Yet the BLS reported that the unemployment rate fell from 5.0 to 4.7 percent, a figure generally regarded as full employment. 

The May jobs increase only covers a small fraction of the monthly growth in the labor force and, therefore, cannot account for the drop in unemployment. 

Moreover, the BLS reported that the labor force participation rate fell by 0.2 percentage points, bringing the decline to 0.4 percentage points over the past two months. Normally, a strong labor market, such as one represented by a 4.7% unemployment rate, causes an increase in the labor force participation rate. 

The question becomes: How real is the 4.7% rate of unemployment?

The answer is: Not at all.