From a Statistics Canada study on competition, firm turnover and productivity growth:
The competitive process that shifts market share towards more
productive firms accounted for about two thirds of aggregate labour
productivity growth in Canadian manufacturing from 1989 to 1999,
according to a new study that examines firm turnover and productivity
growth.
[emphasis mine]
Here is a breakdown of the contributions to labour productivity growth:
Worthwhile Canadian Initiative 
Productivity and Competition
Prof. Gordon from Worthwhile Canadian Initiative points out an interesting statistical study, Canadian data, on the connection between productivity growth and competition: Competition, Firm Turnover and Productivity Growth (theres a PDF v…