lördag 20 april 2013

The Simple Job of the Swedish State Bank

The Swedish State Bank supposedly controlling inflation by repo rate (with the sign indicating that the repo rate is now approaching 0%)

In the previous post I questioned the stated mission of the Swedish State Bank (Riksbanken) led by Stefan Ingves, to control the rate of inflation through the repo rate, as being unphysical in the sense that the cause-effect is rather the opposite: The State Bank passively sets the repo rate after the inflation, rather than actively controlling the inflation by the repo rate.

So what is then the truth? Well, in equilibrium it is hard to say which is the cause and which is the effect, which is the hen and the egg or the dog and the tail, but in a dynamic situation this comes out through the relation between changes in inflation I and repo rate R. Let us study this relation in the simplest case of a linear relation between I and R of the form
• R = S x I + R0       (here I is the cause and R the effect)
• I = 1/S x R + I0     (here R is the cause and I the effect)
where S is a positive sensitivity coefficient, R0 is the repo rate at zero inflation and I0= - R0/S.

If S > 1, then we can view I as the control, with perturbations in R requiring a smaller correction from I.

Conversely, if S < 1, then we can view R as the control, with perturbations in I requiring a smaller correction from R.

The steering wheel of a car or rudder of a boat functions as control mechanism, because small changes of the control suffice to counteract perturbations in the direction of travel; if heavy turning back and forth of the steering wheel was needed, controlled driving would be impossible.

What is then the value of S? Is S < 1 or S > 1, or S = 1?  Let us look at historical data for repo rate and inflation:

We see that after the economical crisis in the early 1990s the inflation has varied between 0% and 2% with a present value of 0%. The repo rate on the other hand has varied between 0.25% and 4.75% with a present value of 1%. These numbers indicate that S ~ 0.5, suggesting that effectively it is the inflation rate which controls the repo rate, that is, Stefan Ingves is the egg or the tail!

When periodically deciding the repo rate at the board meeting of the Swedish State Bank, the boss Stefan Ingves thus asks about the inflation rate and then determines the repo rate to follow the inflation rate. It seems to me that Stefan Ingves has a pretty simple job to do: Just set the repo rate after the inflation rate. I could do that myself at half the salary of Stefan Ingves.

PS At present the inflation is 0% and the repo rate 1%, while the targeted desired inflation is 2%. Is it then possible to increase the inflation from 0% to 2% by lowering the repo rate? No, it does not seem to help much to lower the repo rate below 1%, and thus it appears that the control is lost. Likewise, suppose the inflation is 4% and the repo rate is say 5%. Is it then possible to lower the inflation to 2% by increasing the repo rate to say 7%? Maybe, but a repo rate of 7% and inflation of 2% would probably have severe negative side effects. It thus appears that the inflation can only be controled by the repo rate if the inflation rate is the targeted 2%  and then control would not be needed.