Thursday's jobs report suggested that the employment recovery sped up in June, with the unemployment rate falling to 6.1 percent.

But with the labor force participation rate stuck at 62.8 percent, the lowest it has been since the late 1970s, the unemployment rate overstates the strength of the labor market -- a point that Federal Reserve Chairwoman Janet Yellen, among other top economic officials, has acknowledged.

It's widely understood that the labor force participation rate is depressed both because of ongoing long-term trends, such as the aging of the baby boomers into retirement, and because the disappointing economic recovery has led many people to quit the job hunt and drop out of the official labor force.

Just how much of the decline in labor force participation is due to long-term, secular factors and how much is due to cyclical weakness is a matter of ongoing debate.

One plausible estimate, from the nonpartisan Congressional Budget Office, is that roughly half of the decline in the labor force participation rate since 2007 is attributable to the poor economy.

Using the CBO's estimate, it's possible to get a sense of the "true" unemployment rate — that is, what unemployment would be if those quitters had continued looking for work and were counted in the labor force by the Bureau of Labor Statistics.

The "true" unemployment rate based on the CBO's estimates was 8.3 percent in June, down from 8.5 percent in May. Although it is higher than the official unemployment rate, it is improving along with the unemployment rate, as shown in this chart extrapolating from the CBO's figures:

One clarification: there is no one true unemployment rate beside the official, U-3 unemployment rate published by the BLS. There are, however, other indicators that allow a sense of the strength of the labor market.

In March, Yellen identified five such numbers she watched to monitor progress in the labor market recovery: The U-6 broader unemployment rate, long-term unemployment, the labor force participation rate, the quits rate and wage growth. All five showed improvement or held steady in the most recent readings.