First of all we must clarify that not any kind of research is useful, see graph below.
Each dot is a region (not a country), 50 for USA, 17 for Spain, etc….
As we can see Public Expenditure in Research is not very related to GDPpc. However if we compare private research to GDPpc, the relation becomes much more clear. Look:
And if we use a proxy for innovation as it could be Patents, the relation to GDPpc still is quite important. Look:
So, it seems that ‘A’ from Solow equation is the origin of growth. And must be an ‘A’ brought by free market and competition.
But what I must say now is… growth relations and causation is much more difficult than this and there are great academic papers arguing about it. Be cautious on this matter.