Every day we hear the news about the number of cases of people dying from Coronavirus.
These numbers are shocking and every death is a tragedy. How can we look at this with more structure?
A classic piece of the Economists toolkit is the cost/benefit analysis. Within this framework we seek to establish the costs and benefits of a particular course of action. Let's start with a very simple example: the purchase of a cup of coffee.
The cost is pretty simple to establish - the price paid for the coffee. Say $4.
The benefit is harder to measure - how do you measure the enjoyment gained from consumption of a cup of coffee? What unit do you use? Here's an example of where the Economics profession has made a conceptual leap. You can measure enjoyment in absolute terms or relative terms and both are used.
Example "Which would you enjoy more - the aforementioned cup of coffee or a brand new iPhone 11?" Many people would rank the new phone ahead of the coffee. Some folks would consider that they could take the iPhone. sell it on a popular online auction site and have enough money to buy many cups of coffee.
This leads us to a commonly used tool - that the measurement of the enjoyment of consumption is measured using money. Consider this - if the cup of coffee was not able to give $4 of enjoyment then in a free market situation, where alternatives exist, the subject f this thought experiment may decided on a cup of tea instead. Or a glass of water...
So, we use money as a proxy for enjoyment, or pleasure.
We can also do the opposite. While more problematic for ethical reasons, we can enquire of a test subject how much they would pay to avoid a disbenefit. Another way to measure this is through revealed preferences, observing behaviour. So, as a simple example, if a do-it-yourself enthusiast spends $50 on circuit breaker to cut the power in the event of a power lead being cut, then we can estimate that the DIYer is willing to spend a minimum of $50 to avoid being electrocuted.
Now we are approaching the topic at hand - how much would a person spend to avoid infection with covid-19?
Let's start to look at some real data...
I have used UK population numbers - available here:
https://www.ons.gov.uk/visualisations/dvc671/pyramids2/datadownload.xls
Below is a chart of male population stratified by age cohort, the y axis can be read as, for example, "m_18_70" meaning males, during 2018 aged between 70 and the next category above - in this case 71. Note that there is no category above age 90, so the category for m_19_90 bulges out as it includes those 90, 91, 92, 93,,, 100+ year olds. Also note that odd numbered categories are not shown on the y-axis, but the bars can be seen.
I have the same representation for the female population below:
Now, what does this show us?
That the UK population displays a fairly normal looking population for a Western society that underwent a post Second World War 'baby boom'.
So, now we have to look at the incidence of Covid-19 - who becomes infected and what is the impact on
(a) morbidity
(b) mortality
We now need more data -
If we look at mortality data we can create a pivot table:
| Sum of NDTHS | Sex | 365 | |||
| Age | 1 | 2 | Grand Total | Male | Female |
| Neonates | 1040 | 811 | 1851 | 2.84932 | 2.22192 |
| <1 | 400 | 320 | 720 | 1.09589 | 0.87671 |
| 01-04 | 215 | 164 | 379 | 0.58904 | 0.44932 |
| 05-09 | 137 | 133 | 270 | 0.37534 | 0.36438 |
| 10-14 | 194 | 116 | 310 | 0.53151 | 0.31781 |
| 15-19 | 561 | 270 | 831 | 1.53699 | 0.73973 |
| 20-24 | 981 | 378 | 1359 | 2.68767 | 1.03562 |
| 25-29 | 1242 | 581 | 1823 | 3.40274 | 1.59178 |
| 30-34 | 1658 | 876 | 2534 | 4.54247 | 2.4 |
| 35-39 | 2260 | 1347 | 3607 | 6.19178 | 3.69041 |
| 40-44 | 3185 | 1835 | 5020 | 8.72603 | 5.0274 |
| 45-49 | 5251 | 3454 | 8705 | 14.3863 | 9.46301 |
| 50-54 | 7870 | 5094 | 12964 | 21.5616 | 13.9562 |
| 55-59 | 10755 | 7425 | 18180 | 29.4658 | 20.3425 |
| 60-64 | 14355 | 9950 | 24305 | 39.3288 | 27.2603 |
| 65-69 | 21232 | 14616 | 35848 | 58.1699 | 40.0438 |
| 70-74 | 31296 | 22884 | 54180 | 85.7425 | 62.6959 |
| 75-79 | 36041 | 29195 | 65236 | 98.7425 | 79.9863 |
| 80-84 | 44735 | 41951 | 86686 | 122.562 | 114.934 |
| 85+ | 84552 | 132229 | 216781 | 231.649 | 362.271 |
| Grand Total | 267960 | 273629 | 541589 |
This shows us that for 2018, we saw 1242 deaths of males between 25 and 29. So roughly 3.4 per day.
On any given day we see a number of people die, in total 541,589.
So, what's the change in mortality, stratified by age cohort, expressed as a standard deviation from the mean mortality expected over any period?
Without that level of granular detail we are simply being bombarded by bad news.
At this stage, I would like to restate the point made above "These numbers are shocking and every death is a tragedy."
I will continue this analysis as time allows...
See also:
The regular reader may note that this really is rather off-topic. And from the perspective of a blog that has traditionally looked at topics such as Fixed Income Trading: New venues ( How many Fixed Income trading venues are there? ) , Product Management and Fintech and What's the difference between an EMS and an OMS? this may seem a little unusual. However, your author was trained as an Economist and took a keen interest in Health Economics and the interface between rationality, efficiency and morality. As such, with the usual topics somewhat becalmed I decided to repurpose this blog for an intellectual diversion. I can assure the reader that normal service will be resumed sooner or later...
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