The relativity of interest and inflation

This post will cover a lot, but in a shallow way, because I think a lot of things are connected.  Each idea discussed involves a deeper line of thinking that I could explain in depth.

The relativity of interest and inflation

I was tempted to say that price indexes are "arbitrary", in the sense that you can choose any one. But the term arbitrary is not quite right.  Price indexes are relative.  If you switch from one index to another, you get the exact same information, it is only framed differently.  This is exactly how classical Newtonian relativity works, you can use any frame of reference, so long as you transform information properly between them.  Calculations can be done in any frame, for the most part.

But given our human experiences are what we use to understand and interpret the world, it helps to have a consistent frame of reference.  Sometimes things can be so muddied that this is impossible.

So the point here is, calling something interest or inflation is completely relative, the real rate of interest is just a relativistic frame.   It just depends on the inflation index you use, and while all frames are valid, some are much amenable for our flawed human reasoning.  

Simple Equations, Contentious Interpretations

While this is a phenomenon that happens in many subject areas, it is perhaps most common in economics.  You have a simple equation with 3 or 4 variables, and while many people may agree the identity is valid, at least given proper definitions, they will disagree on how to interpret and apply the identity, in real world situations.

Some examples are the equation of exchange/quantity theory of money, or the fisher equation.  Instead of EoE/QTM, I use what I will call "the total valuation identity":

Bad(EoE/QTM):

 MV = PY, MV= PT 

Good(total valuation identity):

  Aggregate Value = Unit Value * Number of Units

The total valuation identity is much simpler and less prone to misinterpretation. In particular, I view money velocity as a completely contrived measurement which is arbitrarily assumed to be stable.  You could take any three variables, invent a fourth variable as a function of the other 3, and then assume the made up variable is constant.

As for the fisher equation, the way I like to remember it is as the definition of the real rate of interest.

Real Rate = Nominal Rate - Inflation.

This is an expression of 3 variables, but a common mistake in misrepresenting such identities is to assume one is constant, or that only two of the three terms have an interdependent relationship.  To appreciate all the possible interpretations of the fisher equation, we must acknowledge that inflation index chosen creates a relativistic reference frame, and that any possible index can be valid.

It is a mistake to assume a particular relationship between the variables, like changing the nominal rate creates a specific response in the real rate.  I could go into more details at length, but let's move on to the evidence in question.

Can we distinguish mechanics from dynamics?

There are two words commonly used in science and engineering when talking about complex evolving systems that can be described mathematically: mechanics, and dynamics.  I would suggest there is a loose rule of thumb for how these terms are used, though by no means this could be considered definitive.

"Mechanics" connotes a closed or engineered or regular system.  "Dynamics" tends to refer to an open irregular chaotic system.  I'm sorry that I'm mixing precise and common language, but I have a hard time knowing how to best describe this distinction precisely right now.

I think such a distinction could be particularly useful in economics, as it involves the intersection of two systems:

 - Accounting: carefully maintained record keeping with regularity and a high degree of integrity.

 - Finance: great uncertainty, chaotic, often psychological or herd dynamics involved.

The integration of accounting and finance is one of the most challenging parts of economics.  Accounting is supposed to be precise and objective. Finance, the attempt to discover and create what has value, while it relies on accounting, is open ended and always has uncertainty.

Distinguishing between mechanics, which we could say is how accounting works, and dynamics, our attempts to describe the motion of finance, is very useful.  The things we can say about accounting are clear and unambiguous, and we can assert them with near perfect certainty.  We can also describe the dynamics of finance mathematically, but it is much more difficult to achieve precise engineering level of analysis. Markets are the engine of price knowledge, as such, they are hard to predict or emulate, like an ant trying to know the mind of God.

So when people say that interest hikes reduce inflation, how that translates to my mathematically trained brain, is that they are making a statement about dynamics, and not mechanics.  Whereas, if one talks about duration, or interest income, or even interest based margin calls, those effects are mechanical.  To say we can reduce the demand for money is a termite attempting to know the mind of God, but to say that when we raise rates these cohorts get more or less income, is a mechanical effect.

Interest inflation control also typically involves the phillip's curve, a tradeoff between inflation and unemployment.  This is taking an adverse aspect of recessions, and trying to use it to create a controlled deflation.  I actually believe this can work! Although saying it "works", may be generous.  If we are going to use fire to fight fire, an intentional disaster to manage an unintentional one, it should be a last resort, and involve extremely careful execution.

This is the taylor rule:

We can factor to get r = 1.5*p + 0.5*y + 1.  While this may not be the most nuanced or advanced form, the idea is simple, try to maintain a positive real rate.  It goes so far as to recommend, setting the rate 1.5 times that of inflation.

What is the risk?

Well, the way I like to describe it, is that the nominal rate sets a benchmark for "real" asset performance.  If you set the nominal rate to 10%, there are two possibilities.

 1. Assets must achieve a 10% inflation adjusted return, or default.

 2. Assets miss the benchmark and have inflation.

If you set a high nominal benchmark, but don't enforce it, then you have just created inflation, specifically a downward re-denomination of currency.

Real Rate Increases Must Outpace Nominal Rate Increases to Achieve Deflation

The thing about the fisher equation, in order for a nominal increase to induce deflation, the real rate must increase by more than the nominal rate increase.  If you hike by 2% nominal, but can only push up the real benchmark 1% higher, then you get more inflation. A 2% nominal hike requires a 3% increase in the real rate, in order to create a deflationary effect of 1%.  So the amount of deflation is always less than the real rate increase. 

The peril of course, is that a good deal of the debt used to create money, is itself the national debt.  Rate increases in all cases are a form of brinksmanship, whether they are done on a borrower with missed payments, or an economy wide rate increase in the face of inflation.  The rate increase alone does not create a real return, it pushes a scenario into extreme outcomes: either the borrower defaults, and enters bankruptcy, sooner being better than later, or they are forced to self motivate and achieve a much higher real return, at the precise time when they have demonstrated themselves least able to do so.

Is it bravery or stupidity to increase nominal rates and have the discipline for an even greater real rate hike? Can we achieve this real return benchmark on the national debt?  This may require a significant tax increase.

So it's not that a nominal rate increase cannot be part of deflationary response, it's the question of whether it's the most prudent method to do so.  Furthermore, if inflation is 30%, do we really want to jack rates all the way up to 35%? If this works, and inflation returns to zero, then you all of a sudden have a 35% real yield until rates are lowered.  Or do we give a chance for markets to correct, for part of the debt to inflate away?

Critics would argue that allowing the debt to inflate would quickly become an accelerating process.  But in financial markets all asset at some point experience drawdowns.  Traditionally, currencies have only gone down in value, whereas debt instruments can be used to provide a closely associated appreciating security.  If an asset always loses value, then it may be much more prone to an accelerating process when it loses more than usual. So there may be some wisdom in allowing modest debt appreciation.

The final question, is whether we can tighten credit without a nominal rate increase? if that is possible, then this would be much less disruptive, and much less costly overall.  Whatever real rate increase we achieve, is deflationary, whereas with nominal hikes, the nominal hike at least partially offsets the deflationary effect of the real rate increase.

How might we tighten credit in this way?  Require larger down payments. Require more collateral against defaults. Perhaps even support on the bottom end of the labor market would allow us to cut much more aggressively on the top?  Maybe I am just daydreaming, but I think we should take some time thinking about this, before we decide we need a 20% output gap to create lasting deflation.