Thursday, March 12, 2009

The Failure of Economic Models


The Financial Crisis and the Systemic Failure of Academic Economics is an interesting exercise in self-flagellation by a far-flung group of academic economists. In this paper, the authors lament the poor state of mathematical modeling in the fields of economics and finance. While they don’t seem to consider or acknowledge that such models may never be adequate for many of their purported tasks, they nevertheless make a number of good critiques of the modeling world in economics. This is an academic paper so it’s filled with jargon and references to models that no one but other academics have heard of. But there are plenty of good points worth highlighting.

In fact, if one browses through the academic macroeconomics and finance literature, “systemic crisis” appears like an otherworldly event that is absent from economic models. Most models, by design, offer no immediate handle on how to think about or deal with this recurring phenomenon. In our hour of greatest need, societies around the world are left to grope in the dark without a theory. That, to us, is a systemic failure of the economics profession.

[…]

Much of the motivation for economics as an academic discipline stems from the desire to explain phenomena like unemployment, boom and bust cycles, and financial crises, but the dominant theoretical model excludes many of the aspects of the economy that will likely lead to a crisis. Confining theoretical models to ‘normal’ times without consideration of such defects might seem contradictory to the focus that the average taxpayer would expect of the scientists on his payroll.

It’s very difficult to model black swan events so the models usually leave out such events and assume that life is always ‘normal’ (in both the casual and statistical uses of the term). And yet, such events aren’t all that rare so there are numerous ways in which the models can and do break down.

Many of the financial economists who developed the theoretical models upon which the modern financial structure is built were well aware of the strong and highly unrealistic restrictions imposed on their models to assure stability. Yet, financial economists gave little warning to the public about the fragility of their models; even as they saw individuals and businesses build a financial system based on their work. There are a number of possible explanations for this failure to warn the public. One is a “lack of understanding” explanation--the researchers did not know the models were fragile. We find this explanation highly unlikely; financial engineers are extremely bright, and it is almost inconceivable that such bright individuals did not understand the limitations of the models. A second, more likely explanation, is that they did not consider it their job to warn the public. If that is the cause of their failure, we believe that it involves a misunderstanding of the role of the economist, and involves an ethical breakdown. In our view, economists, as with all scientists, have an ethical responsibility to communicate the limitations of their models and the potential misuses of their research. Currently, there is no ethical code for professional economic scientists. There should be one.

Here is a point that applies throughout economics. It is often thought that the field itself is and ought to be amoral. Like Dr. Mengele, human social interaction is reduced to an object of study and experimentation. Moral requirements and proscriptions are rarely seen as relevant.

For structured products for credit risk, the basic paradigm of derivative pricing – perfect replication – is not applicable so that one has to rely on a kind of rough-and-ready evaluation of these contracts on the base of historical data. Unfortunately, historical data were hardly available in most cases which meant that one had to rely on simulations with relatively arbitrary assumptions on correlations between risks and default probabilities. This makes the theoretical foundations of all these products highly questionable – the equivalent to building a building of cement of which you weren’t sure of the components. The dramatic recent rise of the markets for structured products (most prominently collateralized debt obligations and credit default swaps - CDOs and CDSs) was made possible by development of such simulation-based pricing tools and the adoption of an industry-standard for these under the lead of rating agencies. Barry Eichengreen (2008) rightly points out that the “development of mathematical methods designed to quantify and hedge risk encouraged commercial banks, investment banks and hedge funds to use more leverage” as if the very use of the mathematical methods diminished the underlying risk. He also notes that the models were estimated on data from periods of low volatility and thus could not deal with the arrival of major changes. Worse, it is our contention that such major changes are endemic to the economy and cannot be simply ignored.

This is consistent with the formula that was used to rate the risk of MBS tranches. The data behind the model were very thin, of dubious relevance, and came from a few years when houses were shooting up in value. Thus, the use of the model to justify pouring billions of dollars into illiquid securities was bound to end badly.

There are some additional aspects as well: asset-pricing and risk management tools are developed from an individualistic perspective, taking as given (ceteris paribus) the behavior of all other market participants. However, popular models might be used by a large number or even the majority of market participants. Similarly, a market participant (e.g., the notorious Long-Term Capital Management) might become so dominant in certain markets that the ceteris paribus assumption becomes unrealistic. The simultaneous pursuit of identical micro strategies leads to synchronous behavior and mechanic contagion. This simultaneous application might generate an unexpected macro outcome that actually jeopardizes the success of the underlying micro strategies. A perfect illustration is the U.S. stock market crash of October 1987. Triggered by a small decrease of prices, automated hedging strategies produced an avalanche of sell orders that out of the blue led to a fall in U.S. stock indices of about 20 percent within one day. With the massive sales to rebalance their portfolios (along the lines of Black and Scholes), the relevant actors could not realize their attempted incremental adjustments, but rather suffered major losses from the ensuing large macro effect.

Not only did Long-Term get so big that its models’ relevance bent under the hedge fund’s weight, it also suffered from “synchronous behavior” that neither the models nor Long-Term’s partners accounted for. Most of the big banks and numerous hedge funds were making many of the same trades as Long-Term (e.g., bond arbitrage, interest rate swaps, Russian bonds, equity vol.). The partners thought that there would be others who would pick up those trades if and when they had to bail but in fact, the opposite occurred. When the other big rats started to jump from the sinking ship, the weight transfer only made the ship sink faster. The partners could only watch helplessly as their illiquid assets plunged in value and the hedge fund quickly burned through its puny capital.

This leads to a related and well known example of synchronous behavior that the models don’t account for: the near truism that in a financial crisis, “all correlations go to one.” In such a situation, portfolio diversification is nearly impossible because even completely unrelated assets fall in lock step with each other. This is because they aren’t completely unrelated. Even though the assets themselves may be unrelated, they are owned by the same parties – hedge funds for example. And when such parties are forced to sell (due to margin calls for example), they can’t be too picky about what they sell. In such cases (which are quite common in crises), unrelated assets get nuked in parallel as the various parties try to raise capital by selling whatever will move. All correlations go to one and the models’ accuracies go to pot.

A somewhat different aspect is the danger of a control illusion: The mathematical rigor and numerical precision of risk management and asset pricing tools has a tendency to conceal the weaknesses of models and assumptions to those who have not developed them and do not know the potential weakness of the assumptions and it is indeed this that Eichengreen emphasizes. Naturally, models are only approximations to the real world dynamics and partially built upon quite heroic assumptions (most notoriously: Normality of asset price changes which can be rejected at a confidence level of 99. 9999…. Anyone who has attended a course in first-year statistics can do this within minutes). Of course, considerable progress has been made by moving to more refined models with, e.g., ‘fat-tailed’ Levy processes as their driving factors. However, while such models better capture the intrinsic volatility of markets, their improved performance, taken at face value, might again contribute to enhancing the control illusion of the naïve user.

The assumption that asset prices are normally distributed was also a major problem with Long-Term’s models even though the error of this assumption was known at the time. Life is full of “fat tails.” In other words, the supposed “once-in-a-thousand-years perfect storm” seems to show up, in one form or another, about every decade or so.

Many economic models are built upon the twin assumptions of ‘rational expectations’ and a representative agent. ‘Rational expectations’ forces individuals’ expectations into harmony with the structure of the economist’s own model. This concept can be thought of as merely a way to close a model. A behavioral interpretation of rational expectations would imply that individuals and the economist have a complete understanding of the economic mechanisms governing the world…. Leaving no place for imperfect knowledge and adaptive adjustments, rational expectations models are typically found to have dynamics that are not smooth enough to fit economic data well.

Technically, rational expectations models are often framed as dynamic programming problems in macroeconomics. But, dynamic programming models have serious limitations. Specifically, to make them analytically tractable, researchers assume representative agents and rational expectations, which assume away any heterogeneity among economic actors. Such models presume that there is a single model of the economy, which is odd given that even economists are divided in their views about the correct model of the economy….

The major problem is that despite its many refinements, this is not at all an approach based on, and confirmed by, empirical research.5 In fact, it stands in stark contrast to a broad set of regularities in human behavior discovered both in psychology and what is called behavioral and experimental economics. The corner stones of many models in finance and macroeconomics are rather maintained despite all the contradictory evidence discovered in empirical research. Much of this literature shows that human subjects act in a way that bears no resemblance to the rational expectations paradigm and also have problems discovering ‘rational expectations equilibria’ in repeated experimental settings. Rather, agents display various forms of ‘bounded rationality’ using heuristic decision rules and displaying inertia in their reaction to new information. They have also been shown in financial markets to be strongly influenced by emotional and hormonal reactions (see Lo et al., 2005, and Coates and Herbert, 2008) Economic modeling has to take such findings seriously.

Mathematical models of human action which contain dehumanizing assumptions that fly in the face of real world experience? Who’d of thunk it. But the illusion of control has a nasty bite to it.

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