Singapore is a notable counter-example: it is located at 1.22° N and is one of the world's most prosperous countries. This prosperity is based on its position as a port. Other exceptions to the paradox tend to have large natural resources. Saudi Arabia is a good example.
One popular theory to explain this phenomenon is that development is less necessary in tropical regions - "you can lie in a hammock and pick bananas", as opposed to the need to invent agriculture and economy in order to prosper and survive. This explanation, while convenient, may not be sufficiently complex to truly explain the equatorial paradox.
Climatic Determinism was intensely studied by Ellsworth Huntington.