Saturday, August 22, 2015

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.

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


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?


  1. Are you seriously suggesting that stock market P and D are functions of U? I would think that P is largely determined as a function of expectations. If the stock market believes that the economy is going to improve very soon, the price will be relatively high. D is a function of the present and future prices. For D to be high relative to P, the future expectations must improve relative to the current expectations. I don't think U decides P or D. U could be very high, but if the market expects U to drop very quickly, P will be high. If the market expects far worse U a year from now P will be low. D will be low if expectations were better a year ago than today and high if today's expectations are better than last year.

    I think Narayana, Paul, and Steve would all agree that R2 = R* does not imply that U = U*. I think they would also claim that this unusual stock market based measure of the interest rate is not a going to be very helpful in determining convergence to long term trends. Why would anyone think R2 = R* implies a macro steady state?

    1. Yes Ben, I am. Imagine two economies in parallel universes. I will call them economy A and economy B. Both economies are populated by identical copies of the same people. They have the same endowments of land labor and capital. And each economy has access to identical technologies for producing goods. In economic jargon: they have the same fundamentals.

      But although these economies have identical fundamentals, the people in economy A are naturally optimistic. They believe that shares in their stock market are worth PA. And PA is a large number. The people in economy B are pessimists. They believe that their stock market is worth PB. And PB is a small number. Importantly, PB < PA.

      In economy A, as a consequence of the optimism of population, households have a high demand for goods and services. To meet that demand, firms require a high labor force. The unemployment rate in economy A is 2%.

      In economy B, as a consequence of the pessimism of the population, households have a low demand for goods and service. To meet that demand, firms require a low labor force. The unemployment rate in economy B is 10%.

      In each economy, the households and firms believe, correctly, that the value of a share is equal to the discounted present value of a claim to the dividends that will be paid by the firm. And in each economy people discount the future at rate 1/R*, where R* is Wicksell’s ‘natural rate of interest’.

      Dividends, in each economy, are a fraction of GDP. Because employment is higher in economy A than economy B, GDP is also higher. And so are dividends. The valuations placed on the stock market in both economies are rational. PA is equal to the present value of the dividends paid in economy A, discounted at rate 1/R*. PB is equal to the present value of the dividends paid in economy B, also discounted at rate 1/R*. Optimism or pessimism is a self-fulfilling prophecy.

      How can this be? Surely the unemployment rate is determined by fundamentals. Not so. I explain in my published academic work, how there can be many unemployment rates, all of which are consistent with the conditions I described in this blog. In a labor market where people must search for jobs, there are not enough price signals, to lead market participants to the optimal unemployment rate.

  2. Clearly, economy A is at its PPF, while economy B has a lot of slack. Imagine a policy whereby the central bank in B holds interest rates below R* so businesses will be willing to borrow to finance capital expansion. Suppose also that helicopter drops of money are evenly distributed amongst consumers. Consumers will increase demand for current goods and services. To meet the demand, businesses will need to hire more employees. This is all possible without causing inflation, because of the slack in economy B. Firms will, however, have higher earnings, which translates into higher dividends and share prices. R2 will increase even as R1 falls. So as long as the central bank can lower interest rates and drop money on consumers shouldn't the central bank not worry about inflation until the economy approaches the PPF? In this sense, the central bank policy can target U* by deliberately holding R1 < R* until inflation starts to pick up. I don't think anyone is saying that when R1 = R* U = U*. They are advocating holding R1 < R* until U approaches close enough to U* to generate inflation.


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