What prediction is shared by the neutrality of money and the natural rate hypothesis (NRH)?

The prediction shared by the neutrality of money and the natural rate hypothesis (NRH) is that in the long run, changes in the money supply do not affect real variables, such as output, employment, or the real interest rate.

The neutrality of money refers to the idea that changes in the money supply only have a temporary effect on nominal variables (like prices and wages), while leaving real variables unaffected. According to this view, increases in the money supply lead to an increase in aggregate prices and wages, but they do not have any impact on real economic activity.

The natural rate hypothesis, on the other hand, posits that there exists a "natural" rate of unemployment (the non-accelerating inflation rate of unemployment, NAIRU) that is determined by structural factors in the economy. In the long run, the actual rate of unemployment will converge to the natural rate, regardless of changes in monetary policy.

So, the prediction shared by both the neutrality of money and the natural rate hypothesis is that changes in the money supply cannot affect real variables in the long run. However, it is important to note that these are theoretical concepts and there is ongoing debate among economists about the validity of these hypotheses in the real world.