1/ It is wrong to believe that the number of excess deaths is necessarily a good measure for COVID deaths.

When the number of excess deaths is lower than the number of COVID deaths it is also wrong to believe that this necessarily means the COVID death count is wrong.
2/ The reason for this is that many things change during a pandemic.

The two beliefs above would be correct if everything else stayed the same as it was in previous years.

But as we now all know from our personal lives this is very much not the case during a pandemic.
3/ If you now look at the death count from different causes over the last year you see just how large these changes can be.

This compares the death rate from homicides, suicides, traffic accidents, and other accidents of women in Peru.

https://www.sciencedirect.com/science/article/pii/S0091743520303625
4/ In the case of Peru the deaths from these causes all declined (for men too).

The consequence of the changing death rate from these and other causes is that it is wrong to believe that excess deaths = COVID deaths.
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