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. 

Fasten your seat belts; the ride is about to get choppy.

Chinese policy makers are concerned with the dramatic recent falls in the value of the Chinese Stock Market. They are right to be concerned. Although we can, and should, allow financial markets to allocate capital across sectors, the market as a whole is a creature of sentiment. And U.S. experience suggests that market crashes often precede deep recessions.

Today, the Peoples Bank of China was given the authority to purchase shares in the Chinese Stock Market. This is a bold experiment; but it is not unprecedented. In 1998, in the midst of the Asian Financial Crisis, the Hong Kong Monetary Authority engaged in a similar exercise. That intervention was large and successful and was the beginning of the end of the Asian crisis.

Chinese stocks are not dramatically overvalued and prospects for growth have recently picked up. I have advocated in the past for  the policy that the Peoples Bank is now engaged in. But the devil is in the details.

Stock market intervention could unfold in two ways. A purchase of shares by the central bank might be financed by money creation (Quantitative Easing). Or it might be accomplished by swapping short-term debt for risky securities (Qualitative Easing). Chinese interest rates, at 4.8%, are still in positive territory although inflation is currently at 1.2% and falling if official statistics are to believed. That leaves room for purchase of shares financed by money creation and it is an option that I would not rule out.

Buying stocks through money creation is not the only avenue. The Peoples Bank also has the option to purchases shares without increasing the monetary base through swaps of shares, either for foreign exchange or through domestic government borrowing.

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.

An alternative strategy would be to issue domestic debt and use it to purchase stocks. That would leave the Bank with liabilities, short-term debt, offset by assets, shares in the Chinese stock market.

It would be a mistake to bet against a Central Bank that is committed to dampening market volatility and a national treasury that is backed by the present value of future tax revenues. But an intervention of the magnitude that China is now contemplating cannot fail to spill over into world financial markets. Fasten your seat belts; the ride is about to get choppy.

Behavioural Economics is Rational After All

There are some deep and interesting issues involved in the debate over behavioural economics. Greg Hill posted a comment on my previous blog where he says:

Now, you really have to ask yourself whether the kind of rationality involved in [Thaler's idea of a nudge], where a minimal change in cost results in a significant change of behavior, is same kind of rationality Lucas and Sargent have in mind.

That led me to explain my views a little further.

The most interesting issue [with behavioural economics] is whether we should continue to accept the neoclassical assumption that preferences are fixed. Let's go with that assumption for a moment.

If preferences are fixed, then we face a second question. What form do they take? For a long time, macroeconomists assumed that people maximize the discounted present value of a time and state separable von Neumann Morgenstern expected utility function. The narrow version of behavioural economics asserts that this assumption is wrong; but people are still utility maximizers.

Finance economists seeking to reconcile macroeconomics with finance theory have already taken up that challenge (see the survey here on Exotic Preferences in Macroeconomics). The dominant view in finance theory is that people maximize the present discounted value of a subclass of preferences first formalized by Epstein and Zin. These preferences drop one of the key assumptions of Von-Neumann Morgenstern; that the date at which information is revealed is irrelevant. There are also more radical possibilities. The original version of the Epstein Zin utility function also allows for dropping a more fundamental assumption, called the independence axiom.

My point here, is that neoclassical economics can absorb the criticisms of the behaviourists without a major shift in its underlying assumptions. The 'anomalies' pointed out by psychologists are completely consistent with maximizing behaviour, as long as we do not impose any assumptions on the form of the utility function defined over goods that are dated and indexed by state of nature.

There is a deeper, more fundamental critique. If we assert that the form of the utility function is influenced by 'persuasion', then we lose the intellectual foundation for much of welfare economics. That is a much more interesting project that requires us to rethink what we mean by individualism.

Greg also asks

“can we understand all the failures of classical macroeconomics without giving up both rational choice and the premise that all markets clear?” If anyone can make a persuasive case for the “yes” answer, I believe you can."

My response. Yes we can and should maintain rational choice, rational expectations and market clearing: but that requires a radical change in the way we define equilibrium. As I have done here.

The Economics of George Orwell

Diane Coyle has a nice review of Richard Thaler's new book,  Misbehaving. Diane's review is, for the most part, appropriately laudatory. But she does voice a concern that I share. Here is Diane...

"Behavioural economics is now one of the most popular areas of the subject, ... but the new embrace by economists makes me uneasy. This is not just because of the well-known debate about paternalism (as discussed by Gilles St Paul in The Tyranny of Utility or Julian LeGrand and Bill New in Government Paternalism: Nanny State or helpful Friend?) It is because the sight of economists delighting in a new tool to engineer society is alarming –"

I agree. Here is a quote from my review of Akerlof and Shiller's 2009 book Animal Spirits, another piece that draws on behavioural economics to engage in social engineering. 

Akerlof and Shiller want to replace rational choice with behavioural economics. And here is what they mean by that...

“Behavioural economists assert that what makes individuals truly happy can be different from what they in fact choose to do. In Akerlof and Shiller’s words, ‘...capitalism...does not automatically produce what people really need; it produces what they think they need...’ (p. 26).”

To a classical liberal like me, this is a scary proposition since it gives a licence to someone else, someone who knows my true preferences, to act on my behalf. Is this the government or the church? Both institutions have claimed that right in the past, with disturbing outcomes. The idea that the government knows my preference better than I do is a little too  Orwellian for me. 

I went on to criticize Akerlof and Shiller for tearing down too much of classical theory and failing to replace it with a credible alternative. You can read my full review here. 

In my view, we can understand all of the failures of classical macroeconomics without giving up on rational choice. Heres what I said in 2009

I personally find it much more credible to believe that markets may sometimes misallocate resources and that this misallocation is directed by self-fulfilling crises of confidence. There is an existing agenda (part of neo- classical economics) that integrates psychology with economics by constructing economic models in which market fundamentals do not uniquely determine outcomes. In these models, it is the self-fulfilling beliefs of market participants that fill the gap. In my view, this idea of a self-fulfilling belief is a more appropriate candidate for what one should mean by animal spirits than the ... alternative meanings proposed by the authors. This narrower established definition is already widely used by a large existing body of researchers.

Here is a link to a survey paper that discusses this alternative approach.

Multiple Equilibria and Financial Crises

In May of this year, Jess Benhabib and I organized a conference at the Federal Reserve Bank of San Francisco with much help from Kevin Lansing at the Fed. Many thanks Kevin!

Kevin has just sent me a link to a website put together by the Fed with links to all of the papers, including slides of presenters and discussants plus a video of Karl Shell's dinner talk on the history of sunspots. The conference was sponsored by the NBER, UCLA and NYU. Many thanks to all who helped make this possible.