I'm not an economic historian, but like most growth economists I am an avid consumer of economic history. Maybe it's our version of "physics envy". Regardless, it isn't always obvious why growth economists look backwards so much for motivation, examples, and inspiration. Let me try to give an example of the usefulness of economic history by looking at recent "big theories" of the British Industrial Revolution (IR).
If you have any interest in learning about the IR, then you could do a lot worse than reading the following two books:
Mokyr's theory is that there was a unique intellectual environment created in Britain during the Enlightenment, and that this generated cultural conditions that valued innovation as a valuable activity in and of itself, as well as a supply of trained engineers that took advantage of these conditions. What made the IR British was its adoption of science and reason as tools of economic progress.
Allen's theory has to do with relative factor prices. The IR was British because Britain had a unique combination of high wages (persisting after the Black Death) and low fuel costs (due to cheap coal) that made labor-saving and fuel-using innovations (e.g. the steam engine) profitable. Other countries failed to adopt, or lagged in adopting, because they had different relative prices for labor and fuel.
There is some sense that these two have set up competing explanations of the Industrial Revolution, diametrically opposed. Mokyr does tend to downplay the "coal made the IR" idea. Allen does tend to downplay the notion that Britain was unique in its potential for innovation. But there is more subtlety to their arguments than that. The theories do not contradict each other, because they are fundamentally concerned with explaining different phenomenon.
There are two different questions about the IR in Britain that we want to answer. First, why did several particularly important innovations take place in Britain, and not in other places? Second, of all the innovations available, why were they adopted first (or with greater speed) in Britain than in other areas of Europe?
Mokyr's theory is very much an answer to the first question, and provides a sound answer to the second. Newcomen and Watt and Arkwright and Darby and Hargreaves were all British. Perhaps more important than these noted innovators, according to Mokyr, is the small army of highly skilled engineers that patiently but steadily made improvements to the steam engine, spinning jenny, coke smelting, and other technologies. What set Britain apart from China (where most of the big innovations had occurred earlier) or France (which quickly had knowledge of the big innovations) were those engineers. Without them, you have curiosities. With them, you have industrialization. Britain led the IR because the Enlightenment took hold and produced both the original innovators and that army of engineers.
Allen's theory is very much an answer to the second question, but is relatively weak on the first. That is, we can use factor prices to understand why Britain adopted the steam engine or spinning jenny first, but they don't explain why those things were invented in Britain. Allen suggests that those same factor prices played a role in inducing innovation, but that is shakier ground. Anton Howes just posted a reaction to Allen's work that focuses precisely on that failure.
So Mokyr's theory is more comprehensive, but it lacks a compelling explanation for the failure of other countries to follow Britain quickly into industrialization. Allen's work is really a theory of growth and development, articulated with examples from the British IR. We can easily adopt his concepts for other time periods and places, whereas Mokyr's work is far more context-specific. Thus Allen's theory is more relevant than Mokyr's to thinking about the general process of development. The second question above - why do some places fail to adopt or lag in adopting new innovations? - is in some sense the central question of development.
Research on development has been focusing a lot lately on the distribution of productivity across firms (see my reading list on misallocation). In China, India, or Mexico, for example, the ratio of labor productivity of the top firms to bottom firms is on the order of 10-1 or more. Even in the U.S. there are productivity gaps of something like 2-1 between the best and worst firms. Not all firms use the best techniques. Poor countries have particularly bad distributions, with the vast majority of their firms using low productivity technologies.
If we could understand that distribution, we could understand a lot about the gap in income per capita between poor and rich countries. So far, most of the explanations hinge on firms facing some implicit distortion to factor costs, which makes them choose a sub-optimal level of inputs. Firms that may be very productive perhaps face high distortions, making factors expensive, and leading them to be too small. Firms that are unproductive face low distortions, making factors cheap, leading them to be too big.
What this literature could learn from Allen is that the choice of technology itself is in play when factor prices are distorted. In particular, distortions that change the costs of materials relative to capital or labor could be instrumental in keeping firms from adopting leading technologies in poor countries. Cheap labor may make a firm inefficiently large in a poor country, yes. But it also removes the incentive to adopt a capital-using, labor-saving high technology production technology, even if the firm has full knowledge of the technology.
This isn't a brand new idea by Allen. Hicks talked about it in 1932. Hayami and Ruttan talked about induced innovation and the choice of technology with respect to agriculture in developing countries long ago. Banerjee and Duflo's chapter on distortions considers the role of borrowing constraints (i.e. expensive capital) in generating a fat tail of small labor-intense firms in India. Daron Acemoglu's theory of directed technical change is basically induced innovation based on differentials in factor prices.
Allen, though, provides a clear and compelling story about the power of factor prices in technology adoption. Think of his work as a "proof of concept" that induced innovation has a lot of explanatory power for differences between rich and poor countries. It is an excellent example of how studying economic history can produce insights into modern questions about development and growth. Factor price differences created decades-long lags in technology adoption across Europe, perhaps we shouldn't be surprised at decades-long delays in adoption in developing countries. Relative factor prices may be a worthwhile avenue to explore, possibly as the lever on which institutions (hypocrite!?) or geography push to generate differences in living standards.
[I appear to have slighted Mokyr's work here in favor of Allen, but right now someone else is reading his book and gleaning from it some idea about culture and development that I missed completely. From the growth economist's perspective, the purpose is not to decide who's right in these economic history debates, it is to mercilessly steal all the good ideas.]