Economic schools and mathematics
andrea.parisi | Published: 17 Jul 2023, 9:54 a.m.
After my first in-depth encounter with economic theories, that is, after reading the first 50 pages of the book "Economics" by P.A. Samuelson and W.D. Nordhaus, I was left with a lot of confusion. As explained here, I could not relate to the contents of the book and I thought that somehow this domain of science was out of my mindset. I could understand books of chemistry, books of geography, epidemiology, biology, history, social sciences (all domains that I somehow touched during my research activity) but not books of economics. Economists seemed to know things I could not understand, and I had to leave them doing their job as they were simply out of my league.
Scientists have the bad habit of not resigning to just "not understanding". Somehow we need to know "why" we cannot understand. So after several months upon declaring defeat, I wondered if I was the only one having had this experience. Happily we live in the era of the World Wide Web, so it was easy to search for answers. And, surprise surprise, I did find answers! A website was actually explaining the problems of modern economic theory and, amazingly, it was doing precise forecasts on economic events (job market, financial crises, stock markets and price of gold) which were quite different from what was found on the news and economic columns. I was surprised to find a clear and perfectly understandable explanation of these forecasts. I was even more surprised to witness, during the financial crisis of 2007-8, the fulfillment of the predictions made, which were occurring for the exact same reasons that had led to formulating the predictions in the first place. What knowledge did the authors had that differed from what was heralded and blindly believed from the rest of the world? The authors were not magicians, nor psychics: they were followers of the Austrian school of economics.
That was the first time I heard the term "school of economics". I had just discovered that modern economic theory is one school of economics: that is a collection of theories with a common underlining base. There is nothing similar in the world of hard sciences: you do not have a school of chemistry rivaling another school of chemistry. I mean, you do have groups of scientists rivaling on certain ideas, but in the end experimental measures are what leads to one side taking the advantage. In economics the scenario is different, as there are competing school, each with its own full set of theories and methodologies. This abundance of competing schools seems natural as economic science is not a hard science, despite acting as if it were. In economics you cannot do an experiment to establish who is right and who is wrong: that indeed leaves a large margin of uncertainty. Once again, the true nature of economics as a social science resurfaces. However, I believe (and I have found no other reference to this anywhere else in the literature or on the web) there is a more profound methodological problem common to many economic schools, and certainly central to the modern economic school, which mines its progress, and is directly connected with the attempt of using a 'hard' science approach without placing adequate foundations. I will try to explain such a problem in forthcoming articles.
The Austrian school of economics is the school that I have come to know better, mostly because I found references to it in several useful books. In recent years I approached the stock market, and I read several books written by successful fund managers. Famously, Peter Lynch, fund manager at Fidelity Magellan Fund and considered one of the most successful fund managers in history, was quite skeptical of academic theory: in his book "One Up on Wall Street" he explains how he ended up ignoring the stock market theory:
It seemed to me that most of what I learned [at University], which was supposed to learn you succeed in the investment business, could only help you fail. [...] Quantitative analysis taught me that the things I saw happening at Fidelity couldn't really be happening.
While Peter Lynch never followed alternative economic schools, other successful fund managers have ignored modern economic theories, and rather followed the logic dictated by the Austrian school, sometimes adding their own insight into the matter. The Austrian school differs from modern neoclassical economic theories on fundamental matters. The neoclassical theory assumes that the economic actors are rational human entities that take decision based on a maximization of their profits, while being subject to scarcity or environmental (including legal) restrictions. These rational entities have, on their side, an optimal knowledge at any time, and take choices based on such knowledge. Economic models thus may describe the economic world mathematically as equilibrium models where economic changes lead to movement from equilibrium states to new equilibrium states, and thus provide a way to produce forecasts into the future.
The Austrian school takes a very different approach: the economic actors are entrepreneurs, that have a subjective view of the world, and take subjective decisions on what to do. They do not have all the knowledge under their nose: knowledge, rather, is sparse and incomplete, which creates opportunities for the economic actors (individuals, companies, etc) to take advantage of. The complex set of interactions between economic actors does not conform to the static equilibrium of neoclassic economics, rather to a dynamic equilibrium which is continuously adjusting, resulting from the free self-coordination of economic actors. The Austrian school assumes that such dynamic equilibrium cannot be explained using the mathematical language of economics. Producing exact forecasts into the future is considered impossible, as the dynamic equilibrium is driven by emerging opportunities, and these are based on knowledge that arises dynamically and is not known in advance. The only possible predictions are qualitative, and based on the consequences of meddling with the free self coordination process among human actors.
While I have come to appreciate the logic of this school of economics, it is hard for me to believe that mathematics cannot have a place in economics. Accounting, resource management, all fields of economics make use of mathematics to some (however simple) level. Thus, mathematics somehow has some relationship with economics. It could actually be possible to connect the complex non-equilibrium dynamics described by Austrian-school economists with a mathematical description: this might have been prohibitive 100 years ago when Merger and Mises, major figures of the Austrian school, wrote their main books, but modern data analysis provides the tools to analyze and understand human behaviour. Even the dynamic equilibria proposed by the Austrian school 100 years ago are similar to the dynamic equilibria observed and described in modern times in other scientific contexts. In other words, modern mathematics and data analysis may be able to formalize concept that were not as easily rendered through a mathematical description 100 years ago. That does not mean that there is a mathematical theory ready. One of the weirdest thing that I noticed in economics is the blank transfer of theory from hard sciences to economics. I once read articles that tried to frame economic equilibrium theory through the formalism of thermodynamics (the science of heat exchange in physics), and more recently I found out about Quantum Economics: again a blank transfer to economics of methods developed to explain specific phenomena observed in physics. Somehow, some economists seem to try alien theories (at random or by cool name) to try to make them work in an environment for which they were not designed to work. This says a lot about the current level of economic progress.
Let us be clear: I am not saying that such theories are necessarily wrong. I have no sufficient in-depth knowledge of the specific theories to judge their limitations and validity: what I find weird, however, is that economists have been unable to build and develop their own models to explain certain features emerging in real world economics. One thing is to develop a model, verify its good performance, observe similarities with Quantum Physics, and then import some of the methods of Quantum Physics compatible with the successful model to further progress on the path of economic knowledge. That is a good thing: it is called interdisciplinary approach, and is behind a lot of progress among sciences of all fields. Another thing is not knowing how to handle certain facts mathematically, and use a completely alien theory that somehow looks usable to handle those facts.
The major problem in economics is of course the lack of experimental proof: this has led to various disputes among schools. In the modern neoclassic approach, theories are tested on historical data. Economists are aware that history is one and unique, which means that historical data cannot provide definitive results. This fact has an important hidden consequence: as clarified from several authors from the Austrian school, history only reports what has occurred, thus it is impossible to evaluate the effects of any economic measure, since we do not know what the alternative to the adopted measures would have been. In "Economics in one lesson", H Hazlitt provides a famous example: a kid breaks the window of a baker's shop. The baker shop will have to buy a new window: in doing so, the window repairer will have new work to do. He will receive money from the baker shop owner, and he will be able to use it to buy new clothes or whatever he needs. As the money that was originally used to replace the broken window moves from hand to hand favouring trades, many people are made happy. Somehow, the action of the kid seems to have benefitted the economy, as money is circulating and goods are being exchanged. However, what we cannot see is what would have happened if the kid did not break the window. In that case, the owner of the baker shop would have used that same money to buy a new coat from the tailor, who would in turn have used the money to buy staff he needed, and so on. In the second case also, the economy would have benefitted from a window not broken: the difference between the two is that in the first case money is used to replace existing staff, while in the second it is used to produce new staff and thus enrich the community at large. If the first case were of any advantage, then it would be easy to have a flourishing economy: just break anything you see in sight, so that new replacements need to be produced, but of course that is not how it works. The lesson from this simple thought experiment is that actions that seem to bring benefit, not always represent the best choice, as the outcome of alternative courses of action are not readily apparent.
An example of actions not providing the best outcome at work in the wider world is, according to Austrian economists, the manipulation of economies engineered by Central banks and politicians. Politicians use taxes to redistribute incomes and wealth to the economically weaker members of the population. What is seen is that the weaker members acquire some benefit from these policies. But does this really favours the economically weaker members of the community? What is not seen is what would have happened following a different action plan. When politicians use taxes to redistribute incomes and wealth, they deprive future economic progress of capital, which is essential for the creation of new business and to invest in future technological advances, thus hindering economic growth. Central banks counter this by providing new capital in the form of newly created money to the main economic actors through a mechanism called credit expansion, where banks are able to create new money.1 This however, results in a net transfer of wealth from the poorer to the richer members of the population, as the receivers from this credit expansion are always the major economic actors (big companies and government), while at the same time the expansion of the monetary mass reduces the purchasing power of the currency, letting the poor being poorer. This manipulation, according to Austrian economists, has a number of consequences, including the creation of economic cycles, inevitably ending in recessions, which end up in unemployment and a general increase in the inequality of wealth distribution. These effects are not immediate, but occur after a while, are inevitable, and result in portions of the population being in a worsened economic situation. This is the reason behind the strenuous fight of Austrian economists against the manipulation operated by governments and central banks.
Modern economists, on the other hand, claim that it is actually their economic engineering that has smoothed the effects of economic recessions, with credit expansion being at the heart of capital creation. According to neoclassic economists, inexpensive capital creation through new credit fuels investments, business activity, commerce. The proof that this is true, according to these economists, is the constant improvement of living conditions that humanity has experienced since the industrial revolution. Austrian economists, however, counter that this improvement is not the result of credit expansion, but the result of technological advance, which has happened because of individual entrepreneurship: credit expansion only creates periods of accelerated growth followed by dramatic crises and increased wealth inequality. Once again, we can take sides for one school of another, but it is hard to show objectively which school is right as we cannot explicitly test the two hypotheses. Without the possibility of experimenting, this becomes more of a philosophical discussion, with the unpleasant feature that if the more accepted theory is actually wrong, we all suffer the consequences.
- The mechanisms that lead to the creation of new money are mostly consequence of the fractional reserve banking system. This is a relatively simple but subtle mechanism that is actively used by central banks to control the amount of money circulating into the economy and is explained in depth by Murray Rothbard in "The Mystery of Banking".
