The controversy surrounding Scott Walker's views (or non-views) on President Obama's patriotism and religious faith have only increased the Wisconsin governor's stature and visibility on the right. And that's probably just fine with many Democrats.

Should Walker win the GOP presidential nod, progressives will surely try to turn him into a symbol of all that's gone wrong with the U.S. economy. Why wouldn't they? If you believe that the decades-long decline of union power is what's been crippling the American middle class, then a union-busting governor makes a perfect foil in 2016. Maybe even better than a job-slashing, private equity investor and banker did in 2012. And indeed, progressives love to tout the connection between unions' decline and middle-class woes. "Middle-class decline mirrors the fall of unions in one chart," garbles The Huffington Post. "Why screwing unions screws the entire middle class," seethes Mother Jones. "Without unions, the middle class withers," claims the Center for American Progress.

Whatever the political smarts of this approach, the underlying economic theory — while popular on the Elizabeth Warren left — isn't as crystal clear as progressives claim. Yet the idea that the slow death of unions also killed the middle class still gets repeated over and over. Here is Lawrence Mishel, president of the progressive Economic Policy Institute, earlier this week in a New York Times op-ed:

Protecting and expanding workers' right to unionize and bargain collectively is also essential; the erosion of collective bargaining is the single largest factor suppressing wage growth for middle-wage workers over the last few decades. … Contrary to conventional wisdom, wage stagnation is not a result of forces beyond our control. It is a result of a policy regime that has undercut the individual and collective bargaining power of most workers. Because wage stagnation was caused by policy, it can be reversed by policy, too. [New York Times]

Shorter version: Since it's become harder for workers to unionize, union membership has declined, and the bosses have increased their share of the corporate spoils.

That's a strong claim. But it's something of an outlier view among economists. Last year, the University of Chicago's graduate business school asked top economists if they agreed with this statement: "Information technology and automation are a central reason why median wages have been stagnant in the U.S. over the past decade, despite rising productivity." A strong plurality, 43 percent, agreed. Only 28 percent blamed a variety of other causes, including trade, the financial crisis, weak education, and yes, the decline in unionization. (If you think the deck was stacked with right-wing economists, consider that left-wing economist and New York Times columnist Paul Krugman has explained the effect of unions on the income gap to be "significant," but "secondary" to technological change.)

Inequality and wage stagnation are problems witnessed across advanced economies. Wages haven't been going up in Canada either, even though the share of the workforce in unions is twice that of America's and holding steady, according to the OECD. An international macro story requires an international macro explanation — like technology, manifested as automation (computerization eliminating "routine" jobs such as assembly line workers and receptionists) and globalization, itself enabled by the IT revolution.

Indeed, the apparent connection between falling unionization and rising income inequality may itself be the result of how "computerization ... and globalization may a have fostered a more dynamic, and unequal, American capitalism to which unions were poorly adapted," according to a 2011 paper out of Harvard and the University of Washington. Even inequality guru Thomas Piketty concedes that "the main policy to reduce inequality is not progressive taxation, is not the minimum wage. It's really education. It's really investing in skills, investing in schools."

If you can't diagnose the problem, you can't come up with an effective remedy. And suggesting that the fall of unions is the biggest factor of middle-class stagnation is a misdiagnosis of our problem.

Many economists would say deunionization matters somewhat. It's just not the everything explanation that Democrats wish it were.