More on the US's August Labour market data
Traditionally, unemployment and the unemployment rate are seen as lagging indicators. For example, even after the economy bottoms, the unemployment rate can continue to climb. It takes a while before businesses and government become confident that the economy has turned and start hiring again. But the change in unemployment isn't a lagging indicator. It coincides quite well with the business cycle, except of course that it is inverted: unemployment falls when the economy strengthens and rises when it weakens.
The chart below shows the three-month change in the US unemployment rate, inverted (so a data point above zero shows a decline in the unemployment rate) compared with the whole-economy ISM (Institute for Supply Management) index, which is a simple average of the manufacturing and non-manufacturing survey headline figures after extreme-adjustment. As can be seen, over the last few months, the decline in the unemployment rate has been getting smaller and smaller, and the most recent data point (August), unemployment in fact rose. Just a little, but enough to extend the declining trend.