Yearly Archives: 2011

201 – Reasoning with probabilities

I’m reading a very interesting book called Reckoning With Risk: Learning to Live With Uncertainty by Gerd Gigerenzer (holiday reading). He is a psychologist who specialises in the way that risk is communicated and perceived, or often mis-perceived.

One of his interesting points is that, even when well educated people (like doctors, for example) have accurate knowledge of probabilities related to a risk, they are often incapable of manipulating those probabilities in fairly simple ways to make sound judgements about the risk.

Here is a striking example. He asked 24 doctors (with an average of 14 years experience) the following question.

The probability that a randomly chosen woman has breast cancer is 0.8 percent. If a woman who has breast cancer undergoes a mammogram, the probability is 90 percent that the mammogram result will be positive (i.e. indicating that she does have breast cancer). If a woman who does not have breast cancer undergoes a mammogram, the probability is 7 percent that she will have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?

See if you can work out the answer, at least approximately. People who are used to working with statistics and probabilities – like, say, academic economists – should find it easy. (It’s an application of Bayes’ law (see appendix), but you don’t need to know that to solve it.)

Not surprisingly, most people find it very difficult to untangle information like this that includes conditional probabilities, even doctors whose job it is to advise people about these sorts of things.

Of the 24 doctors who responded to the question, only four got close. Most were wildly inaccurate, giving probabilities that were far too high. It seems like they had no idea how to tackle the question. The most common answer, but far, was 90 percent. But that obviously can’t be right because that would be the answer if all women had cancer, whereas 99.2 percent of them don’t!

This lack of probabilistic reasoning among doctors is a pretty concerning finding. You’d like to think that your doctors could provide sound advice about medical risks, if you wanted it, but in this case, at least, you’d be disappointed. It actually reinforces a feeling I’ve had a number of times that doctors who were advising me did not have a good understanding of probabilities.

Gigerenzer then did something quite clever. He reformulated the question in a way that made it much easier for people to think about, as follows.

Eight out of every 1000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don’t have breast cancer, 70 will still have a positive mammogram. Imagine a randomly selected sample of women who have positive mammograms. How many of these women actually have breast cancer? ____ out of ____.

This is the same information as in the earlier question (with some rounding). From this description, it is much easier to see that, of the 1000 women we are considering, 77 will have positive mammograms, and of those 77, only 7 will actually have cancer. Thus the answer is that 7/77 = 1/11 = 9% of women with a positive mammogram would actually have cancer.

Gigerenzer argues that this approach of reformulating probabilistic information into absolute numbers (i.e. it talks about 8 women with breast cancer, rather than 0.8% of women) will generally improve people’s understanding of risk. It certainly worked pretty well with another sample of 24 doctors. Almost half got the second version of the question exactly right, and most got it approximately right. Only 5 of the 24 were highly inaccurate.

That’s a big improvement, although I’m still worried that 20% of doctors could still get the answer completely wrong when the question is posed in such a transparent and intuitively obvious way. I hope they aren’t my doctors!

In follow up research, Gigerenzer investigated what the doctors actually did when they were trying to answer these questions – which numbers from the problem description did they use and how did they combine them. For the first more difficult description based on conditional probabilities, it became even clearer that the doctors didn’t have a clue what to do. Only 20% of them used the same reasoning strategy again when the question was repeated for a different medical test. Clearly, they were just guessing, and overwhelmingly guessing wrong.

Given the intuitive problem description, more doctors used the right reasoning strategy and applied it consistently, but there was still a disturbing number who didn’t.

It certainly will make me want to explore the probabilities more deeply with my doctor when I next have a medical diagnosis.

Appendix: Using Bayes Theorem to solve the problem

Bayes Theorem: P(a|b) = P(b|a)*P(a)/P(b)

where
a = has breast cancer
b = has positive mammogram

From the problem description:
P(a) = 0.008
P(b|a) = 0.9
P(b) = 0.008*0.9 + 0.992*0.07 = 0.077

So
P(a|b) = 0.9*0.008/0.077 = .094

That is, if a woman at random has a positive mammogram, the probability that she has breast cancer is 9%. The intuitive approach, based on absolute frequencies, is clearly much easier to think about than this, although it amounts to the same thing in the end.

Further reading

Gigerenzer, G. (2002). Reckoning With Risk: Learning to Live With Uncertainty, Penguin, London.

200 – Blog

This is Pannell Discussion number 200. To mark the occasion, I am finally responding to many requests from readers and converting the site to a blog format, with a facility for readers to comment on each post.

My main motivation for starting Pannell Discussions in 2004 was to communicate economic ideas, principles and theories to a wide audience, in a way that engages people and gets the ideas across clearly. I wanted people to see the relevance and interest of economics, and to dispel myths, misconceptions and misunderstandings about it.

I also wanted to raise awareness about my research that might otherwise have sat relatively unread in academic journals.

Seven years later, judging from the number of readers and the feedback I get, the site has achieved those objectives quite well. There are 600 subscribers, and the more popular articles get read by over 1000 people (or at least loaded onto their computer screens).

I think the benefits have been greater than I anticipated. On the cost side, I aim to spend no more than an hour on each one, so it’s not a big burden. And, anyway, I quite enjoy writing them.

I also haven’t found it difficult to identify topics to write about. They often seem to present themselves.

So here we are in blog land. I resisted moving to this format for a long time because I was put off by the tone and quality of ‘debate’ you see on some blogs and because of the extra work it might generate. For the time being I am going to approve each comment before it gets posted. I’ll see how it goes.

Some blogs have rules for commenting, and I think that’s probably a good idea, so here are mine.

  1. No abusive comments. No ad hominem attacks, slurs or personal insults. Do not attribute motives to another participant.
  2. Restrict comments to the topic of the Pannell Discussion.

People are still welcome to email me with comments that they don’t wish to make public.

Not all of the old posts have been converted to the new format yet. We’ll be working on that over time.

My other little celebratory gesture for reaching 200 issues is that I’m nominating the site for the 2012 Quality of Research Communication Award of the Australian Agricultural and Resource Economics Society. If anyone would like to quickly email me or post below a comment about Pannell Discussions that I could include as an attributed quote in the entry documentation, that would be much appreciated. The closing date is 30 November 2011. NOTE: I have submitted the nomination now.

199 – Three Gorges Dam

The Three Gorges Dam is an amazing construction, with major benefits for the Chinese people. However, like any large project, it also has large costs and risks.

As revealed in PD198, I was lucky enough to visit the Three Gorges Dam in October. It was a fantastic experience. The group I was with (led by Professor John Langford and Dr Yongping Wei from Melbourne University) was able to get amazing access to the dam and the organisation that built and operates it. The Three Gorges Corporation was a remarkably generous host, particularly its Vice President, Dr Fan Qixiang.

I’ll never forget my visits to the top of the dam wall and to the operating room for the hydro-electric power station, nor my ride on the reservoir in a large boat. The sheer scale of the dam is staggering. The dam wall is 2.3 km long, and its top is 180 m high above the rock base. The reservoir is about 660 km long and averages 1.1 km wide.

Being an economist, my natural tendency is to think about the dam from the perspective of a Benefit: Cost Analysis (BCA). Here is a summary of what seem to be its main benefits, costs and risks.

(Of course, it’s too late for a BCA of the dam to be useful. I’m just using the Three Gorges Dam to illustrate BCA-style thinking about a large, complex project.)

Benefits

(a) Flood prevention. This is seen by the Chinese as the biggest single benefit. Last century, major floods on the Yangtze led to losses of tens of thousands of lives, disruption and dislocation for many millions of people, and massive losses of production and infrastructure.

(b) Electricity generation. It’s the largest power station in the world. At full capacity, the dam generates around 22,000 MW of electricity. This alone will be sufficient to cover the dam’s full financial costs within a decade or so of reaching full operating capacity.

(c) Reductions in CO2 emissions. According to one estimate, the dam avoids 100 million tonnes of CO2 emissions per year (plus reductions in other air pollutants). If these emission reductions are valued at $30 per tonne, this benefit is worth $3 billion per year.

(d) Enhanced navigation of the river. From 2004 to 2007, 200 million tonnes of goods passed through the ship locks. It is estimated that transport costs have been reduced by 25% compared to trucking.

Benefits (b), (c) and (d) would be relatively straightforward to quantify in dollar terms, so long as their predicted levels were accurate. Benefit (a) is more challenging, of course. Economists use the “value of a statistical life” concept, inferring the value of life from the costs that people are willing to bear to reduce their own risks of dying, or the additional risks they are prepared to take in return for financial compensation. This approach is not without debate, but it is at least a useful starting point. The benefits of avoiding the temporary movement of millions of people might be possible to estimate with a survey-based approach, including a non-market valuation component.

Costs

(a) The financial cost of dam construction. This was something of the order of $15 billion.

(b) The financial cost of resettling around 1.2 million people to new accommodation so that they weren’t inundated or endangered by the dam. This also cost around $15 billion. It was interesting that the Chinese spent about as much on this as on constructing the dam itself.

(c) Social costs. In the west, we view forced movement of people of such a scale with amazement, perhaps even more so than the dam construction itself. But in China this is by no means the only example of such mass movements of people. The cost of the inconvenience of moving would be high, but it should be remembered that without the dam, that cost would be even higher as many more people would be forced to move due to floods. The main social cost specific to building the dam is the permanent loss of connection to the particular places where these people grew up, and loss of connection to particular communities of people. Someone said to us that it was mainly the older people who felt this, which seems plausible to me. Given that China is urbanising at a rapid rate, it’s likely that many of the younger affected people would have moved anyway, at their own expense, sooner or later.

Including this cost in a BCA would require it to be estimated using non-market valuation studies.

(d) Environmental impacts. Any construction of this scale is bound to have environmental impacts. In 2008 Scientific American magazine published an article about the dam using language like “environmental catastrophe” and “environmental cataclysm”. While the reality of serious environmental impacts is officially acknowledged, I reckon that article is particularly unbalanced, and includes some rather woolly thinking. They really needed a BCA framework to help them think through the issues in a more logical and balanced way.

Likely environmental costs include extinction of endemic species from the area that has been inundated (there are 57 endangered plant species growing in the region that may be adversely affected to some extent) and loss of fish species by changing the physical environment and reducing the ease of migration (there are 25 endangered fish species in the river, mainly due to over-fishing). The biggest challenge we would face in trying to include these impacts in a BCA would be estimating how many species would actually be lost. Even in the Scientific American article, which leans very much towards a negative perspective, it is pretty clear that we have very little idea what has been lost, or will be lost, due to the dam.

(e) Loss of archeological sites. According to http://china.org.cn/english/culture/66021.htm, artifacts present in the area that was inundated included prehistoric cultural relics dating back to the Old Stone Age more than two million years ago, and cultural sites of ancient dynasties from the Xia Dynasty (21st Century BC to 16th Century BC) to the Qing Dynasty (1644-1911). Huge quantities of archeological material were moved before the dam was filled, but no doubt much is now deep under water. And archeologists say that a moved artifact is not as valuable or informative as one that remains in situ.

Risks to the benefits

(a) Landslides and sedimentation. Sedimentation is a risk to most dams. Over time, it reduces the capacity of a dam to do what it was built for. There have been a number of significant landslides reported, contributing to this sedimentation. However, the Three Gorges Corporation said to us that the rate of sedimentation so far has been less than predicted.

(b) Earthquakes. The region is subject to earthquakes. It has been suggested that the weight of water in the dam may cause an increase in the frequency of quakes, or that a major earthquake might cause the dam to fail. That would potentially be an almost unthinkable tragedy, given the millions of people who live downstream.

(c) Water quality. Building the dam provided an impetus for authorities to improve the quality of water that leaves settlements and cities upstream of the dam. Nevertheless, problems with water quality remain a risk. When we were there, the water quality appeared to be pretty good, but this is something that typically fluctuates.

Quantitatively weighing up all these positives, negatives and risks would be exceptionally challenging. Nevertheless, organising our thoughts using the framework of benefits, costs and risks is helpful.

If it is true that the revenue from electricity is sufficient to cover the project’s financial costs, then an overall assessment would come down to whether the benefits of reduced flooding, reduced CO2 emissions and enhanced navigation are sufficient to outweigh the costs of social, environmental and archaeological losses, allowing for the three risks.

I don’t have a good feel for the risks, but I know that they were studied intensively before the dam was approved, so presumably they are not excessive. If that’s true, my hunch would be that the benefits are easily sufficient to outweigh the costs. But I’d readily concede that that’s just one person’s partially informed judgment.

198 – Chinese air pollution

China impresses visitors with what a “can do” place it is. One thing they haven’t decided to do yet is fix their air pollution problem. Beijing residents seem to be fairly oblivious to it but I found it hard to ignore.

In the 19th century, London was famous for its air pollution. The endless smog made its residents sick (and sometimes killed them), put a layer of grime on everything in the city, and reduced visibility drastically. The main cause was burning of coal in homes and factories. After about 1890, thanks to reductions in living density, the growing use of gas for cooking, and, to a small extent, the Public Health Act of 1891, air quality in London began to improve. Pollution fell steadily over the following century, reaching about 3% of its 1890 level by 2000 (Fouquet, 2011).

Air pollution in Beijing today is actually not as bad as it was in London 120 years ago, but it’s pretty bad. I spent three days there last week, and found the pollution endlessly fascinating. At times, one could not even see a block away. Apart from the physical feeling of having something bad in my chest, and the need to cough regularly to clear it, the smog affected me psychologically. The fact that I couldn’t see far enough to get any sort of perspective of the lie of the land, and couldn’t see whether it was sunny or cloudy above the murk, made me feel closed in.

Just like in London, a major contributor to the problem in Beijing is coal, although this time it is being burnt in power stations rather than homes and factories. As well, there are many other sources, as you’d expect in a city of 21 million people.

In the second half of the 20th century, regulation made important contributions to reducing air pollution in London and in other western cities. Environmental economists also convinced some governments to use market approaches, particularly in the US. These too have been very successful in some cases, with the most famous example of this approach being the use of a cap-and-trade system to reduce sulphur dioxide pollution in the US. (This scheme has recently fallen over for administrative/legal reasons, rather than economic ones, but that’s another story).

I expected the bad air pollution in Beijing, as it’s been widely reported. What I wasn’t prepared for was how bad it was outside major cities. I visited the Three Gorges Dam — perhaps the ultimate example of “can do” in the world. From the tourist lookout built to help tourists admire the dam, one’s ability to appreciate this awesome engineering achievement was somewhat hampered by an inability to actually see it!

Here is a photo, taken from the lookout, of the dam wall.

And here is a shot from the dam wall across the reservoir towards the scenic gorges.

One of our guides told us that the main problem was a phosphorus mine nearby. Another said that the area had always been subject to fog, but that it had got worse recently. To the extent that it is caused by pollution, it is, perhaps, surprising that they allow it to occur here, shrouding such an an iconic symbol of national achievement.

Nevertheless, this being China, every problem is an economic opportunity. I was originally bemused to see, just near the lookout, a booth offering to take photos of tourists with the dam behind them. It seemed like a forlorn venture, given the poor visibility. I couldn’t understand why they seemed to be doing a steady trade.

But look at the name of the business. They aren’t joking. Realising that people would be mighty disappointed to come to the dam and walk away without a decent photo, someone hit upon the brilliant idea of photographing people and then using Photoshop to add them to a photo of the dam taken on a rare clear day — well, relatively clear. How could I resist! Giggling madly, I bought the following totally fake picture. Priceless!

I expect that, sooner or later, China will apply its “can do” approach to environmental management. Perhaps it has already started. The China Daily while I was there had an article titled ‘Environmental rule set to shift’. It said, “Local governments at all levels are expected to face stronger obligations to protect the environment, and polluters will face much heavier fines, according to a draft proposal to amend China’s decades-old Environmental Protection Law” (China Daily, 10 Oct 2011, p.7). It will be fascinating to see whether this is the start of a new environmental commitment.

David Pannell, The University of Western Australia

 Further reading

Fouquet, R. (2011). Long run trends in energy-related external costs, Ecological Economics 70: 2380-2389.

197 – The Danish fat tax

About a week ago, Denmark introduced a new tax on fat in foods, in an effort to improve the health of Danes. The general idea is consistent with the sort of thing that environmental economists often recommend for other bad things, like pollution (e.g. a carbon tax). But is it sensible in this case? I have my doubts.

My daughter is currently living in Denmark and struggling a bit with the high cost of living there. So a further cost increase is the last thing she wants.

The system involves a tax of 16 kroner ($A3.00) per kilogram of saturated fat. Economists recognise two effects of this sort of tax: (a) it makes fatty foods more expensive relative to other goods, so people change how they allocate their income between alternative purchases (a “substitution effect”), and (b) as a result of having to pay the tax, people have less disposable income, and this leads to a reduction in their consumption of all goods, including of fatty foods (an “income effect”). Both result in less consumption of the good that’s being taxed, although the substitution effect is far more important in practice.

So the idea sounds OK, but it’s worth asking, would the approach really work in this case? The effectiveness of such a tax depends mainly on how responsive people are to the prices of the goods in question. It’s well known that responsiveness to price (which economists refer to as “price elasticity”) varies a lot between different goods.

Consumer demand for fat in foods strikes me as the sort of thing that is unlikely to be responsive to price. My reasoning includes that:

  • Fat is only one ingredient of a food, so changes in the cost of fat would have a less than proportionate effect on the cost of the food as a whole.
  • In developed countries, food is only a small proportion of our total expenditure. If its price goes up a bit, it would be possible to cope without greatly altering one’s consumption patterns.
  • People already know that fat is bad for them, but they still choose to buy fatty foods, basically because they taste good. I would not have thought that a modest increase in prices would change that much.

There is some empirical evidence to support my feeling that increasing the price of fat won’t change behaviour much. For example, Chouinard et al. (2007) find that a tax on milk in the USA in order to reduce fat consumption would have to be enormous to have much impact. For example, they say that “a 50 percent tax only lowers fat intake by 3 percent.” That’s a 50 percent tax on the milk as a whole, not just the fat component. Whole milk is about 3.3 percent fat. By my rough calculation, a 50 percent tax on milk would be about 10 times bigger than the new Danish tax, for a really small impact.

Similarly, Brownell et al. (2009) also concluded that moderate sized taxes on soft drinks basically have no impact on consumption.

Although it wouldn’t change behaviour much, these taxes would collect plenty of revenue. Indeed, if revenue collection was the aim, fat might be the ideal target for a tax, specifically because people would keep buying it, even with the tax.

This means that there is potentially an important negative consequence of the tax: it would have a disproportionately large impact on people with low incomes. They spend a larger proportion of their income on food, so the tax would have a larger proportional impact on them. Actually it might have a larger absolute impact on them, because the incidence of obesity is higher among low income groups, so presumably they spend more on fat. Chouinard et al. (2007) argued that “these fat taxes are unattractive because they are extremely regressive, and the elderly and poor suffer much greater welfare losses from the taxes than do younger and richer consumers.”

Ineffective and regressive doesn’t sound like a good tax to me.

A third problem is the specific way that this tax is designed. Apparently, the level of the tax is based on the amount of fat used in making the product, rather than the amount in the end product. If that’s true, it seems ridiculous. If the point is to improve health, why would you want to tax fat that people aren’t actually eating?

Finally, I would imagine that the system would have quite high transaction costs, such as costs of administration, reporting, monitoring, enforcement, learning, and so on. If the system would really work, they could be worth bearing, but probably not in this case.

On a more positive note, it may be that revenue from the tax could be used for other purposes that would contribute to improved health outcomes, such as research or health education. I suspect that this is the most likely route for the system to generate worthwhile benefits, although, of course, governments could use the existing tax collection system to invest in those things and thereby avoid the regressive nature of this tax.

David Pannell, The University of Western Australia

Further reading

Hayley H. Chouinard, David E. Davis, Jeffrey T. LaFrance, and Jeffrey M. Perloff (2007) “Fat Taxes: Big Money for Small Change”, Forum for Health Economics and Policy 10(2): Article 2. http://www.bepress.com/fhep/10/2/2

Kelly D. Brownell, Ph.D., Thomas Farley, M.D., M.P.H., Walter C. Willett, M.D., Dr.P.H., Barry M. Popkin, Ph.D., Frank J. Chaloupka, Ph.D., Joseph W. Thompson, M.D., M.P.H., and David S. Ludwig, M.D., Ph.D. (2009). The Public Health and Economic Benefits of Taxing Sugar-Sweetened Beverages, New England Journal of Medicine 361:1599-1605.