That wealth causes education (because wealthy people can afford it) rather than education causing wealth is a familiar notion to regular readers of this blog. Now here is some writing (from Alison Wolf's Does Education Matter?) about how job success might also cause job training. The ususal nothing being that job training causes job success (pp. 149-150 of my Penguin edition).
What little we know about training practices suggests another scenario as well. Training is more frequent for those higher up the hierarchy; but perhaps much of it follows from success at work, rather than causing it. It may not be about adding skills with a general economic pay-off but rather something that comes with certain jobs. For example, some research I have been doing recently shows that interviewing skills are a very common topic of in-company training for managers. Companies take these courses very seriously, partly because they want managers to make effective hiring decisions, but mostly because they are terrified of ending up before an employment tribunal. Attending such courses is part and parcel of promotion, and so is very likely to be associated with success and higher pay; but it is training that tags along with a successful career, rather than training that leads to one.If a significant amount of training follows from, rather than causes, people's career success, this would certainly explain some puzzling findings. Remember that a major reason to expect systematic under-spending on training is fear of poaching. Employers supposedly train less for fear that trained employees will be snapped up (for higher wages) by other companies which didn't incur the training costs. Yet in practice individuals who receive training are less likely to move than those who do not, and the pay-off to training appears, on the whole, to be higher when you stay with the employer who provided it.
Which means that just spraying job training all over the people who are not now getting it, or who are thought not now to be getting enough of it, is unlikely to make any difference other than to spread confusion, waste and cynicism.
Note also the point about how some (lots of?) training is about legal requirements rather than about the work itself. Regulation regulation regulation brings forth education education education, in self defence. Which might account for why so many educated people - by which I mean schooled people - are so fond of regulation.
Wolf's book is one of the best I've ever read for getting a broad sense of the various educational policies our government has pursued over the years and decades, and of what expensive and counter-productive flops they've mostly been.

