Written by John Lounsbury
This week we are repeating a video from last November that I consider one of the most important we have present on this website.. It addresses what Lars Syll has called a wonkish subject. Be that as it may, the concept is so important in financial and economic analysis, and so often abused, that it should be repeatedly studied until it is no longer wonkish, or until you become a wonk. If you pursue this recommendation you will have the tools to become a rich wonk, should you so chose.
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From the earlier post of this video:
Ergodicity is a property sometimes misapplied in economics. A system is ergodic if the time average of a process and the position average are identical. This week’s video is a lecture that explains just what that means in simple processes and how economics is impacted. Hat tip to @LarsPSyll who has this video on his blog. Prof. Syll refers to the subject as “wonkish” (which it may well be), but its understanding is of fundamental importance for anyone interested in economics and financial systems.
Here is what Prof. Syll says on his blog:
Time irreversibility and non-ergodicity are – as yours truly repeatedly has argued – extremely important issues for understanding what are some of the deep fundamental flaws of mainstream economics.
[This lecture] gives further evidence why expectation values are irrelevant for understanding real-world economic systems.
This documentary is a lecture by Ole Peters at Gresham College in November 2012. Here is a bio for Dr. Peters from the Santa Fe Institute:
I’m a Fellow at the London Mathematical Laboratory, and the Principal Investigator of its economics program. I’m also an External Professor at the Santa Fe Institute. I work on different conceptualizations of randomness in the context of economics. My thesis is that the mathematical techniques adopted by economics in the 17th and 18th centuries are at the heart of many problems besetting the modern theory. Using a view of randomness developed largely in the 20th century I have proposed an alternative solution to the discipline-defining problem of evaluating risky propositions. This implies solutions to the 300-year-old St. Petersburg paradox, the leverage optimization problem, the equity premium puzzle, and the insurance puzzle. It leads to deep insights into the origin of cooperation and the dynamics of economic inequality. I maintain a popular blog that also hosts the economics lecture notes.
Wikipedia has a useful discussion of ergodicoty. Here are three excerpts:
Ergodicity occurs in broad settings in physics and mathematics. All of these settings are unified by a common mathematical description, that of the measure-preserving dynamical system. An informal description of this, and a definition of ergodicity with respect to it, is given immediately below.
Wikipedia has a useful discussion of ergodicoty. Here are three excerpts:
Ergodicity occurs in broad settings in physics and mathematics. All of these settings are unified by a common mathematical description, that of the measure-preserving dynamical system. An informal description of this, and a definition of ergodicity with respect to it, is given immediately below.
The mathematical definition of ergodicity aims to capture ordinary every-day ideas about randomness. This includes ideas about systems that move in such a way as to (eventually) fill up all of space, such as diffusion and Brownian motion, as well as common-sense notions of mixing, such as mixing paints, drinks, cooking ingredients, industrial process mixing, smoke in a smoke-filled room, the dust in Saturn’s rings and so on.
Formal mathematical proofs of ergodicity in statistical physics are hard to come by; most high-dimensional many-body systems are assumed to be ergodic, without mathematical proof.
From The ergodicity problem in economics (Ole Peters, Nature Physics, December, 2019):
Abstract
The ergodic hypothesis is a key analytical device of equilibrium statistical mechanics. It underlies the assumption that the time average and the expectation value of an observable are the same. Where it is valid, dynamical descriptions can often be replaced with much simpler probabilistic ones – time is essentially eliminated from the models. The conditions for validity are restrictive, even more so for non-equilibrium systems. Economics typically deals with systems far from equilibrium – specifically with models of growth. It may therefore come as a surprise to learn that the prevailing formulations of economic theory – expected utility theory and its descendants – make an indiscriminate assumption of ergodicity. This is largely because foundational concepts to do with risk and randomness originated in seventeenth-century economics, predating by some 200 years the concept of ergodicity, which arose in nineteenth-century physics. In this Perspective, I argue that by carefully addressing the question of ergodicity, many puzzles besetting the current economic formalism are resolved in a natural and empirically testable way.
From YouTube:
An exploration of the remarkable consequences of using Boltzmann’s 1870s probability theory and cutting-edge 20th Century mathematics in economic settings. An understanding of risk, market stability and economic inequality emerges.
The lecture presents two problems from economics: the leverage problem “by how much should an investment be leveraged”, and the St Petersburg paradox. Neither can be solved with the concepts of randomness prevalent in economics today. However, owing to 20th-century developments in mathematics these problems have complete formal solutions that agree with our intuition. The theme of risk will feature prominently, presented as a consequence of irreversible time.
This lecture is an essential view for anyone who wants to understand some of the fundamental fallacies in modern economics. It is also important for investors who want to extend their knowledge of investment risks, randomness in markets, and limits of leverage. I have watched the lecture twice and will certainly watch a few more times. It is important to internalize this information if you want to have instant recall whenever problems arise to which it applies.
A transcript of this lecture is available here.
Source: YouTube.
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