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Monday, 6 April 2020

Policy frameworks for pandemics - part 2 - benefit evaluation...

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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