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.

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

  1. I think the absolute level is irrelevant. What matters is how interest rates compare to time preferences in the real economy. Time preferences and interest rates are measures of the same thing namely expectations of future returns; however, time preferences measure such expectations as expressed in terms of actual spending and investment decisions while interest rates measure such expectations in terms of the supply and demand for money. Because of fractional banking and exogenous monetary base those two measures do not have to match. When time preference is higher than the Fed funds target, there is excess supply of money hence asset booms and/or inflation. When the Fed funds target is above time preference there’s a shortage of money which causes deflation and asset busts. These relationships are best described with endogenous money ISLM as I show here tinyurl.com/k4vjswm

    Something else, which is notable, is that examination of the historical record reveals that in the mid-80s a shift occurred in how excess money balances affect the economy. Under fiat regime without central bank with credible anti-inflation stance (Fed pre-Volker), excess money supplies cause inflation. Under gold standard or credible central bank (Fed post-Volker), excess money supplies cause asset booms. The implication for policy is that inflation target may be fundamentally flawed. Instead, central banks should manage the exogenous monetary base aggregate to match endogenous demand for asset money.

  2. JF says:

    “at their natural floors” What is “natural” when banks establish accounts (creating money in use) and predominate in the setting of the pricing for these accounts? The FED probably does want a “natural” inflation and they will intervene if banks are acting unnaturally because of their power to create money and control its pricing. The FED will also intervene if general pricing is “naturally” inflationary but they appear to be telling people that this “natural” inflation idea is tied more to an employment-population ratio type trigger. In light of what has happened in the financial sector we ought not spend much time agonizing over data sets defining something called a “monetary base” and I doubt that the FED and other regulators will be driven by such analyses at this time. Let us be cautious in using the thinking of the late ’70s and ’80s, not sure this was natural.

  3. Metatone says:

    I know you can model everything through interest rates – but if we’re interested in “what’s happening out there in the real economy” it seems basically the wrong way to look at the problem.

    Fundamentally, there are at least 4 “sources” of inflation/deflation which shouldn’t be expected to create the same interactions with interest rates:

    1) Cost-push on vital imported raw materials (typically energy)
    2) Wage-price spiral
    3) Reinforcing circle of aggregate demand increase/decrease (sometimes called animal spirits but often set off by some kind of real shock)
    4) Changes in technology

    I have to suggest that some of the “indeterminacy” in many results comes out of mixing up these differing situations…

  4. Z says:

    Proposed equilibrium condition -> fixed relation -> policy prescriptions

  5. Dan Davies says:

    ” 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].”

    Surely “just deciding to ignore it” is exactly the right thing to do with a model that’s giving such a silly answer?

    • Tony Yates says:

      Well, you can’t just take the conclusions from the bit of the parameter space you like, and ignore the rest. The rest, if it clashes with sound priors, might be telling you that the whole model is crazy.

  6. toby_n says:

    If the level of the short term nominal policy rate determines, or at least meaningfully influences, the average real interest rate paid on term and demand inside and outside money (ex notes and coins) with variable lags (that might be associated with the term structure of debt), is there a case for thinking about the marginal propensity to consume of debtors and creditors (perhaps split by cohorts defined by age, income, and wealth) in understanding the inflationary impacts of changes and levels in rates? Or has this work been done anywhere?

    Basic intuition is that creditors have lower MPCs than debtors, but that interesting stuff happens as folk get older that may have implications for inflation targeting CBs. Understanding the demography of the creditor-debtor landscape could deliver insights.

    Apologies if the question is hopelessly naive and/ or ignorant of basic literature. I only learn stuff by asking stupid questions…

  7. Pingback: Understanding the neo-fisherite rebellion | Bruegel

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