A bit of a civil war has broken out within the left-leaning wing of the economics blogosphere. Gerald Friedman, an economist at the University of Massachusetts at Amherst, recently wrote a paper summarizing Vermont Sen. Bernie Sanders's economic proposals. But many economists and bloggers are criticizing the presidential candidate's spending proposals for including unrealistic assumptions about growth.

A group of economists who worked in the Clinton and Obama administrations have written an open letter to Sanders and Friedman, warning that Friedman's claims "cannot be supported by the economic evidence" and urging a return to evidence-based policy. Obama's former chief economic adviser Austan Goolsbee puts it rather more floridly, saying that Sanders's plans have "evolved into magic flying puppies with winning Lotto tickets tied to their collars."

What are these magic flying puppies? Much of what Sanders is proposing consists of more government spending on public services, such as education and health care, and higher taxes on the rich. But the latter are not big enough to pay for the former if the economy stays on its current moderate-growth path.

For Sanders's proposals to be feasible in the long term, they must avoid putting the U.S. fiscal deficit on an unsustainable path. The only way that will happen is if productivity grows at a historically rapid rate and labor force participation rises to historic highs. Specifically, Friedman assumes that under Sanders, real gross domestic product growth will increase to a torrid 4.5 percent from its recent rate of just over 2 percent. That is even higher than the 4 percent being promised — unrealistically, I might add — by the Jeb Bush campaign. Friedman projects that under Sanders, median household income will soar to more than $82,000 by 2026, up from the current level of around $55,000. That would be an unprecedented bonanza.

To get to 4.5 percent growth, Friedman assumes that in a Sanders presidency, productivity growth will double from its current rate of around 1.6 percent, to around 3.2 percent. To justify this, Friedman relies on the historical correlation between unemployment and productivity. Historically, times of strong growth in productivity also tended to be times when most people had jobs. So Friedman's logic is this: Sanders will reduce unemployment, and higher productivity growth will be the result.

But Friedman is misinterpreting correlation as causation. How will lowering unemployment actually cause productivity to rise? If anything, we'd expect the reverse — the last workers to get jobs as unemployment goes down are usually the least productive, meaning that falling unemployment will usually put a little bit of a drag on productivity.

Even accepting this highly unrealistic idea, a sustained 3.2 percent growth rate in labor productivity would be historically unprecedented:

Only for very brief periods has productivity ever reached the level that Friedman assumes it will average under Sanders for the foreseeable future.

Friedman also assumes that under Sanders, the employment-to-population ratio will rise to 65 percent. As Kevin Drum at Mother Jones points out, that has never happened.

In addition, Friedman doesn't take aging into account. The population is a lot older than it used to be, and it's getting older. Older people don't work very much, because they retire. That means that we should expect the maximum employment-to-population ratio to be lower than in the past. Friedman ignores this completely.

So not only does Friedman make some very dodgy theoretical assumptions, but he also assumes that Sanders's plans will be so good for the economy that they will make both productivity and employment much stronger than they have ever been in the postwar period — much, much better than in the booming 1960s or the late 1990s.

But it gets worse. Even if Sanders were able to produce all of these pie-in-the-sky results, they won't be enough to pay for his spending proposals in the long term. A rise in the employment ratio only lifts GDP growth temporarily — after that, all available workers have been employed. But Sanders's spending proposals would last forever. Eventually, growth must slow, even allowing for the magical productivity increases that Friedman promises. At that point, the deficit will start rising on an unsustainable path once again.

In other words, the assessments of Goolsbee and other economists are correct: Sanders' economic promises, as expressed by Friedman, are highly unrealistic.

Some left-leaning commentators contend that it's OK to make unrealistic promises, since the Republicans do this all the time. Fight fire with fire, right? But Paul Krugman argues — correctly, in my view — that Democrats have benefited quite a bit from taking the path of economic realism over the last few decades. The Republicans' fantasy that tax cuts pay for themselves has probably not served them well electorally. It would be a shame if Democrats were to conclude that they need an equal and opposite form of voodoo economics.

Noah Smith is an assistant professor of finance at Stony Brook University and a freelance writer for finance and business publications.