Real Rate Increases Must Outpace Nominal Rate Increases To Achieve Deflation

They say that higher interest rates reduce the demand for money. It is probably more precise to say that higher rates reduce the demand for debt.  Borrowers tend to be spenders, after all, that is why they borrow.

However, there is at least one way that higher rates actually increase the demand for debt: existing borrowers must cover their outstanding debts or default.  At least one of these borrowers is the country itself.  Unless the treasury can reinforce the contraction of debt based money, by shrinking the national debt, it is hard to imagine that high interest rates can fight inflation on their own. 

But there is a much simpler and direct way that a nominal rate hike may add difficulty to the task of inflation reduction. For a nominal hike to be deflationary, the real rate increase must outpace the nominal rate increase.

To demonstrate this, let's look at the fisher equation again.  I like to first recall the fisher equation as the definition of the real rate of interest.  It is important to remember that this version is an approximation based on treating interest additively instead of multiplicatively.

Real Rate = Nominal Rate - Inflation

In my last article The Relativity of Interest and Inflation, I pointed out that the choice of inflation index is equivalent to choosing a relativistic frame in physics, provided that you can calculate correctly.  Just like newtonian inertial frames, each one has the same information, although our intuitive reasoning may work better in some frames than others.

After we express the fisher equation as the definition of real rate, we can then do a little algebra to convert the equation to isolate inflation.

 Inflation = Nominal Rate - Real Rate

Well known economist blogger Noah Smith once claimed 

Neofisherism assumes that in the long run the nominal rate does not affect the real rate.

This is not true.  For a nominal rate increase to be inflationary, it is only necessary for the real rate increase to be less than the nominal rate increase over the long run. 

 

Nutty Macroeconomic Theories Will Ruin Your Country's Economy. 

Noah's claim is close, but actually misses the mark in a significant way, and given that he is talking about a subject trying to claim mathematical seriousness and the academic high ground, we should at least challenge him on it. 

A nominal rate that does not affect the real rate, over the long run is certainly a sufficient condition for a neofisher effect, but it is not a necessary condition.  It is only necessary for the real rate increase to be less than the nominal rate increase.  If you increase the nominal rate by 2%, but over the long run the real rate only stays 1% higher, you end up with more inflation.  Congratulations, welcome to a neofisher timeline.

The simplest way to put this is the following:

If real rates and nominal rates change by the same amount, then there is no effect on inflation. 

So when a central bank hikes rates by 2%, what they are actually hoping for is that real rates increase by even more.  The problem with real rate increases, is that are expensive in two ways.

1. Create additional interest income for asset / capital holders
2. Increase financial defaults and instability

And this #2 is the real trick to increasing real rates: somebody has to default.  If you aren't willing to let someone default, then you haven't actually decreased money creation, especially considering the national debt, if there is not some kind of fiscal disciplining adjustment made for realized inflation.

So we go back to the title of this post "Real Rate increases must outpace nominal rate increases to achieve deflation".  If the effect of a "shock" ie raising rates, only elevates the real rate above the nominal rate for a short period of time, then the rate hike will eventually cause net inflation.

A fairly plausible shock response to a hike, that ultimately creates more inflation, might be the following:

In this hypothetical, inflation rises from 0.5% in t0, to 1.5% in t1.  In response to inflation, whatever central bank we are talking about, decides to raise rates from 0.5% to 2.5%(most banks have a 2% inflation target, but pretend the target is lower).  Initially, the real rate goes from -1% to 2%, bring inflation immediately back down to 0.5%.  The rate of inflation, is simply the gap between the red and blue line.

But in our invented hypothetical, the impact of the rate hike, or "shock", declines over time.  Even though initially the real rate increased by more than the nominal increase, eventually this comes down so that our 2% hike, only results in a 1% elevated rate over the alternative universe.

• Initially, the rate of inflation is brought down to 0.5% at t1.
• Halfway between t1 and t2 inflation reaches 1.5%, exactly where it would be without the hike.
• By the time we get to t2, the amount of cumulative deflation from the rate hike is zero.
• By the time we get to t3, we have cumulative inflation from hiking(1% for 1 time period).

So while long run real rate, which is unaffected by the nominal rate, is sufficient to create a neo-fisher effect, or net inflation as a result of a rate hike, it is not a necessary condition.  All that is required is that the real rate increase be less than the nominal increase.

There are a good deal of papers investigating the effects of what are called "shocks" of monetary policy.  I have taken a cursory look at a few of these papers, and while statistics is not my strong suit, what stands out to me, is that they claim to observe a deflationary effect over long time lags.

The suspicious thing about these claims, is that the longer you go between cause and effect, the more uncertainty involved, in essence like looking several moves ahead in chess.  While these papers appear to involve a serious level of analytical statistical effort, extraordinary claims require extraordinary evidence.  From what I can tell, the papers do not sufficiently consider alternatives or control variables, such that they can make these claims.  One such paper is Romer and Romer 2004 "A new measure of monetary policy shocks", although there are numerous others.  Most of them do not appear to seriously consider the costs of elevated real rates, nor perform the superhuman feat of controlling for macro uncertainty across up to 2 years of time lag.

Central banks have followed a pattern of hiking rates in response to inflation.  To know if these hikes work, you have to know what would have happened if there were no hike. The central problem of econometrics is to do science without experiments, without the ability to explicitly create controlled alternative treatments.   This is an incredible challenging and sometimes fraught endeavor. While autoregressions can sometimes emulate a properly controlled experiment, I am not convinced they have achieved that in this case, especially based on what I hear from monetarists.

But I do want to give them some benefit of the doubt, and that is by bringing in the issue of accelerating inflation.  If currencies decline rapidly enough, this can negatively affect many factors, including how the currency is used.

As an asset, national debts need to have a real yield during some periods, to stabilize the negative yield of others.  But I think it is a mistake to suppose they always need to have a positive real yield, or inflation will rapidly deteriorate. Here is an interesting article on that subject. 

In standard theory, the focus on is an accelerating inflation.  If we were only looking at currency, and not national debt valuations, then rate hikes might make more sense, although they would still involve a great deal of pain.    For the post 2020 covid era inflation, accelerating inflation is not very plausible, as the U.S. dollar was a strong performing currency compared to other currencies, despite elevated inflation.

In the future I want to talk about alternatives to the taylor rule, for setting interest rates. But for now I will say a few things.

•  I think we can let real debt values draw down for short periods.
•  I think that elevating nominal rates too high can easily create more inflation, as it is more difficult for real asset returns to hit that target.
• The mechanisms of hikes matter: whether that is interest on reserves, or something that coordinates better with fiscal discipline.
• Everyone is required to use dollars, including the treasury.  Competitive domestic note issue, could even lead to lower rates and lower yields on treasuries, as other entities could compete to create their own currencies to buy treasuries.