A fishy conclusion from a Fisher relation

Interesting.  Both a Fed economist and Stephen Williamson (the author of one of my undergrad macro books) have been saying that persistently low interest rates “cause” deflation in the long run (ht Economist’s view) [Lots of others, WCI *, Money blog, Angry Bear, Paul Krugman, Money Illusion].  This seems a little counter-intuitive, but this doesn’t mean anything is wrong – I’m going to write down a few of my thoughts to see if I can figure out what is going on.

I mean, I agree that the Fisher equation must hold, and I agree that the long-run real interest rate will be exogenous.  But this ain’t enough to tell me that having the Fed keep rates at 0.25% forever “causes” deflation.

Why?  The average Fed rate and inflation expectations are both endogenously determined – they seem to be treating the Fed’s choice as exogenous, when they follow a decision rule. Yes it is true that the cash rate at a point in time is a choice variable – but the average cash rate in the long-run should effectively be determined by the real interest rate and long-run inflation target. [Update Think of it this way, I’m really assuming the central bank follows a Taylor rule and that determines the nominal rate given the inflation target.  The big kicker for any argument like this will be the way inflation expectations are formed].

As a result, we could just as easily interpret rates staying at 0.25% forever as an indicator that inflation expectations are -1.75% -> in other words we observe a low nominal interest rate BECAUSE there is deflation.  Fundamentally, this tells us nothing – as the Fisher relationship is an equilibrium statement, not a casual relationship.

In fact, if there is indeed a forecast of rates staying at 0.25% forever there is a STRONG argument for making policy more stimulatory now – is that what the guy is trying to say?

If we want to discuss a causal relationship we need a causal model of our endogenous variables right – the Fisher equation is not this.

Update: I see where they are coming from now.  However, I believe the key issue is with regards to current policy – fundamentally the mentioning of deflation was taken in context of the CURRENT disinflation going on in the USA, and it seemed like a statement that was pushing for an increase in rates to avoid deflation.

I’m also nervous about the use of the word “cause” when any observed relationship in the data will not necessarily be clear – but I’m always nervous about causation so oww well.  Namely, if I see an average cash rate of 0.25% and average -1.75% inflation I wouldn’t say “aha, having the cash rate at that level caused that” – I would want more information on how inflation expectations got there in the first place …