Institutions are endogenous
From Jared Diamond’s review of Why Nations Fail:
But it’s obvious that good institutions, and the wealth and power that they spawned, did not crop up randomly. For instance, all Western European countries ended up richer and with better institutions than any tropical African country. Big underlying differences led to this divergence of outcomes. Europe has had a long history (of up to nine thousand years) of agriculture based on the world’s most productive crops and domestic animals, both of which were domesticated in and introduced to Europe from the Fertile Crescent, the crescent-shaped region running from the Persian Gulf through southeastern Turkey to Upper Egypt. Agriculture in tropical Africa is only between 1,800 and 5,000 years old and based on less productive domesticated crops and imported animals.
As a result, Europe has had up to four thousand years’ experience of government, complex institutions, and growing national identities, compared to a few centuries or less for all of sub-Saharan Africa. Europe has glaciated fertile soils, reliable summer rainfall, and few tropical diseases; tropical Africa has unglaciated and extensively infertile soils, less reliable rainfall, and many tropical diseases. Within Europe, Britain had the further advantages of being an island rarely at risk from foreign armies, and of fronting on the Atlantic Ocean, which became open after 1492 to overseas trade.
It should be no surprise that countries with those advantages ended up rich and with good institutions, while countries with those disadvantages didn’t. The chain of causation leading slowly from productive agriculture to government, state formation, complex institutions, and wealth involved agriculturally driven population explosions and accumulations of food surpluses, leading in turn to the need for centralized decision-making in societies much too populous for decision-making by face-to-face discussions involving all citizens, and the possibility of using the food surpluses to support kings and their bureaucrats.
The more interesting question is not how institutions support economic growth, but rather why growth promoting institutions arise in some places and not in others. As Diamond notes, there are some strong patterns in this.