**Something important** was overlooked in the post on Spanish mortality statistics: the time scale over which the official statistics are updated.

Because statistics are compiled from a large number of sources, the total evolves over time as the contributions from these various places across the country reach the central compiling authority. Hence, for a given year, even if the counting stops on December 31st, the contributions keep coming in well into the next year.

Let’s take a look at that.

What we see in this figure is how the estimate of the total mortality for 2019 evolves *after* 2019. The timeline is from February 2020 (first update in 2020) up to then end of July 2021. It therefore spans almost 20 months from the year’s last update in December 2019.

The first point is at 394k and the second at 411k. But although the total continues to grow as seen in the inlay that shows a zoom on the last part of the curve (Jan to Jul 2021) rescaled to emphasize the variation between consecutive estimates, it is clear that the evolution beyond July 2020 and over the following 12 data points in the time series is minimal.

In July 2020 (5th point) the estimate was 416.3k. And one year later in July 2021 (last point) the estimate was 418.7k. This is a difference of 0.57%.

The conclusion we can draw from this observation is that we can expect a sizeable difference in the estimate over the first 6-7 months, but a very slow evolution, of the order of half a percent, beyond that.

**Let’s now look at the 2020** data from the start of the year in January up to July 2021. In this case, because we are starting from the very first estimate of mortality for the year, we see the full range of values starting from zero.

As in the first figure, we see here that the curve flattens at the end. But even with a rescaling to emphasize differences as shown in the inlay, it is evident that the curve is essentially flat over the last four updates.

The last point from July 2021 is 492.5k. Applying what we observed for 2019, and *augmenting* that estimate of 492.5k by half a percent gives 495k. This, we can be quite confident, is a both robust and conservative value of what we expect to get as the estimate of total mortality for 2020 one year from now in July 2022.

Hence, to recap, we expect the total mortality for 2019 to be around 420k, and for 2020 to be around 495k.

**Mortality is proportional to population**, and naturally fluctuates as all statistics do. Interestingly, as we saw when we first looked at these data, mortality displays a slowly rising trend in time.

Looking at the last 5 years, we see that 2020 (in red) stands out a little.

The average of the last five years is 9k per million. In 2020 the total was 10.5k. This is a difference of 16.7%. And if we use the *augmented* value of 495k instead of 492.5k, then the difference is 17.8%.

Looking at the data for the years between 1995 and 2005 we can see a very large range of values. The amplitude of the change is largest from the peak in 1999 to the valley in 2002 where it goes from 9.2k to 7.8k per million. This is a 15% drop from 9.2 to 7.8, and an 18% difference from 7.8 to 9.

The largest jump from one year to the next is from 2002 to 2003 where mortality went from 7.8k to 9k per million. This is a 15.4% increase. These fluctuations are very similar in magnitude as the one in 2020.

**What is apparent** is that ups tend to be followed by downs, and downs tend to be followed by ups. Moreover, the larger the change tends to be, the larger the counter-change also tends to be. This is, of course, entirely expected.

In a given population, it is natural to expect that the most vulnerable will be most likely to perish. This is true no matter what the challenge is, be it a change in temperature or a viral agent. The most vulnerable are typically the youngest and the oldest, but for different reasons.

Both the youngest and oldest portions of the population grow steadily as babies are born and as adults age. As we get older, and in particular as we reach the average life expectancy, we tend to pass on.

If in one year the conditions are favourable to the vulnerable, less of us will pass on. If several years are favourable, then the mortality rate will be lower than average, and more vulnerable people will survive. When the conditions are less favourable, then more vulnerable people pass on.

Hence, even if it is very hard if not impossible to make precise predictions from one year to the next, we can nevertheless easily see how the mortality curve takes its shape: small and short-lived dips tend to lead to small and short-lived peaks; larger or longer-lasting decreasing trends tend to lead to larger and longer-lasting rising trends.

Therefore, we can conclude that because we have experienced in 2020 a moderate rise of about 17% with respect to the average of the previous 5 years, and because we know that this increase in mortality was almost exclusively from the oldest and most vulnerable portion of the population, it is inevitable that we will see a significant drop in mortality over the coming few years, exactly as was seen in the years from 1999 to 2002, and again from 2003 to 2006.

**The initial conclusions** based on the preliminary statistics were incorrect. I apologize for that. The final conclusions and prediction presented here, however, I believe will prove to be entirely robust. And the one thing we can be supremely confident about in this matter is that time will tell.

Very nice and precise way to describe it. Thanks Guillaume!

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You’re very welcome.

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