Looking at current uk employment numbers[1] , it seems that healthcare , education accommodation and food services count as 23% of the economy.
But :
1. Will they grow under new conditions ?
These sectors historically didn't enjoy more productivity due to technology. Economists called this "baumol's disease". But this is changing. We're seeing higher education and maybe some lower education being automated. In japan we saw a robotic hotel, there's plenty of efforts to automate the food industry(both making and serving food), and in healthcare we're on the way to become much more effective at a fast rate with many(hundreds of genetic treatments in clinical trials,great improvements in targeted cancer therapies, artificial pancreases and continuous glucose monitoring are on the way to solve diabetes , etc ,etc) .
2. How much more can they grow ? Will said growth be enough to stop job decline in other sectors ?
All those sectors grew due to stuff like cheap credit, degree inflation, more expandable income, growing country budgets, etc.
But will those conditions continue to be true in a world with a lot of unemployment in other sectors - much more than we saw in the past ?
Also - all those three sectors are 23% of the economy. We're talking about 40% of jobs at risk due to automation in 20 years. So those sectors would have to double/triple themselves to compensate. Is this realistic ?
[1]http://www.ons.gov.uk/ons/rel/bus-register/business-register...