John Baldwin at Statistics Canada has been very active in estimating the impact of trade on the economy, and on productivity in particular, but also in terms of the performance.
A firm that becomes an exporter, in John Baldwin's finding, becomes substantially better in all aspects of firm performance, including productivity, research and development, higher wages, and so forth. There are very complex interactions between a firm entering an export market, being subjected to international competition, gaining access to international technology and knowledge, and then improving its own performance at home. Of course, this impacts on its ability to generate exports, domestic sales, and domestic employment.
There are some studies of that nature.