Animal Spirits and the Two Natural Rates

In my last post I pointed out that it is not enough for monetary policy to guide the economy back to the natural rate of interest. Central banks and national treasuries must use financial policy to guide us back to the natural rate of unemployment.

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 the 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 example. 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.

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 coincidencecannot 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?

Somebody at the PBC blinked

In a recent post I made this comment about China’s decision to intervene in its own stock market.

China is holding more than $1.2 trillion dollars of U.S. government debt. If the Bank were to tap those funds to stabilize the Chinese stock market it could not simultaneously maintain an exchange rate peg. If China goes that route, look out for upheaval in the foreign exchange markets.

Chinese policy makers are now learning that lesson. The Peoples Bank of China (PBC) has allowed the Renminbi to tumble by more than 3% in the last few days. The ride may not yet be over.

What’s happening and why? It's my guess that there are investors on the margin who are pulling money out of the Chinese market and moving it into the world capital markets. Those investors are betting against the valuation that the PBC is putting on domestic assets. The outflow of funds  puts downward pressure on the RMB and if the PBC were to maintain its previous parity they would be obliged to sell their holdings of dollar denominated assets to support the currency.

The PBC blinked! But that's a good thing. They’ve chosen a domestic target over an exchange rate target and to make that work, the world needs to keep buying Chinese goods.

I have advocated a policy of Treasury and Central Bank intervention to stabilize domestic asset markets. What we are seeing in the Chinese case is that this policy is inconsistent with a fixed exchange rate.

Playing Chess with the Devil

I love this quote (with my amendments for economists)  from the NY Times article about Terrence Tao. 

The true work of the mathematician economist is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof piece of research. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical economic research is to be completely stuck.

It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.

That's pretty much how I feel about research. Another analogy is that research is like solving a Rubik's Cube: You're about to put the last piece in place and you find you have to go back 25 moves and start over.

Why the Belief Function Matters

A debate on the monetary transmission mechanism was recently reignited on the blogs with a post by Noah Smith, posts from Nick Rowe and Brad De-Long and a response to Noah from John Cochrane. This was all triggered by a set of slides prepared by Michael Woodford and Maria Garcia Schmidt for a Riksbank Conference in June 2015. A good starting point is the summary here back in 2014 by John Cochrane. 

The question: If the Fed raises the interest rate will it cause more or less inflation? The answer is complex and the topics that must be dealt with in formulating that answer are at the heart of monetary economics. 

In my own work, I emphasize two central points.

1. Monetary rational expectations models always have multiple equilibria.

2. The right way to deal with this is by explicitly modeling how people form beliefs using a concept that I call the belief function.

Flash back to 1968. Rational expectations was not part of our vocabulary but economists still needed to model the passage of time. The standard approach was the temporary equilibrium model that John Hicks developed in Value and Capital.

In the temporary equilibrium model, time proceeds in a sequence of weeks. Each week, people meet in a market. They bring goods to market to trade. They also bring money and bonds. The crucial point of temporary equilibrium theory is that the future price is different from our belief of the future price. To complete a model of this kind, we must add an equation to explain how beliefs are determined. I call this equation, the belief function.

Now jump forward to 1972. Robert Lucas wrote an influential paper that changed the way we think about monetary economics. Lucas was concerned that a variable called expectations was floating around in our models and that this variable had the potential to influence outcomes through its impact on the beliefs of people. That was messy and it was inconsistent with Lucas’ intuition that prices and quantities should be pinned down by fundamentals: preferences, endowments and technology. He suggested that we model the future price as a random variable with a probability distribution.

How do the people  deal with this possibility? They must form subjective beliefs about what will happen. Instead of forming a point belief about the future price, they form a complete subjective probability distribution. Now comes the coup de grace. Lucas argued that, if people live in a stationary world where the same events are repeated again and again, that rational people will come to learn the true distribution.

Lucas argued that, although we may not know the future exactly: we do know the exact probability distribution of future events.
Following the work of John Muth, he called this idea, rational expectations.

Rational expectations is a powerful idea. If expectations are rational, then we do not need to know how people form their beliefs. The belief function that was so important in temporary equilibrium theory can be relegated to the dustbin of history. We don’t care how people form beliefs because whatever mechanism they use, that mechanism must be right on average. Who can argue with that?

That is a clever argument. But it suffers from a fatal flaw. General equilibrium models of money do not have a unique equilibrium. They have many. This problem was first identified by the English economist Frank Hahn, and despite the best attempts of the rational expectations school to ignore the problem: it reappears with a alarming regularity. Rational expectations economists who deny an independent role for beliefs are playing a game of whack a mole.

More recently, the multiplicity problem arose in a paper by Jess Benhabib, Stephanie Schmitt-Grohé and Martín Uribe (BSU). In new-Keynesian models with rational expectations, the central bank sets the interest rate in response to inflation using a response function that is called a Taylor Rule.  If the Fed chooses a rule that is aggressive in response to inflation, the New-Keynesians thought that the equilibrium would be unique. BSU showed that they are wrong.

This is not an esoteric point. It is at the core of the question that I pose at the beginning of this post: If the Fed raises the interest rate will it cause more or less inflation?  And it is a point that policy makers are well aware of as this piece by Fed President Jim Bullard makes clear.

What is the solution? It is one thing to recognize that the world is random, and quite another to assume that we have perfect knowledge. If we place our agents in models where many different things can happen, we must model the process by which they form beliefs. I made this argument in my 1993 book, the Macroeconomics of Self-Fulfilling Prophecies   where I referred to the mechanism that selects an equilibrium in a rational expectations model as a belief function. It is time to embrace the idea that the belief function matters.