The labor market is weaker than the unemployment rate suggests. Just how much weaker, however, is a subject of debate.

The official unemployment rate has fallen fairly steeply over the past year, from 7.5 to 6.3 percent.

Federal Reserve Chairwoman Janet Yellen, tasked with promoting maximum employment in the U.S., has said that the unemployment rate is the best indicator of the jobs situation. But she has acknowledged that other measures show that the recovery isn't as strong as that drop would suggest. Specifically, she has pointed to the number of people forced to work part time, the highly elevated rate of long-term unemployment, and slow labor market churn as evidence of the lingering effects of the financial crisis.

But perhaps the biggest caveat to the decline in unemployment is that it has been accompanied by a significant decline in labor force participation. Because the size of the labor force -- that is, the total number of Americans who have or want jobs -- is the denominator in the Bureau of Labor Statistics' calculation of the unemployment rate, a shrinking labor force drives down the unemployment rate.

The labor force participation rate has fallen from 66 percent on the eve of the recession in late 2007 to 62.8 percent in April — the lowest it has been since the late 1970s.

Some of that drop is attributable to long-term trends that predated the recession, such as the aging and retiring of the baby boomers.

But a lot of it reflects the severity of the recession, as millions of Americans who couldn't find work quit the job search. Because they were not looking for work, they were no longer included in the official labor force.

"It’s hard to know definitively what part of labor force participation is structural versus cyclical, so it’s something to watch closely," Yellen said at a press conference in March.

The minutes from the April meeting of the Fed's monetary committee, released Wednesday, show that Fed officials continue to wrestle with interpreting the decline in labor force participation. In particular, some participants (the minutes don't name them) "suggested that there is more slack in the labor market than is captured by the unemployment rate alone."

Different analyses have reached varying conclusions about the extent to which the decline in labor force participation is cyclical, meaning related to the business cycle, as opposed to structural. One representative study is the one released by the Congressional Budget Office in February, which found that roughly half the decline in the labor force participation rate is due to cyclical factors.

Assuming the CBO's conclusion is accurate, the "true" unemployment rate — what the rate would be if all the cyclical labor force dropouts were included among the unemployed — is not 6.3 percent, but 8.5 percent. Furthermore, the official unemployment rate has been falling faster than the "true" unemployment rate, as this graph with illustrative data based on the CBO's estimates shows:

The level of unemployment suggested by the unemployment rate factoring in cyclical labor force dropouts would be indicative of an ongoing labor market crisis, not an economy that is close to full health.

The April minutes, however, suggest that at least one Fed official thinks that such fears are overblown. The minutes describe the unnamed official as saying that "labor underutilization" is consistent with past periods in which the headline unemployment rate was 6.3 percent and falling at the same pace as it has after previous recessions. The official cited an "index that takes employment transition rates into account."

We won't know for sure who the official was until the Fed releases the transcript of the meeting five years from now. But one guess would be that it was Jeffrey Lacker, the president of the Richmond regional Fed bank.

In April, researchers at the Richmond Fed introduced a measure of underemployment similar to what the unnamed official described in the Fed minutes.

This metric, called the "non-employment index," accounts for the "substantial differences in the employability of non-employed individuals" by how likely different categories of jobless Americans are to move from unemployment to employment from one month to the next, according to the researchers.

That is, the non-employment index measures the odds that everyone who wants a job, no matter whether they are classified by the BLS as in the labor force or not, will get one. It then uses those odds to create an index of labor underutilization.

The bottom line is that this measure "does not suggest that the standard unemployment rate understates how much slack there is in the current labor market," the Richmond Fed analysts wrote.

The chart below shows the non-employment index (the solid blue line), taking into account involuntary part-time workers, relative to the unemployment rate (in black).

The non-employment index roughly tracks the unemployment rate, the paper's authors note. As officially measured unemployment has declined, so has the index, suggesting that the labor market is indeed as healthy as the headline numbers suggest.

It's just one more data point in the debate over the underlying strength of the U.S. labor market and the economy. If the Richmond Fed researchers are right, the country is a lot closer to full employment than Yellen and other Fed members think, and further central bank stimulus is likely to spur higher inflation sooner rather than later. If they're wrong, there's still a long way to go.