De minimis

Paul Chambers' absurd conviction for sending an ill-judged joke tweet has finally been quashed.  (Jack of Kent has covered the case extensively.)   After the judgment, a spokesperson for the Crown Prosecution Service said:

Following our decision to charge Mr Chambers, both the magistrates' court and the crown court, in upholding his conviction, agreed that his message had the potential to cause real concern to members of the public, such as those travelling through the airport during the relevant time.  Neither the courts nor ourselves thought it relevant that no member of the public is known actually to have been so concerned.

Presenting our case obliged those courts and the High Court, as well as the defendant and his lawyers and supporters, to waste an extraordinary amount of time and money, and caused real damage and distress to an actual person, the defendant. We have noted and accepted the court's reasoning in quashing the conviction.  All of us responsible for this case at the CPS resign our positions with immediate effect, being resolved to spend the rest of our lives in poverty, doing such good works as we can, in the hope of mitigating in some small way the damage we have done.

There seem to be some not insignificant transcription errors in the BBC's reporting of the statement.

The Second Amendment

From time to time, a nutter with a gun in the USA goes postal.  Everyone mourns the lives lost.  Europeans reflect that if everyone has guns, homicidal nutters have guns.  Americans observe that good people need guns to defend themselves from bad people, and that the Second Amendment says they're entitled to bear arms.

It's worth looking at what the Second Amendment actually says.

A well regulated militia being necessary to the security of a free State, the right of the People to keep and bear arms shall not be infringed.

 Its meaning has been debated on three counts.  First, there are additional commas in the version passed by Congress: Geoffrey Pullum recommends ignoring them.  Since no one at the time seems to have troubled themselves over whether the commas should be there or not, that seems sound to me.

Second, what does "bear arms" mean?  It's been argued, notably in the linguists' brief in D.C. v. Heller, that it means to carry weapons in an army or militia.  The majority view of the Supreme Court prefers the more general meaning that one might expect; the minority view dissents, each side citing persuasive examples of usage to support its case.  It's clear to me that the meaning of "bear arms" depended then, as it does now, on the context, which doesn't get us very far since our problem is to understand what the context might be.

Third, and to me most importantly, what is the prefatory clause about the militia doing there at all?  Why not keep it snappy and just put "The right of the People..."?  The linguists' brief explains that grammatically the opening clause is an 'absolute construction' which should be interpreted by prefacing "Because", and the majority view of the Supreme Court was happy to agree with that.  Eugene Volokh argues powerfully that in explaining its objective the Second Amendment does not mean to restrict its scope to the satisfaction of that objective.

I suggest that another reading is possible.  Consider this:

The weather being so hot, staff are permitted to take off their jackets in the office.

Everyone would agree that the permission to undress applies only for the duration of the hot weather. This sort of interpretation has been considered in detail by Stump (p62), whose work is explained in less technical language by Fernald (p21).  The summary seems to be that if the absolute clause is time-limited, the operative clause applies only for the limited time.  So if the necessity of a well-regulated militia was envisaged not to be permanent at the time of the enacting of the Second Amendment, and if it has now lapsed, then the Amendment is now null.

So what was understood by the legislature at the time it passed the Amendment, and by the States when they  ratified it?  We might look at James Madison's earlier draft:

The right of the people to keep and bear arms shall not be infringed; a well armed and well regulated militia being the best security of a free country: but no person religiously scrupulous of bearing arms shall be compelled to render military service in person.

It's clear that he envisaged no temporal restriction.  But that's largely irrelevant.  The legislature in adopting the Amendment chose not just to delete the 'Conscience Clause' but also to move the absolute clause to the beginning, thus making the meaning less clear.  Why did it do that?  I can think of only one reason, which is that a certain ambiguity was required to get the Amendment passed - political fudge is not a recent invention.  The legislature did not agree to create an unambiguous constitutional right for the individual to keep and bear arms.  Very probably many of its members would have been in favour of such a right, had they considered the question at all, but then very probably they would have been in favour of all sorts of things that are not part of the US constitution.  (This is an example of the general weakness of interpretation according to original intent.)

I suggest that in this case, where the legislature has wilfully declined to make itself clear, it is the duty of the Supreme Court to consider present circumstances rather than to seek to divine what a majority understanding of the original meaning might have been in 1791.  And present circumstances strongly suggest that it is not best to permit the general population to keep and bear semi-automatic weapons.

The Price of Milk

It's important for politicians to know the retail price of a pint of milk - it's 49p in the supermarkets, or 29.5p per pint if you buy a four-pint (plastic) bottle.  That's equivalent to 86p and 52p per litre.

However, the producer price is substantially less.  Marks & Spencer, Waitrose, Sainsbury's, and Tesco sign up farmers to medium-term contracts which link the price they pay for milk to production costs: this gives prices currently in the range 29-32p per litre.  Otherwise prices are below that: the average in May was 27p per litre.  Dairy farmers complain that at prices below about 30p they are making a loss.

So what's going on?  Tim Worstall is ready as ever with a neo-liberal analysis:

This is how the system is supposed to work. Too many dairy farmers producing too much milk? Some should go produce something else: that loss is the stick with which to beat them into it. It's not the supermarkets causing these losses. It's not us being mean when considering the price of a bowl of cornflakes either. It's that dairy farming has become more efficient:

The latest provisional figures from Defra show a 4.7 per cent (331 litres per cow) increase in the average yield per cow from 2009/10, to 7,406 litres per cow in 2010/11.

Is this a one off, a single year's blip? No:

The average yield in 2010 was 22.4 per cent (1,336 litres per cow per annum) higher than ten years previously when the average stood at 5,979 litres per cow per annum.

Assume that milk demand stayed static: a 22 per cent rise in output per cow means that we need 22 per cent fewer cows...

I don't know whether Worstall is being careless or disingenuous, because he's skipped past a table (on the page he links to) which shows that total UK milk production fell by 5% in the nine years to 2010.  To be fair, we should include the change in 2000-1, which according to this document (which gives similar but not identical data) was a 2% increase, so the fall over the full 10-year period would be 3%.  The increased yield and falling production implies a decline by 20% of the number of dairy cows (percentages don't work quite as simply as Worstall guesses, a 20% fall in one factor cancels a 25% increase in another, 0.8*1.25 = 1).  (This page reports a decline in dairy cow numbers of 7.2% in the last five years.)  And the number of dairy farms has fallen by about 35% over the eight and a half years - production has concentrated in larger, presumably more efficient, farms.

What these figures show is that whereas yields have risen, falling numbers of cows and farmers have more than compensated for it.  The system has already worked as Worstall says it is supposed to.  Low producer prices are not as he claims due to rising milk yields.

Are British farmers being outcompeted by the rest of the EU?  No.  UK producer prices are lower than in any country we could plausible import fresh milk from.

Are producer prices falling because consumers are getting a great deal?  No, over the last ten years the Consumer Prices Index has gone up by 28%.  The price of a pint of milk has risen by the same 28%.

What about demand for milk?  Liquid milk consumption per person fell by 17% over the ten years.  The UK population rose by 6%, implying a 12% fall in liquid milk consumption.  However, there was increased consumption of yoghurt, cheese, and butter.  I can't be precise about the amount of milk that went into making those products, but I estimate it would compensate for about half the fall in demand, implying a net fall in demand of 6%.

So it does seem that over a decade, demand has fallen slightly more than supply.  Is that the cause of falling producer prices?  If it is, the market must be rather unstable.  Why?

I suggest that the explanation lies in the structure of the milk market, and that it's possible for producer prices to fall below production costs even if there is no oversupply.  First, fresh milk is a perishable product - you have to sell it almost as soon as you produce it, you can't hold out for the best price.  And if a farmer fails to sell his milk he loses its entire value.  Second, while overseas supplies are more expensive, they're not ruinously expensive, even including transport costs, compared with retail prices.  So if a retailer fails to buy milk from a UK farmer, he has viable alternative, it costs him just a few pence more per litre.  Third, retailers have diversified businesses and are not dependent on profits from milk sales, unlike dairy farmers.  And fourth, you can't turn dairy production off and on at will.

The effect of these factors is that all the bargaining power is in the hands of the retailers - they can drive prices down to levels at or below production costs, and farmers have no choice but to accept.  And retailers, who operate in a competitive market, have every reason to cut their costs when they can.

So where are we heading?  If dairy farmers aren't exaggerating their problems, several - more than 3% - will go out of business soon.  Producer prices will then rise, and retailers will have to import some of the milk they sell.  The cost to the retailer will go up, and very likely they'll pass that on to consumers.  Everyone will lose, except for the continental farmers who get a higher price for their product, and the providers of refrigerated transport who bring it here.

The fundamental point is that markets do not always produce efficient outcomes, at least not on a time-scale we care about.

Which brings us back to the supermarkets mentioned above who pay contracted farmers relatively generously.  I doubt that that's just because they're caring human beings, or because they think it good public relations.  My guess is that they are concerned about a collapse in UK production, and they think it worth paying a modest premium now to secure cheap supplies in the future.  Perhaps former dairy farmers would manage half a smile at the sight of the Asda paying up for imported milk while Tescos get the stuff cheap from the farmers they've kept in business.

Bunhill Fields

Carlisle Rainey and David Spiegelhalter, among others, have been chiding the press for sloppy reporting on the search for the Higgs Boson.  The context is the recent experiments using the Large Hadron Collider which seem to have identified a particle consistent with the expected properties of the Higgs Boson, with only a very small probability - one in 3.5 million - that the observed results would be seen if we were just observing random noise.  Rainey and Spiegelhalter's point is that this small probability is not at all the same as the probability that we have not discovered some new particle, or the Higgs Boson in particular. They cite sundry reports which fail to appreciate the difference.

Whereas I am not much concerned about the general grasp of the Standard Model of particle physics which predicts the existence of the Higgs Boson, I think it quite important that as many people as possible should understand the scientific notion of hypothesis testing.  So I'm going to make my own attempt to convey the message.

Suppose we have a hypothesis A which we wish to test.  We devise an experiment which will always give result B if A is true, but will sometimes give that result B if A is not true.  We can calculate the probability of getting B when A is not true, call it p.  We conduct the experiment and get result B.  What now is the probability that A is true?

The answer is that there's not enough information.  If we had been almost sure that A were true before we did the experiment, we'd be even more sure now.  Whereas if we'd thought it fantastically unlikely that A were true, we'd think it only somewhat less unlikely now.

The extra information we need is an estimate before doing the experiment of the probability that A is true.  Call that probability q.  Now we have the information we need.  Once we get result B, we are interested in the relative likelihood of getting the result because A is true - probability q - or because A is not true but the random numbers lined up that way - probability (1-q)p.  Our new estimate of the probability that A is true, in the light of the experimental result, is therefore q / (q + (1-q)p ).  Note that if we were already certain that A was true - q = 1 - then our new estimate is still 1.  And if we were already certain that A was false - q = 0 - then our new estimate is still 0.

The important thing to grasp is that the probability in isolation that we get a particular result from random data is not the same as the probability in a given experiment that gave that result that the data were random.  The latter probability depends on what competing, non-random explanations are available and how likely they are to be true.

Let's take a concrete example.  We take a penny coin at random from the change we're given in a high-street shop.  We wish to test the hypothesis that his has heads on both sides.  So we toss it ten times and observe whether we get ten heads.  (Yes, I know, it would be easier just to look at both sides, but bear with me).   Suppose that we'd estimated the probability of having a double-headed penny as one in ten million.  The probability of tossing ten heads and no tails with a standard coin is one in 1024, which is about ten thousand times as probable as the double-headed penny, so our new estimate of the probability of having a double-headed penny is about one in ten thousand - the formula gives one in 9767 to the nearest whole number.  Although the likelihood in isolation of getting ten heads was small, we are forced by the result to believe something unlikely has happened, and we prefer the very unlikely explanation - ten heads out of ten by chance - to the extremely unlikely explanation - a double-headed penny.

Let's take another example: a proposed drug.  We employ a team of expert scientists to research into a particular biochemical pathway and to devise a drug to interfere with it in some desirable way.  We find that the drug works perfectly in vitro.  Then we test it in humans, using a carefully devised double-blind trial, and find that it outperforms a placebo to an extent we would expect to equal or exceed with another placebo one time in twenty (i.e a p-value of 0.05).  If our prior estimate of the probability of the drug's working was 40%, our new estimate will be 93%.

Alternatively, we might pick a naturally occurring substance by guesswork, dilute it out of existence with water, drip the water onto a sugar tablet, and allow the tablet to dry.  We observe no in vitro activity with this tablet beyond the effect of the sugar.  But suppose that when we conduct a similar double-blind trial we get a positive result meeting the same p-value of 0.05 .  If our prior estimate of the probability of the drug's working was one in a billion, our new estimate is one in 20 million.  Homeopathists might see this stark difference in interpretation of the data as unfair: a scientist would merely observe that the experiment wasn't nearly powerful enough to give useful support to such a fantastically unlikely hypothesis.  (In practice, drug investigators never publish their own estimates of prior probabilities: instead they give qualitative reasons why they thought the drug worth testing; the reader can form a view of their own.)

Back to the Higgs Boson.  Physicists generally tended to think that the Higgs Boson would be there in the energy range they were looking at, say with probability 75%.   If we ignore the possibility that they may have discovered a different particle in that range, and accept the announced value of the probability of getting the result from observing noise, then the probability now that the observed results are not due to the Higgs Boson are a bit less than one in 10 million.  We'd get a different estimate if we started from something else than 75%: the point is that only if we started from about 50% would we be able to say that the probability that the Higgs Boson has not been found is now one in three and a half million.
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What I've been writing about is a simple application of Bayes' Theorem.  It's less well known than it might be that Thomas Bayes himself is buried at Bunhill Fields in the City of London (as are Daniel Defoe, William Blake, and John Bunyan, among others).  If you're a quant in the City and you're finding it difficult to think clearly about some question of probability, I recommend a walk there.  Not out of any mystical faith in the powers of the bones of long-dead nonconformists, but because it's there and the walk will do you good.

Their lips were moving

Having pointed out that Barclays was one of the least culpable banks in the understatement of Libor at the height of the liquidity crisis, I wondered how it came about that all the banks were lying at once.

I think there's a clue in the submissions data.  Look at the charts for UBS, Royal Bank of Canada, and WestLB (ignoring one point that looks like an error).  The deviations from Libor are tiny.  It's impossible for UBS in particular that this bears any relation to its actual borrowing costs: it had reported massive losses on mortgage derivatives in 2007 and 2008 and it would have had to pay higher interest rates than Barclays.  I suspect that it had little interest in borrowing in the interbank market, and wasn't getting quotes at all (or if it was, the people getting them weren't the ones responsible for BBA submissions).  In that case, the Libor quotes for BBA would have been generated by phoning a few brokers and asking them where they thought the market was, not specifically for UBS.  If several banks did the same thing, they would all generate very similar quotes without any sort of collusion.

My speculation is that many of the banks ignored the precise wording of the BBA question "At what rate could you borrow funds...", and answered instead the question "At what rate could a bank with good credit borrow funds..."  And that they did it not as a result of any instruction from on high that they should submit low quotes, but because that was a convenient way to get the numbers.  Generally it's considered poor manners to ask for a specific quote if you're not interested in trading, but quite normal to ask for information about the market.

So we could be in a bizarre situation where the banks who submitted quotes closest to the truth are deemed to be the worst liars, because they are the ones who made a conscious decision to distort the data.

Je me fous du passé

Listening to Edith Piaf, it struck me for the first time that it doesn't make sense to parse "Je me fous du passé" as something about madness.  The literal meaning has to be something surprisingly vulgar, at least to English sensibilities.

I put the phrase into Google Translate and it came up with "I care about the past".  That doesn't make sense either.  So I put a line break in after "fous", and it changed to "I do not care"/"the past".

I deduce that "I don't care about the past" is an acceptable translation, and that Google Translate est fou et foutu.  But in a good way.

The curious case of the high low submissions

One of the two charges against Barclays in the Libor fixing scandal is that during the banking crisis it submitted, on the instructions of senior management, artificially low quotes in order not to stand out as a poor credit risk by comparison with the rest of the Libor panel.

Barclays has today issued nine pages of "supplementary information", starting with a further statement of contrition.  The document explains that the instruction to lower the quotes was issued by Jerry del Missier, then President of Barclays Capital, following a telephone call on 29th October 2008 between Bob Diamond and Paul Tucker, the Deputy Governor of the Bank of England.  Barclays reports that there was some misunderstanding between Diamond and del Missier about exactly what Tucker had said.  (This is all consistent with paragraph 176 of the FSA report.)  Both Diamond and del Missier resigned from Barclays today.

Barclays' document includes a chart of its rankings relative to the rest of the panel submitting 3-month dollar Libor quotes during November 2008, at the peak of the liquidity crisis following the failure of Lehman Brothers in September that year.  It was almost always the highest quote of the 16-bank panel.

The Guardian has helpfully published an interactive chart of dollar Libor up to the end of 2008.  It shows that  the spread to the fixing of Barclays' quotes for the 3-month rate more than halved on 30th October, and fell to zero at the beginning of December.  Barclays' chart is true but not the whole truth.  And James Mackintosh of the FT has this chart of sterling Libor showing a quicker and more dramatic change.  (The FSA report says, somewhat opaquely, that "After 6 November 2008, changes in market conditions affected Barclays’ LIBOR submissions such that the instruction became redundant.")  Nevertheless, it does seem unfair to give Barclays a kicking for this dishonesty when they were lying less than most of the rest of the panel.

The Bank of England knew in October 2008 that Libor fixings were artificially low, not just from market data but because Barclays (and very possibly other banks) were telling them so.  But there's no sign that they did anything much about it.  We need to know if and when the BoE took action to tell the banks to tell the truth about interbank rates.  If the BoE did nothing, it seems quite reasonable for Barclays and others to suppose that the BoE was more concerned about financial stability than about accurate Libor fixings.  There are many situations in life when an untruth is expected and as such not immoral.  It's not clear to me that this wasn't one of them.

I repeat however that Barclays' manipulation of Libor submissions for trading advantage was truly scandalous.  There's no injustice about the consequences of that.

Race for Life

Team Helen will be Racing for Life this morning.  Please give generously.