This may sound a bit strange but I developed an argument while writing my economi history comp that I am somewhat interested in taking up in a more serious fashion. There was a question on the relationship between institutions and productivity, specifically the link between "free" labor and slavery generally.
You can do a simple comparison of Southern and Northern GDP growth prior to the Civil War to test this theory. And, I would argue that you can more than simply show a correlation (which may or may not imply causation!). Specifically, after testing for a correlation you could analyze the micro-evidence on the (firm- and institution-specific) sources of productivity in the North and South. The story goes as follows.
Before the Revolution, indentured servitude was a pretty common labor contract form in the North. Basically, a worker would sell anywhere from 2 to 7 (or more) years of his labor power in exchange for wages and food, shelter, training in some skill or craft, etc. The Revolution changed this institution. The Revolution was carried by the bourgeois but also represented a set of ideas of freedom that were fundamentally incompatible with indentured servitude, especially in the case of white males. Thus, in the North we saw a gradual shift from this "unfree" labor to a more "free" labor where the employer did not have complete control over the worker: contracts were freely entered into and, increasingly, workers could leave before a contract's terms were up (say, a stipulation that the worker must stay with the employer for a year). This gradual shift really was gradual, encompassing 4-5 decades of post-Revolutionary U.S. history.
Indeed, this is one very important part of this story, of this shift from unfree to free labor: it was not an "overnight" phenomenon. To use, Steinfeld's characterization, it was bound in the political, legal and cultural struggles of the post-Revolutionary northeast, as workers came to terms with their own freedoms and the extent of those freedoms at the same time that new modes of organization of work were being introduced by entrepreneurs. A rough marker of the official change over to free labor is the case of Mary Clark in 1821 who was not required to serve out the full term of her contract and received compensation for the time she did seve; this is covered by Steinfeld. But throughout the 1820s and 1830s, what free labor really meant was still being debated. For example, if a worker in a northeast textile mill agrees to work for one year but quits after six months, is he or she entitled to compensation for these six months? The answer was not so clear cut during this time. But things did gradually change, and disputes such as this were not very common in the 1840s and afterward.
So if we can establish that labor contracts in the North were in a kind of limbo for the first part of the 19th century, while in the South slavery as an institution contineued to survive and perform well, our next question is: what was the performance like of the two economies during this period? We have an answer, and although it would be nice to have earlier numbers they are difficult to come by:
GDP per capita 1840 1860
North 109 141
Northeast 129 181
North Central 65 89
South 74 103
S.Atlantic 66 84
E.South Central 69 89
W.South Central 151 184
(Data taken from Fogel and Engerman, Time on the Cross p. 248.)
Northern economic performanace was clearly outstripping the South by the 1840s, but two additional points should be made from this table. First, the Northeast experienced the greatest boost in growth between 1840 and 1860. This is in conjunction with the rise of "free" labor as a contractual norm. Second, the West South Central had some of the highest levels of per capita growth in any region. This outlines the movement of slavery from first along the coasts (Virginia, South Carolina) into the "cotton belt" by the 1840s, as soil was being exhausted and more land was being taken from the Native Americans.
What I would argue that this shows is the relation between labor markets/institutions and productivity growth. The South had always been ahead of the North since the first decades of colonization, due to the thriving plantation economy and trade with the West Indies and Africa. Slavery, it is argued, was a very productive institution given the South's emphasis on agriculture. When compared to a "mixed" institution of some unfree, some free labor (as was the case following the Revolution and into the 1830s) it is clearly superior. But, the birth of the proletarian and all that comes with it (capitalism: the employer owning the means of production; labor organized in increasingly large and centralized factories; various forms of regulation of labor's behavior; and so on) is the engine of the rapid economic growth that gripped the U.S. economy in the second quarter of the 19th century.
So, in the end we find more than a simple correlation: homogeneous institutions provide the best performance within any one economic system, but capitalism is the mother of them all in terms of being able to harness the full productive capacity of the worker and turn out the greatest profits and change possible.