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Three decades ago this month, the economists Richard B. Freeman and James Medoff published a classic book, "What Do Unions Do?" If they wrote it today, they would have to call it "What Did Unions Do?"

Unions are dying in the United States. The share of private-sector workers who are union members dropped from about 35 percent in the 1950s to 6.7 percent in 2013. That gradual decline was highlighted Friday, when workers at Volkswagen's Chattanooga, Tenn., plant voted against unionization by a count of 712 to 626.

That loss was more than just symbolic. The United Auto Workers framed it, as Alec MacGillis of the New Republic has pointed out, as a fight for "the future of organized labor." That was only a slight exaggeration. A win in Tennessee would have also made it far easier to unionize Southern auto plants, where the future of the U.S. industry lies.

Trying to pin this on Republicans like Tennessee Sen. Bob Corker or Gov. Bill Haslam — both of whom made public threats against the workers if they unionized — won't get you very far. Unions have been undermined by a combination of worker hostility and the rising power of capital over labor. Their demise raises a question: Is the U.S. better off without them?

Freeman and Medoff's conclusion still stands. Unions have two roles to play in the American economy: They balance power between employers and workers, and they provide a voice for workers that management can hear.

Freeman and Medoff thought the first role was important but not entirely positive, and they're right. Union power comes from turning labor into a cartel. Although it helps union members, it's inefficient and bad for the economy as a whole, and it's especially bad for nonunion workers. But that's not the union's only job, Freeman and Medoff responded — their role as a worker voice reduces job turnover and may boost productivity. That end is unambiguously good.

Whether to mourn unions depends on whether you believe the good outweighs the bad. Wherever you land on that question, though, the U.S. must find ways to replace what good unions did. It must restore power to labor in a world without Labor.

And that couldn't be much more urgent. Workers' share of income, which until recently had been so stable that fundamental economic models are premised on its stability, is plummeting. Wage growth and median incomes seem locked in a slow- to no- growth zone. The strength of capital seems ever greater than of labor; just take a look at corporate profits.

"There is this nagging sense that the loss of the union has happened with the rise of inequality, the rise of money, that somehow it's created an imbalance in society," Freeman told me in a phone interview. "That sense is right. We need some other way that restores power to workers."

What the Chattanooga defeat should tell us is that labor unions probably can't be an answer to those problems. Economic change, particularly the rise of global competition, killed them. U.S. policy must aim to replace unions, not revive them.

One replacement might focus narrowly on the role of unions Freeman and Medoff gave their highest praise: worker voice. Economics bloggers Adam Ozimek and Matt Yglesias, for example, have recommended that the change U.S. labor laws to allow for "works councils" in nonunion workplaces.

That's the model Volkswagen wanted to bring to America. And, had U.S. law not prohibited them, they would have done so. They are small organizations that create a forum for worker- management communication at the level of the individual shop or factory. The lawmakers of the 1930s feared they would crowd out unions, a concern that's no longer relevant without any unions to crowd out. The U.S. should change that law.

"Works councils have been very successful in Europe, helping employers and employees discuss problems in a non- conflictual way," Freeman said.

Another smart response would be to stop businesses from abusing labor laws by classifying their employees as independent contractors. This trick gets the employer off the hook for payroll taxes, exempts them from overtime and minimum wage rules, and weakens the employees' legal protection against discrimination. President Barack Obama's Labor Department can do this by itself, though Congress could help by clarifying the legal distinction between employee and independent contractor.

Freeman also had a recommendation of his own: passing laws that encourage employee ownership of companies and profit- sharing agreements. To rebuild labor's share, he suggests, help labor play capital's game.

Yet nobody thinks these incremental ideas are enough to restore the power of labor. That will take some bigger policy guns: monetary and fiscal policies aimed at full employment. A new book by economists Dean Baker and Jared Bernstein showed that workers do best — their inflation-adjusted incomes rise most quickly — in times when labor markets are tight.

And while there's no shortage of options on this front, my view remains that the Federal Reserve should lead the way by establishing a policy target for the level of nominal income in the U.S. economy. By stabilizing nominal income, the Fed can keep the U.S. closer to full employment without hampering its goal of low and stable inflation. In a modern open economy, full employment is the only way to give workers true power.

Unions can no longer solve labor's woes. That's not terrible, because the way unions gave workers power created its own problems. Yet the U.S. will be much worse off without labor unions if it doesn't replace what they once did.