Learning by doing, the idea that people get better at a job after they've done it for longer, is somewhat of a conundrum in that it is both useful to theory and almost self-evidently exists but has proven so empirically challenging that it has not gone far in the literature without running into trouble.
The scale of learning by doing is important because it can, theoretically, provide a competitive advantage to incumbent firms that have more experienced and learned employees. If learning by doing provides a competititive advantage for some firms then it can create a path dependency which would form a barrier to entry and be anti-competitive. If, on the other hand, it exists but not on a scale sufficient to provide a significant competitive advantage or is impossible for firms to capture by holding onto more experienced employees then all it will do is act as a slight and rather inconsequential delay to the introduction of new technologies.
The problem for economists and economic historians seeking to answer this question is that it is fiendishly difficult to do so. A classic example of how this has been studied in the past is a study by David in 1973 which examined improvements in productivity in the Lawrence Mill, no.2 in 1830s Massachusetts. This mill managed a superb increase in productivity without commensurate changes in capital or labour and David attributes this to learning by doing. However, Lazonick and Brush responded in 1985 suggesting that the most important factor driving productivity increases and decreases may really have been changes in the amount of effort put into production as companies became more or less powerful with new, more or less transient, workers and, hence, more or less able to squeeze harder work out of their employees.
Maybe this explanation is too technical. This viral ad I found via 18DoughtyStreet explains it very well:
In my experience, this is one of the most pleasant results of an academic education. I saw the ad on 18DoughtyStreet and it set me thinking about the broader implications of the process of control the programme was satirising. The great joy I have taken from my academic training is that constant stream of thoughts and ideas provoked by everyday experiences and stories. I love it and hope it isn't a habit I lose over time.
Anyway, back to learning by doing: Whether it is power that explains gains in productivity isn't really what is crucial to the learning by doing debate. There could be a host of reasons why productivity growth was more or less than that expected by a simple analysis of the amount of capital and labour in the plant. There are a thousand factors that David might not have thought of that might be the 'real' explanation of the productivity gains in the No. 2 Mill. Thompson, in 2001, examined another classic case of learning by doing, the Liberty Ship programme during the Second World War when the US rapidly expanded production of merchant ships. He includes measures for capital deepening and changes in quality but still accepts that there may be other factors he has not thought of in the residual that he wishes to identify as caused by learning by doing.
The only study that might get around this is one by Leunig, an academic from the LSE who authored a housing policy misunderstood by Iain Dale. He found data sufficiently detailed that it would allow him to study the production of individual workers as they gained more experience and, hence, avoid using a big, aggregate "everything else" residual as his measure of learning by doing. Unfortunately he has studied an industry, cotton spinning, with high labour turnover and piece rates that mean firms could not take a competitive advantage from learning by doing. We live in hope that a similar study can be attempted on an industry, like British shipbuilding up to the First World War, that does appear to have suceeded through learning by doing.
I think the difficulty robustly empirically answering this simple question should give us all pause when we are tempted to make too definitive statements about the lessons of history. There are thousands of similarly complicated questions (Was market irrationality the cause of the 1920s crash? Are patents crucial to innovation?) that people like to assume are settled. History is so complex and controversial that it should rarely be used to end debate (the "look what happened when..." argument is used too confidently, too often). One example of why the argument from historical analogy can be wrong is highlighted by the Lucas Critique. Only when we combine experience with coherent logic as to why that experience came to pass can we really claim to have a decent understanding of what is going on in the world and what might happen in the future if we change policy.