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.