Hiring difficulties drive companies to increase productivity in the United States: Will this also be the case in the euro zone?

When hiring difficulties are significant in the United States (from 2017 to 2019 before the COVID crisis, currently), companies react by making greater productivity gains, which preserves growth and prevents wage inflation. Can we expect the same reaction from companies in the euro zone? What factors could lead to such a lack of productivity growth in the euro zone? The fact that hiring difficulties are less severe than in the United States; we can clearly see that the participation rate has fallen in the United States and not in the euro zone; The fact that European companies are far less inclined to digitalise and automate than US companies.