Wednesday, September 23, 2015

Beliefs are Fundamental: Whatever your Religion

A couple of weeks ago, I had the pleasure of attending a very interesting conference at the Federal Reserve Bank of Saint Louis. The topic
of the conference was the relationship between income inequality and monetary policy, but the papers, more broadly, were all trying to cope with the intellectual problem of rebuilding monetary economics to incorporate the lessons of the Great Recession.

I discussed a fascinating paper, presented by Jim Bullard, joint with Costas Azariadis, Aarti Singh and Jacek Suda (ABSS). ABSS Built a 241 period overlapping generations model in which the people who inhabit the model are permitted to trade one period nominal bonds: but nothing else. They focused on one particular equilibrium of their model and they showed that, conditional on this equilibrium, a central bank can help the economy to function efficiently. Here is a link to the paper and here is a link to my discussion.

In this blog post I am going to give a synopsis of some general points that I made in my discussion, with a slight change of notation to make it blog friendly. 

Gather round and I will tell you a story. It is a story of how classical economists from the dark side bamboozled the Keynesian children of the light into accepting their dark version of the truth.

I don’t see how to discuss this issue without a little notation. So bear with me, and you will be rewarded. I promise.

For the past thirty years, most monetary models were built around a three equation New Keynesian monetary model.

Eqn 1. R – (PF-P) – (YF-Y) = Rstar + Dshock
Eqn 2. R = beta1*(PF-P) + beta2*(Y-Ybar) 
Eqn 3. H(PF-P,Y-Ybar) = Sshock
Here, P is this year’s price index, PF is next year’s price index (the F is for future) Y is GDP this year, YF is GDP next year and R is the money interest rate. Rstar is Wicksell's natural rate of interest and Ybar is potential GDP. 

Dshock and Sshock are random variables that represent demand and supply shocks. All variables are written as natural logarithms so PF-P is the inflation rate and YF-Y is the growth rate of real GDP. The star means multiplication and beta1 and beta 2 are numbers that describe policy.

Equation 1 (sometimes called the Fisher equation) is derived, in New Keynesian models, from the choices made by a representative person with superhuman powers of perception who chooses to optimally allocate resources between the present and the future. It says, in words, that the price of future goods, relative to current goods, is proportional to the ratio of consumption this year to next.

Equation 2 reflects central bank policy and it is sometimes called a Taylor Rule after John Taylor who showed that an equation like this does a pretty good job of describing how the Fed actually behaved in the period preceding the Great Recession.

Equation 3 specifies how the real and the monetary economy interact, and, in the New-Keynesian model, it takes the form,
Eqn 3A. P-PL = PF-P + k(Y-Ybar) + Sshock
where k is a number and PL is last year’s price index. This is called the New Keynesian Phillips curve and it plays the same role in New Keynesian economics that the Nicene creed plays in Christianity.

Almost all of the papers at the conference last week accepted equation 2 and most of them accepted some version of equation 3. 

The focus of pretty much every paper at the St. Louis Fed conference was on how to replace Equation 1. That is an interesting development, which reflects the fact that monetary economists have woken up to the fact that there is a problem with the representative agent assumption.

That is a start. And it is a good start. But, as I argued, in my discussion of ABSS, the problem with monetary economics is deeper than replacing the representative agent assumption: although that is certainly a big part of the problem. The problem is with the rational expectations assumption.

The New Keynesian monetary model is a child of the rational expectations revolution. In the dark days, before Robert Lucas wrote his game changing paper, Expectations and the Neutrality of Money, economists had a more nuanced approach to super-human powers of perception. Here is the monetary model we worked with back then.

Eqn 1B. R – (EPF-P) – (YF-Y) = Rstar + Dshock
Eqn 2B. R = F(EPF-P,Y-Ybar)
Eqn 3B. H(P-PL,Y-Ybar) = Sshock
This looks superficially like the New Keynesian model. But the differences are deep. First, I have replaced PF, the realization of the future price, with EPF, our current belief about what PF will be.  (I could have done the same with YF, but changing PF to EPF is sufficient to make my point.) Second, back in the dark days, we worked with a version of the Phillips curve that was purely backward looking. More on that point in a future blog.

Let me deal first, with expectations. By replacing PF with EPF I have added a new variable. The belief about what the future price will be is NOT the same as what it actually is. And because beliefs are not always correct, we need another equation. That equation, pre Lucas, was called adaptive expectations and it took the form

Eqn 4B.  EPF-P = F1(X)
where X is stuff we observe this year.

In words, expected inflation between this year and next year is some function of things we can observe this year. For example, Friedman used the following form for the function F1( )

Eqn 5B.  EPF-P = lambda*(P-PL) + (1-lambda)*(EPFL-PL)
which says that our belief of inflation is a weighted average, with weight lambda, of last period’s belief of this year's inflation rate and the inflation rate that actually happened. People don’t have superhuman powers of perception. They do, pretty much, what econometricians do.

So how were we bamboozled into accepting rational expectations? Bob Lucas argued that, just as econometricians add random shocks to their models, so should theorists. And if the theorists’ model has shocks: the people who inhabit the model should recognize that fact. According to Bob, EPF is not the same as PF because PF is a random variable.

If people inhabit a stationary environment, they will learn that every time they see X, P is equal to P(X). The rule that they use to forecast PF is irrelevant. In equilibrium, people will learn to forecast in a way that is unbiased. In equilibrium, PF will not equal EPF every time. But these two variables will be equal on average.

This was a brilliant and beautiful argument. But Bob slipped in an unwarranted assumption. He assumed that for given fundamentals, there is a unique rational expectations equilibrium. That assumption is false in every monetary general equilibrium model that anyone has ever written down. And it was false in the model that Bob used to make his point as Mike Woodford and I pointed out at the time and as I have tried to hammer home in pretty much everything I’ve ever written since then.

So how does this relate to the papers at the St Louis Fed conference? And how should it shape the way we move forward?

Let me be clear. Rational expectations is a great assumption. In the words of Abraham Lincoln: you can’t fool all of the people all of the time. But, even in a stationary environment where the world is not changing in unpredictable ways, RATIONAL EXPECTATIONS IS NOT ENOUGH TO DETERMINE BELIEFS. The forecast rule, equation 4B, is a separate independent equation that represents beliefs. 

The moral of my story is this: Beliefs are fundamental: whatever your religion.

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