Since the demographic transition is far from over yet, there is no reason to believe that a "normal situation" would imply a much higher level of r* in the coming years. (Graph 5 – Inflation rate, long time series). The real rate of interest is low, but so is inflation.
In classical economic thinking, growth in prosperity is linked to labour productivity, labour supply, hours worked etc., while inflation is considered to be a purely monetary phenomenon – this is also called classical dichotomy. While monetary policy cannot be decoupled from labour market developments, the link to inflation has become weaker. This is often referred to as a flattening of the Phillips curve.