Small effects

Here's Boyd Swinburn defending sugar taxes in the Herald, in his usual charitable style:

A report by the New Zealand Institute of Economic Research (NZIER) concluded that a sugary drinks tax by itself would not significantly reduce obesity. This has fuelled the merchants of doubt who are opposed to including it in a multi-strategy approach to reduce our appallingly high rates of childhood obesity and dental caries.

The report drew the wrong conclusions because it dismissed the estimated changes of body weight as trivial when in fact, applied across the whole population, they are substantial. For example, an 800g reduction in weight from a 20 per cent tax would have an impact equivalent to halting the rise in population weight gain for three years.

I suppose that's the conclusion you get if you think the world's a Manichean struggle of heroic public health people against some evil conspiracy.

Let's leave the battles of good and evil and go back to the study. The NZIER report surveys a pretty wide literature.

The specific one that Swinburn is here citing in from John Gibson at Waikato. The Gibson study takes a prior simulation model of Grogger's and corrects an overestimate of the demand elasticity. Grogger doesn't really look at obesity though. Grogger rather estimates the effect on obesity of a reduction in soda consumption using models of energy intake and expenditure.

Gibson shows that Grogger massively overestimated the effect of tax on consumption, and so Grogger's modeled effects on obesity were too large. The steady state weight change should have been about 0.4kg, not Grogger's 2-4 pounds. The Mexican tax has been characterised as a 10% tax (close, but it's really a peso-per-litre excise), so I guess doubling that gets you the 800 grams.

Gibson corrects the demand elasticity part, but doesn't look at the soda-to-obesity part. He just says that if Grogger's model of the consumption-obesity relationship is right, then the effect of tax on obesity is much smaller than Grogger estimated.

NZIER cites a pile of studies that do try to get more direct links from consumption to obesity outcomes.

NZIER cites Maniadakis et al, 2013, a metastudy of 55 studies on sugar taxes. NZIER summarises:

The relationship between prices and taxes on food and beverage items and health outcome measures was found to be very weak. Results suggested that a 10 percent increase in prices (including by imposition of a tax) would be expected to reduce energy intake by a maximum of 50 calories per day, resulting in a weight loss of up to 0.3 kilograms per year, which was deemed to be insignificant.

But it would be a misreading to say they deemed it insignificant because 300 grams per year is small. They deemed it insignificant because it was the largest effect found in the eleven studies in that category, with other ones finding smaller effects or zero effect. Here's Maniadakis et al:

Moreover, six studies 28,29,31–34 and five studies 35–39 examined the association between beverage/food prices and taxes and energy and weight outcomes, respectively. These studies indicated that there is a very small impact of prices and taxes on energy intake and weight outcomes. These studies indicated that the caloric effect of a 10% increase in prices or a corresponding imposition of a tax reduces energy intake by a maximum of 50 calories per day, 450 per month, and up to 0.3 kilograms or 1.5 pounds per year, which cannot be considered significant. The specific studies also indicated the regressive nature of taxes and that their use is promoted mostly in order to generate revenue for the public purse.

NZIER also cites Backholer et al, another metastudy suggesting insignificant effects. Here's NZIER:

Backholer et al. (2016) reviewed studies estimating the effects of an increase in the price (or a tax) of sugar-sweetened beverages on purchases or consumption and weight outcomes regressivity, within high-income countries. Price elasticity estimates varied considerably across studies as did resulting consumption changes and weight changes. The review found that few studies statistically tested differences in outcomes between socio-economic groups. Seven studies reported on changes in weight outcomes for the total population following an increase in SSB prices. Studies either found no association between a tax on sugar-sweetened beverages and BMI or a very small association, with insignificant weight loss implications of up to less than 2kg over ten years. Some found similar reductions in weight for all socio-economic groups while others found greater reductions for lower income groups compared to higher income groups. A tax on sugar-sweetened beverages was associated with a wide range of estimated impacts on the population obesity rate: from a less than 0.1 percentage point decrease in obesity prevalence to a more than 10 percent (3 percentage point based on a 30 percent obesity rate) prevalence reduction. All studies that examined the average household tax burden reported that tax on sugar-sweetened beverages would be regressive, but with small differences between higher and lower income households (0.10-1.0% and 0.03%-0.60% of annual household income paid in tax by low- and high-income households, respectively). 

The problem isn't that 2kg over ten years is deemed small, it's that it's the largest effect in a field of either smaller effects or no effects.

Swinburn then goes on a bit of a rant about the inapplicability of rationality models, but I don't see the relevance - or at least I don't see that it goes the way Swinburn wants it to go. Whether people are wholly rational, or completely barking mad, the studies aren't showing any particular effect of sugar taxes on sugar consumption - at least in the ranges that have been tried so far.

But it's worse than that. The rationality assumptions are what make sugar taxes a plausible intervention in the first place. If people are completely irrational, there's no necessary relationship between demand and prices except through an income effect. And in that world, why would we even be thinking about sugar taxes?