Colwell made an estimate based on the available census data and with reference to state data. Even if his estimate was wrong -- off by half, if you like -- his basic point, that the states surrounding New York contributed more to its economy than the Deep South cotton states -- holds up, and you can see that in his figures.
Kettell's approach was based on the idea that you could trace all wealth back to agriculture or natural resources. He left out the value added by manufactures and services. It's not hard to see where he went wrong. Plenty of resource-rich countries have failed to develop because they failed to diversify and remained tied to a single crop or commodity.