This article has no one topic that it aims to cover, but does have a general theme running through it. Some of the topics touched are model error, limits to knowledge, heterodox ideas in economics, anti-fragility. It is a sort of a menagerie of ideas that have been bouncing around in my head of recent. Let’s dive in:
We use models as a way of thinking about the world and by their very nature they make certain assumptions about the world, which could be about underlying statistical distribution or assuming away some “frictions” that exist in the real world. Now models come with model errors. These errors are harmless in certain domains where the payoffs are linear, but under non-linearity small departures can lead to large changes in outcomes. The situation gets worse when the payoff is concave the idea is illustrated in the picture below. The idea was introduced by Nicholas Nassim Taleb in his book Anti-Fragile. The idea has been mathematically formalized by Taleb and a co-author.
Taleb has introduced a simple heuristic to check the robustness of the models, it basically involves re-running the model with slight perturbations, which reminds me of a practical maxim in Hindi thok baja ke dekhlo (transliterates to: stress test it but not too much). In fact, such practical maxims from traditional times are a common theme in Taleb’s work as they have proven to be robust through centuries.
Speaking of practice, I would like to point to a whole body of knowledge especially in finance that have been developed by practitioners of the field, tinkerers and experimenters , who evolved these ideas through trial and error. These ideas do not enter academic curriculum mostly because of a lack of structure. A great example of ideas developed by practitioner are the ideas of the mathematician Edward Thorp. Thorp worked in the field of probability and initially tested out his ideas in Vegas. He even wrote a book Beat the Dealer based on his experiments, but it did not sell well. He later applied his ideas to Wall Street, and found success. He went on to develop an investment technique called the Kelly Criterion, which has been somewhat of a controversial topic. Another amazing tinkerer was the mathematician Benoit Mandelbrot, who employed his mathematical ideas in combination with computer simulations to gain deep insights in working of financial markets. His work has consequences for effectiveness of orthodox theories like mean-variance portfolio optimization, which are a quint-essential part of any finance curriculum.
The idea here is not to reject orthodoxy in our disciplines completely, but to embrace more ideas to have a better understanding of behaviour of the system and the risks involved – the bottom line is to make a better more informed decision.
Moving on, I would like to discuss very specific idea, which I feel should receive more attention. The idea was developed Pia Malaney in collaboration with Eric Weinstein in her Ph.D. thesis at Harvard. Malaney developed a new way of measuring economic variables like the CPI Index which is more robust and accurate. The idea ran into trouble since the very beginning as it was rejected by the economics department at Harvard, and was buried until recently it resurfaced in the aftermath of the financial crisis as people began to look for alternative ideas as orthodox economic theory failed. Employing Differential Geometry the authors showed there was a way to construct an inflation index that could account for changing basket of goods through time as a result giving a more accurate measure of cost of living. It also allows us to overcome the assumption of static preferences, which is central to a lot of economic theory. It was presented to an audience of physicists and economists at the Perimeter Institute in Waterloo, where the authors seemed to have been heckled (by economists of course). It was again presented at the Field’s Institute in Toronto where it was received better. The idea was mentioned by Waterloo’s own Lee Smolin in his book, who has investigated the idea and sees its merits.
Again, the idea is not to reject existing theory, but to extend our understanding by accepting new ideas into the discipline even if they may be at odds with the existing ones. This is just one idea there are whole fields like complexity economics, which are well worth learning and applying to real world decision making.
Finally, it is important to understand the limits of knowledge i.e. what we can know depends on the capability of our tools of discovery. In case of social sciences the tool we have is statistics. It is important to understand the limits of the statistical tools in terms of what can be concluded from them. When applying statistics to decision models it is important to be sure of robustness as these models need to perform under stress. In conclusion, there will continue to be uncertainty, and we should be able design systems that can withstand shocks without blowing up, which requires all the information and insights we can fathom.
There are many more ideas like the precautionary principle, power laws, scaling, and narrative economics I would like to discuss, but I cannot fit them here. I will try to keep this piece a dynamic one to which I can continue to add.