Foreign Competition and Domestic Innovation

Difficult question where the answer depends significantly on the particular circumstances being considered.

This is neither clear theoretically (scale effects versus escape competition effects) nor empirically (see Autor et al. versus Bloom et al.)
-see background information here
-see background information here

Trade and competition is a long established driver of innovation. Autarkies - like North Korea - have little innovation.

It depends on the capabilities of firms in the home market; if they are too far behind the frontier they won't be able to compete
-see background information here

The relationship between competition and innovation is non-linear

Evidence in both directions, differing for Europe & US. Difference could depend on domestic comp or labor markets (e.g., trapped factors)
-see background information here
-see background information here
-see background information here
-see background information here

My understanding of the literature both in theory and empirics is that this relationship is ambiguous.

R&D will increase the quality of the product or lower its costs and comparative advantage will be restored

Depends on the nature of the industry (monopoly, network effects...).

Bell labs? I think there is little reason to expect something really systematic here