S2 File -

Objectives
The improvement of the manufacturing industry’s total factor productivity depends not only on innovation factor double circulation, but also on cross-border mobility to a large extent.
Methodology
This paper constructs a model that demonstrates the impact of innovation factor double circulation and cross-border flow on the manufacturing industry’s total factor productivity, and it seeks to estimate this impact by using panel data from China’s manufacturing industry taken from the period 2009–2020.
Findings
It finds the path dependence of innovation factors significantly increased their double circulation cost, and did not significantly improve the manufacturing industry’s total factor productivity.
Conclusion
It finds the path dependence of innovation factors significantly increased their double circulation cost, and did not significantly improve the manufacturing industry’s total factor productivity. Cross-border flow improves the marginal efficiency of innovation factors, realizes the spatial agglomeration of high-end innovation factors and greatly promotes the double circulation of innovation factors in a way that effectively improves the manufacturing industry’s total factor productivity.
Implications
These conclusions have profound policy implications: cross-border flows can promote the incremental adjustment of innovation factors; fully release the development potential and toughness of the dual circulation of innovation factors; and are essentially conducive to improving the manufacturing industry’s total factor productivity.