Of course, other traditions of economic thought have emphasized the role of the market in fostering economic growth as well. In the Marxian circuit of capital, markets are central to the accumulation process, providing the means for businesses to reinvest the surplus value gained from selling their goods back into the labor process, in turn creating the conditions to extract even more surplus from workers. In this framework, markets are also important but in a slightly different way: markets are only necessary insofar as they allow the initial accumulation process (the really important part of the Marxian theory of growth) to expand on ever-larger scales. In other words, they are an intermediate agent in capitalist expansion -- where the primary role comes from the labor process itself.
Which answer, or model, is right? It depends, in part, on your view and understanding of the rise of capitalism -- an issue which involves theoretical debates which are extremely important to political economy. But aside from the theory, it's true that each answer or model definitely possesses a set of testable hypotheses. For example, to show that markets were the primary source of economic growth, one may want to look at statistical connections between market integration and economic growth. Of course, causality would have to be tested for and established -- usually a very difficult phenomenon to pin down.
Indeed, this is the approach taken by the neoclassical study mentioned above, by Winifred Rothenberg, and she ultimately fails in giving good scientific reasons for thinking that markets were primary to understanding the growth of the economy. Markets can still be an important part, but the question of whether markets caused growth or the other way around -- a scenario in which wealthy producers may set out to develop and expand the market in society -- is not addressed. In other words, while Rothenberg certainly shows the presence of market integration between 1750 and 1850, in the end it is simply a correlative relationship. To really get at the effects of markets on growth, we have to think about employing alternative methodologies.
One possibility is the skillful use of the counterfactual. What would have happened, say, if British economic growth ultimately came to a halt by the middle of the eighteenth century? What would the neoclassical model predict about this phenomonon? Well, given the central role that markets supposedly play in fostering growth, then neoclassical economists would argue that markets most likely were not as integrated, or as large, or as important in society. If there was someway to test this hypothesis, then it would be one way of getting at a causal relationship: if markets were indeed dead in Britain (in the case of British failure), while they were quite alive in America (the case of success), then it would be more persuasive to argue that market integration is a primary variable.
Of course, the problem with the counterfactual is that it's very difficult to find! In "Domestic Trade and Market Size in Late-Eighteenth-Century France" (Journal of Economic History, September 2010), Guillaume Daudin utilizes the methodology of the counterfactual by considering the role markets played in the relatively-slower developing late-eighteenth and early-nineteenth France.
But as you can see from the title, Daudin focuses on market size, not market integration. Nevertheless, Daudin brilliantly uses market data to measure market size, and finds that markets were relatively larger than their British counterparts. Market size is determined by a two-stage process: first, Daudin measures the probability that any particular town would have been consuming a particular good (textiles, hardware, and so on). The probability is based on the amazing dataset used in the study -- a per-district, as well as national, report on transport costs, populations, and other relevant market-size and market-access variables. These probabilities are used as weights on the town population sizes to establish market size.
As Daudin notes at the end, "our claim is that size-innovation relationships do not explain the course of the Industrial Revolution.... Adam Smith could certainly not predict the emergence and future form of the Industrial Revolution by describing the division of labor in a French pin factory. But he still uncovered an important path to higher productivity" (739). While not a complete refutation of Smith, for reasons mentioned above and emphasized a bit more below, the use of the counterfactual here is an intriguing method for understanding the real causal mechanisms behind economic growth.
I want to return briefly to the comparison between Rothenberg's discussion of market integration, and Daudin's analysis. Rothenberg seems to have it on the mark that the question is about market integration. Some discussion of this by Daudin may give a more convincing account -- for example, were prices also converging across markets in France during the period in question? If so, then the fact that French growth is slower means that we should search for other variables to explain the relative success of Britain.
Nevertheless, just as Ogilvie's article (commented on a while back on this blog) criticized the Industrious Revolution model by showing how demand is constrained by local institutions, so does this model ultimately come to the conclusion that demand simply cannot explain economic growth.
When will the profession convincingly move toward supply-side phenomena which focuses on the labor process in the context of a transforming social system? More to come on that in the upcoming weeks!
UPDATE: You can find a copy of the paper here: http://web.mac.com/gdaudin/Guillaume_Daudins_homepage/Research_Papers.html