I wanted to get something out quick about the USDA’s soda report and its implication that a modest soda tax could cause children to loose 4.5 lbs.

I assumed that the 4.5 number came from an equilibrium METs analysis. Basically to do that you note that living one’s life requires burning some number of calories per pound of body weight. The units we use are Metabolic Equivalent Tasks (METs).

Then the embarrassingly simply model says that if we reduce calories by X we will get weight loss. However, as the body looses weight it will burn fewer calories in daily activities. Thus calories-out will be reduced. This rate is determined by your METs assumption.

At some point calories-in and calories-out will re-equilibrate and we think of that as net equilibrium weight reduction. Now setting aside all of the endogeneity / partial equilibrium problems with this simplistic analysis, the USDA report doesn’t even go that far.

No what it does reads to me as unthinkable. They multiply 43 calories per day times 365 days a year and divide by 3500 calories per pound of fat to suggest that children will loose 4.48 ~ 4.5lbs of fat per year!

Per year my friends. Per year!

I often sense from the comments that the extremity of these types of claims fails to sink in. Lets just do a little abstraction.

So, child is loosing 4.5lbs per year. Mind you child’s weight is nowhere in this analysis even implicitly. 4.5lbs a year – that sounds pretty good. Indeed at that rate an eight year old formerly soda guzzling kid could loose 45lbs of fat by her 18th birthday.

But wait a second. What if our child only has 15 lbs of excess body fat. What then. Does she become gymnast level ripped, incapable of menstruating?

Does she fail to grow? We know that mass balance is a fundamental law of nature not a social convention. The laws of physics don’t know if she’s “too thin.” If the calories don’t come from fat, of which she only has 15 lbs, they have to come from somewhere. Perhaps, her growth is permanently stunted? Perhaps, her brain development is impaired? Perhaps she suffers all of the maladies associated with underweight childhood development?

All of these thing are possible from persistent caloric restriction but they seem a bit strong as a result of a soda tax?

“Well that’s taking it to extremes.” you say. This analysis doesn’t work at the extremes. Its just about averages and point estimates.

Here is the important point, however: this analysis makes no distinction between moderate and extreme extrapolation. There is no “distance from baseline” component.

The fact that you know this analysis doesn’t work in extremes means that at minimum the model is imprecisely constructed with relation to scale. Further, I would add, there is simply no reason to assume that the model works over “reasonable” scales but simply fails over extreme ones.

The model can, I would argue does, begin to breakdown as soon as the first gram of fat is lost.

This is a large part of why weight loss science looks and acts like voodoo.

Someone takes a really complex equilibrium system. They indentify a property or set of properties. Re-inserting that property into the entire system is mathematically intractable and indeed, we don’t completely understand the system anyway.

So the analyst linearizes the assumption. If all else is held equal they say. Yet, the scale over which the human metabolism will match a linear approximation is tiny. The body immediately acts to undue whatever effect you tried to create.

So maybe, maybe if you are lucky and you hit the body with the equivalent of sledge hammer’s worth of adjustment you can temporarily squeeze out five, ten maybe even 20 lbs of pure adipose tissue. However, the metabolism soon adjusts and acts to overcome even that enormous effort.

This is the core of the problem we face. Any effort to address this problem that does not recognize this difficulty is doomed to failure.

I cannot beat this drum enough, because people continue to try these types of methods, continue to fail and continue to be shocked at that failure. And, even if that type of hamster wheel insanity was ok as a private choice, if definitely shouldn’t form the basis of public policy.

Let me say will all the force I can: We must not pick winners and losers based on analysis that fails to recognize key elements of the public problem.

It is deeply, deeply irresponsible to do so.

Note: A previous version of this post attributed the report to the FDA when in fact it was from the USDA