A Student Among the Econ: Seeing Through Mathemagics
Asad Zaman
In my article Education of an Economist, I explained how I gradually came to realize that all I had learnt during my Ph.D. training at Stanford University was false. I would like to make this more specific and concrete by providing some examples. A leading example is a paper on Power and Taxes which I studied as a graduate student. But, let me start from the beginning.
Leijonhufvud, in his classic narrative Life Among the Econ explains how the priestly caste of the Math-Econ is the most admired and revered among the Econ. With a math degree from MIT, I was eager to join the ranks of Mathematical Economists, the most prestigious among the alternatives facing me. But a few experiences soured me on this idea. I ended up with a degree in Econometrics, which also makes heavy use of mathematics, under the illusion that this may be closer to reality. I learned much later that all of the theory I studied at Stanford pertains to a fantasy world created by economists, which has no relationship to the real world.
The first among the many shocks that disillusioned me about Mathematical Economics occurred within a course on Game Theory taught by Mordecai Kurz. In the course, he exposited a model under development with Robert Aumann, later published in Econometrica (see: Power and Taxes). The goal of the model was to understand taxation structures. The model sets out a game in which coalitions of players are allowed to form, and any coalition which has a majority can make the tax laws. Aumann and Kurz “solve” the game using a highly technical concept known as the Harsanyi-ShapleyNash Non-Transferable Utility Value. Sadly, this game has a trivial solution. A majority coalition will form, tax away everything which the minority has, and redistribute it equally among themselves. The Shapley value is calculated by taking the average payoff to each player, where averaging is done over all possible coalitions. This leads to a trivial solution: each player will receive exactly equal shares of total endowments. This is a highly unrealistic tax structure – no match to reality. What to do? Aumann and Kurz came up with an ingenious idea: Allow those who are being taxed to burn their endowments, instead of giving them up.
Once this move is introduced into the game, the mathematical solutions become more interesting. In particular, the majority allows the minority to retain enough to prevent a revolt (corresponding to burning their endowments).
Aumann and Kurz make analogies between the game and real-world concepts. The ability of the majority coalition to impose its will on others is called democracy, and the ability of the minority to burn their endowments is likened to farmer’s rebellions. The idea that the game has any resemblance to reality can only fool naïve readers, who have no knowledge of politics or history. Unfortunately, the vast majority of economists have only disdain for these disciplines. As a result, economists have no clue as to realism, or lack thereof, of their models. As a student, I was flabbergasted by the attempt to match the outcomes of this completely artificial game to real world tax structures. Surely, it should be obvious to all that this is a vain enterprise. I can make up thousands of games with different structures. It is possible to do reverse engineering, and make a model which would perfectly match the data. Surely, studying solutions of this game is fascinating mathematics, but it gives us no insights into the operation of the real world. In the concluding remarks of the paper, Aumann and Kurz argue that the game shows that concentration of power in a few hands leads to inequality of wealth, while Western democracies create equitable wealth distributions. At one level, this is bland truth which has no relationship to the model: more power in fewer hands will lead to more wealth in fewer hands. A thousand other games, with a thousand different interpretations of power, and radical variations in details, would all lead to the same result.
At a deeper level, when judged empirically, the result itself is quite false. For example the communist societies of Russia and China had substantially better income distributions than those in democratic-capitalist USA. But this is not my concern here. I was amazed that any sane person could think that the mathematics of Harsany-ShapleyNash NTU game theory, applied to a simple game, under highly unrealistic assumptions, could have anything to say about real world taxes. It seems intuitively obvious that if one wants to learn about tax structure in the USA, one should study the Congressional debates on taxation, and the legislation which led to the creation of the tax structure. Power struggles would be reflected in these debates, as different parties would (or should) attempt to pass rules which would give them greater votes. As it turns out in practice, votes depend more on campaign contributions than on the ability of a politician to appeal to a mass of voters. As a result, tax structure has become increasingly favorable to the rich and powerful. During my studies, I found that economists not only lack knowledge in these areas, but also are supremely indifferent to acquiring this knowledge. According to the dominant methodology, economics consists of the study of theoretical models; and the relationship to reality is of no importance.
Due to my facility with mathematics, Mordecai Kurz actually approached me and asked if I wanted to do a PhD thesis in this area. There was ample room to play with variations of this game in a fantasy world, unconstrained by real world considerations. I told him that I found the completely artificial assumptions required to create and work with mathematical models of the economy repulsive, and planned to work in econometrics. At least that deals with real world data. He was a bit hurt, and responded by criticising the highly artificial assumptions that econometricians must make, to enable data analysis. It is worth noting that he did not defend mathematical economics; instead, he argued that econometrics is also based on artificial and unrealistic assumptions! It was years later that I realized the truth of his remarks. Econometrics is based on false assumptions, and is more damaging because it deals with real data, creating the illusion that it is about the real world. Econometric models basically extrapolate from past correlations to the future, and routinely break down when something real changes. Fancy mathematics cloaks crude assumptions, preventing the public from recognizing the flawed foundations upon which sophisticated computer outputs depend. I hope to provide more details later (see: A Realist Approach to Econometrics). It seems appropriate to conclude with a quote from Krugman, in the aftermath of the Global Financial Crisis, “The profession as a whole went astray, because they mistook the beauty of mathematics for truth.”
Source: WEA Pedagogy, 23 May 2023
