The wreckage left by the housing collapse is well known: The unemployment rate in the construction industry is more than17 percent. About 1.4 million workers in the field are unemployed.

So: Are unemployed construction workers worse off than the rest of the jobless?

This simple question has become a matter of fierce contention among economists because of what it says about the economy and how best to fix it. Last week, it spurred a rather unusual public disagreement between economists in the Federal Reserve.

“Construction workers are not experiencing relatively worse labor market outcomes,” concluded an online article by economists at the Federal Reserve Bank of New York, Richard Crump and Aysegul Sahin.

Within days, their colleagues at the Atlanta Fed issued on their Web site what they called “an alternative view of the fate of unemployed construction workers.”

“Unemployed construction workers are generally experiencing relatively large wage declines relative to what they earned before becoming unemployed,” wrote Pedro Silos and Lei Fang, economists at the Federal Reserve Bank of Atlanta.

Why so much attention on construction workers? The reason is that they have become the focus of a much broader political debate among economists over how best to address lingering joblessness.

On one side of the debate, some say that a significant chunk of the current unemployment stems from shifts in the economy that have created a “mismatch” between the skills that workers have and the skills that the economy needs.

In this view, now that the housing boom has ended and the industry has shrunk, there are simply too many people with construction skills. Likewise, there may be an excess of mortgage brokers. In order to work again, these people may have to go into other professions for which they are unprepared.

“You can’t change the carpenter into a nurse easily, and you can’t change the mortgage broker into a computer expert in a manufacturing plant very easily,” as Charles Plosser, president of the Philadelphia Federal Reserve Bank, has put it.

This explanation suggests that merely stimulating the economy with monetary policy or government spending won’t work.

“Monetary policy can’t retrain people,” Plosser said last year.

On the other side of the debate are those who believe that more government stimulus is the right way to reduce unemployment.

These economists minimize the role of skills mismatch as a cause of unemployment, and say instead that unemployment persists because the economy needs to be stimulated — and they favor government policy to do that.

They note that after every recession, a significant number of workers shift from one part of the economy to another — say from construction to manufacturing or services. But the economy and workers make adjustments, as they already are doing.

“We need to have more job openings and more jobs in every sector,” says Lawrence Mishel, president of the Economic Policy Institute, a liberal think tank. “And a wide array of policies can make that happen.”

For example, he suggests that more stimulus spending on infrastructure projects – roads, bridges, railways – would help employ construction workers, who, newly employed, would spend and stimulate the economy further.

Moreover, Mishel notes that while construction workers suffer from high unemployment, their troubles account for only a few tenths of a percent in the uptick in the nation’s unemployment rate during the recession.

“Construction has lost a lot of jobs and construction workers are struggling – I don’t deny that,” he said. “But they are not the whole story of unemployment in the U.S.”

So how are those construction workers really doing?

It depends partly upon which statistics are examined.

Crump and Sahin, who opined that they are not faring worse in unemployment, bring to bear several numbers. They note that the unemployment rate in the construction industry, though it rose to a very high level, has come down faster than the overall unemployment rate. Where it once stood at 27 percent in February 2010, it had fallen in two years to about 17 percent, according to Bureau of Labor Statistics data.

Similarly, they point out that since mid 2010 the rate at which unemployed construction workers have found work has improved faster than the rate for other unemployed workers.

Silos and Fang however, examine different federal data, which show that construction workers leaving the industry for jobs in other industries are suffering wage losses of about 19 percent compared who found jobs in construction.

“Unemployed construction workers who took jobs in other sectors seem to have done so at a considerable loss of income,” they write. “The reason may well be a mismatch between the skills they possess and those required by their new job.”