The title for this post arises because Dr No has idly been playing Shorter Titles, the I’m Sorry I haven’t A Clue game in which panellists are invited to submit film (or song) titles where a single letter omission changes the meaning – Oldfinger, The King’s Peech, Rear Widow, The Godfarter, The Tird Man, that sort of thing – but as Jack Dee would say, they don’t work in print – the original title here being Left Shift, the hypothetical statistical fancy much beloved of the medical Islingtonistas who favour alcohol minimum unit pricing. Left shift is the notion that in populations the body wags the tail: the mean determines the extremes. Applied to alcohol minimum pricing, left shift has it that if average consumption falls because of raised minimum unit prices, then so too will heavy consumption fall. Populations, according to this hypothesis, behave like a blancmange made with excess gelatine: a nudge in the middle, and the whole pud moves across.
One can be confident that in the drawing room at Downton, Lord G would have something Imperial to say about shifty left footers. Meanwhile, back in the real world, blancmanges of course are rather less well behaved. Putting aside the thorny question of what happens to teetotallers when they get left shifted – presumably they move to negative consumption, and start excreting alcohol – there is no guarantee that the other tail – the heavy drinkers – will feel any great attachment to the body. As anyone who has tried to smooch a blancmange sideways knows, blancmanges have a mind of their own. So too do heavy drinkers.
Left shift may have gained traction amongst Islingtonistas, but we must recall that it is just a hypothesis that has yet to gain empirical support. It started life in the 1950s as the Ledermann single distribution theory, which held that drinking behaviour is distributed lognormally: a skewed lop-sided bell-shape, with an extended right tail. As observations go, this descriptive approximation is fair enough, a ‘good enough’ fit to the reported data. Where the left shift hypothesis/theory/model starts to loose the plot is when what is an observational approximation is given magical predictive powers.
It is a matter of simple sums to show that if we reduce the number and consumption of heavy drinkers, then the average (mean) and spread (scatter, variance, standard deviation) will also fall. We have changed the borders of the distribution, and so the summary numbers that describe it are bound to change. But does it follow that if we change the summary numbers – average consumption, by changing behaviour in the middle of the distribution – then consumption at the tails, the extremes, will also change?
We have already contemplated the black hole of alcohol negative equity that teetotallers face, if only to alert ourselves to the possibility that something dodgy may be going on. The Ledermann/Left Shift hypothesis, and later recipes by Rose, who added the chilling ingredients of first sick and then deviant individuals to the mix, is – to recap – the notion that there is an invisible glue that connects all the individuals in the population together. A movement at the centre will be reflected by a similar movements at the tails: reduce average consumption, and consumption at the tails will also reduce.
For this to work, two connected conditions must be met. Firstly, the population must be homogeneous, that is, one population of like individuals, who all behave in similar ways. The second, which is in its way a statistical expression of the first, is that the spread (scatter, variance, SD) must remain fixed. Indeed, this binding is the glue that connects the tail to the body. Without the glue, the curve (distribution) can become elastic: the body can left shift, while the upper tail remains pinned where it is. Where this leaves the inelastic teetotallers, already facing a negative consumption black hole, doesn’t bear thinking about.
Unless, that is, the fundamental condition for left shift to work – homogeneity, specifically for alcohol-price elasticity – doesn’t apply. As it happens, there is clear evidence it doesn’t. Putting aside for now questions of substitution (switching to a cheaper source to maintain supply, which – by the bye – further weakens the case for minimum pricing), ‘global’ alcohol price elasticity varies greatly by consumption group. Determined teetotallers are, in effect, perfectly price inelastic: no change, however large, in alcohol price will persuade them to touch a drop; and thus they save themselves from negative consumption. Overall, global mean elasticity is around –0.5 (a ten percent increase in price will cause a five percent drop in consumption), while for heavy drinkers, the elasticity is less, at around –0.28. It has even been suggested – not entirely implausibly – that the heaviest drinkers go full circle and join teetotallers with an elasticity of zero – perfect inelasticity: no increase in price, however large, will stop them drinking. The rock on which minimum pricing is built is bust. Minimum unit pricing will never work: it will never achieve its declared aim of delivering left shift, for the simple reason that, in this particular beast, the body and tail are not connected.
To be fair to Rose (the later English proponent of the single distribution theory – Ledermann was French), he worded his classic papers carefully. In Sick Individuals, there is mention of ‘large potential’ – albeit wrapped in hot talk of ‘powerful advantages’, while in Deviants he says: ‘The close link between mean and prevalence [of deviants] implies that to help the minority the “normal” majority must change’ and ‘The way that most people eat, drink, and behave, even if it were harmless to themselves (which is often not the case), may determine how many others, more vulnerable, will suffer as a consequence [italics throughout added]. Rose was careful to sound pious, and yet describe possibilities, not certainties. The pity is that today’s medical Islingtonistas, high on opinion and lite on evidence, have embraced fanciful certainty, and ignored practical reality. That is why, even when he is not playing ShorterTitles, Dr No calls Left Shift left shit.