If the same percentage of adults were in the workforce today as when Barack Obama took office, the unemployment rate would be 11.1 percent. If the percentage was where it was when George W. Bush took office, the unemployment rate would be 13.1 percent.

That helps explain a seeming contradiction in the unemployment numbers — the rate keeps dropping even though job creation has been soft.

In April, the U.S. economy added a mere 115,000 jobs, according to Bureau of Labor Statistics data released Friday. In a normal month, that would not even be enough to keep up with new entrants into the labor market. But in this economy, it was enough to drive unemployment from 8.2 percent down to 8.1 percent, the lowest point since January 2009.

The explanation is a little-watched measure known as the “labor force participation rate.” That tracks the number of working-age Americans who are holding a job or looking for one. Between March and April, it dropped by 342,000. But because the official unemployment rate counts only those workers who are actively seeking work, that actually made the unemployment rate go down.

Critics of the Obama administration have been quick to seize on this as the real reason for the falling unemployment rate. In February, the Republican National Committee released a research note on “The Missing Worker,” arguing that “over 3 million unemployed workers have called it quits due to Obamanomics.”

Economists say the story is considerably more complicated. For one thing, the trend predates President Obama. And while part of the story is clearly that the labor force is shrinking because the bad economy is driving workers out, another significant factor is that baby boomers are beginning to retire early — a trend that has worrying implications for future growth.

An accelerating trend

The percentage of Americans in the labor force has been declining for more than a decade. In January 2000, 67.3 percent of Americans had a job or were actively seeking work. By 2007, just before the recession, that had fallen to 66 percent. In January 2009, the month Obama assumed the presidency, it was 65.7 percent. Since then, it has fallen to 63.6 percent, a level not seen since the first year of the Reagan administration.

The implications for returning to what economists call “full employment” are significant. According to calculations by Michael Greenstone of the Hamilton Project, if the labor force grows by 90,000 a month, then an economy creating 200,000 jobs a month would take about eight years to return to full employment. If the labor force grows by 125,000 a month — plausible if discouraged workers begin returning to the labor force — it will take almost 14 years to return to full employment.

The ‘discouraged worker’ story

It’s easy to see why some workers would, in the current environment, get discouraged and stop looking for work altogether. There are about 3.7 job seekers for every available opening.

“We’re not going to see the labor force tick back up until there are enough opportunities that the people who enter aren’t faced with months of fruitless job searches,” said Heidi Shierholz, an economist at the Economic Policy Institute.

Once the economy improves, the theory goes, more workers will start searching for jobs and the unemployment rate will go back up.

The more worrying possibility is that workers discouraged by bleak job prospects will find themselves unable to return to the labor market even after it improves. About 41 percent of the unemployed have been out of work for more than 27 weeks, and economists have found that as workers remain jobless for extended periods of time, their skills erode, their work contacts move on, their motivation wanes and they have difficulty returning to the labor force when the economy picks back up. They move from being unemployed to being almost unemployable.

The ‘demographics’ story

But a number of economists are arguing that the recession is distracting people from the real story — long-run demographic trends that have nothing to do with the current economy. Baby boomers are starting to retire en masse, which means that there are fewer eligible American workers.

Demographics have always played a big role in the rise and fall of the labor force. Between 1960 and 2000, the labor force in the United States surged from 59 percent to a peak of 67.3 percent. That was largely due to the fact that more women were entering the labor force while improvements in health and information technology allowed Americans to work more years.

But since 2000, the labor force rate has been steadily declining as the baby-boom generation has been retiring. Because of this, the Federal Reserve Bank of Chicago expects the labor force participation rate to be lower in 2020 than it is today, regardless of how well the economy does.

In a March report titled “Dispelling an Urban Legend,” Dean Maki, an economist at Barclays Capital, found that demographics accounted for a majority of the drop in the participation rate since 2002.

A smaller workforce means less growth

And what about the most recent downturn? Based on survey data, Maki found that about 35 percent of Americans who have dropped out of the labor force since the recession began in 2007 do want a job, but they have become too discouraged to fire off résumés. That’s a sign of a weak labor market. But the other 65 percent are people who have left the labor force and do not want a job. The biggest chunk of that group seems to be composed of baby boomers, those 55 and older, who have decided to retire early.

That suggests, Maki and his colleagues wrote, that unemployment will not necessarily start ticking up again as the economy keeps adding jobs, as many people expect.

“Such an event has not happened in the past and we do not believe it will this time either,” they argued.

Other reports find a smaller — but still significant — role for demographics. The Chicago Fed estimates that retirements accounted for only about one-quarter of the drop in labor force participation since the recession began.

One thing that makes it hard to predict future retirement trends, Greenstone says, is that it is unclear how many older Americans will postpone retirement and work longer to rebuild their 401(k)s and retirement savings that were battered by the recession. That would increase the size of the labor force in the coming years.

“We’ve seen some indication of this recently,” Greenstone said. “But we still don’t know if it’s a short-term blip or long-term trend.”

How fast the labor force shrinks will also have implications for future U.S. growth prospects. The Barclays report, which argues that older workers are retiring more quickly than most economists had assumed, projected long-run economic growth at around 2 percent. That’s significantly lower than the Federal Reserve’s forecast of somewhere between 2.3 percent and 2.6 percent.