Charts: What's the real unemployment rate?

The U.S. unemployment rate fell to 4.7 percent in May, even as job growth failed to meet expectations. But does that tell the whole story?

Every month on jobs day, the Labor Department's Bureau of Labor Statistics puts out a ton of employment-related data, each of which tells its own story about the state of the economy. Economists look past the official unemployment rate — known as the "U-3" number — to other metrics that provide more nuanced views of the employment situation.

The U-3 rate is defined as the "total unemployed, as a percent of the civilian labor force," but doesn't include a number of employment situations. A broader figure is the U-6 rate, which many economists rely on as a more accurate portrayal of employment in the country.

The U-6 rate remained unchanged at 9.7 percent in May.

The U-6 rate is defined as all unemployed as well as "persons marginally attached to the labor force, plus total employed part time for economic reasons, as a percent of the labor force." That means the unemployed, the underemployed and the discouraged.

While the U-6 rate has made substantial gains in the past years, it remains stubbornly at pre-recession levels. It's also been more volatile than the U-3 rate. The U-6 is down 100 basis points over the past year, versus a 80-point drop in the U-3.

Market watchers are paying close attention to the jobs report this month to see what effects it will have on the Federal Reserve's decision on whether to raise interest rates in June. Fed Chair Janet Yellen has repeatedly said the committee is looking to the data to see evidence of improvement in the economy.

In recent remarks at the Radcliffe Institute for Advanced Study, Yellen said that a rate hike is "probably" appropriate in the coming months if economic data continue to show signs of strength. She highlighted improvement in the labor market, but also pointed to employment weakness, like in the area of wages

As more of the unemployed find work, you'd expect wages to rise as employers compete against each other for the remaining qualified candidates. Wages have not come back in recent months as strongly on other employment indicators. In May, average hourly wages increased by 5 cents to $25.59. Average weekly wages rose to $880.30.

As unemployment rates have returned to more typical pre-recession levels, economists have focused on other indicators such as wages and labor participation.

A rise in the unemployment rate is not always a bad thing. The one-tenth point rise in the U-3 rate in March, for example, was a function of more potential workers getting out and looking for jobs. That could mean that previously marginalized workers are seeing progress in the job market and are coming in off the sidelines.

But despite the improvement that government statistics show, some economists think that the employment situation is much more dire, partly because of the sluggish participation rate. That rate fell by 0.2 percentage points in May to 62.6 percent.

The participation rate has fallen since the recession, but economists don't agree on why. Some suggest that demographic shifts — mainly the retiring baby boomers — is the main cause. Others think it's more cyclical factors or changes in the economy.