Jan Boone has suggested using the derivative of profit with respect to marginal cost as an indicator, which has some of the same features as the OP covariance. Also some advantages if technologies aren't constant returns. I've only really seen it used very much in banking contexts but I don't know why it wouldn't apply to other industries.
Perhaps the model would benefit from considering where the market is in its life cycle? Some markets have been around forever, others are closer to the technology frontier. In those tech markets, it may take a few years for a superior firm to prove its worth and capture market share. The change in OP Covariance over time of the smaller firms may signal the level of competition they will provide over time.
This is a great point and I should have been explicit. You definitely shouldn’t compare 2 industries, just as you shouldn’t compare 2 industries on their concentration either. You’d want to compare across countries for the “same industry” (as much as that is possible) or across time for the same country. Technology definitely could mess it up still but again that’s true for all the measures.
Jan Boone has suggested using the derivative of profit with respect to marginal cost as an indicator, which has some of the same features as the OP covariance. Also some advantages if technologies aren't constant returns. I've only really seen it used very much in banking contexts but I don't know why it wouldn't apply to other industries.
Someone else recommended that as well. I need to look at his paper more carefully.
Perhaps the model would benefit from considering where the market is in its life cycle? Some markets have been around forever, others are closer to the technology frontier. In those tech markets, it may take a few years for a superior firm to prove its worth and capture market share. The change in OP Covariance over time of the smaller firms may signal the level of competition they will provide over time.
Interesting!
But, if I got it right, it's necessary to assume that every firm in the market has the same technology.
So, if A and B has the same technology, but A is more productive than B, A would have more market share than B.
And the marketshare is correlated with the covariance between the average productivity of the two firms.
This is a great point and I should have been explicit. You definitely shouldn’t compare 2 industries, just as you shouldn’t compare 2 industries on their concentration either. You’d want to compare across countries for the “same industry” (as much as that is possible) or across time for the same country. Technology definitely could mess it up still but again that’s true for all the measures.