Australia and greenhouse gas emissions

Two people (one friend, one student) have sent me this story about Australia’s bad environmental placing. I did, to be fair to them, see it first in the Sydney Morning Herald (i.e. before these two emails, by a long way, and before the BBC had it, I believe).

The story: a study/database, Carbon Monitoring for Action (CARMA – aren’t they clever?) has been stitched together for the purpose of figuring out, globally, whose industries are up to what. Alley-oop:

Australia’s contribution to global warming may be much greater than first thought. New research shows our power stations are the world’s highest per capita producers of carbon dioxide.

…

shows the two biggest producers of CO₂ in Australia are in NSW – the Bayswater station at Muswellbrook and Eraring near Lake Macquarie, which each produce 18.325 million tonnes of CO₂ a year.

Their level of CO₂ to power output is comparable to many of the power stations in China often criticised for being dirty plants.

The survey shows Australians each produce more than 10 tonnes of CO₂ emissions for every person just through generating power, compared to nine tonnes for each American and two tonnes for each Chinese.

I’ll just assume they meant each Chinese person (wtf? Get an editor, people).

This is not news, really. Comparing ecological footprints, the US, Australia and Canada place 1^st, 2^nd and 3^rd. It would stand to reason, then, that a rank of greenhouse gas emissions would replicate that. Canada manages to stay clean, though, or at least outside the top five (in emissions per capita):

1. Australia – 10.0 tonnes
2. US – 8.2 tonnes
3. UK – 3.2 tonnes
4. China – 1.8 tonnes
5. India – 0.5 tonnes

That list from the BBC – I can’t get the CARMA site up. The list in total terms changes, of course: the US and China are the top two (unsurprisingly).

The SMH story closed on some interesting details:

Dr Wheeler said his data had been compiled from public records and by extrapolating from a commercial database used by the power industry. Where disclosures of CO₂ emissions were not publicly available, the researchers used modelling based on the age and size of the power station.

“Information leads to action,” he said. “We know that this works for other forms of pollution and we believe it can work for greenhouse gas emissions, too. We expect that institutional and private investors, insurers, lenders, environmental and consumer groups and individual activists will use the data to encourage power companies to burn less coal and oil and to shift to renewable power sources.”

I would like to see which countries/power plants required that inferencing. China’s lack of any sort of pollution controls at the plant-level are well-enough known – do these numbers under-estimate their carbon-load? Method can make a lot of difference. Not that it matters a great deal. For us to even be on such a list is as great a shame as it is entirely not surprising.

Also, much as I like the idea that information leads to action, one can only hope: information has, one would think, been sufficent to prompt action before now, yet the likes of Australia, the US, China and the UK are clearly not giving up on coal. Hell, we’re building more plants at mines.

To the extent that this information has an effect, I would expect, just as cynically as is reasonable, to see more palliative efforts at pollution control (probably not including China), but no less use or demand for coal-fired energy.

Hannah Montana fan club members to sue the fan club. Hopefully the judge is a Bayesian

This is a re-post. For some reason pieces of the original did not upload and I was too tired to even check. This morning I added the regression stuff.

While I’m in the mood to update old stories: here’s the latest one about Hannah Montana

Thousands of “Hannah Montana” fans who couldn’t get concert tickets could potentially join a lawsuit against the teen performer’s fan club over memberships they claim were supposed to give them priority for seats.

The lawsuit was filed on behalf of a New Jersey woman and anyone else who joined the Miley Cyrus Fan Club based on its promise that joining would make it easier to get concert tickets from the teen star’s Web site.

…

“They deceptively lured thousands of individuals into purchasing memberships into the Miley Cyrus Fan Club,” plaintiffs’ attorney Rob Peirce said. His Pittsburgh firm and a Memphis firm filed the suit Tuesday in U.S. District Court in Nashville.

The fan club costs $29.95 a year to join, according to the lawsuit, which alleges that the defendants should have known that the site’s membership vastly exceeded the number of tickets.

What an interesting club they have. At least they like to do things together? It seems these are people who either (a) honestly did purchase membership with this club in order to get preferential access to concert tickets, or (b) are now saying they did because taking responsibility for things just not working out is so unfashionable, these days. Who knows.

I guess it’s just a lawsuit, like any other. I’ve looked around: I don’t see any mention of the actual number of members of this fan club (perhaps it’s made known once you are a member and log in?). If this number was known then, yes, I would say it should be clear to members that more people will want tickets than will get them. “Thousands” are in on this lawsuit, so I figure it ought to be a lot.

The solution is simple: compare the two sets of people, members and non-members. There must be some measure of the non-member fans of the girl – perhaps people who tried and failed to get tickets via the members’ site? If, conditional upon being a member, one was in fact more likely to have gotten tickets than the general public, there is no lawsuit. If the opposite is found (i.e. if there appears to have been no advantage), there there is a lawsuit.

Bayes’ Theory

Enter Bayes’ theory: suppose we want/need the probability of getting tickets conditional upon being a Miley Cyrus Fan Club member. We don’t have that, per se. What we do have is the probability of being a Fan Club member conditional upon (a) getting tickets, and (b) not getting tickets. With this, we can work.

First, define A₁ = Getting Tickets, A₂ = Not Getting Tickets, B₁ = Fan Club Member and, finally, B₂ = Not A Fan Club Member.

So, the probability we need is

to compare to

What we observe (or can observe) are , , and , where (for example)

and so forth. Now, the probability

for example, gives us

Repeating that, we see that the probability that we need is given by

This is because our outcomes are clearly defined: they are mutually exclusive, and they are exhaustive – i.e.

Same for B₂. Thus will we get the two numbers that need to answer the questions: (1) what was the probability of getting tickets conditional upon being a Miley Cyrus Fan Club member; and (2) was it greater than the probability of securing tickets conditional upon not being a fan club member? I should point out here that the tricky part of this is going to be finding A₂ and Pr(A₂ ). Less so, perhaps for members of the Miley Cyrus Fan Club than for the general population. The value of that information will make a very big difference to our conditional probabilities: what if, for example, they are different numbers, but very similar numbers? How different do they have to be? Enter the (pronounced ky, to rhyme with sky) test for independence.

Chi-squared

The test for independence will test for us the null hypothesis (the default hypothesis) that , versus the alternative that . For this we need all four possible joint observed cells:

If the two probabilities are in fact equal, then we would expect to see (for example):

Then we calculate our test statistic:

(This equation refuses to convert. I’ll fix it later). Here you go (anyone want to explain why the equation beats the WordPress renderer?):

I.e. the sum of the squared values of the (observed – expected) cells for each of the two outcomes. This could also be done the other way around, or using the Tickets columns, rather than the Membership rows. With n – 1 = 1 degree of freedom, we just need that statistic to be greater than 3.84:

to reject our null hypothesis and conclude that the distribution of ticket-getting was in fact different for Miley Cyrus Fan Club members than for non-members. If the members had a higher conditional probability of securing tickets then, again, there is no case. If they are not statistically significantly different, they’ve been ripped-off. Again, whether they should have known this beforehand is a matter for a jury: we just do the numbers.

Done? Not even close. What if there was more to it than that?

Regression

Regression analysis: regression analysis will offer two distinct advantages in this instance; one for the prosecution, and definitely if the defence has demonstrated, above, than Miley Cyrus Fan Club members did in fact get a better deal on tickets than non-members, and one for the defence, for the same reason:

1. Regression analysis will be able to quantify the degree to which being a member of the fan club increased the probability of securing a ticket to the show(s).
2. Regression analysis will be able to identify the statistical significance of the relationship between fan club membership and ticket-securing, controlling for other factors.

Our regression model appears thus:

Keeping it simple Ordinary Least Squared. That is part (1): this model will positively identify whether being a member of the fan club (a dummy variable: 0 = not a member; 1 = member) affects the probability of securing tickets. For purposes of compensation, it will also quantify the degree to which that probability increased (if it increased at all).

However. What if there was some other difference? We know, for example, that scalpers landed on these tickets like (insert joke here – who don’t you like?). Suppose Miley Cyrus Fan Club members differed in some specific other respect? Perhaps they just didn’t log on as quickly? Do they have a slower connection? Was a child doing it with their parents credit card (the assumption being that they were slower to manoeuvre the system)? On to multiple regression! Controlling for these factors, our model becomes:

The more statistically significant explanatory variables we introduce into our model, the less statistically significant (and, probably, economically significant) will become, and the weaker will become the class action lawsuit against the Hannah Montana people.

Seems like a waste of perfectly good econometrics/statistics, one might think. The suit will probably contain every fan club member who did not get a ticket, though, asking for triple damages plus legal fees. I reckon it’s worth the effort for the companies being sued.

I keep telling my students that econometrics can do everything…

China, iron ore and how to just be crap at economics and diplomacy

Updating my odd and new-found interest in iron ore: an interesting story by way of the Sydney Morning Herald.

China’s fragmented steel industry is approaching a consensus that it can do nothing to stop BHP Billiton from swallowing Rio Tinto.

…

A merged BHP and Rio would control close to two-fifths of traded iron ore and almost one-fifth of traded alumina.

China’s steel companies are seen as too small to afford a meaningful stake in Rio Tinto and too parochial to combine their resources effectively.

“It is the most fragmented steel industry in the world – to band them together has proved impossible,” said the Steel Business Briefing spokeswoman.

Many of the largest steelmakers, including Baosteel, Angang and Wugang, say they have no plan to buy Rio shares and they don’t expect to snap up “spare” iron ore assets either because they will be expensive or there won’t be any.

The argument in favour being one of vertical integration (comma, backwards): since China’s steelmakers are in the market for so much of the iron ore, and if Rio Tinto is still non-subtley inviting offers, why not have Chinese companies get control of Rio Tinto? They can

1. keep iron ore prices down (as they want to do), and
2. prevent Australian ores from falling into a monopoly (and nothing ruins the fun of monopsony purchasing power faster than monopolies – just ask Wal-Mart).

If BHP can use the merger to save as much money as it’s suggesting, so can PetroChina, surely.

According to the Sydney Morning Herald, though, (a) Chinese firms just can’t get along well enough for to work itself out, and (b):

… the Chinese Government is redoubling efforts to artificially dampen iron ore demand during the secret but all-important contract price negotiations.

The official Xinhua news agency says the Government is prepared to use macro-economic controls to dampen demand as well as steep steel export tariffs.

“It is expected that the spot market for imported iron ore will be greatly influenced by the policy,” said Xinhua.

This would be par for the course, for the Chinese government – but really, can a government be so oblivious to (a) basic economics or (b) basic requirements of getting along with others? I’ve posted several times, with respect to the Yuan, that China will do that which is in her interests, just like any other country will. They have the people, the standing army, the cash, the macroeconomy – is there anything, either stick or carrot, that we have? Not really, no. I’d like to see us try our hand at, say, kicking them out of the WTO: we bloody need them, and they’ve got us right where we wanted to be.

I will, nevertheless, be interested to see the Chinese government employing macroeconomic policy tools in an attempt to suppress their entire macroeconomy in order to dampen the demand for iron ore (that would be the derived demand for iron ore, following the derived demand for steel).

For a start, I must assume it is a bluff: if China could slow their economy down, they’d probably be trying to do so – stable prices kind of make the single-party rule acceptable; not being able to afford food is going to cause a lot of friction.

Secondly, though, perhaps they see a better after-effect. If the Chinese government credibly threatened to play the bench-mark negotiations on this sort of scale, I can’t imagine anything more likely to push Rio Tinto and CVRD into a free market. This would benefit China (assuming it hadn’t, in the process, completely bollocksed-up its economy and pissed off every country in the OECD, WTO, NATO – it’d be a long list).