If the central bank rate falls, does inflation rise or fall? The limits of verbal reasoning.

Noah Smith and Ryan Avent got his debate going again, a conversation whose last incarnation was an exchange between Steve Williamson and Paul Krugman, essentially, sparked by Steve asserting that inflation was too low because Fed rates were too low.  Chris Dillow has offered his own contribution.

The latest exchange, for my money, shows the limit of verbal reasoning about questions in monetary economics, and lack of prior exposure to the long past literature on this.  This literature isn't necessarily right (about what would happen in the real world).  But it offers a menu of what ifs, a menu to which these blog posts are essentially trying to add.  Noah and Ryan wrestle with the impact of expectations on current prices.  Chris wrestles with different 'mechanisms'.  All of them seem to me to get trapped by the pitfalls of the initial thought experiment.

First thing to say.  If expectations are rational - in the jargon this means if agents know how the model works, what the central bank is doing - then under either sticky prices, or flexible prices, a wide class of models gives the answer that if the central bank holds the interest rate down at a fixed level for ever (even for a long time) ANYTHING can happen to inflation.  You have what is known as 'indeterminacy'.   There are infinitely many values for inflation expectations and thus inflation consistent with any given value for the shocks hitting the economy.    This has been known since Sargent and Wallace.  And was later studied by McCallum, Woodford, Evans and Honkapohja, Bullard and many others.

It may well be unrealistic to suppose rational expectations for an experiment like this.  If expectations follow processes generated by least squares learning, or similar, then holding the interest rates down for a long period, or forever, is highly likely to generate violent instability in inflation.  So, in a slightly different way, if we were to ask what inflation might turn out to be some time down the road, we would have to say : who knows, anything could happen.

Holding inflation constant, we can then only really ask questions about what would happen if interest rates were held temporarily lower than were dictated by a monetary rule that, once followed subsequently, were sufficient to guarantee determinacy or stability.  The answer to that question we know in a wide class of models.  Inflation rises if interest rates fall.  Temporarily.  Thereafter, interest rates rise to combat the unwanted loosening, and the rise in inflation, and eventually all settles back to steady state.  So far as I know, none of this depends on whether expectations are rational, or prices are sticky.

We can ask questions about what would happen if the inflation target were to change permanently.  If it were to fall, then in the long run, so would nominal interest rates, by the same amount [leaving aside, as most of the models I am subblogging [term coined to mean blogging without referencing properly, derived from subtweeting] do, the costs of inflation].  In the mean time, what happens to nominal rates depends on whether prices are sticky or not.  If they are flexible, then nominal interest rates would fall immediately, and correspondingly.  If sticky, then initially nominal rates would have to rise before settling back to a lower steady state.   I don't think this result would depend on expectations.

I recall being mystified by Steve Williamson's cryptic suggestion that the Fed is causing low inflation with low interest rates.  Because presumably he meant 'despite telling everyone that their inflation target was 2 per cent, roughly'.   I was mystified because I know he understands the models I have just cantered through better than I do, where this isn't true.  These models exclude models in which money is modelled in a way that would satisfy Steve and the other 'new monetarists'.   I don't know what happens in these models.  Or if versions of them have been developed that are sufficiently realistic in other respects to allow us to compare.

A final nihilistic contribution was made by Cochrane, in his JPE paper of a few years ago.  If I can offer the most ridiculously short summary of a long and hard paper ever attempted, I'd say that this paper says 'even when modellers using the rational expectations sticky price model say that things are determinate, they may not be, though they are certainly not when they say they aren't.'  Which means that you have to go back over what I said, and note that where I said we might get a definite answer, instead of 'anything', we might actually just get 'anything'.

Anyway, that was a rather hurried post, offered really as an elaboration on a few tweets I have sent out.  I don't pretend that they describe the real world, but I hope that they ring some alarm bells about the care that bloggers need to take when they pose and try to answer the question 'what happens to inflation if the central bank cuts rates?'  You need to say:  for how long, and why exactly is it cutting rates?  Is that part of a revision of the monetary rule?  And you may have to ask yourself whether you can decide on whether prices are sticky or not, and on whether the change is comprehended or believed by the private sector.

Update.  [This is why I should stick to the Simon Wren Lewis rule of only posting what you wrote yesterday].

This discussion is not of purely academic interest, though it sounds nerdy and pointless.  Recall where it started.  Core inflation is sliding in the US and the ECB [and possibly in the UK too].  Does this mean that central banks should double down and keep rates lower for longer [this is how central bankers would see it, and this is how monetary econ as summarised above would have it], or is low inflation, by contrast, caused by the low rates?  It's pretty crucial to settle this.

Relatedly, the discussion connects with recent efforts by the Bank of Canada, Fed and the BoE to stimulate the economy by announcing that rates will be held low, and fixed, at their natural floors, for long periods of time, before eventually rising, a policy they have dubbed 'Forward Guidance'.  We know that the rational expectations, sticky price models used by central banks behave VERY weirdly indeed as we vary the number of quarters for which interest rates are held fixed.  Work by my former colleague Matthias Paustian and coauthors shows, for example, that you can get that a loosening implemented this way can generate a massive inflation, or, if the number of quarters is changed just a little, a massive deflation.  One presumes that central bank modellers have found some kind of fix for this [or have decided to just ignore it].  But these results must leave us with some disquiet about i) whether the models are the final word on the matter and ii) whether the central bank policymakers really can say that they have a clue what will happen to the economy under Forward Guidance.

I will revise this post with links later tonight.