However, as yesterday’s quote noted – sometimes we need to temper our warm hearts with cold heads in order to understand social phenomenon and discover truths that lead to the improvement of society.  If we are interested in understanding the risks to a country associated with coronavirus, we need good information on how the virus spreads and the fatality rate, in order to set appropriate policy.   

In that way I’d like to talk about selection bias in the coronavirus figures – how this may overstate the death rate and understate the number of people catching it, and how the cruise ship – as well as being an incubator – may be (in part) a natural experiment which allows us to correct for this bias.  

As my economics PhD thesis consider health related questions, this is an issue I like to think through, and which I think is valuable.

The bias

Looking at the gross numbers alone there appear to be a number of “facts” (as at 5pm NZT 19/02/2020):

1. 75,216 people are or have been infected.
2. 16,645 closed cases – with a gross death rate of 12%
3. Of the remaining cases 21% are serious or critical.
4. Of those that have died 10.5% have cardiovascular issues.

Assuming the death numbers are accurate, this is a very high death rate.  However, the WHO states that they estimate a fatality rate of 2%. This issue also generates hot debate.

But there is a good reason why the true fatality rate may be so much lower than the currently measured rate, which has nothing to do with a lack of preparation or it initially occurring in a poor community. In my view the number of cases is understated!

This would be due to sample selection bias and the missing individuals with no or limited symptoms.

We need to think about how this sample was selected in order to understand whether these measures are representative of the whole population.

The key issue is that someone is noted as having the virus after being checked by a doctor, this tells us that:

1. This is an individual showing symptoms,
2. This is more likely to be an individual that is disproportionately impacted by the symptoms

As a result, we would expect the following biases in the numbers:

1. People with no symptoms or with limited symptoms that didn’t lead them to seek out a doctor will not have been counted – so the number of infections could be much higher.  Furthermore the spread rate (Rho) may be higher.
2. If the vast majority of those with major symptoms do seek help, and so are measured, this indicates that the death rate would be much lower.
3. Furthermore, the serious and critical rates would also be lower.
4. Interestingly, if a given condition is more likely to lead to symptoms being serious (such as those with pre-existing cardiovascular conditions) then we will relatively overestimate how many people with those conditions catch the disease.

The ship

As we know, the Diamond Princess cruise ship has been quarantined in Japan due to the coronavirus outbreak.  This quarantine is now ending, with countries getting their citizens home.

On February 18 worldometers noted the following:

“88 new cases on the Diamond Princess cruise ship in Japan were confirmed as a result of 681 people being tested (13% infection rate). Of these, 65 people (74%) have no symptoms. So far, a total of 542 infected people were found among 2,404 passengers and crew members tested (23% infection rate) out of 3,711 total people on the ship”

This isn’t the same as testing the “population of the ship” – or a random sample.  As they will have tested everyone who was showing symptoms, and then some number of people who had not.  If the additional people were selected on the basis of their closeness with those with symptoms, rather than randomly, that would generate further selection bias.

However, 65% of all passengers were tested even with a large number of these individuals not showing symptoms – as a result although selection bias still exists it is not as strong.

If the last days data were representative of the rest of the sample, this means that 74% of people who have tested positive for the virus showed no symptoms. [Note: It may not be representative of the sample, especially if those showing symptoms were tested first – I am just using this for the sake of argument].

There are three biases in estimating population statistics given current sampling around the world – a) a downward bias in the % of people not showing symptoms relative to total infected, b) a downward bias in the number of people infected (so in the infection rate), and c) an upward bias in the infection rate among those tested.

Given selection bias we would expect a LARGER % of people with the virus to show no symptoms – as the sample includes those showing symptoms (who make up 100% of the population showing symptoms) and a random selection of individuals some of which are infected.  As some of the unsampled individuals not showing symptoms will be infected, this implies that the percentage not showing symptoms of the total infected is larger.

In addition, this figure as a population estimate of the number infected is biased downwards.  As the worldwide sample is based on only testing those who have symptoms, people not showing symptoms who have the virus are excluded from the sample.

Furthermore, the infection rate among those tested is biased upwards, as your chance for being selected for sampling is related to having the disease.

For the sake of argument let’s pretend that they did test everyone on the boat to get a 75% figure – and assumed the people on the boat was a random selection of the global population (which cruise ship passengers aren’t, eg they tend to be older and likely more likely to show symptoms). Furthermore, assume that the only testing that has occurred around the rest of the world is on people showing symptoms.  

This implies that we have a potential correction to current world-wide estimates based on the “natural experiment” on the boat where there is no selection bias. Specifically, the current case number is equal to only 25% of the total – or around 300,000 people are infected.

There are two ways to read this figure:

1. We may think that many of these infections just haven’t manifested in symptoms YET and as a result this is very scary.
2. Seeing how long the boat was quarantined we may view this as saying that 75% of individuals that catch the virus don’t ever have symptoms.  As a result, the true fatality rate is lower.

Let’s assume that the gross death rate for the above figures is going to be 12% – so around 9,000 poor souls pass away based on the 75,000 who are recorded to have caught the virus.  If the real number of cases is 300,000 then the fatality rate is instead 3%, much closer to the WTO estimates.

All the links focused on how the article made the case for a tax on sugar.  That is fine and all, it was an externality case that we can discuss, appeal to evidence and value judgments on, and then decide whether we agree or not.  In fact, I get the impression that is the exact point that the authors are raising after setting up the pro-argument.

However, I didn’t get the impression that many people made it to the second half of the article (given the way it was used) – and the second half was absolutely glorious.

The second half starts with this:

But a major focus of the calls from many “health” campaigners is the impact that taxing these drinks might have on the contested term “obesity”.

The focus on obesity reveals the other public health fantasy: socially engineering perfect bodies.

This is true – a focus on obesity rather than externalities stemming from consumption is a different argument.  And seems to crawl towards rhetoric used by those who want others to take on some ideal form.

Then there is this:

If, for instance, we decided to tax sugar-sweetened beverages and had a subsequent reduction in diabetes and improvement in dental health, would the tax be judged unsuccessful if BMI didn’t change?

In fact, diabetes and poor dental health affect people of all body sizes, who can all be healthier, regardless of BMI. But if a sugary drink tax collected enough healthcare funding to pay for diabetes and dental care, would public health campaigners still demand more just to make people slimmer?

These are important questions.  If we are actually thinking about the externality, an “output target” in terms of rates of obesity and the average BMI makes very little sense.  Instead, the focus should be on the link between consumption and disease – the change in BMI’s or obesity rates is symptomatic here.

This leads to the question:

What we must ponder is why public health campaigners and researchers feel the need to complicate a very simple relationship by dropping in the term obesity whenever possible, despite its longstanding logical and ideological problems.

Or, put differently: why are they so determined to define and control body mass when they could just target disease?

I also struggle with this question – why does it often feel that the “costs” are ex-post justifications for targeting something that a group of people just don’t like?

The entire idea of determining social policy on the basis of an idealised form for how individuals should be is an incredibly strong normative assumption.  The same argument holds for other target based measures, such as GDP targets.  And the use of economic language to “justify” and obsfucate this  violates the fact economics is supposed to make these value judgments, regarding individuals, transparent.

This IS NOT an argument against active policy based on improving individual well-being and based on clear knowledge of the value judgments involved – in fact I am a huge fan of the introduction of mechanism design in this area, as there is a lot of self-reporting by individuals that obesity is something they are very unhappy with in their own lives.

But the reason I keep reiterating this is that:

1. Many of the underlying justifications for targeting obesity are being based on the authors normative belief’s about whether others should be obese – same arguments hold with alcohol, tobacco, and other “sin goods”.  Yes there are significant issues of choice and reasonable knowledge, but it is a long bow for this to lead us to an oversimplistic tax argument.
2. As an individual I strongly, and totally, disagree with this inherent value judgment.  A willingness to justify social action to punish individual difference is something I find morally abhorrent.  Banning and constraining individual choice because it doesn’t fit our view of what a sensible individual would do is something that is ethically wrong, prior to any consideration of outcomes.  I know that is a pretty deontological view of policy, but if we are going to consider things normatively without just thinking our view of societies social welfare function is totally an utterly right it is necessary.

But why couldn’t Big Food’s processing and marketing genius be put to use on genuinely healthier foods, like grilled fish? Putting aside the standard objection that the industry has no interest in doing so—we’ll see later that in fact the industry has plenty of motivation for taking on this challenge—wouldn’t that present a more plausible answer to America’s junk-food problem than ordering up 50,000 new farmers’ markets featuring locally grown organic squash blossoms?

It is an issue I see a lot of my friends talking about, and one which has led Gareth Morgan and Geoff Simmons to write a book.  Seems like an interesting and important issue to think about

Note:  I have no interest in trying to define what people should be doing here – and I aim to have a little chat about choice at some point in the future as I think it is an important issue that can get lost in this (eg I feel it gets lost here).  However, I can tell the food issue is, and is going to be, an issue that people want to look into – and would like to hear your thoughts

Oregon’s experience with methamphetamine manufacture and abuse since 2006 does not stand out from its neighbors or other parts of the United States. This potentially calls into question whether Oregon’s Rx-only law had any independent effect on these key measures. Moreover, this law does come at some cost to consumers and government and private payers.

So the ban on selling effective cold medicine over the counter had no observable effect upon the P problem, but does cause inconvenience for people with a cold. It will be interesting to see comparable studies for New Zealand in a few years time, although the lack of neighbouring states makes it harder to find control groups to compare with.

Lets ignore the fact that the slope of the  “regression line” appears very sensitive to the addition of a few countries.  Lets instead focus on the fact that it is a poor regression and that there isn’t a clear “theoretical background for causation”.

Dim Post sums up the choice of countries on the basis that “so while the first graph picks countries in order to test a hypothesis”.  Interesting, lets think about how this regression works at testing a hypothesis.

Firstly, we are saying that our dependent variable (Life expectancy) is in some way related to our independent variable (Inequality).  In order to move to saying that inequality CAUSES life expectancy we really need two things:

1. A causal theory – both to give us the direction of causation, and a reason for the causation to exist,
2. The regression to not be a big steaming pile of icky things.

I would say that we have neither.

Causation

How in the name of frik himself does inequality cause life expectancy – is it because poorer people do not live as long, the relationship in non-linear (specifically additional income has a diminishing return on life expectancy), and as a result for the same level of national income, inequality will drag down the average?  Hell I guess I can buy that.

I can also buy the fact that life expectancy causes inequality – society that generally live longer need to co-operate for longer, and so will share resources.  I guess we need to really sit down and figure out the direction of causation then.

Steaming piles

However, this is NOWHERE NEAR the worst point.  The worst point stems from omitted variable bias.

In the above discussion we mentioned some other variables, such as the actual income level.  Well what about the amount spent on healthcare.  What about inherent genetic factors.  What about country specific factors – and any cross-country bias stemming from those.  If any of these other variables that impact upon life expectancy are also related to income inequality we have a serious problem here!

And the fact is that some of them are – the income level of a nation is most definitely related to both income inequality and life expectancy.

Furthermore, what happens if BOTH of our causal interpretations are true at some level – well frik me then we have an endogeniety problem, awesome.

Conclusion

Overall, we aren’t clear on the nature of any causation AND our estimate of any correlation is biased because we have ignored endogeniety/omitted variable issues.  I would also add that there is “time-series” data out there that could be used to substantially improve the amount of information we have – and try to work out the nature of many of these problems.

Another fundamental issue I have is that I hate cross country comparisons as:

1. Data is often wildly incomparable between nations – the “same stat” is so often measuring different things.
2. There are so many unobserved, relevant, factors that differ between nations that is boggles my head how we can have much faith in such studies.

I don’t know too much about statistics – but given this stuff is compulsory to cover in the 2nd year of training as an economist I certainly hope it has been answered somewhere.

Note:  I have read their responses to critics BUT I haven’t read the book, or even paid much attention to it before now. My first hope is that the book largely discusses this issue, and actually ran regression that corrected for this area of bias AND came up with a clear conceptual framework that can be used to explain causation.

And before anyone says “of course they must have” I would like a source – actually I would prefer it if I could have a copy of the actual statistics they did.  At the moment all I see are 2D graphs with lines drawn through them, which seem to imply they ran a simple linear regression and reported the results …

Furthermore in the responses, the only time I saw someone raise the issue of omitted variables they also rose causation – and the answer was only on causation.  I haven’t actually seen any response to the omitted variable issue.  Given the importance being given to this book I HOPE they have covered the issue – and that I can update this post with a correction.

I know it has had a serious impact on me during this years flu season – given that all the alternatives suck.  And I know a lot of people who feel the same.

Dumb policy with a very obvious and high cost and pretty much no benefit.  What is this!  How does this rubbish get passed.

(Source Marginal Revolution)

Note: I am joking, this is not causality.  For one we don’t have a quantity measure of drinking, and the impact of drinking on intelligence is no doubt non-linear.  In fact, you could make the argument that “smarter” people know how control their own alcohol consumption, and so do not face the severe negative impacts of drinking – in a way smart people are more likely to find ways to control, or are not subject to, time inconsistency problems in liqour.

However, I think we should also use this as a reminder that it the link between the consumption of a drug and the drugs impact can be very poorly estimated if we aren’t very careful to control for these sorts of issues – hence why I do not trust a lot of studies out there, especially the ones made by interest groups where all they do is draw lines (95% of studies according to my casual observation).

Update:  CPW sent me the link to the full set of graphs with alcohol involved – it is beautiful.

In essence this sort of discussion is saying that we discount our future selves TOO steeply (compared to whatever the underlying presumption of a “fair discount factor” is).  Is this a fair value judgment to make in policy?  It is not one I would make, but it appears to be the basis of some overaching policies such as universal healthcare and superannuation.

In this case, we don’t need to worry about a “moral hazard problem” even though (empirically) the actions of moral hazard will appear.  Why?  Because the actors aren’t thinking about the future selves and so these “inefficient” outcomes would have occurred in the first place!  Policy helps to correct this by transfering resources to our future selves to improve outcomes relative to the REAL counterfactual (rather than the idealized one where agents choose on the basis of our subjectively fair discount rate).

I think it is important to keep this issue in mind, because it is a closet behavioural assumption behind most policy.  If we buy this value judgment, then we will believe in a larger role for government then if we didn’t.

However, even if all the premises are correct and even given significant social justice goals, I think we have to be clear regarding why we think an exemption is the way to go – and in the end I still disagree regarding any exemption.

Lets assume there is a negligible administration cost from removing the tax on certain types of food.  Even given the lack of a cost why are we taxing one good differently to another here?

The justification used is that GST is a regressive tax – well it isn’t in standard terms.  In fact it punishes those with more volatile income, not with lower lifetime income.  The more apt justification used is the fact that the poor spend more of their income on food.  However, in this case we are merely saying we want to give more money to the poor directly rather than indirectly.  If we think the income of our lowest citizen is too low as a society, we should transfer income to them – not fiddle with prices.  As a result, I do not agree with doing this on the basis of social justice – if this is what society wants just increase income transfers!

Fat tax

The only reason we would want to cut the GST off food is if we decided we wanted the relative price of food to be lower.  In the piece it is mentioned that if we cut the price of supermarket food the consumption of healthy food goes up.  Accepting the strong relationship they find (although, I would like to see the study directly – given the magnitude of the lift) we could justify some cut in the GST on supermarket food if we felt there was an externality from the consumption of healthy food.  Essentially this is the a fat tax vs non-supermarket, fattier foods.

Now for a fat tax (or non-fat subsidy) to work, we need an incredible amount of targeting.  This will either lead to a much larger administration cost (and the govt. hires people to look around and check things) or a significant increase in tax avoidance (by “recategorising” foods).  In order to adjust the relative price of food types, we have to accept that administration issues will become important!

As mentioned earlier, the fat tax is at best a second best option – in reality the problem stems from the governments refusal to make hospital policy in line with social values.

Given this, I would be against arbitrarily imposing a “anti-fat subsidy” through the guise of a cut of GST on some foods even if the administration cost was very small.

Not a fat tax?

Now it doesn’t appear that the study actually looked at a fat tax.  From the article we have:

The main findings from the survey? People, Blakely explained, kept on buying almost the same amount of saturated fats, regardless of the price and regardless of the educational material they were given. However, they used their 12.5% price discount to buy a significantly higher amount of healthier foods, and were still doing so at the end of the survey.

So a 12.5% drop in the price of supermarket goods lead people to buy A LOT more healthy stuff.  Four things:

1. This does not take into account what people spent their “higher income” on outside the supermarket.  Could it be that higher real income lead to more takeaways.  Without a more detailed look at incomes this is tough.
2. What income group were these shoppers?  Given that the relative price of goods INSIDE the supermarket were unchanged, why doesn’t a standard boost in income lead to this sort of massive increase in healthy food consumption (makes me suspect) – and why don’t we see these huge benefits overseas when they do have lower GST on food.
3. Incidence of tax.  If demand for healthy foods rises on the back of a cut in price, we will see the price of healthy food fall LESS than the price of unhealthy food.  This will cancel out some of these gains (even if they actually attempt to occur).
4. I would seriously like to take a closer look at the data in this study, as it is hard to tell exactly what they did solely from an article that mentions it.

Now, even if these huge estimates of the benefits of moving GST away from food are true I am forced to ask, what is the social benefit of the individuals actions here?  I understand that eating better is great for the person, however this choice set for the person could be achieved by giving them more money in the first place.

If a person then decides to spend any additional income on an xbox instead of healthy food THEY ARE SAYING they value Halo more than a longer healthier life.  Good for them – if it is that good maybe I should play Halo one day too.

The government should only subsidise if there is a social benefit – and again we come down to the second (at least) best world of it being like a fat tax.

And as I said earlier, I would be against arbitrarily imposing a “anti-fat subsidy” through the guise of a cut of GST on some foods even if the administration cost was very small.

However, then inside the article I saw it was written by a nutritionist – the worst of the prescriptive disciplines in my opinion.  Furthermore, they decided to take an entirely holistic approach to weight gain, removing any individual responsibility and blame the environment.  Namely:

Professor James said that in countries such as Britain and New Zealand, the reason for many people’s obesity was a genetic predisposition in an environment which allowed it to happen with an “out-of-control” food industry and the constant use of cars

What is this.

Like all individual choices, weight gain has several elements:

1. There are individual preferences, which are determined by genetics, history, and society.
2. There is the choice set/constraints, which is determined by society and natural endowment.
3. There is the nature of individual choice – which is determined by the person choosing.

Ultimately, the third element ensures that weight gain IS someones choice.  However, given that it is their choice we know that it is fine – as long as the individual has access to information.

The nutritionist is blaming society as he believes that people are being “forced” to consume by the very nature of the choice set they are being given.  Ok, this is a value judgment – and one I strongly disagree with.  Why?  People still choose to consume, they could physically eat less, exercise more, or change the makeup of their diet – but they don’t.  This implies that people prefer to have a higher weight than incurring the cost to have a lower weight.

Now we have to remember that there is NO social cost from people putting on weight (unless it comes from other policy distortions), and there is no “co-ordination problem” in society involving weight so there is no market failure for us to correct.  Being fat is not a crime, it is not a bad – and trying to “reduced obesity” misses the point of what policy should be doing.

Note:  You will notice I assumed no co-ordination problem.  I would like to hear people try and build up possible co-ordination problems if they have some in mind.  Implicitly, the nutritionists argument relies on a sufficiently strong co-ordination problem to function.