A serious problem: The lack of a long-run theory of inflation

There is much debate at present about whether the inflation that has appeared in the United States and to a lesser degree in the euro zone is temporary or permanent. But this debate is complicated by the fact that we no longer have a long-run theory of inflation that is consistent with the facts. The traditional theory is that inflation in the long run is a monetary phenomenon, that it depends on the rate of money supply growth. But this theory does not tally at all with the facts observed over the past 30 years. If inflation in the long run does not depend on growth in the quantity of money, what does it depend on? Nominal interest rates set by the central bank (neo-Fisherian theory)? Expected inflation in a self-fulfilling and therefore inevitably unstable equilibrium ?