Economists, Fat Taxes, and the 3500kcal rule

Economists are often sought out to help determine the effects of fat and soda taxes.  We are generally well-equipped to estimate how much less of a particular type of food will be eaten when prices increase as a results of a tax.  However, we are much less well-equipped to go the next step and figure out how changes in the consumption of a food results in a change in weight - the key statistic of interest.  That last step requires some knowledge of nutrition, biology, and metabolism.  

Unfortunately, it turns out that one of the critical "thumb rules" that we economists have used from those literatures, that a change in 3500 kcal will equate to a change in 1 pound of body weight, is likely highly misleading and overstates the effects of the tax (not to mention that it says nothing of when the weight change will happen or how long it will take to happen).  

I've previously blogged about some of the issues with this thumb rule but I'm not sure how widely the problem is understood or recognized among economists.  For example, here are some quotes from some recent, otherwise well-done papers.     

Okrent and Alston in the American Journal of Agricultural Economics in 2012 (free version here) said:

One frequently used relationship in textbooks (e.g., Whitney, Cataldo, and Rolfes 1994) and academic articles that address the potential impacts of fiscal policies on weight (e.g., Chouinard et al. 2007; Smith, Lin and Lee 2010) is that a pound of fat tissue has about 3,500 calories. We used this multiplier to convert changes in annual calorie consumption into changes in body weight.

Dharmasena and Capps in the Health Economics in 2011 said:

Finally, using the conversion ratio of 3500 cal per pound of body weight, we calculate the induced change in the per capita body weight in pounds as a result of aforementioned change in the per capita caloric intake.

Kulcher et al in Applied Economic Perspectives and Policy (formerly the Review of Agricultural Economics) in 2005 said: 

Assuming that no food would be substituted, at 3,500 calories per pound of body weight (American Dietetic Association), the [estimated] reduction translates into less than a fourth of a pound.

To be fair, I didn't appreciate the problem till only recently.  My own paper with Schroeter and Tyner in the Journal of Health Economics in 2008 stated the following (although we used a different calculation to derive weight changes):

On average, in order to gain (lose) one pound, a person needs to consume (burn) 3500 calories in addition to the typical caloric intake (expenditure). Overall, a surplus (deficit) of 500 kcal a day brings about a gain (loss) of body fat at the rate of one pound per week and a surplus (deficit) of 1000 kcal a gain (loss) of two pounds per week (Whitney et al., 2002).

In this context, I was pleased to see this recent article in the International Journal of Obesity, which we economists can use to derive better weight effects.  Here is the abstract

Despite theoretical evidence that the model commonly referred to as the 3500-kcal rule grossly overestimates actual weight loss, widespread application of the 3500-kcal formula continues to appear in textbooks, on respected government- and health-related websites, and scientific research publications. Here we demonstrate the risk of applying the 3500-kcal rule even as a convenient estimate by comparing predicted against actual weight loss in seven weight loss experiments conducted in confinement under total supervision or objectively measured energy intake. We offer three newly developed, downloadable applications housed in Microsoft Excel and Java, which simulates a rigorously validated, dynamic model of weight change. The first two tools available at, provide a convenient alternative method for providing patients with projected weight loss/gain estimates in response to changes in dietary intake. The second tool, which can be downloaded from the URL, projects estimated weight loss simultaneously for multiple subjects. This tool was developed to inform weight change experimental design and analysis. While complex dynamic models may not be directly tractable, the newly developed tools offer the opportunity to deliver dynamic model predictions as a convenient and significantly more accurate alternative to the 3500-kcal rule.

Finally, I will end by noting that there are many papers that use economic models to project how a tax/subsidy will change the consumption of certain nutrients, and similar thumb rules are used to translate to changes in heart attacks, diabetes, etc.  Although I don't know for sure, I suspect many of the exact same sorts of problems exist with these thumb rule extrapolations as exists with the 3500kcal=1lb rule, not to mention the larger difficulty of ascribing causation in those models.