Economists love their models; can too much loving be dangerous?
Recent financial crises have prompted many to rethink the nature of mathematical modeling of financial markets. There is a widely popular joke that whenever you see a group of economists, there is an “orgy of mathematics,” and that economics is the only science in which people are awarded the Nobel Prize for saying completely contradictory things. If you work in this field or have taken courses in economics or its subspecialty, financial economics (commonly known as finance), you probably know what I mean. Let’s briefly understand the rationale for financial and economic models through a personal example and then examine some of their effects on the real world.
Although it has been 20 years since I started learning economics, I still vividly remember my first day in an introductory course where we learned about the scientific method and how to apply it to real-world economic phenomena.
The goal of the lecture was to illustrate supply and demand, the cornerstone of economic theory. A mathematical model was quickly introduced to help predict how sellers and buyers would respond to changes in the price of a good.
At the end of the lecture, we were expected to be able to “forecast” the impact of a price increase of a competing product on the quantity demanded of another good.
In one of the homework assignments, I was eager to apply this model to other economic situations, only to find out that our model’s predictions were inaccurate if any of the assumptions (some are extremely unrealistic) from the model was violated.
A few years later in my Ph.D. program, our models got much more interestingly seductive and complex. We once spent an entire month deriving the formula to price European-style stock options (proving the Black-Scholes formula), employing some of the most advanced methods in stochastic calculus, real analysis, topology, partial differential equations and other esoteric math.
To give you an idea of the level of mathematical rigor, I recall asking several of my classmates, whom I will call Bob (a then recent graduate with a master’s degree in applied math at perhaps the world’s leading engineering university), Joe (a young fellow with an advanced degree in physics from an elite university in the East), Harry (a graduate degree holder in economics from a top 10 U.S. university) and Johnny (who scored perfectly on the math and analytical sections of the Graduate
Record Examination). Not too surprisingly, this rather bright group of graduate students could only follow our professors (many of whom had studied under theorists who won the Nobel Prize in the field), especially the hundreds of assigned journal articles, at most 70% of the time, based on my estimate. In fact, researchers in one subspecialty (financial markets and institutions, for instance) often have a difficult time comprehending the models in another subfield within the same discipline, such as investments, and vice versa.
The Black-Scholes model has been one of the primary tools in the investment community globally for about three decades and is responsible for, according to some commentators, the collapse of longterm capital management, the stock market crash of 1987 and recent global financial crisis (a topic I discussed extensively in the last three articles in the Gazette). One of the reasons the model fails is its reliance on some rather unrealistic assumptions about financial markets, to make the math more tractable. It is often necessary to assume, for example, a normal (Gaussian) distribution in many financial models to obtain closed-form solutions, a practice that can lead to detrimental consequences in the real world. Rationality of economic agents (consumers, investors, speculators…), one of the core assumptions in financial theory, has been shown to be questionable in some realworld scenarios. Despite the shortcomings, those assumptions (among others) have been the backbone of financial theory for decades. And, if my hunch is right, financial models of the future will be even more sophisticated, including additional assumptions and novel techniques absent in prior theoretical and empirical models.
Financial economists have a “physics envy.” Unlike physics, which is an extremely precise science, financial economics is not, no matter how much fancy math is involved. In physics, laws can be derived from physical experiments whose results are predictable and repeatable. The same cannot be said of financial markets. The value of a financial asset such as a stock, for instance, is dependent on many factors, including investors’ perceptions (which are highly unpredictable) of the firm issuing the stock. Further, past financial values are hardly good predictors of future ones. Finance practitioners, therefore, have to make do with the available tools—their beloved models, which are necessarily an abstraction of (highly complex) reality. And to make the models behave well, certain assumptions must be made. Therein lies the rub.
Financial economics is a difficult but worthwhile subject to explore, not to mention the relatively well-paid jobs available to finance graduates, especially those with an advanced degree in the field. It is one of the most popular majors at top universities. Despite its limitations, it can be argued that our knowledge of the financial markets has vastly improved over the last few decades and made life measurably better. If you ever doubt this, just imagine for a few seconds what the world would be like without finance!