Is Economics Just Another Applied Math Field?

Lynne Kiesling

I highly recommend Arnold Kling’s Tech Central Station article today on the implications of the very mathematical methodology of modern economics. Arnold’s article is inspired by this recent Cato Journal article from Dartmouth economist Meir Kohn, which I also recommend to you.

Actually, I have to say that I find Kohn’s paper to be a strikingly articulate analysis of a fundamental dissonance that I’ve been trying to reconcile for as long as I’ve been an economist. Being a Northwestern Ph.D. I am of course deeply embedded in Kohn’s “value paradigm” and the game-theoretic math approach that accompanies its expression in industrial organization. But increasingly as I have continued to work and read and think and write and talk economics, I have found Kohn’s “exchange paradigm” to be a better description of how I think economics should be done. One aspect of why the value paradigm doesn’t work (at least for me) any more is that there is no place for institutions in it.

Kohn (p. 310) provides a nice summary of the institutionally sterile nature of the value paradigm:

There is no explicit role for economic institutions in the theoretical approach of the value paradigm. Economic institutions are the organizational structures within which exchange takes place. In a trading environment characterized by price taking, there is nothing for them to do and no reason for them to exist. Some real-world institutions do make a nominal appearance in the value paradigm, but they do not function as institutions. The firm is not an institution but a maximizing individual. The market is not an institution but an abstraction—an algorithm that magically coordinates the plans of individuals. Government is not an institution either. It is either an exogenous force or yet another type of individual that in this case maximizes social utility.

These characterizations of institutions sit uncomfortably with the principle of methodological individualism. In reality, firms and governments are aggregates of many individuals, each of them greedy and purposive. However, the interaction of these individuals within firms and governments is ignored by the value paradigm and the aggregates themselves are treated as though they had motives and intelligences of their own. The characterization of the market is even more of a problem. It is seen as a disembodied spirit (sometimes called the “Walrasian auctioneer”) that produces, without action by any individual, the prices that individuals take as given.

However, from a more exchange-oriented perspective we derive a different theoretical focus:

Exchange opportunities are not given, but must be found or created. Prices are not provided by magic, but must to be set by someone. Exchange involves interaction not with an impersonal market but with other individuals. Promises of future performance are not always kept. Goods and traders are heterogeneous, so that individuals require information not only on prices but also on the quality of goods and the trustworthiness of counterparties. Such information is scarce and often asymmetric. Individuals are not always insignificant relative to the market: markets are often thin, and prices may be set strategically or be subject to bargaining. …

In this trading environment individuals are characterized not only by resources and technology but also by information—the information they possess and the information that others possess about them (their reputations). Purposive behavior is much richer.

Kohn then argues that the exchange paradigm is better equipped to address inherently dynamic questions of growth, change, and uncertainty, and that it yields different positive and normative policy prescriptions. I leave the rest to you, gentle reader, but I think this is a really important paper that has crystallized a lot of ideas that have been rumbling around in my head for a while.

Arnold’s take on these ideas in his TCS article synthesizes Kohn’s arguments with those in his own book. I particularly like how he puts the growth point:

The fundamental economic question in the learning paradigm is how we came to be so rich relative to our ancestors. In my book, I use the example, based on calculations of Brad DeLong, of the fact that if you measure productivity in terms of bags of flour, we can produce over 400 times as much today as we did 500 years ago.

We did not achieve these spectacular increases in our standard of living by re-allocating what was known in 1500. Instead, it was exploration of the unknown, and the millions of discoveries and adaptations involved in that exploration, that led to the production techniques and consumer goods and services that are available today.

One might say that economic growth involves the transition from the unknown to the known. We go from an inferior set of production techniques to a superior one as the economy learns and adopts the better methods. How to achieve this transition from the unknown to the known is a different problem than that of allocating a known set of resources.

Given that economic growth cannot be understood in terms of a known set of resources and production techniques, it is not surprising that mathematics fails to explain differences in the average standard of living across time and across countries.

One challenge I think we face in economics is simultaneously to focus on real-world questions and issues while maintaining a systematic analytical methodology that enables us to construct and test hypotheses. That’s been relatively easy to do with math tools over the past century for many pressing questions. But for the questions that are of increasing importance having to do with knowledge, networks, and open-ended unknowable change, the math is not helping us be systematic and analytical and still focus on the important questions.

2 thoughts on “Is Economics Just Another Applied Math Field?

  1. Economists have “science envy”. They make up for this by being overly analytical.

    You guys need to get over it. Personally, I find the more ideological, even metaphysical aspects of economics the most appealing.

    Just because something isn’t a true science doesn’t mean that it can’t be useful, or even truthful.

    And as economics proves, just because a concept is mathematically based, doesn’t mean that it is scientific. Garbage in, garbage out.

  2. The question of how we became so rich relative to our ancestors (and relative to other cultures) is the thing I find most intreging about economics as I understand it today. In “Guns, Germs and Steel”, Jared Diamond starts his inquiry of the evolution of cultures to answer a question posed by friend of his in New Guinea, “Why do the white men have all the cargo?”

    In addition to the luck of geography that favored certain locations and peoples for the beginnings of civilization, the rest of the answer is about the evolution of culture, and the sorting process of what works, and what doesn’t work. (Not perfection, but advantage.) From here I went on to read about evolutionary biology and animal behaviors as related by Richard Dawkins. The ideas he presented have close paralles to the ideas of spontaneous order discussed by economic thinkers such as Hayek and Adam Smith.

    Given that individuals’ utility functions are so highly variable, the mathematics behind developing reasonable simulations of the collective behaviors is daunting. Much like prediciting future evolutionary paths in biology.

    Another example, a little closer to what I do every day, concerns traffic simulations done by engineers to model the capacity of roadway segments. In the last five years these simulations have become much more realisitic and useful, as the models included a range of driver and vehicle responses based on the population of drivers and vehicles. Driver behavior varies widely based on aggresiveness and other factors (as anyone from a rural area or small city knows when the first try to drive in a city like Chicago or New York.) The simulations of macro behavior have improved with the ability to model micro level behavior with a degree of diversity that more closely resembles the real world.

    So what this means to economics is our understanding of it will increase as we are better able to model the decisions and tradeoffs made by individuals, with different knowledge, motivations, temperaments, goals, etc. This diversity of individual behaviors is a clear challenge to the regulatory frameworks erected in most fields of economic activity because of the uniformity of treatment applied to diverse players by regulations. This gets back to the theme of one of the recent posts about competition that is good enough, but not perfect.

    In dynamic systems, the pursuit of perfection is taken incrementally with ideas (regulations) (or genes) being adopted because they are somehow better than the previous alternative.

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