Wednesday, June 15, 2011

The Fear Index rises...

So far this month the so-called Fear Index -- the Chicago Board Options Exchange's volatility index, the VIX -- has risen by 24%. The VIX is a measure, roughly speaking, of how volatile market participants expect the markets to be over the next month, and these people, apparently, have growing uncertainty about a whole lot of things. What's going to happen with Greece and is the Eurozone itself safe? In the US, what happens now that the Federal Reserve has stopped its program of "quantitative easing" -- i.e. increasing the supply of money?

In the Financial Times, Gavyn Davies suggests the world's economic leaders are "out to sea" and simply unable to coordinate in their actions. The situation, he suggests, has been...
...triggered by the realisation that policy-makers around the world are no longer in any condition to rescue the global economy from a further slowdown, should that occur. Economies, and therefore markets, are currently flying without an automatic safety net from either fiscal or monetary policy.  And that brings new risks, compared to the situation which has been in place for most of the period since the 2009.
This is the world as reflected in the financial press -- one in which emotions and fears and hunches and uncertainty play a huge, indeed central role. Hardly surprising.

What is surprising and rather odd, is how far this is from the view of academic economists who assume (most of them, at least) that irrational fears and crazy expectations have little to do with market outcomes, which actually reflect in some way individuals' rational assessments of future prospects. This is the Rational Expectations view of economics, currently still considered, amazingly enough, as the gold standard in economic theorizing. It's been dominant for around 40 years, since first proposed by economists John Muth and Robert Lucas. Fortunately, it is finally giving way to a more realistic and less rigid view (more on this below) which takes note of something that is quite important to human beings -- our ability to learn and adapt.

I've long found it hard to understand how the Rational Expectations idea has come to be taken seriously at all by economists. It's primary assertion is that the predictions of individuals and firms about the economic future, while they may not be completely identical, are not on average incorrect. People make random but unbiased errors, the idea goes, and so the average expectation is rational -- it captures the true model of how the economy works. This is indeed patently absurd in the face of historical experience: the average view of the future in 2005, for example, was not that a global financial and economic crisis lay just around the corner. Perhaps a determined Rational Expectations enthusiast would disagree. What evidence is there after all about what peoples' expectations really were at the time?

The standard defense of the Rational Expectations framework follows the same three-tiered logic used in defense of the Efficient Markets Hypothesis (not surprisingly, given the close link between the two ideas). The first defense is to assert that people are indeed rational. Given evidence that they are not, the second defense is to admit that, OK, people make all kinds of errors, but to assert that they make them in different ways; hence, they are not irrational on average. Of course, the behavioral economics crowd has now thoroughly trashed this defense, showing that people are systematically irrational (over confident, etc) in similar ways, so their errors won't cancel out. Hence, the third line of defense -- arbitrage. Starting with Milton Friedman and continuing for decades, defenders of the rational core of economic theory have argued that competition in the marketplace will drive the irrational out of the market as the more rational participants take their money. The strong prey upon the weak and drive them out of existence.

For example, in 1986, Robert Lucas wrote the following, expressing his view that anything other than rational expectations would be weeded out of the market and ultimately play no role:  
Recent theoretical work is making it increasingly clear that the multiplicity of equilibria ... can arise in a wide variety of situations involving sequential trading, in competitive as well as finite-agent games. All but a few of these equilibria are, I believe, behaviorally uninteresting: They do not describe behavior that collections of adaptively behaving people would ever hit on.
Alas, this evolutionary or adaptive defense turns out not to work either. As Andrei Shliefer and others have shown, an arbitrager would need access to an infinite amount of capital to be able to drive the irrational (so-called "noise traders") from the market, essentially because market "inefficiencies" -- mispricings due to the stupid actions of noise traders -- may persist for very long times. The market, as the famous saying goes, can stay irrational longer than you can stay solvent.

None of this has stopped most economists from plodding right on along behind the Rational Expectations idea, and they may well continue this way for another 50 years, stifling macroeconomics, with the rest of us paying the price (well beyond our tax dollars that go to fund such research). But there is fresh air in this field, let in by researchers willing to throw open some windows and let high theory be influenced by empirical reality.

It is obvious that expectations matter in economics. What happens in the future in markets or in the larger economy often depend on what people think is likely to happen. The problem with RE (Rational Expectations) isn't with the E but with the R. A far more natural supposition would be that people form their expectations not through any purely rational faculty but through a process of learning and adjustment, adaptively, as we do most other things. Indeed, a number of people have been exploring this idea in a serious way, through both models and experiments with real people. The results are eye-opening and demonstrate how much has been lost in a 40 year trance-like distraction at the (supposed) mathematical beauty of the rational expectations theory.

Cars Hommes has written a beautiful review of the area that is well worth close study. As he notes, there have been about 1000 papers published in the past 20 years on "bounded rationality" -- the finite mental capacity of real people -- and learning. These include agent-based models of markets in which the agents all use different, imperfect strategies and learn as they go, and other studies looking more closely at the process by which people form their expectations. Here are a few highlights:

* Studies from about 10 years ago explored the actual strategies followed by traders in a hog and beef market, and found empirical evidence for heterogeneity of expectations. One study estimated that "about 47% of the beef producers behave naively (using only the last price in their forecast), 18% of the beef producers behaves rationally, whereas 35% behaves quasi-rationally (i.e. use a univariate autoregressive time series model to forecast prices)."

Think of that -- in an ordinary hog and beef market we have roughly half the market participants behaving on the basis of an extremely simple heuristic.

* More recently, a number of researchers have used agent models to characterize data from markets for stock, commodities, foreign exchange and oil. As the review notes, "Most of these studies find significant time-variation in the fractions of agents using a mean-reverting fundamental versus a trend-following strategy."

That is, not only do the participants have distinct expectations, but those expectations and the basic strategies they follow shift over time. Not surprising really, but clearly not consistent with the rational expectations view.

* The review also points to recent seminal work by a team of physicists led by Fabrizio Lillo. This study looked at investors in a Spanish stock market and found that they fell into different groups based on their strategies, including trend followers and contrarians who bought against trends.

* And who says simple surveys can't be instructive? Various studies over 15 years using this traditional technique have found that financial experts "use different forecasting strategies to predict exchange rates. They tend to use trend extrapolating rules at short horizons (up to 3 months) and mean-reverting fundamentalists rules at longer horizons (6 months to 1 year) and, moreover, the weight given to different forecasting techniques changes over time." Similarly, for peoples' views on inflation, a study found that "heterogeneity in inflation expectations is pervasive..."

So then, why does the use of rational and homogeneous expectations continue in economics and finance? The review doesn't answer these questions, but in view of the massive quantities of data pointing to a much richer and complex process by which people form their expectations, the persistence of the rational expectations view in mainstream macroeconomic models -- this is my understanding, at least -- seems fairly scandalous.

So what's going on with the VIX? No one really knows, and I'm absolutely sure that the answer cannot emerge from any general equilibrium model with rational expectations. Times of uncertainty lead, in general, to two effects -- 1) a growing diversity in views, given the lack of information that would push most people toward one, and 2) a growing urgency to find some clue about the future, some guide to future behaviour. Urgency in the face of uncertainty leads many people -- as this study in Science from a couple of years ago showed -- to see what they take to be meaningful patterns even in purely random noise. Hence, we need a theory of adaptive expectations, and it needs to include irrational expectations. The good news is that this idea is finally getting a lot of attention, and the old faith that evolutionary competition in some form would enforce the tidy picture of rational expectations can be consigned to the dustbin of history.

         *** UPDATE ***

I just want to clarify that what I've written in this post doesn't begin to do justice to the rich material in Cars Hommes review article. I mentioned some of the earlier empirical work he discusses, but much of the paper reviews then results of extensive laboratory experiments, by his group and other groups, exploring how people actually do form expectations in situations where the experimenter has close control on the process in question. For example, a price fluctuates from period to period and volunteers are asked to predict it over 50 periods. They are told very little, except some facts about where the prices come from -- from a speculative market such as a stock market, or instead from a very different market with perishable goods. Skeletal information of this kind can make them expect positive feed backs, hence the potential for self-reinforcing trends, or quite the opposite.

There's nothing in these experiments that explains why they weren't done 30, 40, 50 years ago. Why didn't someone in the 1970s start such a program to really test the Rational Expectations idea? (Did they and I'm just not aware of it?). It's a shame because these experiments yield a wealth of insight, as well as directions for future work. I'll just quote from Hommes conclusions (my comments in brackets):
Learning to forecast experiments are tailor-made to test the expectations hypothesis, with all other model assumptions computerized and under control of the experimenter. Different types of aggregate behavior have been observed in different market settings. To our best knowledge, no homogeneous expectations model [rational or irrational] fits the experimental data across different market settings. Quick convergence to the RE-benchmark only occurs in stable (i.e. stable under naive expectations) cobweb markets with negative expectations feedback, as in Muth's (1961) seminal rational expectations paper. In all other market settings persistent deviations from the RE fundamental benchmark seem to be the rule rather than the exception.


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