Sen. Bernie Sanders and Hillary Clinton have been in a war of words over who is most pro-poor and anti-soda.

Hillary Clinton voiced her support Wednesday for Mayor of Philadelphia Jim Kenney’s plan for a three cents per ounce tax on soda to fund universal pre-school.

“It starts early with working with families, working with kids, building up community resources — I’m very supportive of the mayor’s proposal to tax soda to get universal preschool for kids,” Clinton said at an event in the Philadelphia. “I mean, we need universal preschool. And if that’s a way to do it, that’s how we should do it.” (RELATED: Philadelphia Prepares For $400 Million Soda Tax Experiment)

But Clinton soon found herself accused by her socialist rival for Bernie Sanders of favoring a tax that would disproportionately hit low-income Americans, while registering barely a blip on the radars of the wealthy.

“Frankly, I am very surprised that Secretary Clinton would support this regressive tax after pledging not to raise taxes on anyone making less than $250,000,” Sanders said Thursday. “This proposal clearly violates her pledge. A tax on soda and juice drinks would disproportionately increase taxes on low-income families in Philadelphia.”

Kenney shot back, accusing Sanders of standing up for the interests of giant corporations. “I’m disappointed Sen. Sanders would ignore the interests of thousands of low-income — predominately minority children — and side with greedy beverage corporations who have spent millions in advertising for decades to target low-income minority communities,” Kenney said on Friday.

According to a research note from the UK’s Institute of Economic Affairs (IEA), Sanders is right on the money when it comes to who is most impacted by a soda tax. Both real-world evidence and economic theory make a mockery of the notion that taxes suffice to substantially tackle obesity, says the IEA’s head of lifestyle economics, Christopher Snowdon.

One of the key reasons sugar taxes don’t work is the demand for sugar-filled drinks and fatty foods tend to be inelastic – meaning people continue to buy the products in large amounts despite the higher price.

Even if people were to change their behavior in response to higher taxes, consumers will often just switch to cheaper brands or buy their groceries from cheaper shops. “This leads to the consumption of inferior goods rather than the consumption of fewer calories,” says Snowdon.

The IEA points to the example of Denmark’s so-called “fat tax,” which was introduced in October 2011. The tax proved so ineffective, with people switching to cheaper brands or buying the products they preferred from across the border, that it was repealed in January 2013. The tax was also hugely unpopular.

A tricky problem for politicians hoping to introduce similar taxes in the US is the poor spend a greater share of their income on the bare necessities, any taxes targeting these goods will have a disproportionate impact on the poor.

The IEA’s previous work on “sin taxes” shows the poorest 20 percent of UK households spend roughly $2,000 per year on sin taxes, amounting to around 11.4 percent of their disposable income.

Leaving aside the harm done to poor pockets, sugar taxes may not even have an impact on people’s health. “No impact on obesity or health outcomes has ever been found,” Snowdon writes. “Early evidence from Mexico suggests that a ten percent tax on sugary drinks led to an average daily decline in consumption of 36ml per person.”

“As Tom Sanders, a professor of nutrition and dietetics, notes, this is the equivalent of 16 calories and is ‘a drop in the caloric ocean. Long-term reductions in total energy in the range of 300-500 kcal/d are probably needed to prevent obesity.’”

Snowdon concludes by citing a systematic review of 880 studies that found “the public health case for using economic instruments to promote dietary and physical activity behavior change may be less compelling than some proponents have claimed.”

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