You write: “The most recent empirical studies show that the world economy overall is in a wage-led demand regime ...”
This is good news in several respects. I focus in the following on verification/falsification, i.e., on the relationship between facts and theory.
You write: “An increase in the wage share has several effects on demand and whether actual demand regimes are wage-led or profit-led is subject to an ongoing academic debate.”
This debate can be quickly resolved. A positive relationship between wage rate, various demand components, and employment and a negative relationship between price/inflation and employment is exactly what the structural-axiomatic Employment Law asserts (see 2014, p. 9, eq. (22)).
I wrote on p. 10: “A general increase in the wage rate increases the factor cost ratio in eq. (22) and effects higher employment. This systemic property follows in direct lineage from the axioms and the condition of product market clearing. It goes without saying that this rectified relationship between wage rate and employment is almost certainly beyond the comprehension of the marginalistic supply-demand-equilibrium mindset. There is no need, though, to discuss contradicting assertions because of eq. (22) is testable. Therefore, an experimentum crucis that settles the matter is possible in principle. There cannot be much doubt about the outcome.”
The outcome is what the most recent empirical studies show. These studies have not yet come to my notice, yet I am quite certain that you can improve the results by applying the structural axiomatic Employment Law Wikimedia AXEC07:
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
Related 'Keynes’ Employment Function and the Gratuitous Phillips Curve Disaster' and 'Essentials of Constructive Heterodoxy: Employment'.
Ramanan — Good Reference On Wage-Led Growth
Chris Dillow — On Wage-Led Growth