Their is an answer to Harrison's essay by Gregory Clark on Cato Unbound.
Again some quotes:
....Harrison’s project seems in this report to be an echo of David McClelland’s work in the 1950s and early 60s. McClelland argued that societies differed culturally in their “need for achievement” which could be diagnosed by personality surveys or even by analysis of the popular literature of the society. High need for achievement was characteristic of Protestant societies. This is not to imply that Harrison is wrong, just to suggest that in fifty years the agenda of introducing culture into analysis of growth has not advanced one step from the state of the art of the 1950s.
The problem with both the Harrison and McClelland approaches is that the responses may reflect just the realities of the institutional framework people live within, rather than their cultural attitudes. A North Korean who reports “fatalism” or “resignation” is plausibly no different culturally from a South Korean who states “I can influence my destiny.” These cultural measures are not a pure probe into the essence of local cultures, but reflect institutions and economic environments that change the real possibilities for people. It is hardly unexpected that people in growing or wealthy societies are more open to innovation, more accepting of risk, and more welcoming of advancement by merit. But which came first, the economic dynamism and wealth, or the social attitudes?
.......So, if we want to measure the effects of culture on economic growth, we need measures of culture that are independent of growth. Earlier attempts to link culture to religious doctrine were in part an attempt to find such a grounding. Recent attempts of those in experimental economics, such as Ernst Fehr, Sam Bowles, and Joe Henrich, to see how subjects from different cultures interact in controlled strategic games show another path to isolating pure cultural differences. Game theory predicts how rational self-interested actors should behave in experiments. By looking at deviations we can identify the existence of cultural norms, and whether they vary across societies. However, the results of these investigations, while suggesting significant cultural differences, so far have not been consistent or informative.
We also find in history clear signs that significant aspects of peoples' preferences—their degree of impatience, their work inputs, and their propensity to violence – changed over time in ways unrelated to economic circumstances, at least in England, as the society moved from stagnation towards modern growth. Further, there is a dynamic in the pre-industrial world—survival of the richest—that might explain these trends.
But, in general, since Harrison has measures of culture that are not clearly independent of economic circumstances, and since he has no clear intervention to alter culture, the path he plots may as much lead us into the undergrowth as into the light.