Efficacy of Fat Taxes and Thin Subsidies

Science News reported the following results from a recent study:

Taxes on soft drinks and foods high in saturated fats and subsidies for fruit and vegetables could lead to beneficial dietary changes and potentially improve health, according to a study by experts from New Zealand published in this week's PLOS Medicine.

and

The authors say: "Based on modelling studies, taxes on carbonated drinks and saturated fat and subsidies on fruits and vegetables are associated with beneficial dietary change, with the potential for improved health. "

My first reaction was "duh."  Clearly if you raise prices of (say sugar or fat) high enough, you will get people to eat less.  In fact, one way researchers often model a ban on a substance is by simulating what happens when the price gets high enough that no one buys the product.  

Thus, the key question isn't whether one can change consumption and nutrient intake with sufficiently high taxes or subsidies.  The better questions are by how much? and at what cost?  An even better question still: where is the market failure that would justify the tax or subsidy?  The answer to that last question is actually much less obvious than most public health professionals presume (see here or here).

On the former question of how much?, let's turn to the original study mentioned at the first of this post.  The study is actually a literature review, pulling together the findings of previously published papers (including one that I co-authored).  Below is a graph showing some of the key results from different studies simulating how much change in consumption (or energy intake) would occur from a change in the price of a good. Pay attention to the scale of the vertical axis.  My take (see the middle chart) is that it would take very large price changes to get energy consumption to change by much (a 20-40% increase in price results in a 0.2-0.4% reduction in calories consumed).  

Stated differently, these sorts of policies are likely very costly in achieving the desired health outcomes.  Moreover, we must ask why - if these health changes are really so inexpensive and beneficial - people are not already voluntarily making them?

Some Obesity Math

When I was in graduate school, we had an old book laying around titled something like How to Lie with Statistics.  I don't remember ever actually reading the book but the title says it all: one can tell two entirely different stories depending on how one chooses to report the numbers.

I fear that much of the rhetoric surrounding obesity has fallen into this trap.  According to CDC data, the average weight of men aged 40-49 has increased roughly 15 lbs in the past 10 to 15 years (compare data in this publication to this one showing the average weight going from about 187 lbs in 1988-1994 to about 202 lbs in 2003-2006; I should also note that more recent data shows these weight gains leveling off).  

Fifteen pounds doesn't seem like a huge number to me (I've personally lost and gained much more than this amount in my adult life).  So, how is it that this small to medium sized increase in average weight gets translated into a message that there is an epidemic?  Part of the answer is that when scientists translate averages into prevalence rates, the numbers look a lot scarier.   

Stick with me while I illustrate with an example.  

Let’s take a hypothetical population of men whose average weight is 180 lbs.  Suppose, men’s weights vary in the population according to a normal distribution with a standard deviation of 30 lbs.  This means roughly 68% of the men will have weights between 150 lbs and 210 lbs.  Suppose also, for convenience sake, that all the men are the same height: 5 ft 10 inches. 

Obesity is defined as BMI greater than 30 (BMI is weight in kg divided by height in meters squared).  In our hypothetical example, where everyone is the same height, a man will be obese if he weighs more than 209 lbs.  Moreover, given our assumptions about the normal distribution, we can readily project that 16.6% of men in this population will be obese (1 minus the cdf of a normal distribution with mean 180 and standard deviation of 30 evaluated at the point 209 is 0.166).

What if all men gain a paltry 5 lbs?  The average weight goes from 180 up to 185 lbs.  Yet, (again given the assumption of the normal distribution), obesity prevalence will go up from 16.6% to 21.1%.

Thus, we have what most of us would consider a rather trivial gain in weight (an increase in 5 lbs or a 2.8% increase in weight); however, we have what appears to be a rather dramatic increase in obesity prevalence (prevalence goes up 4.48% or a 27% increase in prevalence of obesity!).

If we run through the same example again assuming men gain an average of 10 lbs, we can find that obesity prevalence goes up almost 58% even though weight only increased 5.5%!

Both statistics are "true" but they tell very different stories.  

Does 1 lb = 3500kcal?

Researchers studying the effect of various food policies on changes in weight often use the simple saying that a change of 3500 kcal via diet or exercise results in a 1 lb change in weight (it is a claim we repeated in our paper in the Journal of Health Economics, which studied the efficacy of fat taxes).

I ran across this interesting post by a Mike Gibney, a public health and nutrition expert, who points out some problems with the 1 lb = 3500 kcal calculation.  Here's what he has to say:

Firstly, a 1lb weight loss will not be 100% fat but will also involve the loss of some lean tissue (muscle and protein elements of adipose tissue and its metabolism). Whereas fat has an energy value of 9 kcal/g, lean tissue has a value of 4 kcal/g. The exact ratio of the loss of lean and fat in weight reduction depends largely on the level of fat in the body at the outset.

and:

The second criticism of this rule is that it ignores time. If you shed 3,500kcal per week every week, that would differ from a deficit of 3,500 kcal per month every month. The former leads to a daily deficit of 500 kcal while the latter is just 117 kcal.

and:

Thirdly, the 3,500 kcal rule assumes complete linearity – in other words the rule equally applies, pound after pound of weight loss. We saw above that progressive weight loss will progressively increase the % of that weight loss as lean tissue but more importantly, the 3,500kcal rule ignores a major adaptation in energy expenditure

and on this topic, he concludes:

Clearly, the continued use of the 3,500 kcal rule in predicting weight loss should cease and the recommendations of the consensus statement of the ASN and ILSI should apply: “Every permanent 10 kcal change in energy intake per day will lead to an eventual weight change of 1lb when the body reaches a new steady state.  It will take nearly a year to achieve 50% and about 3 years to achieve 95%”.

Finally, I'll point out the importance of taking into account these kinds of issues when calculating the effects of fat taxes.  He says that according to one study, a 20% soda tax would lead to;

 a reduction of energy intake of 34-47 kcal per day for adults. Using the 3,500 kcal rule, an average weight loss of 1.60kg would be predicted for year 1 rising to 8kg in year 5 and to 16kg in year 10. However, when the dynamic mathematical model is used, the corresponding figures for years 1, 5 and 10 are, respectively, 0.97, 1.78 and 1.84 kg loss. The % of US citizens that are over-weight is predicted to fall from existing levels of 66.9% over-weight to 51.5% over-weight in 5 years time using the 3,500 kcal rate but using the dynamic mathematical model, the 5-year figure for the over-weight population in the US would be just 62.3%.

 

Greg Gutfeld on the Food Police

Greg Gutfeld at his hilarious and satirical best . . .

My favorite lines:

The LA City Council just adopted a resolution for meatless Mondays.  This is while around most of this awful brutal world they have meatless weeks and months.  They'd be happier with 'please don't let me starve Mondays.'

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How hilarious is it that the left accuses the right of invading their bedrooms just as they climb onto your plate.

and

This is Solindra for your belly which is why I feel like throwing up.

The Fat Tax that Wasn't

A while back Denmark passed a law to implement one of the first comprehensive "fat taxes."  A year after its implementation, it looks like they've changed their mind.  

One of the biggest drivers of the reversal was apparently public opinion, not to mention the negative economic impacts.  

I am often amazed at how easy many public health professions believe it is to change weight and corral bad behavior simply by just slapping a tax on things they don't like.  Just today, the folks over at Freakonomics discuss a recent conference where fat taxes were thought a really good idea (I've been a many of these kinds of meetings too).  

We economists often come across as uncaring , negative Nellies when we point out that such taxes often have very little effect on weight, have unintended consequences (as Denmark just realized), and are regressive (meaning that food taxes hit the poor the hardest).  

But, at the end of the day, who is more caring?  The folks pushing for costly taxes that wont materially change weight and health or those of us trying to prevent bad policies from affecting those who can least afford to pay the effects?