A Tale of Two Natural Rates

Narayana Kocherlakota makes the case for more public debt. Paul Krugman and Steve Williamson agree. (I have to keep rereading that sentence before I believe it). What is this argument all about and how does it relate to the soul of Keynesian economics?


Let's start with a key premise in the Kocherlakota speech. There is a theoretical concept called the ‘neutral real interest rate’ and one of the jobs of a central bank is to get us back to that rate of interest as quickly as possible. The ‘neutral rate’ is what Wicksell called the ‘natural rate of interest’ and I'm going to stick with Wicksell’s terminology here.


Wicksell’s natural rate of interest inspired Milton Friedman to coin the term ‘natural rate of unemployment’. In classical economics and in the brand of New Keynesian economics that inspires central bankers, there is a one-to-one correspondence between these concepts. If we could only ensure that we were at the natural rate of interest, it would simultaneously be true that we were at the natural rate of unemployment. That is, to use a technical term, poppycock.

Let's consider two possible definitions of ‘the’ gross real interest rate.

Definition 1: R1

R1 is  the number of apples you could buy one year from  today if you sell one apple today, invest the proceeds in one year treasury bonds, and convert the interest and principal, one year from now, back into apples.

Definition 2: R2

R2  is the number of apples you could buy, one year from today, if you sell one apple today, invest the proceeds in the stock market, and reinvest the quarterly dividends. One year from now, you sell your shares and convert the proceeds back into apples.

These two real interest rate concepts will always be different because the stock market return is far riskier. But economic theory says that they should be connected by the equation,

R2 = R1 + RP

where RP is a positive number that represents the extra return you require to compensate you for risk.

So far so good.

Now let's look at the connection between R2 and the stock market price. Imagine that we repeat the experiment of selling an apple many times and that we compute the average return. That's a bit of an artificial experiment because technically, I am thinking of the return earned in a billon parallel universes, all with the same initial conditions. That's a technicality that lets me abstract from uncertainty.

How would R2 be related to the price dividend ratio?

Here’s the answer.

R2 = 1 + D/P = 1 + (1/pd)

where  pd is the price dividend ratio, P is the price of the stock and D is the dividend averaged over all of these parallel universes.

Now let's get back to original question. Let R2* represent the natural rate of interest earned in the stock market. Let U be the unemployment rate,  let U* be the natural rate of unemployment and let pd* be the price dividend ratio when we are at the natural interest rate.

QUESTION 
Here is my question to Narayana, Paul, Steve and anyone out there who wants to throw in their two cents. 

If:

R2 = R*

is it necessarily true that

U = U*?

My answer is a resounding no. And that is what distinguishes my work from new Keynesian economics. The reason is that for every U there will be a P(U) and a D(U) where D(U) is the dividends you would earn on the stock market, and P(U) is the price you would pay for a share  if the unemployment rate was U. In my world, there are multiple equilibrium unemployment rates. That is, after all, the essence of Keynesian economics. And that premise implies that there are multiple values of U such that

pd* = P(U)/D(U)

The answer to this question matters. And it matters a lot. During the Great Moderation, unemployment and inflation came down together. There was no apparent conflict between the goal of 2% inflation and full employment. That divine coincidence cannot be expected to continue. We need two tools for two targets. As I have argued here; we must use financial policy to target the unemployment rate and monetary policy to target inflation. 

So my question to wannabe Keynesians is: Are you a Neo-paleo Keynesian? Or are you a watered-down-Samuelsonian-MIT-Hicks-Hansen-1950s-IS-LM kind of guy?