En leiu of GDP you might investigate tariffs and trade in that period. 'The Harmony of Interests' by Henry Cary has some contemporary data on these matters. As Polanyi noted, economics did not properly apply to the 19th Century USA, as economics was then conceived as the science of the allocation of scarce resources to various competing ends, while land, labor and money were essentially free. Land was free due to the availability of vast tracts for homesteading until the 1890s, labor was abundant and cheap due to the constant flow of immigrants, and money could be dug from the earth in the form of gold and silver.

Of course the benefits of these factors accrued primarily to white males with the wealthy benefiting disproportionately, as always. How these considerations applied could become quite complex and law was a sometime thing.

"It is not necessary to have hope in order to persevere."