The economics profession has faced harsh criticism since the financial crisis of 2007-09 – not least from its own members –for relying on mathematical models that failed to foresee the crisis and in some cases abetted its onset.
These models rested on assumptions that have little to do with reality. For example, here is a description of the Dynamic Stochastic General Equilibrium model, the dominant macro model, from a U.S. House of Representatives sub-committee report on economic models in July 2010:
The agents populating DSGE models, functioning as individuals or firms, are endowed with a kind of clairvoyance. Immortal, they see to the end of time and are aware of anything that might possibly ever occur, as well as the likelihood of its occurring; their decisions are always instantaneous yet never in error, and no decision depends on a previous decision or influences a subsequent decision. Also assumed in the core DSGE model is that all agents of the same type – that is, individuals or firms – have identical needs and identical tastes, which, as “optimizers,” they pursue with unbounded self-interest and full knowledge of what their wants are. By employing what is called the “representative agent” and assigning it these standardized features, the DSGE model excludes from the model economy almost all consequential diversity and uncertainty – characteristics that in many ways make the actual economy what it is.
In his testimony at the hearing, Nobel laureate and Massachusetts Institute of Technology professor emeritus Robert M. Solow said the DSGE model has “essentially nothing to say” about the problems surrounding the financial crisis, despite its dominance at elite universities, central banks and influential policy circles.
Is the criticism justified, and what can be done about it?
The tradition of mathematical modeling in academia
Given the criticisms above, it is no wonder that the mathematical models of economics didn’t foresee the crisis. But are they as bad as they seem?
Purely theoretical exercises are not uncommon in academia. The findings of pure mathematics are intended to contribute to abstract mathematics and not to applied mathematics, which is often housed in an entirely different department at a university. The current fashionable model of physics, string theory, occupies much of physicists’ efforts but is criticized for being both untested against actual physical phenomena and untestable.
Economics suffers from the same disconnect between theory and application. Economist David Colander says in his textbook Economics, “Modern macroeconomists see their models as only indirectly relevant for policy. For example, when Robert Lucas, a Nobel Prize-winning modern macroeconomist at the University of Chicago, was asked what he would do if he were appointed to the Council of Economic Advisers, he said that he would resign.”
The justification for abstract models with unrealistic assumptions is that they remove the observer from the trees in order to assess the forest. Observing the forest from a distance can cause the viewer to miss many of the facts on the ground, but it can sometimes bring about a new perspective. If the new perspective helps uncover new principles, those principles can be taken back into the forest to improve its study.
For example, the theory of efficient markets allows academics to study price movements at the level of the forest. But the trees in those forests – investors – often act in ways – such as herding behavior – that can only be explained through new paradigms, such as behavioral finance, or the framework that financial writer John Cassidy calls “rational irrationality.”
However, theoreticians often stay in make-believe land forever, never even caring to apply their theory to the real world. In pure mathematics, no one would ever make the mistake of thinking that theories should be applied to the real world, but in other fields, like economics and physics, it is assumed that they do apply to the real world. If abstract theories don’t and are not meant to apply to real-world scenarios, then theoreticians need to do a better job of letting people know that.
Meanwhile, the need for a theory with actual relevance and practical value for real-world economics goes a-begging.
What can be done about it?
In response to this appalling paucity of genuinely practical economic theory, a burgeoning field, or fields, of “heterodox macroeconomics” has sprouted since the financial crisis.
I interviewed one prominent researcher of a cluster of those heterodox economic ideas recently. Matheus Grasselli, deputy director of the Fields Institute for Research in Mathematical Sciences at the University of Toronto, is studying the application of nonlinear dynamical systems – also known as chaos theory – to economics. His work is funded by a grant from George Soros’s Institute for New Economic Thinking.
The mathematics Grasselli is using bears little resemblance to the classical mathematical models of economics and finance. Before we explore the difference, let’s review what is missing in the standard models.
The gaping hole in economic and financial theory
Models like DSGE hold their position at the center of economic modeling because economists have become intoxicated with their version of Adam Smith’s “invisible hand.” If the invisible hand operated perfectly, then everybody acting individually in their own self-interests would add up to an economy that always operated optimally, as if some all-seeing power had designed it to do that. The theory that the economy operates like a single agent with hyper-rational powers is possible only if you believe that the individual agents in an economy act as if they were one gigantic optimizing, all-seeing organism. This was, in fact, the assumption – or the result, it is hard to tell – of the theory of perfect markets.
The most glaring and canonical exception to this assumption is the fact that bank runs can occur even if a bank is perfectly solvent. A bank run could be caused by a rumor that the bank is insolvent, or a rumor that other depositors believe it is insolvent. Even if no individual depositor believes it is insolvent, every depositor could act on the rumor in the belief that others will. These actions are rational.
Why, otherwise, would it be so necessary for CEOs of financial companies to declare with the greatest of confidence (most notoriously just before they go bankrupt) that their firms are perfectly sound? Because if just one little chink in the armor shows, the demise of the institution is assured.
This does not sound like the way a small spherical ball comes to rest at the bottom of a bowl after rolling around for a while, which is the common conception of how diversified economic forces in a perfect market achieve equilibrium.
Instead, this sounds like the way a ball achieves equilibrium when perched at the apex of a pyramid and it is slightly perturbed – by falling straightway off the edge.
That kind of equilibrium, a sudden precipitous downfall – one which can be illustrated by innumerable practical real-life examples – has found almost no representation in mainstream economics, let alone in its mathematical models. For example, at the heart of the global financial crisis was an event in which many overnight lenders like money market funds suddenly decided they couldn’t trust the CDOs that collateralized their lending and precipitously withdrew their support.
A separate branch of economics has long understood that this can be a serious problem. Non-cooperating, independent market participants can interact in such a way as to create an optimal equilibrium, as if guided by an “invisible hand,” but they can also interact so as to create a “tragedy of the commons” for all of them.
For an example of a tragedy of the commons, suppose a hundred families’ homes have lakefronts on a small fish pond and each could take a fish a day without depleting the population. But if each family assumes that other families are non-cooperating and will compete to gain an advantage over others, then each family will rationally have an incentive to take more than its quota before others do. This would result in the extinction of the fish population – a tragedy of the commons.
Environmental and resource economists, in response, research ways that intervention and regulation could cause only the sustainable quantity of fish to be taken.
In finance and its relation to the macro economy, there has been little study of an analogous nature. Yet it is now glaringly obvious – as it should have been, at least to theoreticians, before the financial crisis – that similar phenomena can occur in that context as well.
Efforts to create a better theory
Grasselli, a mathematical physicist, understands that mathematical modeling, and over-mathematization in particular, has been blamed for the failures of economics. However, it is possible that the problem is that the wrong mathematical models have been studied, or that some models have been studied to the near-exclusion of other models, or that mathematical modeling is not understood in the proper light. Modeling should be seen as a means of gaining insight to practical solutions, not as a miraculous engine that produces practical solutions by itself.
Grasselli makes the distinction between local modeling, in which consumer and producer decisions occur “on the margin” in a local framework, and global modeling, in which global macroeconomic variables are considered.
Modern portfolio theory (MPT) is set in a local framework. It is not only “spatially” local but temporally local as well. With rare exceptions, all of its mathematical formulations apply to very short time periods.
In Grasselli’s modeling, local models take account of global macroeconomic variables, such as the aggregate level of debt, in ways that maintain “stock-flow consistency” – that is, aggregate balance-sheet and cash-flow entries must be consistent with each other over time. We know some of these necessary consistencies from aggregate econometric variables. For example, aggregate consumption must equal aggregate production. Some of the new macroeconomics disciplines argue that current mainstream economic models do not have stock-flow consistency.
For example, when global circumstances are taken into account, a local model of the stochastic process of securities pricing could be affected by the values of the global variables.
One of Grasselli’s models, for example, presents what has become the standard model of securities prices over time, “geometric Brownian motion”, but with a difference. In Grasselli’s model, downward price jumps can occur randomly but with higher likelihood when the economy’s level of highly-speculative debt financing, or “Ponzi finance,” is high. To make up for these downward jumps, the geometric Brownian motion must be further adjusted to have a “momentum effect”. That is, an upward trend will tend to continue until a random downward jump occurs.
Furthermore, Grasselli’s models produce one of two equilibria – a good one, like the ball at the bottom of the bowl, or a bad one, like the ball falling off the apex of the pyramid. Very small perturbations in the economy – the proverbial “butterfly effect” of Edward Lorenz – triggered by some small event can lead a model to one equilibrium or the other. This fork in the road, which can lead to an optimal “wisdom of crowds” equilibrium or to a bad equilibrium, is called a “bifurcation.”
Grasselli and I discussed whether a bifurcation and its consequence could be foreseen in advance. The models cannot make this prediction, because the timing and the path taken are so dependent on tiny unpredictable turns of events. But we agreed it might be possible to develop an indicator – ideally a single figure of merit or warning level – that measures the susceptibility of the economy or the financial system to a bifurcation. This indicator could show the likelihood that a bifurcation may be on the horizon. For more information about this field of research, an example is provided in this article.
Practical implications of the new modeling
These new modeling efforts have very important practical implications. They provide pointers for how to better regulate the macro economy and individual banks or institutions using monetary and fiscal instruments. A measure of a global or even bank-specific level of susceptibility to a bifurcation could be developed, and sensitivity to specific characteristics of the economy or the institution could be modeled.
This would surely be better than the current value-at-risk (VaR) model, which does not take into account the possibility of bifurcations or negative equilibriums.
A body of theory and the academic apparatus surrounding it is like a battleship – hard to turn around, even if it is going in the wrong direction. It will take a while to turn this battleship around, not to mention the entire regulatory and risk-management framework that has been built around it. But the heterodox economists are numerous, fruitful, vocal and highly innovative. Let us all hope they develop something soon to replace the defunct economic thinking that led to the catastrophe from which we continue to struggle to recover.
Michael Edesess is an accomplished mathematician and economist with experience in the investment, energy, environment and sustainable development fields. He is a senior research fellow with the Centre for Systems Informatics Engineering at City University of Hong Kong and a project consultant at the Fung Global Institute, as well as a partner and chief investment officer of Denver-based Fair Advisors. In 2007, he authored a book about the investment services industry titled The Big Investment Lie, published by Berrett-Koehler.
Read more articles by Michael Edesess
