Two renowned economists engaged in a fierce debate at the IMCA New York Consultants Conference on Tuesday on a question that both admitted had no concrete answer: What can the government do to repair the economy?

That question comes several years after a massive federal bailout in the U.S., and as some European nations totter on the brink of requiring rescue of their own. But the discussion titled “Keynes vs. Hayek,” in honor of the famed debate between economists John Maynard Keynes and Friedrich Hayek more than 80 years ago, shows that different approaches to those problems exist just as much today.

The debate included Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities who was a member of President Barack Obama’s economic team, and Russell Roberts, a professor of economics at George Mason University.

Bernstein argued on behalf of Keynes’ philosophies that economies sometimes require outside intervention to run smoothly. Roberts argued for Hayek’s beliefs that economies should mostly have the opportunity to correct themselves.

For Bernstein, who was a newly named member of President-elect Obama’s economic team in December 2008 when the U.S. economy was losing jobs at a rate of 800,000 per month, the choice was clear to create a stimulus package, he said.

Shortly after the stimulus funds were applied in 2009, the rate of GDP contraction got smaller, Bernstein said. While the unemployment rate actually increased from 7% when the stimulus was passed to 9.5% a year later, Berstein cautioned that it’s important to think about where that rate could have been, at 10% or 11%.

Bernstein argued that the opposite of Hayek’s free market theory would be central planning, which has also proven it cannot work. What is needed instead is a hybrid, Bernstein said, where large government can sometimes take a lead role when necessary.

“There are times when the economy’s in a bust, when there’s a recession, where you need to do more stuff that looks a bit like central planning,” Bernstein said.

Roberts, the professor of economics, sought to dispel the notion that government spending directly promotes economic growth.

“The New Deal didn’t end the Great Depression. It was the war time spending,” Roberts said. And even that injection did not benefit the economy evenly, Roberts argued. While weapons manufacturers saw a boost, the private sector did not.

Japan, which has also weathered its own prolonged downturn, has spent trillions on paving projects. The result has been good for contractors, Roberts said, yet has not resulted in a lift for the economy. The American Recovery and Reinvestment Act may follow that same pattern.

“Did it work? The right answer is we don’t know. But we don’t have any evidence that it was successful,” Roberts said.

That comes as the Congressional Budget Office estimates that, as of the third quarter of 2011, 400,000 to 2.4 million new jobs were created. Having a six-fold difference between those estimates—from .4 to 2.4—makes for an “imprecise world,” according to Roberts.

“We should not put our children in debt … in the name of jump starting the economy where there’s no evidence that the jumper cables are actually connected to anything,” Roberts said.

Bernstein rebutted Roberts, saying he saw stimulus funding directly help job creation while he was working with Vice President Joe Biden. In an area of Florida where the unemployment rate was 20% among construction workers, one project helped put a few hundred individuals to work.

“This is what actually happened. It’s not philosophy,” Bernstein said. “When the government temporarily steps in and helps to replace some of the lost demand, some of the lost jobs, its helps to make people’s lives a little more comfortable while the private sector is getting its act back together.”

Tuesday’s debate began with a viewing of a hip hop economics video, “Fight of the Century,” that Roberts created with John Papola.

Lorie Konish writes for On Wall Street.