Reflecting on the Fisher relationship

Irving Fisher’s famous relationship is written , in the long run : Nominal interest rate = Real interest rate + Inflation It is an identity that necessarily holds . But how should it be interpreted? Conventionally : The real interest rate results from structural features of the economy (the savings-investment equilibrium); Inflation is determined by money supply growth (from which real potential growth is subtracted); Knowing the real interest rate and inflation, we then have the nominal interest rate. But this traditional view is incompatible with the fact that there is no longer any link between money supply growth and inflation. One may then look to the neo-Fisherian view, where: The real interest rate still results from structural features of the economy; But the central bank chooses the nominal interest rate, even in the long run ; And inflation results from the nominal interest rate and the real interest rate. Under the neo-Fisherian view, a long period of restrictive monetary policy with low nominal interest rates leads in the long run to lower inflation. But empirical estimations show that even in the long run, monetary policy has an effect on the real interest rate. We then have a “monetary policy” view. Under this view, an expansionary monetary policy, for example, leads to a lower real interest rate even in the long run. In the event of monetary expansion, we may then have: A low nominal interest rate; A low real interest rate; And rising inflation if the reaction of the real interest rate is greater than the change in the nominal interest rate.