Neo-Fisherites

22 Dec

The neo-Fisherite view is that a higher target for the interest rate will result in higher inflation, and a lower target for the interest rate will result in lower inflation.

The Fed has kept its target interest rate at close to .02% for some years now, and it has been saying that they will stay there for some time.   The inflation rate has remained a bit low during this period.

So, evidence tells us that a low target for the interest rate results in low inflation.

This follows from a very simple theory–the Fisher relationship.   The nominal interest rate is equal to the real interest rate plus the inflation rate.

             .
R = r + P

                                   .          
And so, obviously, P = R – r.

If we have the Fed follow a rule of targeting the nominal interest rate, which is realistic, and the real interest rate depends on some kind of real economic factors independent of monetary policy, then a higher target for the interest rate will generate a higher inflation rate, and a lower target for the interest rate will generate lower inflation.

While it is only a model, we can test it.   And the low target for the nominal interest rate set by the Fed recently has generated low inflation.   The model predicts the data.

Rowe especially, but also Sumner have responded to this nonsense.

From a monetarist perspective, the Fisher relationship holds in the long run.   If the quantity of money grows more quickly, then the inflation rate rises.   For any given nominal interest rate, this reduces the real rate.   This benefits debtors and injures creditors.   The demand for credit rises and the supply falls, raising the nominal interest rate, and shifting the real interest rate back towards its initial value.  With all sorts of somewhat implausible assumptions, the real interest rate returns exactly to its initial value, and so the nominal interest rate is now equal to the initial real interest rate plus the new, higher inflation rate.   All of these implausible assumptions are necessary for “super neutrality” to hold, which means that the real economy is independent of the growth rate of the the quantity of money.

Suppose the central bank had the following rule for the growth rate of the money supply:

 .                           .       .
M     =  R* – rn + yp – V
                                                                                                                      .
 Where R* is   target for the nominal interest rate, rn is the natural interest rate,
 .                                                            .
M is the growth rate of the money supply, yp is the growth rate of potential output, and
 .
V is the growth rate of velocity.
                                                                   .         .       .     .
The inflation rate in the long run is P  = M + V – yp

So, by substitution:
 .
P   =    R*  – rn

This rule requires that when the target for the nominal interest rate rises, the central bank raises the growth rate of the quantity of money and so the inflation rate rises.

If one assumes that the natural interest rate is equal to the growth rate of potential output and the growth rate of velocity is zero, then the rule for the money supply is:
 .        
M   = R*

If the target for the nominal interest rate is just taken as fixed, then the economy is stable.   It is just a fixed quantity of money rule.   Sure, inflation will change with productivity shocks and inflation and real output will change with shifts in velocity,, but as long as prices and wages adjust to surpluses and shortages as they ought, then real output should adjust to potential in the long run.

If velocity growth, potential output growth, or the natural interest rate change, then the appropriate growth rate in the money supply will change–if the goal is really to keep nominal interest rates fixed?

And why would that be?   Right.. optimal quantity of money.

The nominal interest rate needs to be zero, more or less, so that there is no opportunity cost from holding hand-to-hand currency.

And if R* is zero, and the natural interest rate is equal to the growth rate of potential output and velocity is constant, then the quantity of money should be held constant!

Of course, actual central banks are not targeting the nominal interest rate in this way..   They adjust the nominal interest rate to target inflation and unemployment.   And they raise their target rate to slow inflation and raise unemployment and lower their target rate to raise inflation and lower unemployment.   And the way their trading desk raises interest rates is to slow money supply growth and the way they lower interest rates is accelerating money growth.

And so, it is difficult to see what the neo-Fisherite theory can tell us about what happened from 2008 to 2014.   It is rather a proposal for how monetary policy ought to operate.   With the only plausible goal being a zero nominal interest rate and so a deflation rate equal to the real natural interest rate.   And the only rationale for the goal is to allow for the optimal use of zero nominal interest rate currency.