You all know the Wicksellian rate of interest, now meet the Hayekian rate of inflation.

Knut Wicksell (1851-1926) could perhaps rival anyone for the title of most influential economist of the last 150 years. When James Buchanan gave his Nobel lecture in 1986, he lauded Wicksell for being the primary inspiration behind his own intellectual journey, which of course lead to the founding of public choice economics. That praise on it’s own would be enough to cement Wicksell’s legacy. However, he is even more well-known today for his contribution to monetary economics than for his work on public finance. Modern macro cannot get far without discussion of the natural rate of interest, popularly known as the “Wicksellian rate”.

The natural rate is considered to be the rate at which desired saving and investment are equilibrated. As Wicksell (p.102) originally explained:

“There is a certain rate of interest on loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower them. This is necessarily the same as the rate of interest which would be determined by supply and demand if no use were made of money and all lending were effected in the form of real capital goods. It comes to much the same thing to describe it as the current value of the natural rate of interest on capital.”

Wicksell concluded that an increasing or a decreasing price level is a signal that the actual rate of interest is divergent from the natural rate. Assuming central banks are setting interest rates, then, if the price level is increasing, the central bank has interest rates below the natural level. Whereas if prices are falling, the central bank is holding rates above the natural level. Only when prices are stable is the actual rate on par with the natural rate. This method of assessment is still used today, as price stability is pervasive in contemporary mainstream thought. Therefore, it is said, neutral money implies a stable price level.

**Neutral money** is another important concept; it is the state of affairs such that a monetary economy is behaving as if it were a barter economy. Simply put, when money is neutral, all demand for goods is satisfied with the existing supply. Money becomes non-neutral when there is too much of it (people demand more real goods and services than exist) or if there is too little of it (supply of goods and services exceeds demand). When money is non-neutral you get harmful inflation and deflation.

In Prices and Production Hayek analyzes Wicksell’s arguments, and agrees that in some cases neutral money means the price level is stable. However, Hayek builds on Wicksell with the observation that a stable price level would only hold money neutral in a special case: a static growth economy. So long as output is stationary, the Wicksellian framework is correct. However, this scenario does not hold true within the context of a growing economy.

**All Velocity Shocks are Demand Shocks, but Not all Demand Shocks are Velocity Shocks**

Where Wicksell was right is that the price level should remain constant in the face of a velocity shock. In other words, a change in the Cambridge *k* should not result in a change in P. If velocity is rightly defined as V = 1/k, then the proportion of wealth held as money is inverse to the speed at which money circulates through the economy. Assuming Ms = Md and MV = PY, then price level movements resulting from velocity movement creates undesirable inflation or deflation which means the real interest rate has diverged from the natural rate. In order to hold P constant, the money supply would have to shrink in order counteract the rise in velocity, lest it effect output in a negative fashion. Of course, holding V constant and shifting the money supply would have the same harmful effects as well.

However, in a growing economy, Hayek argues that the alignment of the actual and natural rate of interest would only be consistent with a decreasing price level. How can this be if shifts in demand to hold money are fully offset by supply?

This is because the Cambridge *k *(what we could call “liquidity preference”) is not all that drives money demand; income also plays a role. My thesis advisor at Cevro, Professor Pavel Potuzak, has summed this idea up nicely by pointing to some simple identities commonly assumed in macro.

If real money demand is described as: Md/P = k(*i*,x1,x2… xn)Y, (where *i *is the interest rate x1 through xn are the many other variables which influence our portfolio decisions), we can still see shifts in Md even when *k *(and therefore, V) is constant. If P is to remain stable as Wicksell endorsed, then there must be an increase in the money supply in the face of output growth. But this monetary expansion would lower the actual rate of interest below the natural rate.

Therefore, what we would need to keep money neutral is a stable MV (what Hayek calls the “money stream”) such that a rise in Y precipitates an equal fall in P. Thus, as Hayek and many others have since pointed out, in a growing economy, for money to remain neutral — and therefore for real and natural interest rates to be aligned — we need to see price deflation.

**Defining the Neutral Rate of Inflation**

So, if ΔP (π) must perfectly oppose ΔY (*g*), then the inflation rate which keeps the loanable funds market equilibrated and money neutral is the inverse of the growth rate in output. For example, if GDP is growing at 3% per annum, then the **neutral inflation rate** is -3% per annum.

The actual, or **real inflation rate,** can be defined as just whatever inflation actually is, as observed by movements in a given price index. If inflation was measured as 2% last year, then the real rate of inflation was 2%, as traditionally stated. But if GDP growth was 3% then, given what we know about the neutral rate, the** inflation gap** was actually 5%, as measured by deviation between the neutral rate and real rate. Thus, we now have two measures of inflation: **the neutral **and** the real: **when these two rates are not equal we can say there is an **inflation gap**.

The real interest rate seems to be the only one garnering any attention in contemporary academic literature. But the inflation gap matters too if we care about monetary neutrality, as this gap measures the economy’s deviation away from neutral money. To use Hayek’s terms, it measures how loose of a joint we have. While, to my knowledge, these two types of inflation have not been explicitly distinguished and named, the idea of a neutral monetary policy certainly has, and these rates are implicit in this idea. In fact, that was one of Hayek’s main points in P&P, and it has since been pointed out again and elaborated upon by many, including Hutt (1979), Selgin (1988), and Horwitz (2000). Implicit in all of these is the idea that a persistent inflation gap is what drives monetary disequilibrium, not necessarily real inflation (as in theory, real inflation could equal neutral inflation and this would mean there was no gap). A neutral monetary policy is thus one which targets the neutral rate of inflation, i.e aims to have a 0% inflation gap.

Wicksell is known for the natural rate of interest, or the “Wicksellian rate” which is currently built into almost all monetary rules. Hayek should be known for the neutral rate of inflation, the “Hayekian rate,” and that too should be built into monetary rules if we wish to minimize the effects of non-neutral money.

**A Hayekian Inflation Target in Practice**

Whether or not a central bank can actually perfectly target the neutral inflation, Hayekian rate, in practice is a different question. Again, Professor Potuzak points out a potential problem. A central bank could only target the neutral rate of inflation (although he does not use this term) if the economy is dynamically efficient – in other words, if the natural rate of interest is greater than the rate of economic growth. We can say that the following condition must hold true if a neutral monetary policy is to be operational, and not get pressed up against the zero lower bound: r*>*g*. For if this were not the case than a central bank would need to set a negative interest rate, which likely would be quite problematic. (If the target interest rate is the natural rate and the target inflation rate is the neutral, then, using Fisher’s equation, the central bank rate will be negative, if real plus inflation is negative).

Therefore, we could say that an inflation target may be warranted, as the best of a bad situation. If we are stuck in a secular stagnation world with a low r*, we may need to tolerate the distortionary effects of monetary injection to keep interest rates above zero. Then we ought to set up an inflation gap target, not a real rate one (as is currently standard practice), in order to keep monetary policy as close to neutral as possible, while still remaining operational.

But note that this simply collapses into a nominal GDP target; the inflation target turns into: x-*g*. Where “x” is the desired percent of inflation gap, chosen to cover variance of r* and *g* , plus perhaps a percentage point or two as a ZLB buffer, to satisfy our earlier condition such that now: r*+x>*g*. This simply mean x% becomes the desired growth trend of NGDP.