Set aside, if you will, the valid and legitimate criticisms of labor force participation and people leaving the labor market. I am merely updating arguably my favorite chart - housing starts vs. unemployment.
I happened upon this chart quite some time ago and noticed that housing stats lead unemployment figures anywhere from 6-18 months. The logic being that housing triggers not just construction hiring, but effects nearly every other industry as a "house" virtually houses products from every other industry. Ergo when housing recovers so too (generally) does employment in every other sector.
Empirically, this relationship is holding, but as mentioned before a large part of the drop in unemployment has been by people leaving the labor force. I may someday compare labor force participation vs. housing starts to see how this compares (though I fear demographic trends - women entering the work force, baby boomers retiring - may mask any relationship)