How might productivity differ between a climate that supports innovation and one that does not?
Productivity will tend to be higher in a climate that supports innovation than in one that does not. The reason for this is that innovations tend to bring about labor saving devices and methods that allow the productivity of each worker to rise.
We can see from American history that innovation is linked to productivity. As one example of this, farming became much more productive on the Great Plains after the Civil War with the introduction of better plows and other mechanical devices. These devices came about through innovation. Similarly, it was innovations like the assembly line (developed by, among others, Henry Ford) that made American industry much more productive in the early 1900s.
Innovation is the major driver of increases in productivity. Firms that want to increase productivity need to create climates where innovation is encouraged.