Tuesday, January 13, 2015

Financial crises as global sunspots

I have just written a new working paper, 'Global Sunspots and Asset Prices in a Monetary Model', that is available on the NBER website here. The paper is a continuation of research on financial markets that I began in 2002, (2002a, 2002b) and it provides intellectual ammunition to support a proposition that I put before the UK parliament in April of 2012. We must develop a new institution that is designed to counter financial market volatility. 

My paper explains three asset pricing puzzles that are difficult to reconcile with the now standard representative agent approach to macroeconomics. First, asset prices are volatile and persistent and price dividend ratios are predictable. Second, long lived risky assets earn 5% more on average than short term government debt. And third, the volatility of asset prices changes through time. I argue that all of these puzzles are caused by the simple fact that we cannot buy insurance over the state of the world we are born into.

Why do market economies go through bouts of expansion and contraction? In the early 1980s, researchers at the University of Pennsylvania came up with a novel explanation. Even when all prices are perfectly flexible and there are no impediments to trade of any kind, financial markets still do a very poor job of allocating resources across different periods in time.  How can that be?

Dave Cass and Karl Shell, in their pathbreaking paper, "Do Sunspots Matter?",  showed that the problem with financial markets is simple but fundamental. We cannot trade in asset markets that take place before we are born.  That simple fact is sufficient to invalidate the central proposition of welfare economics: that free trade in competitive markets leads to outcomes that cannot be improved upon by government intervention.

The University of Pennsylvania, in the early 1980s, was an exciting place to be. The Cass-Shell paper relied on the idea that general equilibrium models typically have multiple equilibria.  Costas Azariadis, exploiting the same idea, wrote a seminal paper, "Self-fulfilling Prophecies", in which he showed that sunspot equilibria are endemic to overlapping generations models and I wrote a joint paper with Michael Woodford which combined this idea with monetary models (where there is always a vast multiplicity of equilibria) to show how sunspots drive business cycles.  My paper with Mike was very close to the model that had been developed by Robert Lucas to introduce the idea of rational expectations.  But in contrast to Lucas' paper, where equilibrium was unique, we showed that there could be an infinite dimensional continuum of equilibria. 

The fact that general equilibrium models have multiple equilibria was an anathema to Lucas,  because it threatened the nascent rational expectations agenda that had begun to take hold. Lucas saw rational expectations as a way of 'solving' the 'problem' of expectations which had an uncomfortable way of asserting themselves as independent variables in contemporary models of the Phillips curve. In contrast, I viewed multiple equilibria as a way of understanding features of equilibrium models that are otherwise inconsistent with the data. 

Lucas strongly disagreed with my approach to multiplicity, a point that he made clear to me in a personal letter, shortly after I published a paper that was a direct challenge to Lucas's eponymous critique of econometric policy analysis. Lucas never embraced the idea (explained here) that multiple equilibria can help us to explain real world phenomena and instead, he supported the embryonic real business cycle agenda that was based on the assumption that business cycles are the optimal responses of rational agents to unavoidable productivity shocks. 

Why weren't sunspot models more widely adopted by the profession? One reason was intense resistance from Lucas and Prescott who viewed models with multiple equilibria as a threat to the idea that expectations are determined by fundamentals. But there was also a strategic issue. What is the most effective way to persuade other economists that your ideas are important? 

The real business cycle agenda was associated with the Minnesota school, a group of like minded academics who made it their mission to spread the gospel.  It began in the early 1980s and, for a period of twenty years or more, no economics department was considered complete until it had recruited a newly minted disciple of the faith.

In contrast, the proponents of the sunspot agenda were disorganized and inwardly focused. Cass and Shell were theorists who did not initially recognize the importance of developing empirically relevant applications of their approach.  As a consequence, sunspots were viewed by the profession as a theoretical curiosity that did not help us to understand the real world. That is a situation that only now is beginning to be corrected

The obsession of macroeconomists with dynamic equilibrium models with a unique equilibrium was a huge mis-step in the history of ideas. But it is not too late to put things right. There is now an active group of researchers who are exploring ways to bring back confidence and self-fulfilling prophecies to the forefront of the policy debate. Sunspots are back and, this time around, sunspots are here to stay.


  1. Some softballs for you. If you had to explain what a sunspot was to a well-educated layman, what would you say? Can you explain what a sunspot equilibria might look like by giving a concrete example? Why was the term 'sunspot' chosen?

    1. Stanley Jevons, writing in 1878, developed a theory in which sunspots influence business cycles. At that time, agriculture was still a substantial part of GDP and the sunspot cycle is known to influence the weather.

      Writing more than a century later, Cass and Shell used the term 'sunspots' as a spoof. By then, agriculture had declined to less than 1% of GDP and Jevon's ideas had been discredited. They meant, instead, any random event that people believe to be connected to the economy, even though it has no fundamental impact. Cass and Shell use the term sunspot to mean a sel-fulfilling prophesy.

      An example would be the influence of a financial journalist who makes pronouncements that investors believe. Because of public confidence in his abilities, an optimistic article about the stock market may cause stock market prices to rise even though was no fundamental reason for this to happen.

  2. First time commenter here. Can I try to ask somewhat technical question?

    I've been reading your new paper and don't quite understand where the indeterminacy comes from. You reduce your model to a difference equation in two variables (sections 5.2 - 5.3), so ordinarily we'd need two initial conditions. If one condition is the linear constraint derived from initial portfolios (eqn. 23), and the other the stable manifold, it seems that we can determine a unique perfect foresight trajectory, and thus there would be no room for sunspots. What am I missing?

    1. It's because government is denominated in dollars and there is nothing to pin down the price level. Indeterminacy of the price level is a property of any general equilibrium model in which the central bank sets the interest rate. Different values of the price level revalue the real value of government debt and shift the burden of tax liabilities between present and future generations.

    2. Eqn 23 is not a constraint because the real value of debt, denoted by b, is a free variable.

    3. Thanks for replying. OK, so both m0 and b0 are not "physically" predetermined. But if eqn. 23 defines a 1-dimensional curve of possible initial points in (m0, b0) space, as the text seems to suggest, and stable manifold defines another one, we'd expect them to intersect at a single point, no?

    4. Yes they intersect at a point. But any initial point on the stable manifold is consistent with equilibrium. There is no unique initial condition.


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