Source: Education at a Glance 2015, section 6.
The British, Australians, and Italians experienced strong growth in tertiary attainment since the year 2000. In the case of the Italians, it was from a low base. There is still a big difference in tertiary attainment between English-speaking and other countries.
Source: OECD Factbook 2015-2016.
I do admire the way in which the USA has been able to have a steadily falling equilibrium unemployment rate since 1984 through thick and thin. The Great Recession had no impact on the US equilibrium unemployment rate. Not only has the largest member been able to do this, the OECD host country (red squares) has had a pretty steady natural unemployment rate too all things considered.
Source: OECD Economic Outlook June 2016 Data extracted on 01 Jun 2016 12:40 UTC (GMT) from OECD.Stat
This data tells more of a story than I expected. Firstly, New Zealand has not been catching up with the USA. Japan stopped catching up with the USA in 1990. Canada has been drifting away from the USA for a good 30 years now in labour productivity.
Australia has not been catching up with the USA much at all since 1970. It has maintained a pretty consistent gap with New Zealand despite all the talk of a resource boom in the Australia; you cannot spot it in this date are here.
Germany and France caught up pretty much with the USA by 1990. Oddly, Eurosclerosis applied from then on terms of growth in income per capita.
European labour productivity data is hard to assess because their high taxes lead to a smaller services sector where the services can be do-it-yourself. This pumps up European labour productivity because of smaller sectors with low productivity growth.