Saturday, May 06, 2006

Science, Axioms, and Economics

UPDATE 05/20/06: Read this related post by Don Luskin (Chronicle of the Conspiracy).

Science is a four-fold process:

1. gathering and analyzing data about observable phenomena

2. theorizing causal relationships from those observations and analyses

3. testing those theories to see if they are accurate predictors of previously unobserved phenomena

4. adjusting old theories, as necessary, and developing new ones in the light of new observations.

Every scientific theory rests eventually on axioms: self-evident principles that are accepted as true without proof. Such principles may be self-evident to scientists who specialize in a particular discipline, even though they may not be self-evident to a non-specialist or non-scientist. The relativity principle of Galileo is an example of an axiom that is not self-evident to most non-scientists. The relativity principle

essentially states that, regardless of an observer's position or velocity in the universe, all physical laws will appear constant. From this principle, it follows that an observer cannot determine either his absolute velocity or direction of travel in space.

Galileo's 400-year-old principle is a fundamental axiom of modern physics, most notably of Einstein's special and general theories of relativity.

One aim of science is to push the boundaries of knowledge outward, away from old axioms and toward a deeper understanding of the causes of observable phenomena and the relationships among those phenomena. But no matter how far scientists push the boundaries of knowledge, they must at some point rely on untestable axioms, such as Galileo's relativity principle.

Self-evident principles notwithstanding, it is possible to discover important and useful quantitative information about physical phenomena. Consider the speed of light, for example. Maxwell's equations, combined with Galileo's relativity principle, tell us that the speed of light is the same for all observers, regardless of their respective velocities. But Einstein's special theory of relativity, which is where Maxwell's equations and the relativity principle are combined, does not define the speed of light, which was determined experimentally, just as Einstein's theory has been confirmed experimentally.

That brings me to economics, which -- in my view -- rests on these self-evident axioms:

• Each person strives to maximize his or her sense of satisfaction, which may also be called well-being or happiness.
• Happiness can and often does include an empathic concern for the well-being of others; that is, one's happiness may be served by what is usually labelled altruism or self-sacrifice.
• Happiness can be and often is served by the attainment of non-material ends. Not all persons (perhaps not even most of them) are interested in the maximization of material goods (or monetary claims on material goods). That is, not everyone is a wealth maximizer.
• The feeling of satisfaction an individual derives from a particular good (a product, service, or activity) is situational -- unique to the individual and to the time and place in which the individual undertakes to acquire or enjoy a good. Generally, however, there is a (situationally unique) point at which the acquisition or enjoyment of additional units of a good during a given period of time tends to offer less satisfaction than would the acquisition or enjoyment of units of other goods that could be obtained at the same cost.
• Work may be a good or it may simply be a means of acquiring and enjoying goods. Even when work is a good it is subject to the "law" of diminishing marginal satisfaction (preceding bullet).
• There is no limit on the feeling of satisfaction that an individual may derive from the acquisition and enjoyment of goods, as long as there is always a greater variety of goods than an individual can enjoy at a given time.
• Individual degrees of satisfaction are ephemeral, nonquantifiable, and incommensurable. There is no such thing as a social welfare function that a third party (e.g., government) can maximize by taking from A to give to B. Whenever a third party intervenes in the affairs of others, that third party is merely imposing its preferences on those others.

It may be possible to test some physical axioms, such as the constancy of the speed of light, but it is not possible to test the axioms of economics. For the purpose of "doing" economics, one must accept (or reject) the idea of personal utility maximization (for example), but one cannot disprove it. Nor can one devise (to my satisfaction) a measure of interpersonal utility that would enable a government to maximize a (non-existent) social welfare function.

My position aligns me (mainly) with the Austrians. The "dean" of that "school" was Ludwig von Mises, about whom Gene Callahan writes at the website of the Ludwig von Mises Institute:

As I understand [Mises], by categorizing the fundamental principles of economics as a priori truths and not contingent facts open to empirical discovery or refutation, Mises was not claiming that economic law is revealed to us by divine action, like the ten commandments were to Moses. Nor was he proposing that economic principles are hard-wired into our brains by evolution, nor even that we could articulate or comprehend them prior to gaining familiarity with economic behavior through participating in and observing it in our own lives. In fact, it is quite possible for someone to have had a good deal of real experience with economic activity and yet never to have wondered about what basic principles, if any, it exhibits.

Nevertheless, Mises was justified in describing those principles as a priori, because they are logically prior to any empirical study of economic phenomena. Without them it is impossible even to recognize that there is a distinct class of events amenable to economic explanation. It is only by pre-supposing that concepts like intention, purpose, means, ends, satisfaction, and dissatisfaction are characteristic of a certain kind of happening in the world that we can conceive of a subject matter for economics to investigate. Those concepts are the logical prerequisites for distinguishing a domain of economic events from all of the non-economic aspects of our experience, such as the weather, the course of a planet across the night sky, the growth of plants, the breaking of waves on the shore, animal digestion, volcanoes, earthquakes, and so on.

Unless we first postulate that people deliberately undertake previously planned activities with the goal of making their situations, as they subjectively see them, better than they otherwise would be, there would be no grounds for differentiating the exchange that takes place in human society from the exchange of molecules that occurs between two liquids separated by a permeable membrane. And the features which characterize the members of the class of phenomena singled out as the subject matter of a special science must have an axiomatic status for practitioners of that science, for if they reject them then they also reject the rationale for that science's existence.

Economics is not unique in requiring the adoption of certain assumptions as a pre-condition for using the mode of understanding it offers. Every science is founded on propositions that form the basis rather than the outcome of its investigations. For example, physics takes for granted the reality of the physical world it examines. Any piece of physical evidence it might offer has weight only if it is already assumed that the physical world is real. Nor can physicists demonstrate their assumption that the members of a sequence of similar physical measurements will bear some meaningful and consistent relationship to each other. Any test of a particular type of measurement must pre-suppose the validity of some other way of measuring against which the form under examination is to be judged.

Why do we accept that when we place a yardstick alongside one object, finding that the object stretches across half the length of the yardstick, and then place it alongside another object, which only stretches to a quarter its length, that this means the first object is longer than the second? Certainly not by empirical testing, for any such tests would be meaningless unless we already grant the principle in question. In mathematics we don't come to know that 2 + 2 always equals 4 by repeatedly grouping two items with two others and counting the resulting collection. That would only show that our answer was correct in the instances we examined — given the assumption that counting works! — but we believe it is universally true. Biology pre-supposes that there is a significant difference between living things and inert matter, and if it denied that difference it would also be denying its own validity as a special science.

What is notable about economics in this regard is just how much knowledge can be gained by hunting down the implications of its postulates. Carl Menger arrived at the great insight that the value of a good to an actor depends on its marginal utility to him based entirely on pursuing the consequences of the assumption that people act with the purpose of improving their circumstances. Mises's magnum opus, Human Action, is a magnificent display of the results that can be achieved along these lines.

The great fecundity from such analysis in economics is due to the fact that, as acting humans ourselves, we have a direct understanding of human action, something we lack in pondering the behavior of electrons or stars. The contemplative mode of theorizing is made even more important in economics because the creative nature of human choice inherently fails to exhibit the quantitative, empirical regularities, the discovery of which characterizes the modern, physical sciences. (Biology presents us with an interesting intermediate case, as many of its findings are qualitative.) . . .

I hope the above considerations will make Mises's apriorism more intelligible to staunch empiricists. But I suspect that some of them still may look askance at the proposal that we have this "oddball" kind of knowledge, one that is neither empirical nor analytical. They still may be inclined to dismiss it, noting that its claim to axiomatic status shields it from further analysis. It also appears suspiciously like those outcasts from post-Enlightenment epistemological respectability: intuitive, revealed, and mystical claims to knowledge. However, a deeper examination of human knowledge, undertaken without a prejudice in favor of the currently sanctioned methods of inquiry, reveals every mode of understanding, including the logical, the mathematical, and the experimental, as ultimately grounded upon our intuitive judgment.

For instance, a person can be presented with scores of experiments supporting a particular scientific theory is sound, but no possible experiment ever can demonstrate to him that experimentation is a reasonable means by which to evaluate a scientific theory. Only his intuitive grasp of its plausibility can bring him to accept that proposition. (Unless, of course, he simply adopts it on the authority of others.) He can be led through hundreds of rigorous proofs for various mathematical theorems and be taught the criteria by which they are judged to be sound, but there can be no such proof for the validity of the method itself. (Kurt Gödel famously demonstrated that a formal system of mathematical deduction that is complex enough to model even so basic a topic as arithmetic might avoid either incompleteness or inconsistency, but always must suffer at least one of those flaws.)

A person can be instructed in mechanical systems of formal logic, but there is no mechanical procedure for deciding which of these possible systems are worth developing. (It is quite possible to specify perfectly consistent, formal systems of logic that yield conclusions that are correct per the rules of the system but that any intelligent person can see are nonsense. For example, we might devise a system in which, if x implies y and z implies y, then x implies z. Within that system, the acceptance of "all men are mortal" and "all slugs are mortal" would mean that all men are slugs. Aside, perhaps, from particularly bitter feminists, we can all see that argument is rubbish, but we can only judge between alternative formalisms based on our intuitive sense of deductive truth.)

Michael Polanyi has shown that intuitive judgment is the final arbiter even in the "hard" sciences like physics and chemistry.

While experimental findings are, quite properly, a major factor in a scientist's choice of which of two rival theories to accept, the scientist's personal, intuitive judgment will always have the final say in the matter. When the results of an experiment are in conflict with a theory, the flaw may be in either the theory or the experiment. In the end, it is up to the scientist to choose which to discard, a question that cannot be answered by the very empirical results in doubt.

This ultimate, inescapable reliance on judgment is illustrated by Lewis Carroll in Alice Through the Looking Glass. He has Alice tell Humpty Dumpty that 365 minus one is 364. Humpty is skeptical, and asks to see the problem done on paper. Alice dutifully writes down:

365
- 1
___
364

Humpty Dumpty studies her work for a moment before declaring that it seems to be right. The serious moral of Carroll's comic vignette is that formal tools of thinking are useless in convincing someone of their conclusions if he hasn't already intuitively grasped the basic principles on which they are built.

All of our knowledge ultimately is grounded on our intuitive recognition of the truth when we see it. There is nothing magical or mysterious about the a priori foundations of economics, or at least nothing any more magical or mysterious than there is about our ability to comprehend any other aspect of reality.

(Callahan has more to say here. For a technical discussion of the science of human action, or praxeology, read this. Some glosses on Gödel's incompleteness theorem are here.)

I omitted an important passage from the preceding quotation, in order to single it out. Callahan says also that

Mises's protégé F.A. Hayek, while agreeing with his mentor on the a priori nature of the "logic of action" and its foundational status in economics, still came to regard investigating the empirical issues that the logic of action leaves open as a more important undertaking than further examination of that logic itself.

There, I agree with Hayek. It is one thing to know axiomatically that the speed of light is constant; it is quite another thing to know experimentally that the speed of light (in empty space) is about 671 million miles an hour. Similarly, it is one thing to deduce from the axioms of economics that demand curves generally slope downward and supply curves generally slope upward; it is quite another thing to estimate specific supply and demand functions.

But one must always be mindful of the limitations of quantitative methods in economics. As James Sheehan writes at the website of the Mises Institute,

economists are prone to error when they ascribe excessive precision to advanced statistical techniques. They assume, falsely, that a voluminous amount of historical observations (sample data) can help them to make inferences about the future. They presume that probability distributions follow a bell-shaped pattern. They make no provision for the possibility that past correlations between economic variables and data were coincidences.

Nor do they account for the possibility, as economist Robert Lucas demonstrated, that people will incorporate predictable patterns into their expectations, thus canceling out the predictive value of such patterns. . . .

As [Nassim Nicholas] Taleb points out [in Fooled by Randomness], the popular Monte Carlo simulation "is more a way of thinking than a computational method." Employing this way of thinking can enhance one's understanding only if its weaknesses are properly understood and accounted for. . . .

Taleb's critique of econometrics is quite compatible with Austrian economics, which holds that dynamic human actions are too subjective and variegated to be accurately modeled and predicted.

In some parts of Fooled by Randomness, Taleb almost sounds Austrian in his criticisms of economists who worship "the efficient market religion." Such economists are misguided, he argues, because they begin with the flawed hypothesis that human beings act rationally and do what is mathematically "optimal." . . .

As opposed to a Utopian Vision, in which human beings are rational and perfectible (by state action), Taleb adopts what he calls a Tragic Vision: "We are faulty and there is no need to bother trying to correct our flaws." It is refreshing to see a highly successful practitioner of statistics and finance adopt a contrarian viewpoint towards economics.

Yet, as Arnold Kling explains, many (perhaps most) economists have lost sight of the axioms of economics in their misplaced zeal to emulate the physical sciences:

The most distinctive trend in economic research over the past hundred years has been the increased use of mathematics. In the wake of Paul Samuelson's (Nobel 1970) Ph.D dissertation, published in 1948, calculus became a requirement for anyone wishing to obtain an economics degree. By 1980, every serious graduate student was expected to be able to understand the work of Kenneth Arrow (Nobel 1972) and Gerard Debreu (Nobel 1983), which required mathematics several semesters beyond first-year calculus.

Today, the "theory sequence" at most top-tier graduate schools in economics is controlled by math bigots. As a result, it is impossible to survive as an economics graduate student with a math background that is less than that of an undergraduate math major. In fact, I have heard that at this year's American Economic Association meetings, at a seminar on graduate education one professor quite proudly said that he ignored prospective students' grades in economics courses, because their math proficiency was the key predictor of their ability to pass the coursework required to obtain an advanced degree.

The raising of the mathematical bar in graduate schools over the past several decades has driven many intelligent men and women (perhaps women especially) to pursue other fields. The graduate training process filters out students who might contribute from a perspective of anthropology, biology, psychology, history, or even intense curiosity about economic issues. Instead, the top graduate schools behave as if their goal were to produce a sort of idiot-savant, capable of appreciating and adding to the mathematical contributions of other idiot-savants, but not necessarily possessed of any interest in or ability to comprehend the world to which an economist ought to pay attention.

. . . The basic question of What Causes Prosperity? is not a question of how trading opportunities play out among a given array of goods. Instead, it is a question of how innovation takes place or does not take place in the context of institutional factors that are still poorly understood.

These are behavioral issues that economists can address legitimately with quantitative methods, as long as they are aware of and honest about the limitations of their methods. One of those limitations is that, while quantitative analysis may reveal certain general relationships and tendencies, those relationships and tendencies are the residue of myriad individual choices that cannot be quantified or predicted. (I am with Kling on the subject of "happiness" research. See also this post by Will Wilkinson.)

Many economists (e.g., "libertarian" paternalists) get around that essential limitation by insinuating their own values into the minds of others. Such economists simply are not content with the notion that A's happiness and B's happiness are unique and incommensurable. They claim to know what makes A and B happy, and they wish to make A and B (and every other "lesser being") act accordingly. We can have a priori knowledge about the axioms of economic behavior, but we cannot presume a priori knowledge about any individual's preferences.

Nor can we repeal the axioms of economics. Wherever quantitative methods yield results that are at odds with those axioms, it is the results that should be rejected, not the axioms.