by China, Italy and the U.S., and extends
the list of countries with trustworthy data to include Brazil, India, Peru,
South Africa, Colombia, Mexico, Spain, Argentina, Chile, France, Saudia Arabia,
and the United Kingdom. However, when they evaluated COVID-19 case data for
Russia, they found cause for concern:
Results suggest high possibility of data
manipulations for Russia's data. Figure 1e illustrates the lack of Benfordness
for the total confirmed cases. The pattern resembles a random distribution: if
we calculate the RMSE related to a constant proability of 1/9 for all first
digits, it shows that the RMSE is 20.5%, a value lower than the one related to
the Benford distribution (49.2%).
Wei and
Vollock also find issues with Russia's COVID-19 data for daily reported cases
and deaths. Here is their chart summarizing the results for total confirmed
COVID-19 cases for each of the nations whose data they reviewed:
To see the
chart, click here.
They also
found issues with Iran's daily confirmed cases and deaths, but not enough to
verify the nation's figures have been manipulated.
Koch,
Christopher and Okamura, Ken. Benford's Law and COVID-19 Reporting. Economics
Letters. Volume 196, November 2020, 209573. DOI: 10.1016/j.econlet.2020.109573.
Wei, Anran
and Vellwock, Andre Eccel. Is the COVID-19 data reliable? A statistical
analysis with Benford's Law. [Preprint PDF Document].
September 2020. DOI: 10.13140/RG.2.2.31321.75365.
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