Often I have heard people bring up “Baumol’s cost disease” as a reason for why labour productivity and wages can be unrelated.
Effectively, the argument is that if labour productivity rises in one sector it increases the demand for labour which in turn drives up wages in other sectors, even though productivity in other sectors is unchanged.
Now this is all well and good, but I’m not sure that this takes away the relationship between productivity and wages. Let us assume that there are an infinite number of sectors, but conveniently there are only two sectors competing for the same labour pool. Furthermore, one of these sectors experiences an exogenous increase in labour productivity and the “other sector” doesn’t.
Effectively, the increase in the cost of labour for the “other sector” will reduce the supply of that good driving up the relative price of the other good. There will be a reduction in the quantity produced and an increase in the relative price, which should imply that there will be an increase in marginal (and probably average) productivity of labour in the other sector.
What this concept DOES tell us is that maybe we shouldn’t be so tough on government for its poor productivity performance (as lamented here and here). Why? Labour productivity in the government sector hasn’t experienced any technological change, the services they provide haven’t become relatively easier to produce.
As a result, with the rest of the economy experiencing an increase in labour productivity wages have been driven up, forcing the government to also drive up wages.
Of course, this also implies that the relative size of the government should have shrunk (which it hasn’t) and that the increase in the price of government labour should have been smaller (which it wasn’t). But it does explain part of the public sector wage inflation that we have seen in recent years.