Wednesday, December 4, 2013

A delicate balance, part 2

Can the interest rate r and the inflation rate i be balanced, maintaining a steady state equilibrium condition r ~ i?

This is an accepted piece of economic theory with proponents from Nick Rowe to Scott Sumner to Paul Krugman to Steve Williamson. Absent external shocks or mistakes by the central bank, you should be able to keep the (nominal) interest rate constant given constant inflation. In an earlier post, I wrote down some of my thoughts about the big controversy that happened last week that all seemed to follow from one unconventional interpretation of an equilibrium condition. Part 1 of this pair of posts discussed what that equilibrium was and how it worked. In this post, I will show that the equilibrium does not exist.

The information transfer model says r ~ i is impossible. Effectively any pairing of constant rates r and i require accelerating nominal GDP (and monetary base), hence accelerating real GDP growth (since inflation is constant).


Using the information transfer model, I constructed a path of the economy with a constant nominal interest rate and a constant inflation rate. On the graph above, the lines of constant interest rate are shown as dotted red, the ∂P/∂MB = 0 line is solid red, the actual path of the economy is black and counterfactual constant r,i path is blue.

Here is the price level (black = model, green = data, blue = counterfactual model):


And here are the NGDP and MB paths:


We can start to see the problem if we look at the RGDP growth rate:


You can see a steady increase in RGDP growth rate. In fact, a constant interest/constant inflation path requires not just a constant increase in NGDP and MB, but an accelerating increase in NGDP and MB that is more apparent in this longer time series:


There are actually no stable paths where the interest rate and inflation rate are constant -- therefore there is no delicate balance enabling the equilibrium to exist in the first place (unless it is a dynamic equilibrium). Of course, there has never been a time with constant inflation rate and interest rate; in recent US history (since 1960) the inflation rate and interest rate have climbed up to ~10% or more and fallen back down.




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