How will the valuation gap between US and European equities correct?

An observation of long-term growth and long-term interest rates shows that the gap between the valuation s (PERs) of US and euro-zone equities is not justified. It results from higher aversion to equity risk when it comes to euro-zone equities. It is therefore reasonable to expect a correction of the valuation gap between US and European equities. But how will it take place? Via a fall in US share prices? Their overall valuation does not seem excessive: US potential growth should be revised upwards and labour costs are barely increasing, which renders a sharp correction unlikely; Via an increase in European share prices? This is more likely, due to investors’ excessive pessimism over the euro-zone economy, which is being boosted by a sizeable demand stimulus.