The idea that "institutions matter" has been embraced by many economists and has garnered a bunch of Nobel prizes, including the most recent ones.
Does culture matter? Dumb question? Comparisons of the two Koreas, the two Germanies (until 1989), the various Chinas as well as Finland vs Estonia have been used to make the point that institutional differences are profound with respect to economic success even when culture is held constant.
Nevertheless, culture is a slippery idea. And it is not simple to isolate culture from institutions. But to think about this problem, look at Eric Jones' Cultures Merging: A Historical and Economic Critique of Culture. Then go back to see what Deepak Lal says about all this.