Remembering Black Monday

The largest single one day decline in percentage terms of the Dow-Jones average (22.6%) happened 30 years ago today, on October 19, 1987.  It was a Monday, hence "Black Monday."  Although unlike after the second largest such one day decline in percentage terms (12.8%) on October 28, 1929, the US economy did not go into a decline, much less anything remotely resembling the Great Depression.  Indeed, the very next day, after starting to decline further in the morning, the market turned around and starting rising, led by the futures and options markets in Chicago.  Although the market would decline far more between August, 2007 and March, 2009 at the front end of the Great Recession, there was no single day during all that when the market fell nearly as much as on either of these two days listed above.

Robert Shiller has written an interesting column in the New York Times about Black Monday (linked to by Mark Thoma on Economists View).  He did a survey after it happened of participants and found that they were driven basically by pure panic.  The Brady Commission report said that it was about the trade deficit and a possible tax change, and also program trading via portfiolio insurance.  Yes, Shiller says that latter was some of it, but in fact he determined that fear of it was probably more important than the actual program trading.  There was very little going on with fundamentals, but vague rumors and reports set off a huge crash, the biggest one day one ever, even if in the end it did not really amount to much.  But Shiller says it can happen again (and, if he were alive, the late Hyman P. Minsky would probably agree).

Let me add a few observations of my own, based on things I was working on back then and have since, if with less attention than Shiller.  In particular I was worrying about how one could model such financial market crashes by considering financial markets as complex nonlinear dynamical systems.  The big candidates for helping to understand such phenomena coming out of that field were catastrophe theory and chaos theory.  As it happened, October 1987 was around the time that chaos theory was at its height as the intellectual fad du jour.  Indeed, it sort of looked like maybe chaos theory might be useful.  It is famous for the "butterfly effect," where supposedly a butterfly flapping its wings in a rain forest in Brazil can cause a hurricane in Texas. So, this apparent lack of anything really major happening in the economy or the markets prior to Black Monday brought forth a lot of commentary along the lines of "Wow, this looks like the butterfly effect and chaos theory!"

Well, the heyday of chaos theory has passed.  For better or worse, the econometrics of identifying whether or not a time series is actually chaotic or not is pretty hairy.  There are no significance tests.  Lots of time series, including plenty of financial ones, that exhibit the basic characteristics of having a butterfly effect (sensitive dependence on initial conditions, a positive Lyapunov exponent, to be more technically precise).  But estimated models based on these do not do well forecasting, not much better than random walks.  Actually, the nature of such butterfly effects is that if they exist, one should not expect to be able to make good forecasts. In any case, even though many such time series look like they might chaotic, we have all lost interest.  But, as it is, quite aside from all that, I do not think chaos theory is(was) really the best explainer of what happened on Black Monday.

Rather, of the family of complex dynamics, I think the relevant one was and is catastrophe theory, which was very much out of fashion at that time.  Let me note that as a sub-part of bifurcation theory, catastrophe theory is back in various parts of economics and ecology and other related disciplines. Pretty much any nonlinear system that shows multiple equilibria will be subject to bifurcations and dynamic discontinuities as they move from one basin of attraction to another.  While the economy did not collapse after Black Monday, and the stock market did not continue to decline, it remained well below where it had been prior to Black Monday for quite a long time.

I note that the very first paper in economics that used catastrophe theory was the second paper ever published in the Journal of Mathematical Economics back in 1974.  Without getting into the technical details, I note that it drew on a much older setup long discussed in the financial markets literature, one where two sets of agents were identified.  One was fundamentalists whose behavior is stabilizing and tends to push the market back toward its fundamental (assuming there really is such a thing), while the other set are the chartists or trend chasers, whose pursuit of bubbles as they rise and their dumping of assets when they fall tend to destabilize the market.  The paper, "The Unstable Behavior of the Stock Exchanges," was written by E. Christopher Zeeman, a major figure in the mathematics of catastrophe theory.  His story was one of a shifting balance of dominance in the market between these two sets of agents, with stability and instability oscillating back and forth within a cusp catastrophe setup, which included the possibility of a market crash.

I note that this basic sort of setup had been modeled in the 1950s by people like William Baumol in long forgotten papers without any fancy nonlinear dynamics.  More recently complexity economists have developed models that follow this Baumol-Zeeman approach, such as the Santa Fe stock market model using agent based modeling in the 1990s, by people like Blake LeBaron and William (Buz) Brock, along with others.  Models with multiple agents who shift their strategies according to recent performance and move back and forth between stabilizing behavior and destabilizing behavior are all over the place and continue to be studied, if not necessarily getting published in the top journals. But these models look pretty good as ways of analyzing these sorts of dynamics.

Addendum:  One other outcome of Black Monday also was that it was the beginning of the end for the dominance in economic theory of the rational expectations axiom.  Yes, it is still around and strong in the whole DSGE modeling world.  But increasingly people take more behavioral assumptions seriously, and Black Monday was a body blow to ratex big time.

Barkley Rosser