Growing consumption of increasingly less expensive food, and especially “fast food”, has been cited as a potential cause of increasing rate of obesity in the United States over the past several decades. Because the real minimum wage in the United States has declined by as much as half over 1968-2007 and because minimum wage labor is a major contributor to the cost of food away from home we hypothesized that changes in the minimum wage would be associated with changes in bodyweight over this period. To examine this, we use data from the Behavioral Risk Factor Surveillance System from 1984-2006 to test whether variation in the real minimum wage was associated with changes in body mass index (BMI). We also examine whether this association varied by gender, education and income, and used quantile regression to test whether the association varied over the BMI distribution. We also estimate the fraction of the increase in BMI since 1970 attributable to minimum wage declines. We find that a $1 decrease in the real minimum wage was associated with a 0.06 increase in BMI. This relationship was significant across gender and income groups and largest among the highest percentiles of the BMI distribution. Real minimum wage decreases can explain 10% of the change in BMI since 1970. We conclude that the declining real minimum wage rates has contributed to the increasing rate of overweight and obesity in the United States. Studies to clarify the mechanism by which minimum wages may affect obesity might help determine appropriate policy responses.
So a decrease in minimum wage, which decreases unemployment when it's an effective price floor, leads to a higher BMI. This has to be a coincidence. It's hard to see the theoretical rationale for this. A change in the minimum wage really represents nothing more than a transfer of money from one group to another.
For instance, short run studies of the elasticity of low skilled labor suggest that its demand is inelastic. That means an increase in the minimum wage, even though it will reduce the level of employment of low skilled workers, will increase the income of low skilled workers taken as a group. But where does that money come from? It doesn't grow on trees. It comes from business profits and from consumer pocketbooks (through price increases). So some groups realize an increase in their money flow while others see a decrease. But they find a negative relationship.
Moreover, the authors find that the effect is significant across income groups. I would expect there to be no effect in the highest income groups. It is most likely a coincidence and what they've found is a simple correlation.