Fat taxes & modeling

NPR covers a Danish move to tax saturated fat:

So when the tiny Scandinavian country announced it would be imposing a 16 Kroner (about $3 U.S.) tax on every kilogram of saturated fat as a way to discourage poor eating habits and raise revenue, we were left scratching our heads.

How’s that going to work?

Ole Linnet Juul, food director at Denmark’s Confederation of Industries, tells The Washington Post that the tax will increase the price of a burger by around $0.15 and raise the price of a small package of butter by around $0.40.

Our pals over at Planet Money took a stab last year at explaining the economics of our version of the fat tax — the soda tax. They conclude that price increases do drive down demand somewhat.

But couldn’t Danes just easily sneak over to neighboring Sweden for butter and oil and simply avoid paying the tax, throwing all revenue calculations off?

Meanwhile, some health studies indicate a soda tax doesn’t work to curb obesity anyways.

First a few obvious problems: oil is typically not saturated and therefore presumably wouldn’t fall under the tax. And sneaking over the border for butter? Seriously? You’d better bring back a heckuva lot, because there’s the little matter of the Øresund Strait, which now has a handy bridge, and a 36 EUR toll to go with it.

More interesting is the use of models in the linked studies. From the second (“doesn’t work”):

But new research from Northwestern University suggests that soda taxes don’t actually help obese people lose weight, largely because people with weight problems already tend to drink diet soda rather than the sugary kind. So taxing full-calorie sodas may not help many Americans make better dietary choices.

Patel ran computer simulations designed to track how soda prices would affect obesity rates. The findings demonstrated that a sugar tax would cause a negligible drop in obesity, about 1.4%, and that obese people would not lose much weight. “For people going from [body mass indexes] of over 30 to below that…most people are not having massive swings,” Patel said.

For the study, Patel’s team collected data on people with “all ranges of BMI” from the Centers for Disease Control and Prevention’s Behavioral Risk Factor Surveillance System, which has tracked health conditions in the U.S. for nearly three decades. They also collected a data set of soda prices and sales to estimate consumer practices, which they used to predict what people would purchase before and after the implementation of a soda tax. Based on the resulting change in total calories consumed per day over a set time period, the team modeled long-term changes in weight using existing nutrition literature.

Kelly Brownell, the director of the Rudd Center for Food Policy and Obesity at Yale University, has doubts about the accuracy of studies such as Patel’s. Simulations of the potential impact of public health actions such as a soda tax are based on a huge number of assumptions — about consumption, spending behavior, weight change — that are, in reality, difficult to make accurately, he explains.

“All of those changes are unknown,” he said. “So it’s not hard to allow those assumptions to create the results you want.”

Patel counters that assumptions are inevitable in research, and that previous studies that have produced results in favor of soda taxes have also made assumptions, typically about consumer preferences. “I’m trying to see if there are any critical assumptions here that really change the results, but so far I haven’t had anything like that,” he said. “It’s a somewhat valid criticism, but the paper is still being fleshed out, and there are a variety of robustness checks.”

But Patel acknowledges that his study could not predict whether a soda tax would help prevent people from consuming sweetened drinks in the first place and becoming fat later on — another point raised by Brownell. “The question of whether a soda tax could prevent people from becoming obese in the future…that’s still kind of an open question because there are some issues on how you model weight change that to my knowledge haven’t been addressed,” he said. “It’s possible that a soda tax could prevent people from becoming obese in the future, but for people already obese it’s not really going to do anything.”

As press coverage of models goes, this is actually pretty good, and Patel is nicely circumspect about the limitations of the work. The last paragraph hints at one thing that strikes me as extremely important though: the study model is essentially open loop, with price->choice->calories->body mass causality. The real world is closed loop, with important feedbacks between health and future choices of diet and exercise, and social interactions involved in choices. I suspect that the net result is that the long term effect of pricing, or any other measure, on health is substantially greater than the open loop analysis indicates, especially if you’re clever about exploiting the various positive loops that create obesity traps.

Brownell’s complaint – that we know nothing, so we can just plug in assumptions to get whatever answer we want – irks me. It betrays an ignorance of models (especially nonlinear dynamic ones), which are typically more constrained than unstated mental models, not less.

There seems to be a flowering of health and obesity models in system dynamics lately, with some interesting posters and papers at the last few conferences. There’s hope for closing those loops yet.