I am confused by this assertion. If they are undocumented, wouldn't they be excluded in the stats? And if they aren't included in the stats, shouldn't we expect an artificial increase in worker productivity? If there is a 4:1 undocumented to documented ratio, then that 1 documented person will get "credit" for the work of 5 people! Even if 4 of those people are relatively unskilled, that's still a big boost.
My initial thought about this is that productivity declines because workers wait around a lot, and they wait around because of ballooning administrative overhead. This would also be consistent with what we know about state of the medical industry and academia during the same time period.