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The Ergodicity Problem in Economics

148 points by ali92hm 6y ago

wrnr 6y ago
Talk by the same author for those that don't like to read: Time for a change - https://www.youtube.com/watch?v=f1vXAHGIpfc https://www.youtube.com/watch?v=f1vXAHGIpfc
- deleted 6y ago
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- RobertoG 6y ago
  They have a webpage: https://ergodicityeconomics.com/ https://ergodicityeconomics.com/
laszlosandor 6y ago
Time to read! https://twitter.com/ben_golub/status/1338175642932715520?s=21 https://twitter.com/ben_golub/status/1338175642932715520?s=2...
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- juskrey 6y ago
  Many words about how economics is like physics, hence Peters makes a terrible insults to generations of respectful academics. And not a single word about how they are still missing the ruin problem, and how ergodicity is a dead simple and exact answer to it
  - drdeca 6y ago
    The main article doesn't seem to refer to "the ruin problem" either. What is that?
    - juskrey 6y ago
      Ole should repeat it on more occasions, since this is what it's all about: economic unit is not an average of the same imaginary economic units following different paths, some of which can end in a bankruptcy. Instead single bankruptcy will end the whole process, this is a ruin problem. That is economic unit is an average on its own timeline, not space.
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    - nullc 6y ago
      #!/usr/bin/python3 import random #100 people start with $100 balances=[100]*100 #They take 10000 bets with an _expected_ return of 1.25x. # ... so they should end up with ~1.2e1000 at the end... for i in range(10000): balances=[0 if x<=0 else random.choice([x*2,x//2]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0]))
      - ulucs 6y ago
        > # ... so they should end up with ~1.2e1000 at the end... Who has ever claimed this? Also, people end up with zero because you are doing integer division in your code (ie the simplified expected return is wrong). Here are my results with 100 bets, and 10000 bet takers. The average return is also on the upward trend, but not really close since CLT doesn't really apply to this distribution: >>> sum(balances)/1000000 24546192.840913434 >>> print(len([x for x in balances if x<=100])) 5426 >>> print(len([x for x in balances if x>=100])) 5381 >>> print(len([x for x in balances if x>100])) 4574
        nullc 6y ago
        Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring division: #!/usr/bin/sage import random balances=[Rational(100)]*100 for i in range(10000): balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0])) The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it. One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing. And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.
  - wazoox 6y ago
    Economics is not like physics at all. It's a social science, rooted in many social assumptions and compromises and power relationships between human beings and groups. Most attempts to negate this are just tortuous ways to justify the current power structure.
    - imtringued 6y ago
      There is a small nugget that is as hard as physics. Namely the tools can be analyzed in their theoretical performance. But economics is deeply tied to politics. What type of economy you have is entirely dependent on current leadership. It's the government that sets the basic foundation and rules upon which the economy is built. Some governments decided to go to either extreme. Communism or capitalism. There is a price equilibrium, assuming one is allowed to exist, which is dependent on your government, but where exactly it lies is also entirely dependent on the laws the government set. If the government bans garbage disposal in rivers then it would be completely unreasonable to insist that the equilibrium price should stay the same. By this same logic if there is an inherent injustice or imbalance it exists in the laws the government created. One prominent example would be the central bank flooding the market in a way that benefits existing asset holders, one could have done the exact opposite as well or maybe even done a little of both. It's not a question of which is the right action, the question is "What kind of economy do you want?" and the central bank has spoken.
      - wazoox 6y ago
        Precisely. "What kind of economy do you want?" is a political question, that has no definite, scientific answer. And more restrictive economic questions, very often, also are political questions that should be democratically debated and decided, but are instead presented as "scientific" in nature, with the pretension that "we should do as our experts said" (whose experts exactly?).
- ssivark 6y ago
  That Twitter thread is tautological trash, to put it politely. It seems more interested in protecting turf than directly critiquing (or even understanding) Ole Peters’ central point. It is absolutely silly, bordering shitposting, to respond to a claim about subtle/hidden assumptions by claiming: > Expected utility theory makes 4 assumptions, which are stated precisely and concisely in every graduate textbook. Ergodicity is not among them. when the whole point is that the conventional economics literature might have ignored a subtlety.
  - QuesnayJr 6y ago
    It's not. You can read the proofs to see that they aren't missing a step. If you don't want to do that, I can give some indirect evidence. The "conventional economics literature" begins with a theorem of von Neumann and Morganstern, published in 1944. This is the John von Neumann of math and physics fame. In particular, von Neumann was one of the architects of ergodic theory. He proved the mean ergodic theorem all the way back in 1932. It would be pretty surprising indeed if it was von Neumann who missed the subtlety.
    - ReflectedImage 6y ago
      It would be more correct to say economists misinterpreted what von Neumann said.
      - QuesnayJr 6y ago
        They didn't, though. Look at von Neumann and Morganstern's "Theory of Games and Economic Behavior". There's nothing in there about time-series averages. It's a theory of games that you might play only once.
        ReflectedImage 6y ago
        It's fairly obvious that in the real world time does play a role. This may shock you but theories advance over time. There isn't a holy paper which can never be improved on (at least not in sensible research fields).
tribler 6y ago
"We therefore have reason to be optimistic about the future of economic theory."
ncmncm 6y ago
This is important. It is disgraceful that economics failed to arrive at this result at any time in the past century.
- dataflow 6y ago
  What result are you referring to, exactly?
- QuesnayJr 6y ago
  And what result is that? Most of this is well-known. Ergodicity is a concept that's covered in econometrics classes. "When are time averages the averages of the underlying probability distribution?" is the first topic in time series. Honestly, the whole approach is a step back. People discussed these ideas back when Kelly first published the Kelly rule, and the conclusion is that most people are not that aggressive in their investment decisions. People still study it, though, (it's called the growth optimal portfolio), and its properties are well-known. Peters also sneaks in a second assumption, which is that the growth rate of wealth is ergodic. Is it? That's not clear to me at all.
  - ReflectedImage 6y ago
    "most people are not that aggressive in their investment decisions" That's because Kelly's criterion is a special case of Ole Peters, where Kelly's is a very aggressive option. There are other criterion that can be used, which are not so aggressive. Ole Peters lists the class of functions that can be used in his paper. So basically economics has rejected it for the wrong reason.
    - QuesnayJr 6y ago
      As far as I can tell, he lists wealth, and log wealth as the two possible criteria. If there are others, I missed them. If you try to match a power utility model with stock market data, to match prices on the stock market, you would reject both the additive model (eta = 0) and the multiplicative model (eta = 1), in favor of an eta greater than 10. This is known as the equity premium puzzle. The thrust of research over the past 30 years in explaining stock prices has been to reject both Peters' models, and expected utility in general. People build their entire careers on investigating alternatives. There are hundreds of experiments to explain, plus all of the real-world data. It turns out that explaining all of this with one unified model is hard.
QuesnayJr 6y ago
I don't get what people find so exciting about his papers, which I find borderline troll-ish. We know that people in general don't reason the way he says he does. If people only cared about log of wealth, they would take much more risks than they do. If everyone did it, the return on stocks would be much lower than it is, because everyone would regard stocks as a great deal despite the volatility.
- kgwgk 6y ago
  You may have seen this already: https://arxiv.org/abs/1101.4548 https://arxiv.org/abs/1101.4548 Funny stuff. They predict that in aggregate 100% of the wealth is invested in stocks and investing more than that would be suboptimal: the optimal leverage is 1. They "submit the hypothesis to a rigorous test" and find that the optimal leverage for the S&P 500 is around 1, given its volatility. There is a small problem with their rigorous test. They forgot to include dividends: "a real investment in the S&P500 outgrew federal deposits at only 2.0% p.a". Including dividends would bring the optimal leverage to 2 or 3. But that's ok. It's close enough to 1 for them, apparently. Even better: ignoring dividends was not so wrong anyway because the S&P 500 overestimates the return of a real equity investment due to survivorship bias. "The S&P500 is an index of five hundred large companies, listed publicly in the United States. We use it as a proxy for a generic diversified investment in US stocks, but we note some caveats. Firstly, the index does not account for dividends paid to stockholders. This means it will tend to underestimate the performance of a real investment. Secondly, the index suffers from survivorship bias, representing a portfolio of the largest and most successful companies in the US, in which less successful companies are routinely replaced. This acts in the opposite direction to the first caveat."
  - QuesnayJr 6y ago
    I hadn't seen that. Thanks.
drdeca 6y ago
I feel that this downplays the justification for theories of expected utility too much? But I still want to keep reading to see where they're going with this. Ok, like, it says that modeling people as trying to maximize expected utility, is like assuming something as if one is interacting with paralell universe copies of onseself. But, surely the author must be familiar with the Von Neumann–Morgenstern utility theorem? It complains that when people fail to act according to the theories, that the people are considered to be irrational, rather than amending the theories. While it is of course true that theories need to be made to account for how people actually behave, it seems to me that people failing to satisfy the vNM axioms, really is a way in which people fail to live up to the correct ideal of a rational agent. Well, maybe for it to make sense, instead there should be a formalization of like, a compute-limited approximation of following the vNM axioms, maybe throw in a dash of sub-agent stuff, and a few things along those lines. Hmm. Ok, well, if this makes better predictions of how people behave, that is valuable. Though, it would raise the question of "why?".
- zwaps 6y ago
  It's really mind boggling if you know the original proofs my Neumann-Morgenstein or Savage for that matter. In his article, Peters immediately rushes into the time domain, whereas the time domain doesn't exist at all in EUT. I feel like Peters could have made a valid point about the application of dynamic EUT, but he severely over-claims the problem he sees. To refute EUT, Peters had to start with one set of EUT axioms. He clearly doesn't want to do that. We can guess why.
  - ReflectedImage 6y ago
    Ole Peters has addressed this. He had a study of real people done, which shows that real people make decisions using the time domain. The behaviour of real people matches Ole Peters maths but not EUT. This means that EUT does not apply to the real world, which makes EUT a pointless theory.
    - QuesnayJr 6y ago
      Even that isn't new. There are hundreds of experiments that point out the limitations of EU. If you're looking for a reason to reject EU, you didn't need to wait until now. Allais published his paradox in 1953. If Peters wants to propose an alternate theory, he needs to explain all of this existing evidence. For example, he needs to explain why historically the return on stocks is so high. If people only cared about the logarithm of wealth, they would hold almost entirely stocks and very little bonds. They would take their weekly paycheck and deposit it directly into their Robinhood account. (And everyone would have a brokerage account.)
timdaub 6y ago
Thanks for posting. I had read Antifragile in parts but I had never heard of Ergodicity. But it's a great technical term to understand! I looked online and found this post that explained it well: https://taylorpearson.me/ergodicity/ https://taylorpearson.me/ergodicity/
- sn41 6y ago
  Ergodic theorist (occasional) here. Ergodic theory is basically studying situations in which the time average of (almost every) trajectory equals the space average of the system. This is a widely studied area in dynamical systems. I am squeamish about such popular accounts. An old account which is readable even today, is by Birkhoff [1]. About Kelly-Bernoulli criterion, the readable account is the book [2]. [1] https://doi.org/10.1080/00029890.1942.11991212 https://doi.org/10.1080/00029890.1942.11991212 [2] "Fortune's Formula" by William Poundstone. https://archive.org/details/fortunesformulau00poun https://archive.org/details/fortunesformulau00poun
- ReflectedImage 6y ago
  Calling it Ergodicity Economics is a bit confusing. Existing economics is ergodicity. Ole Peters is claiming that the ergodicity assumption in economics is false. His corrected version of economics should be called Non-Ergodicity Economics.
- hfkgktkrlfk 6y ago
  Taleb did write about ergodicity: > A central chapter that crystallizes all my work. Time to explain ergodicity, ruin and (again) rationality https://medium.com/incerto/the-logic-of-risk-taking-107bf41029d3 https://medium.com/incerto/the-logic-of-risk-taking-107bf410...
  - tomjakubowski 6y ago
    n.b.: Taleb in this chapter cites Ole Peters, who is the author of the featured article.
dools 6y ago
Microeconomics is meaningless unless everyone gets macroeconomics right
- offby37years 6y ago
  It is easier to macro bullshit than it is to micro bullshit.
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oli5679 6y ago
(1) their insight is not novel, they have independently reinvented Something that started with the Kelly Criterion https://en.m.wikipedia.org/wiki/Kelly_criterion https://en.m.wikipedia.org/wiki/Kelly_criterion (2) Expected utility theory makes no assumptions about ergodicity. In intertemporal setting, portfolio allocations maximising expected utility will chose something close to their metric as well as giving some insight into the split between investment and consumption. https://en.m.wikipedia.org/wiki/Intertemporal_choice https://en.m.wikipedia.org/wiki/Intertemporal_choice (3) with intertemporal analysis, the rate of discounting is important. This has been heavily discussed by economists and philosophers already. If you don't have heavy discounting, the future becomes much more important relative to the present than would be consistent with many people and government's actions.
- juskrey 6y ago
  Kelly here is the only way which is addressing the ruin, other two are (bad) tricks around initially wrong assumptions
  - kgwgk 6y ago
    Their result is not an alternative to expected utility maximization. It is expected (logarithmic) utility maximization.
  - hntrader 6y ago
    In practice, utility theory works well. Poker players adopt a utility function similar to u(x)=x and apply some very basic risk management heuristics (bankroll management) on top in order to handle ergodicity. Their whole thought process is centred on E[u(x)] (E[x]), and they have much more affinity for expected utility theory than the more "correct" Kelly. Professional investors adopt a slightly risk-averse u(x) (not quite ln(x) in my experience) and do just fine with that. Risk of ruin is managed again using simple practical heuristics, such as capping the maximum downside on each decision, and sizing up only when confident (in Kelly-like fashion - but very subjective). That it doesn't explicitly handle ergodicity isn't a huge flaw in practice. It's still a useful (although imperfect) mental model of what's going on in people's brains and offers some practical usefulness. It's also not a wrong assumption technically, because it's not claiming to model such phenomena, its claim is to model the utility of a single discrete choice.
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ReflectedImage 6y ago
I looked into this. The economists have really screwed up here. Basically, Expected Utility Theory (EUT) is wrong. It happens to give the right result by coincidence when you set the fudge factor U to log(wealth), which all economists do without any justification. Well EUT is corrected using the fudge factor, other parts of economics built using it are not. The nobel prize winning Prospect theory, when you correct the maths, dissolves away into nothing. The theory says people deviate away from the expected rational answer due to psychological reasons. It turns out people use the rational answer, the maths in Prospect theory is just wrong. Additionally, the famous St. Petersburg paradox isn't a paradox and has an exact answer. This is a pretty big blow for economics and the economists on social media aren't actually being mature about it.
- zwaps 6y ago
  Economists have since refuted the points above: https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x Read both sides!
  - ReflectedImage 6y ago
    I have, the economists completely failed to refute Ole Peters' points. As a Comp Sci PhD I'm telling you Ole Peters is correct.
    - zwaps 6y ago
      As a stats PhD, I am telling you Ole Peters is misunderstanding what EUT is ;-) EUT was developed by von Neumann, someone slightly familiar with ergodicity. It simply is not based on dynamics of out-of-equilibrium systems. Any such thing is an application that adds assumptions to the construct. Ergodicity is an obvious addition in the time domain, it is so obvious that the insight is not even new. However, Peters restricts the problem to a very simple dynamic gamble and then claims that all of economics must be wrong. The very first sentences of Peter's article already get this completely wrong. If you insist on his results, despite the quoted article, the most one can say is that the application of EUT to these problems is questionable. To put it in terms you may be more familiar with. It's like saying that Object Oriented Programming is "wrong", because Python doesn't work for my problem at hand.
eclat 6y ago
https://www.luca-dellanna.com/ergodicity/ https://www.luca-dellanna.com/ergodicity/ I found this to be an excellent overview of ergodicity and its implications.
smitty1e 6y ago
From undergraduate Control Systems theory those decades ago, the point of Ergodicity seems to be that, as long as we reach a steady state, we can ignore the transients. Which seems a great simplifying assumption where applicable.
bobcostas55 6y ago
A reply by some economists: "Economists’ views on the ergodicity problem" https://sci-hub.se/https://www.nature.com/articles/s41567-020-01106-x https://sci-hub.se/https://www.nature.com/articles/s41567-02...
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irotatori 6y ago
Reactions/rebuttals by economists here: https://old.reddit.com/r/badeconomics/comments/kcmtce/guy_with_a_degree_in_theoretical_physics_and_a/ https://old.reddit.com/r/badeconomics/comments/kcmtce/guy_wi...
- ReflectedImage 6y ago
  The issue is that the rebuttals are wrong. They have just objected for the sake of objecting.
ilaksh 6y ago
Is there a field that is similar to economics but is empirical and about building working systems rather than just theories, and incorporates recent high tech advances, and accounts for sustainability by incorporating things like finite resource tracking? Personally I think almost all of it is outdated and have no respect for economists. To back systems that perpetuate such gross inequity it seems most must have a very dated and reductionist Social Darwinist mindset. The first thing we need is to start to incorporate technology into society, such as by comprehensively tracking resources. Things like distributed technologies are the best starting point for this. Then when we use point systems for distributing control over resources (money) that should be a high tech system that is integrated with resource tracking and regulation. The way the current system works is kind of like if someone built an MMORPG and only included one stat --- money. Then, instead of server code for managing things, the powerful Economic Cult characters estimated what was happening and tried to regulate everything by controlling the spawn of gold coins.
- dash2 6y ago
  > Is there a field that is similar to economics but is empirical and about building working systems rather than just theories, and incorporates recent high tech advances, and accounts for sustainability by incorporating things like finite resource tracking? Yes. It's called "economics". Empiricism is absolutely central to modern economics. Here's the latest AER, the top journal.[1] 7 out of 8 articles are empirical. 4 out of 8 actually use the word "Evidence" in the title; by now this is practically a meme. Incorporates high tech advances: interested in machine learning? Here's an overview for you: https://www.nber.org/system/files/chapters/c14009/c14009.pdf https://www.nber.org/system/files/chapters/c14009/c14009.pdf Accounting for sustainability? First, environmental economics is an entire subfield. William Nordhaus won the Nobel prize[2] for estimating the costs of global warming, oh, and have you heard of the Stern Review? More broadly, the field of economics was famously defined as "Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses" (my italics). Sounds like it might be relevant to finite resource tracking. Lastly, I'm not sure why you think economists support the current level of inequality. I'd wager most don't. Maybe you've heard of Capital in the 21st Century, which put inequality squarely back on the political agenda. It's by Thomas Piketty, an economist. [1] https://www.aeaweb.org/issues/625 https://www.aeaweb.org/issues/625 [2] I beseech you not to tell me how It's Not Really The Nobel Prize. Everyone knows. Nobody cares.
penstroma 6y ago
I love reading critiques of articles by Hacker News readers in their fields of expertise, and finally feel I may be able to make a small contribution to the community. Below are some of my thoughts after a glance through the paper: 1. The critique of the article by Doctor et al. (linked from Ben Golub's Twitter) summarizes my thoughts succinctly. I am left wondering: if everyone used "ergodicity" as the basis of their decisions, doesn't this imply that, given some scenario with risk, everyone would make the same decision? But this is certainly not true. The author mentions that different people might care about "additive growth" vs. "geometric growth", but this is equivalent to using different functional forms of utility (e.g. CARA vs CRRA). Perhaps the author is saying that his ergodicity-derived decisions are "optimal"? But in what sense? It seems to me that his maximization of the growth rate is equivalent to using log utility. This result is well-known (see the Kelly criterion). 2. Ergodicity is covered in first-year graduate econometrics (at least where I was taught). See Hayashi Chapter 2. Perhaps not everyone reads it this way, but the tone of the article seems to suggest that this topic is completely foreign to economics. 3. There is a rich economics literature in decision theory. Savage's work on subjective expected utility shows that under a certain set of axioms of rationality, the decisions that a person makes can be completely captured by a subjective probability distribution and a personal utility function. The sentence "expected utility theory implicitly assumes that individuals can interact with copies of themselves, effectively in parallel universes" is completely misguided. 4. There are a number of well-known documented violations of expected utility (e.g. the Allais paradox). These represent challenges to the axioms of rationality. Nevertheless, the point of using expected utilities is to model human behavior, even if it is only approximate. From Rubinstein's great book "Economic Fables": "I remember the moment as a student when I realized that the models in economic theory do not assume that the decision maker consciously tries to maximize his preferences, but only assume that the behavior of a decision maker can be described as if he had maximized some objective function" (emphasis mine). 5. It is true that time-separable utility (usually with constant relative risk aversion, or CRRA) is often assumed for many mainstream models for tractability reasons. However, in recent years substantial progress has been made in extending utility to recursive preferences, e.g. Epstein-Zin. In fact, Epstein-Zin is essentially as tractable as the conventional time-separable CRRA utility, and allows for the separation of elasticities between risk and time. I expect that these more sophisticated preferences will soon be the norm. There are even stranger preferences in use, for example hyperbolic discounting. A whole field (behavioral economics) is founded on the notion that humans are not rational. The point is, lots of work has been done on generalizing utility functions. 6. I am not exactly sure what point the author is trying to make with Figure 2. This appears to be nothing more than a demonstration of Ito's Lemma (the convexity adjustment necessary for solving stochastic differential equations). In fact, the author mentions as much in the last paragraph of the third section. 7. My (ungenerous) interpretation of the experiment section: "Look, experiments calibrate the coefficient of relative risk aversion to be about 1 (log utility). And there doesn't seem to be much heterogeneity in risk aversions across people. This is consistent with my ergodicity-derived decisions, which is essentially log utility. Hence my model is supported!" (For reference, the usual calibrations I encounter for CRRA range from 1 to 5.) 8. Finally, the "Outlook" section. This section definitely rubbed me the wrong way. The author patronizes the entire field of economics, boasts of the ingenuity of his invention, and claims to somehow link together everything from the equity premium of the stock market to optimal monetary policy. It sounds too overconfident of itself and dismissive of others. References to works I expect to see are absent, and self-citations are abundant. After reading this paper, I was gently reminded of Baez's "Crackpot Index". I imagine that what I am feeling is similar to what a physics professor might feel after reading an idea for a perpetual motion machine. There is a mixture of correctness and sophistry, with a dash of illusions of grandeur. It is comprehensible enough to understand and reasonable-sounding enough to require some effort to criticize. Looking back, writing such a lengthy critique might not have been the best use of my time. I am rather surprised this paper was published. I am not familiar with Nature Physics, but based on this article alone, my regard for it is not high. In my opinion, this paper would not be sent out for refereeing, let only pass the referees, at any reputable economics or finance journal.
dash2 6y ago
I'm an academic in an economics department. This paper is trash. The published version of Peter Wakker et al's critique [1] is remarkably polite. You have to read their supplementary information [2] for the full, hilarious horror. Here are some juicy quotes to tempt you: "The EU [expected utility] value does not actually have to be realized or consumed in any sense.... However, Peters erroneously thinks that the EU value must actually be realized in some sense.... EU involves imagining, a priori, some outcomes that later may not have actually been received. This procedure involves imagining consequences that will never happen. But we do this every day, and such is the nature of every probabilistic decision. We do not need to believe in “parallel universes” or the existence of “multiverse clones"...." "A more fundamental problem in dynamic decisions is that we do not just maximize our entire wealth at the end of our life, but intermediate consumption patterns virtually always play a role. For nonquantitative outcomes, growth rates cannot even be defined. Dynamic questions as discussed here are central, for instance, in economic growth theory and in life-cycle consumption theory." "Peters suggests that economists should primarily study intertemporal processes, the topic of ergodic theory. For example, he suggests that risk attitudes and risky variance are not important and that interpersonal variations are not important, and then, in one blow, that neither is any economic theory." "Peters’ claims that, because of the ubiquity of time, we should always study intertemporal growth. Similarly, a risk theorist can claim that we always face uncertainties and, therefore, we should always study risk theories.... In the annotated bibliography Wakker (2020), the keyword “own small expertise = meaning of life” gives references to other authors falling victim to this ubiquity fallacy. ... and then there's the experiment. Oh boy, I'd forgotten that part! "Meder et al. applied expected utility and prospect theory in a way that we call static: they applied EU and PT to each choice in each round separately, as if it was the only choice made and as if intermediate outcomes were actually received. This static analysis is incorrect. The intermediate outcomes are not outcomes received and consumed by subjects." Translation: Sorry, kid, you failed your midterm. tl:dr; This is nonsense, an embarrassment to the authors, and an embarrassment to physics. Yet it pops up on Hacker News from time to time as a Deep Mathematical Takedown of Economists by Physicists!!!!... No.[3] [1] https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x [2] https://static-content.springer.com/esm/art%3A10.1038%2Fs41567-020-01106-x/MediaObjects/41567_2020_1106_MOESM1_ESM.pdf https://static-content.springer.com/esm/art%3A10.1038%2Fs415... [3] https://hn.algolia.com/?dateRange=all&page=0&prefix=false&query=ergodicity&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
Pyramus 6y ago
This is a fascinating example of 'if you have a hammer, all you see is nails'. It seems odd that this has been published at all - but then again, it is most likely to be published in journal that is not domain-specific. The author seems to miss that "economics" is a vast field spanning the whole spectrum from applied economics, over theoretical economics, mathematical finance, financial mathematics, to pure mathematics (with physicists working along the whole spectrum, so this is not a consequence of the author's background per se). He fails to engage at the right level. From a theoretical mathematician's point of view all models are wrong - they are just deductions from assumptions. From an applied economist's point of view are models are right - they explain some observed phenomena. Ergodicity is not a niche topic, most intermediate courses on stochastic processes will cover it. Will loosening an assumption about the properties of stochastic processes yield different, potentially better models? Maybe. Will it lead to a revolution in economic theory? Unlikely. Again, odd that this has been peer-reviewed. See also the reply here, which is rather damning [1] And the author's reply to the reply. [2] [1] https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x [2] https://www.nature.com/articles/s41567-020-01108-9 https://www.nature.com/articles/s41567-020-01108-9
- deleted 6y ago
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- xapata 6y ago
  While I am sympathetic to the author's claims, I was surprised to see that the author didn't "strong man" the prevailing economics views. Anyone trying to keep up with recent macroeconomics research could randomly sample papers and probably half would analyze only the equilibrium growth path as if it were a certainty that the equilibrium were stable.
- javitury 6y ago
  Thanks for sharing the economics' reply, I found it very interesting. All the good stuff is in the supplement. They argue that Peters' model produces extreme risk aversion in lotteries with (near) zero payoffs, and such risk aversion is not backed by empirical work or even by intuition. "Would a person ever prefer a process [A] that, after three rounds, diminishes wealth from US$10,000 to 0.5 cents over one [B] that yields a 99.9% chance of US$10,000,000 and otherwise US$0? Ergodic theory predicts [A] [... but] [v]irtually everyone will prefer B" That is, growth models don't behave well at or near zero. Personally, I enjoyed reading Peters solution to the St. Petersburg paradox and how the ergodicity framework is applied to economics in such a concise and intuitive manner. But I am reluctant to think that this ergodicity framework will completely remove the "psychological" aspects of economics. The utility of agents still needs to be accounted for. The ensembles that Peters describes are heterogeneous, and agents can derive different amounts of utility even if wealth or growth rates are equal. Think about insurance.
fraserphysics 6y ago
Chapter 6 of "Elements of Information Theory" by Cover and Thomas is "Gambling and data compression". It explains that maximizing expected utility almost always leads to ruin. I didn't believe it when I first read it. Of course it is exactly correct. I reccomend it.
Xcelerate 6y ago
Could someone summarize what everyone in the comments is arguing about in less technical terms? I don’t have a background in economics but do have a background with physics.
- H8crilA 6y ago
  It's some hilarious turf/flame war. The paper itself is pretty interesting if you know some maths and haven't thought about non-linear utility functions. You can also read that "original" paper by Bernoulli, he has some simple examples there (for example why does it make sense to buy insurance despite it having negative expected payoff, he brings the example of ship cargo insurance but it applies to any kind of insurance really). EDIT: Daniel Bernoulli's paper: https://www.semanticscholar.org/paper/Exposition-of-a-New-Theory-on-the-Measurement-of-Bernoulli/ef512f15aa1c294c7575aa329a7fecd80be6633b https://www.semanticscholar.org/paper/Exposition-of-a-New-Th...
  - rmbeard 6y ago
    Exactly.
- fallingfrog 6y ago
  I think what’s going on is that “hard sciences” people in physics etc have a strong feeling that most of economics (and behavioral science and psychology) is bunk, given that economists in particular seem to have all sorts of mutually contradictory theories, are always making predictions that turn out to be wildly wrong, and seem to disagree with one another on basic facts. This paper gives them ammunition to support these feelings that the emperor has no clothes. I am not qualified to judge whether those feelings are correct however.
- ReflectedImage 6y ago
  Economists have been using ensemble average where they should of being using time average. Using the wrong type of average mildly screws up everything in very subtle ways as you can imagine. A lot of the important results in the field including one that got a nobel prize turn out to be wrong. The economists are responding to this in a very mature way and have told Ole Peters "he can go kick a rock".
dellannaluca 6y ago
Here is a short introduction to ergodicity in non-mathematical terms: https://twitter.com/DellAnnaLuca/status/1339621378765537282?s=20 https://twitter.com/DellAnnaLuca/status/1339621378765537282?...
sjg007 6y ago
I see the stock market as an interesting non-linearity that can decouple the value of a company from its monetary performance. Then there is the idea of technology and transformation which can happen in a short amount of time and be bigger than you expect. The market, like the Universe continues to expand and I guess smaller ones go through collapse from time to time but unlike physics we don't have universal forces defining trajectories.
m0rc 6y ago
I remember the first time I heard someone (N. Taleb) expressing a negative opinion about economists because they were not "getting" the concept of ergodicity (in addition to other issues not relevant for this discussion). Initially, I didn't get the idea either. At some later point in time, I read Kelly's and Gellman's papers [1][2] with some effort, and although I was able to follow the arguments I didn't found anything surprising. That is, I didn't get the idea nor the implications. It was during the reading of O. Peters and A. Adamou "Ergodicity Economics" [3] that I better understood the idea. Imagine a basic gamble that repeats indefinitely. In each iteration and with equal probability, the player can win 60% more or lose 40% of the initial capital. For this gamble, the ensemble average (aka expectation) of the player's wealth one step ahead is simply 1/2 x 160% + 1/2 x 60% = 110%. A good gamble, right? However, the time average of the same step (i.e. the average gain of a single individual playing) is sqrt((1.6)x(0.6)) x 100 = 98%. So, the individual looses money with time. This was quite surprising to me although obvious a posteriori given that the multiplicative stochastic process is not ergodic. In other words, this simple gamble shows that the expectation does not have the intuitive meaning we sometimes assign to it specially for some repetitive gambles. In other words. the time and ensemble average differ in general for non-ergodic stochastic processes and in particular for multiplicative stochastic processes (note that for additive processes the expectation of the wealth increment can be used). And here comes the important implication... Given that several economic processes can be modeled as a first approximation as multiplicative random processes (e.g. stock markets, real investments, GDP growth, etc.), it is not a rational strategy to use the ensemble average (aka expectation of wealth increment) to take some economic decisions. There are several implications of the above simple fact including the optimality of the Kelly criterion; the optimal leverage being below 1 in all cases involving multiplicative processes; the incorrect measurement of inequality; or the known inadequacy of the average income, instead of the median, to measure the average well-being to name a few. A possible controversial corollary of the above is that the concept of utility is unnecessary and incorrect as a first approximation to the micro-economic behaviour. Instead an ergodic measurable should be used. In the specific cases of multiplicative stochastic processes the difference of the walth logarithm is ergodic and a rational decision maker should use it to optimize his wealth. This will require further debate within the scientific community because it is not clear that what is an optimal decision is a good model for the people's behavior. In any case, if the expected utility is not optimal, it also does not make much sense as a model for the Homo Economicus. In any case, I really recommend reading instead of rushing to conclusions [3]. [1] J. L. Kelly, A new interpretation of information rate. Bell System Technical Journal, 35 (1956), 917-926. [2] O. Peters and M. Gell-Mann. Evaluating gambles using dynamics. Chaos, 26:23103, February 2016. [3] Peters, Ole, and Alexander Adamou. "Ergodicity economics." London Mathematical Laboratory (2018).

148 points by ali92hm 6y ago

wrnr 6y ago

Talk by the same author for those that don't like to read: Time for a change - https://www.youtube.com/watch?v=f1vXAHGIpfc https://www.youtube.com/watch?v=f1vXAHGIpfc

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RobertoG 6y ago
They have a webpage: https://ergodicityeconomics.com/ https://ergodicityeconomics.com/

laszlosandor 6y ago

Time to read! https://twitter.com/ben_golub/status/1338175642932715520?s=21 https://twitter.com/ben_golub/status/1338175642932715520?s=2...

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juskrey 6y ago
Many words about how economics is like physics, hence Peters makes a terrible insults to generations of respectful academics. And not a single word about how they are still missing the ruin problem, and how ergodicity is a dead simple and exact answer to it
- drdeca 6y ago
  The main article doesn't seem to refer to "the ruin problem" either. What is that?
  - juskrey 6y ago
    Ole should repeat it on more occasions, since this is what it's all about: economic unit is not an average of the same imaginary economic units following different paths, some of which can end in a bankruptcy. Instead single bankruptcy will end the whole process, this is a ruin problem. That is economic unit is an average on its own timeline, not space.
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  - nullc 6y ago
    #!/usr/bin/python3 import random #100 people start with $100 balances=[100]*100 #They take 10000 bets with an _expected_ return of 1.25x. # ... so they should end up with ~1.2e1000 at the end... for i in range(10000): balances=[0 if x<=0 else random.choice([x*2,x//2]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0]))
    - ulucs 6y ago
      > # ... so they should end up with ~1.2e1000 at the end... Who has ever claimed this? Also, people end up with zero because you are doing integer division in your code (ie the simplified expected return is wrong). Here are my results with 100 bets, and 10000 bet takers. The average return is also on the upward trend, but not really close since CLT doesn't really apply to this distribution: >>> sum(balances)/1000000 24546192.840913434 >>> print(len([x for x in balances if x<=100])) 5426 >>> print(len([x for x in balances if x>=100])) 5381 >>> print(len([x for x in balances if x>100])) 4574
      - nullc 6y ago
        Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring division: #!/usr/bin/sage import random balances=[Rational(100)]*100 for i in range(10000): balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0])) The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it. One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing. And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.
- wazoox 6y ago
  Economics is not like physics at all. It's a social science, rooted in many social assumptions and compromises and power relationships between human beings and groups. Most attempts to negate this are just tortuous ways to justify the current power structure.
  - imtringued 6y ago
    There is a small nugget that is as hard as physics. Namely the tools can be analyzed in their theoretical performance. But economics is deeply tied to politics. What type of economy you have is entirely dependent on current leadership. It's the government that sets the basic foundation and rules upon which the economy is built. Some governments decided to go to either extreme. Communism or capitalism. There is a price equilibrium, assuming one is allowed to exist, which is dependent on your government, but where exactly it lies is also entirely dependent on the laws the government set. If the government bans garbage disposal in rivers then it would be completely unreasonable to insist that the equilibrium price should stay the same. By this same logic if there is an inherent injustice or imbalance it exists in the laws the government created. One prominent example would be the central bank flooding the market in a way that benefits existing asset holders, one could have done the exact opposite as well or maybe even done a little of both. It's not a question of which is the right action, the question is "What kind of economy do you want?" and the central bank has spoken.
    - wazoox 6y ago
      Precisely. "What kind of economy do you want?" is a political question, that has no definite, scientific answer. And more restrictive economic questions, very often, also are political questions that should be democratically debated and decided, but are instead presented as "scientific" in nature, with the pretension that "we should do as our experts said" (whose experts exactly?).
ssivark 6y ago
That Twitter thread is tautological trash, to put it politely. It seems more interested in protecting turf than directly critiquing (or even understanding) Ole Peters’ central point. It is absolutely silly, bordering shitposting, to respond to a claim about subtle/hidden assumptions by claiming: > Expected utility theory makes 4 assumptions, which are stated precisely and concisely in every graduate textbook. Ergodicity is not among them. when the whole point is that the conventional economics literature might have ignored a subtlety.
- QuesnayJr 6y ago
  It's not. You can read the proofs to see that they aren't missing a step. If you don't want to do that, I can give some indirect evidence. The "conventional economics literature" begins with a theorem of von Neumann and Morganstern, published in 1944. This is the John von Neumann of math and physics fame. In particular, von Neumann was one of the architects of ergodic theory. He proved the mean ergodic theorem all the way back in 1932. It would be pretty surprising indeed if it was von Neumann who missed the subtlety.
  - ReflectedImage 6y ago
    It would be more correct to say economists misinterpreted what von Neumann said.
    - QuesnayJr 6y ago
      They didn't, though. Look at von Neumann and Morganstern's "Theory of Games and Economic Behavior". There's nothing in there about time-series averages. It's a theory of games that you might play only once.
      - ReflectedImage 6y ago
        It's fairly obvious that in the real world time does play a role. This may shock you but theories advance over time. There isn't a holy paper which can never be improved on (at least not in sensible research fields).

tribler 6y ago

"We therefore have reason to be optimistic about the future of economic theory."

ncmncm 6y ago

This is important. It is disgraceful that economics failed to arrive at this result at any time in the past century.

dataflow 6y ago
What result are you referring to, exactly?
QuesnayJr 6y ago
And what result is that? Most of this is well-known. Ergodicity is a concept that's covered in econometrics classes. "When are time averages the averages of the underlying probability distribution?" is the first topic in time series. Honestly, the whole approach is a step back. People discussed these ideas back when Kelly first published the Kelly rule, and the conclusion is that most people are not that aggressive in their investment decisions. People still study it, though, (it's called the growth optimal portfolio), and its properties are well-known. Peters also sneaks in a second assumption, which is that the growth rate of wealth is ergodic. Is it? That's not clear to me at all.
- ReflectedImage 6y ago
  "most people are not that aggressive in their investment decisions" That's because Kelly's criterion is a special case of Ole Peters, where Kelly's is a very aggressive option. There are other criterion that can be used, which are not so aggressive. Ole Peters lists the class of functions that can be used in his paper. So basically economics has rejected it for the wrong reason.
  - QuesnayJr 6y ago
    As far as I can tell, he lists wealth, and log wealth as the two possible criteria. If there are others, I missed them. If you try to match a power utility model with stock market data, to match prices on the stock market, you would reject both the additive model (eta = 0) and the multiplicative model (eta = 1), in favor of an eta greater than 10. This is known as the equity premium puzzle. The thrust of research over the past 30 years in explaining stock prices has been to reject both Peters' models, and expected utility in general. People build their entire careers on investigating alternatives. There are hundreds of experiments to explain, plus all of the real-world data. It turns out that explaining all of this with one unified model is hard.

QuesnayJr 6y ago

I don't get what people find so exciting about his papers, which I find borderline troll-ish. We know that people in general don't reason the way he says he does. If people only cared about log of wealth, they would take much more risks than they do. If everyone did it, the return on stocks would be much lower than it is, because everyone would regard stocks as a great deal despite the volatility.

kgwgk 6y ago
You may have seen this already: https://arxiv.org/abs/1101.4548 https://arxiv.org/abs/1101.4548 Funny stuff. They predict that in aggregate 100% of the wealth is invested in stocks and investing more than that would be suboptimal: the optimal leverage is 1. They "submit the hypothesis to a rigorous test" and find that the optimal leverage for the S&P 500 is around 1, given its volatility. There is a small problem with their rigorous test. They forgot to include dividends: "a real investment in the S&P500 outgrew federal deposits at only 2.0% p.a". Including dividends would bring the optimal leverage to 2 or 3. But that's ok. It's close enough to 1 for them, apparently. Even better: ignoring dividends was not so wrong anyway because the S&P 500 overestimates the return of a real equity investment due to survivorship bias. "The S&P500 is an index of five hundred large companies, listed publicly in the United States. We use it as a proxy for a generic diversified investment in US stocks, but we note some caveats. Firstly, the index does not account for dividends paid to stockholders. This means it will tend to underestimate the performance of a real investment. Secondly, the index suffers from survivorship bias, representing a portfolio of the largest and most successful companies in the US, in which less successful companies are routinely replaced. This acts in the opposite direction to the first caveat."
- QuesnayJr 6y ago
  I hadn't seen that. Thanks.

drdeca 6y ago

I feel that this downplays the justification for theories of expected utility too much? But I still want to keep reading to see where they're going with this. Ok, like, it says that modeling people as trying to maximize expected utility, is like assuming something as if one is interacting with paralell universe copies of onseself. But, surely the author must be familiar with the Von Neumann–Morgenstern utility theorem? It complains that when people fail to act according to the theories, that the people are considered to be irrational, rather than amending the theories. While it is of course true that theories need to be made to account for how people actually behave, it seems to me that people failing to satisfy the vNM axioms, really is a way in which people fail to live up to the correct ideal of a rational agent. Well, maybe for it to make sense, instead there should be a formalization of like, a compute-limited approximation of following the vNM axioms, maybe throw in a dash of sub-agent stuff, and a few things along those lines. Hmm. Ok, well, if this makes better predictions of how people behave, that is valuable. Though, it would raise the question of "why?".

zwaps 6y ago
It's really mind boggling if you know the original proofs my Neumann-Morgenstein or Savage for that matter. In his article, Peters immediately rushes into the time domain, whereas the time domain doesn't exist at all in EUT. I feel like Peters could have made a valid point about the application of dynamic EUT, but he severely over-claims the problem he sees. To refute EUT, Peters had to start with one set of EUT axioms. He clearly doesn't want to do that. We can guess why.
- ReflectedImage 6y ago
  Ole Peters has addressed this. He had a study of real people done, which shows that real people make decisions using the time domain. The behaviour of real people matches Ole Peters maths but not EUT. This means that EUT does not apply to the real world, which makes EUT a pointless theory.
  - QuesnayJr 6y ago
    Even that isn't new. There are hundreds of experiments that point out the limitations of EU. If you're looking for a reason to reject EU, you didn't need to wait until now. Allais published his paradox in 1953. If Peters wants to propose an alternate theory, he needs to explain all of this existing evidence. For example, he needs to explain why historically the return on stocks is so high. If people only cared about the logarithm of wealth, they would hold almost entirely stocks and very little bonds. They would take their weekly paycheck and deposit it directly into their Robinhood account. (And everyone would have a brokerage account.)

timdaub 6y ago

Thanks for posting. I had read Antifragile in parts but I had never heard of Ergodicity. But it's a great technical term to understand! I looked online and found this post that explained it well: https://taylorpearson.me/ergodicity/ https://taylorpearson.me/ergodicity/

sn41 6y ago
Ergodic theorist (occasional) here. Ergodic theory is basically studying situations in which the time average of (almost every) trajectory equals the space average of the system. This is a widely studied area in dynamical systems. I am squeamish about such popular accounts. An old account which is readable even today, is by Birkhoff [1]. About Kelly-Bernoulli criterion, the readable account is the book [2]. [1] https://doi.org/10.1080/00029890.1942.11991212 https://doi.org/10.1080/00029890.1942.11991212 [2] "Fortune's Formula" by William Poundstone. https://archive.org/details/fortunesformulau00poun https://archive.org/details/fortunesformulau00poun
ReflectedImage 6y ago
Calling it Ergodicity Economics is a bit confusing. Existing economics is ergodicity. Ole Peters is claiming that the ergodicity assumption in economics is false. His corrected version of economics should be called Non-Ergodicity Economics.
hfkgktkrlfk 6y ago
Taleb did write about ergodicity: > A central chapter that crystallizes all my work. Time to explain ergodicity, ruin and (again) rationality https://medium.com/incerto/the-logic-of-risk-taking-107bf41029d3 https://medium.com/incerto/the-logic-of-risk-taking-107bf410...
- tomjakubowski 6y ago
  n.b.: Taleb in this chapter cites Ole Peters, who is the author of the featured article.

dools 6y ago

Microeconomics is meaningless unless everyone gets macroeconomics right

offby37years 6y ago
It is easier to macro bullshit than it is to micro bullshit.
- deleted 6y ago
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oli5679 6y ago

(1) their insight is not novel, they have independently reinvented Something that started with the Kelly Criterion https://en.m.wikipedia.org/wiki/Kelly_criterion https://en.m.wikipedia.org/wiki/Kelly_criterion (2) Expected utility theory makes no assumptions about ergodicity. In intertemporal setting, portfolio allocations maximising expected utility will chose something close to their metric as well as giving some insight into the split between investment and consumption. https://en.m.wikipedia.org/wiki/Intertemporal_choice https://en.m.wikipedia.org/wiki/Intertemporal_choice (3) with intertemporal analysis, the rate of discounting is important. This has been heavily discussed by economists and philosophers already. If you don't have heavy discounting, the future becomes much more important relative to the present than would be consistent with many people and government's actions.

juskrey 6y ago
Kelly here is the only way which is addressing the ruin, other two are (bad) tricks around initially wrong assumptions
- kgwgk 6y ago
  Their result is not an alternative to expected utility maximization. It is expected (logarithmic) utility maximization.
- hntrader 6y ago
  In practice, utility theory works well. Poker players adopt a utility function similar to u(x)=x and apply some very basic risk management heuristics (bankroll management) on top in order to handle ergodicity. Their whole thought process is centred on E[u(x)] (E[x]), and they have much more affinity for expected utility theory than the more "correct" Kelly. Professional investors adopt a slightly risk-averse u(x) (not quite ln(x) in my experience) and do just fine with that. Risk of ruin is managed again using simple practical heuristics, such as capping the maximum downside on each decision, and sizing up only when confident (in Kelly-like fashion - but very subjective). That it doesn't explicitly handle ergodicity isn't a huge flaw in practice. It's still a useful (although imperfect) mental model of what's going on in people's brains and offers some practical usefulness. It's also not a wrong assumption technically, because it's not claiming to model such phenomena, its claim is to model the utility of a single discrete choice.

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ReflectedImage 6y ago

I looked into this. The economists have really screwed up here. Basically, Expected Utility Theory (EUT) is wrong. It happens to give the right result by coincidence when you set the fudge factor U to log(wealth), which all economists do without any justification. Well EUT is corrected using the fudge factor, other parts of economics built using it are not. The nobel prize winning Prospect theory, when you correct the maths, dissolves away into nothing. The theory says people deviate away from the expected rational answer due to psychological reasons. It turns out people use the rational answer, the maths in Prospect theory is just wrong. Additionally, the famous St. Petersburg paradox isn't a paradox and has an exact answer. This is a pretty big blow for economics and the economists on social media aren't actually being mature about it.

zwaps 6y ago
Economists have since refuted the points above: https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x Read both sides!
- ReflectedImage 6y ago
  I have, the economists completely failed to refute Ole Peters' points. As a Comp Sci PhD I'm telling you Ole Peters is correct.
  - zwaps 6y ago
    As a stats PhD, I am telling you Ole Peters is misunderstanding what EUT is ;-) EUT was developed by von Neumann, someone slightly familiar with ergodicity. It simply is not based on dynamics of out-of-equilibrium systems. Any such thing is an application that adds assumptions to the construct. Ergodicity is an obvious addition in the time domain, it is so obvious that the insight is not even new. However, Peters restricts the problem to a very simple dynamic gamble and then claims that all of economics must be wrong. The very first sentences of Peter's article already get this completely wrong. If you insist on his results, despite the quoted article, the most one can say is that the application of EUT to these problems is questionable. To put it in terms you may be more familiar with. It's like saying that Object Oriented Programming is "wrong", because Python doesn't work for my problem at hand.

eclat 6y ago

https://www.luca-dellanna.com/ergodicity/ https://www.luca-dellanna.com/ergodicity/ I found this to be an excellent overview of ergodicity and its implications.

smitty1e 6y ago

From undergraduate Control Systems theory those decades ago, the point of Ergodicity seems to be that, as long as we reach a steady state, we can ignore the transients. Which seems a great simplifying assumption where applicable.

bobcostas55 6y ago

A reply by some economists: "Economists’ views on the ergodicity problem" https://sci-hub.se/https://www.nature.com/articles/s41567-020-01106-x https://sci-hub.se/https://www.nature.com/articles/s41567-02...

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irotatori 6y ago

Reactions/rebuttals by economists here: https://old.reddit.com/r/badeconomics/comments/kcmtce/guy_with_a_degree_in_theoretical_physics_and_a/ https://old.reddit.com/r/badeconomics/comments/kcmtce/guy_wi...

ReflectedImage 6y ago
The issue is that the rebuttals are wrong. They have just objected for the sake of objecting.

ilaksh 6y ago

Is there a field that is similar to economics but is empirical and about building working systems rather than just theories, and incorporates recent high tech advances, and accounts for sustainability by incorporating things like finite resource tracking? Personally I think almost all of it is outdated and have no respect for economists. To back systems that perpetuate such gross inequity it seems most must have a very dated and reductionist Social Darwinist mindset. The first thing we need is to start to incorporate technology into society, such as by comprehensively tracking resources. Things like distributed technologies are the best starting point for this. Then when we use point systems for distributing control over resources (money) that should be a high tech system that is integrated with resource tracking and regulation. The way the current system works is kind of like if someone built an MMORPG and only included one stat --- money. Then, instead of server code for managing things, the powerful Economic Cult characters estimated what was happening and tried to regulate everything by controlling the spawn of gold coins.

dash2 6y ago
> Is there a field that is similar to economics but is empirical and about building working systems rather than just theories, and incorporates recent high tech advances, and accounts for sustainability by incorporating things like finite resource tracking? Yes. It's called "economics". Empiricism is absolutely central to modern economics. Here's the latest AER, the top journal.[1] 7 out of 8 articles are empirical. 4 out of 8 actually use the word "Evidence" in the title; by now this is practically a meme. Incorporates high tech advances: interested in machine learning? Here's an overview for you: https://www.nber.org/system/files/chapters/c14009/c14009.pdf https://www.nber.org/system/files/chapters/c14009/c14009.pdf Accounting for sustainability? First, environmental economics is an entire subfield. William Nordhaus won the Nobel prize[2] for estimating the costs of global warming, oh, and have you heard of the Stern Review? More broadly, the field of economics was famously defined as "Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses" (my italics). Sounds like it might be relevant to finite resource tracking. Lastly, I'm not sure why you think economists support the current level of inequality. I'd wager most don't. Maybe you've heard of Capital in the 21st Century, which put inequality squarely back on the political agenda. It's by Thomas Piketty, an economist. [1] https://www.aeaweb.org/issues/625 https://www.aeaweb.org/issues/625 [2] I beseech you not to tell me how It's Not Really The Nobel Prize. Everyone knows. Nobody cares.

penstroma 6y ago

I love reading critiques of articles by Hacker News readers in their fields of expertise, and finally feel I may be able to make a small contribution to the community. Below are some of my thoughts after a glance through the paper: 1. The critique of the article by Doctor et al. (linked from Ben Golub's Twitter) summarizes my thoughts succinctly. I am left wondering: if everyone used "ergodicity" as the basis of their decisions, doesn't this imply that, given some scenario with risk, everyone would make the same decision? But this is certainly not true. The author mentions that different people might care about "additive growth" vs. "geometric growth", but this is equivalent to using different functional forms of utility (e.g. CARA vs CRRA). Perhaps the author is saying that his ergodicity-derived decisions are "optimal"? But in what sense? It seems to me that his maximization of the growth rate is equivalent to using log utility. This result is well-known (see the Kelly criterion). 2. Ergodicity is covered in first-year graduate econometrics (at least where I was taught). See Hayashi Chapter 2. Perhaps not everyone reads it this way, but the tone of the article seems to suggest that this topic is completely foreign to economics. 3. There is a rich economics literature in decision theory. Savage's work on subjective expected utility shows that under a certain set of axioms of rationality, the decisions that a person makes can be completely captured by a subjective probability distribution and a personal utility function. The sentence "expected utility theory implicitly assumes that individuals can interact with copies of themselves, effectively in parallel universes" is completely misguided. 4. There are a number of well-known documented violations of expected utility (e.g. the Allais paradox). These represent challenges to the axioms of rationality. Nevertheless, the point of using expected utilities is to model human behavior, even if it is only approximate. From Rubinstein's great book "Economic Fables": "I remember the moment as a student when I realized that the models in economic theory do not assume that the decision maker consciously tries to maximize his preferences, but only assume that the behavior of a decision maker can be described as if he had maximized some objective function" (emphasis mine). 5. It is true that time-separable utility (usually with constant relative risk aversion, or CRRA) is often assumed for many mainstream models for tractability reasons. However, in recent years substantial progress has been made in extending utility to recursive preferences, e.g. Epstein-Zin. In fact, Epstein-Zin is essentially as tractable as the conventional time-separable CRRA utility, and allows for the separation of elasticities between risk and time. I expect that these more sophisticated preferences will soon be the norm. There are even stranger preferences in use, for example hyperbolic discounting. A whole field (behavioral economics) is founded on the notion that humans are not rational. The point is, lots of work has been done on generalizing utility functions. 6. I am not exactly sure what point the author is trying to make with Figure 2. This appears to be nothing more than a demonstration of Ito's Lemma (the convexity adjustment necessary for solving stochastic differential equations). In fact, the author mentions as much in the last paragraph of the third section. 7. My (ungenerous) interpretation of the experiment section: "Look, experiments calibrate the coefficient of relative risk aversion to be about 1 (log utility). And there doesn't seem to be much heterogeneity in risk aversions across people. This is consistent with my ergodicity-derived decisions, which is essentially log utility. Hence my model is supported!" (For reference, the usual calibrations I encounter for CRRA range from 1 to 5.) 8. Finally, the "Outlook" section. This section definitely rubbed me the wrong way. The author patronizes the entire field of economics, boasts of the ingenuity of his invention, and claims to somehow link together everything from the equity premium of the stock market to optimal monetary policy. It sounds too overconfident of itself and dismissive of others. References to works I expect to see are absent, and self-citations are abundant. After reading this paper, I was gently reminded of Baez's "Crackpot Index". I imagine that what I am feeling is similar to what a physics professor might feel after reading an idea for a perpetual motion machine. There is a mixture of correctness and sophistry, with a dash of illusions of grandeur. It is comprehensible enough to understand and reasonable-sounding enough to require some effort to criticize. Looking back, writing such a lengthy critique might not have been the best use of my time. I am rather surprised this paper was published. I am not familiar with Nature Physics, but based on this article alone, my regard for it is not high. In my opinion, this paper would not be sent out for refereeing, let only pass the referees, at any reputable economics or finance journal.

dash2 6y ago

I'm an academic in an economics department. This paper is trash. The published version of Peter Wakker et al's critique [1] is remarkably polite. You have to read their supplementary information [2] for the full, hilarious horror. Here are some juicy quotes to tempt you: "The EU [expected utility] value does not actually have to be realized or consumed in any sense.... However, Peters erroneously thinks that the EU value must actually be realized in some sense.... EU involves imagining, a priori, some outcomes that later may not have actually been received. This procedure involves imagining consequences that will never happen. But we do this every day, and such is the nature of every probabilistic decision. We do not need to believe in “parallel universes” or the existence of “multiverse clones"...." "A more fundamental problem in dynamic decisions is that we do not just maximize our entire wealth at the end of our life, but intermediate consumption patterns virtually always play a role. For nonquantitative outcomes, growth rates cannot even be defined. Dynamic questions as discussed here are central, for instance, in economic growth theory and in life-cycle consumption theory." "Peters suggests that economists should primarily study intertemporal processes, the topic of ergodic theory. For example, he suggests that risk attitudes and risky variance are not important and that interpersonal variations are not important, and then, in one blow, that neither is any economic theory." "Peters’ claims that, because of the ubiquity of time, we should always study intertemporal growth. Similarly, a risk theorist can claim that we always face uncertainties and, therefore, we should always study risk theories.... In the annotated bibliography Wakker (2020), the keyword “own small expertise = meaning of life” gives references to other authors falling victim to this ubiquity fallacy. ... and then there's the experiment. Oh boy, I'd forgotten that part! "Meder et al. applied expected utility and prospect theory in a way that we call static: they applied EU and PT to each choice in each round separately, as if it was the only choice made and as if intermediate outcomes were actually received. This static analysis is incorrect. The intermediate outcomes are not outcomes received and consumed by subjects." Translation: Sorry, kid, you failed your midterm. tl:dr; This is nonsense, an embarrassment to the authors, and an embarrassment to physics. Yet it pops up on Hacker News from time to time as a Deep Mathematical Takedown of Economists by Physicists!!!!... No.[3] [1] https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x [2] https://static-content.springer.com/esm/art%3A10.1038%2Fs41567-020-01106-x/MediaObjects/41567_2020_1106_MOESM1_ESM.pdf https://static-content.springer.com/esm/art%3A10.1038%2Fs415... [3] https://hn.algolia.com/?dateRange=all&page=0&prefix=false&query=ergodicity&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

Pyramus 6y ago

This is a fascinating example of 'if you have a hammer, all you see is nails'. It seems odd that this has been published at all - but then again, it is most likely to be published in journal that is not domain-specific. The author seems to miss that "economics" is a vast field spanning the whole spectrum from applied economics, over theoretical economics, mathematical finance, financial mathematics, to pure mathematics (with physicists working along the whole spectrum, so this is not a consequence of the author's background per se). He fails to engage at the right level. From a theoretical mathematician's point of view all models are wrong - they are just deductions from assumptions. From an applied economist's point of view are models are right - they explain some observed phenomena. Ergodicity is not a niche topic, most intermediate courses on stochastic processes will cover it. Will loosening an assumption about the properties of stochastic processes yield different, potentially better models? Maybe. Will it lead to a revolution in economic theory? Unlikely. Again, odd that this has been peer-reviewed. See also the reply here, which is rather damning [1] And the author's reply to the reply. [2] [1] https://www.nature.com/articles/s41567-020-01106-x https://www.nature.com/articles/s41567-020-01106-x [2] https://www.nature.com/articles/s41567-020-01108-9 https://www.nature.com/articles/s41567-020-01108-9

deleted 6y ago
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xapata 6y ago
While I am sympathetic to the author's claims, I was surprised to see that the author didn't "strong man" the prevailing economics views. Anyone trying to keep up with recent macroeconomics research could randomly sample papers and probably half would analyze only the equilibrium growth path as if it were a certainty that the equilibrium were stable.
javitury 6y ago
Thanks for sharing the economics' reply, I found it very interesting. All the good stuff is in the supplement. They argue that Peters' model produces extreme risk aversion in lotteries with (near) zero payoffs, and such risk aversion is not backed by empirical work or even by intuition. "Would a person ever prefer a process [A] that, after three rounds, diminishes wealth from US$10,000 to 0.5 cents over one [B] that yields a 99.9% chance of US$10,000,000 and otherwise US$0? Ergodic theory predicts [A] [... but] [v]irtually everyone will prefer B" That is, growth models don't behave well at or near zero. Personally, I enjoyed reading Peters solution to the St. Petersburg paradox and how the ergodicity framework is applied to economics in such a concise and intuitive manner. But I am reluctant to think that this ergodicity framework will completely remove the "psychological" aspects of economics. The utility of agents still needs to be accounted for. The ensembles that Peters describes are heterogeneous, and agents can derive different amounts of utility even if wealth or growth rates are equal. Think about insurance.

fraserphysics 6y ago

Chapter 6 of "Elements of Information Theory" by Cover and Thomas is "Gambling and data compression". It explains that maximizing expected utility almost always leads to ruin. I didn't believe it when I first read it. Of course it is exactly correct. I reccomend it.

Xcelerate 6y ago

Could someone summarize what everyone in the comments is arguing about in less technical terms? I don’t have a background in economics but do have a background with physics.

H8crilA 6y ago
It's some hilarious turf/flame war. The paper itself is pretty interesting if you know some maths and haven't thought about non-linear utility functions. You can also read that "original" paper by Bernoulli, he has some simple examples there (for example why does it make sense to buy insurance despite it having negative expected payoff, he brings the example of ship cargo insurance but it applies to any kind of insurance really). EDIT: Daniel Bernoulli's paper: https://www.semanticscholar.org/paper/Exposition-of-a-New-Theory-on-the-Measurement-of-Bernoulli/ef512f15aa1c294c7575aa329a7fecd80be6633b https://www.semanticscholar.org/paper/Exposition-of-a-New-Th...
- rmbeard 6y ago
  Exactly.
fallingfrog 6y ago
I think what’s going on is that “hard sciences” people in physics etc have a strong feeling that most of economics (and behavioral science and psychology) is bunk, given that economists in particular seem to have all sorts of mutually contradictory theories, are always making predictions that turn out to be wildly wrong, and seem to disagree with one another on basic facts. This paper gives them ammunition to support these feelings that the emperor has no clothes. I am not qualified to judge whether those feelings are correct however.
ReflectedImage 6y ago
Economists have been using ensemble average where they should of being using time average. Using the wrong type of average mildly screws up everything in very subtle ways as you can imagine. A lot of the important results in the field including one that got a nobel prize turn out to be wrong. The economists are responding to this in a very mature way and have told Ole Peters "he can go kick a rock".

dellannaluca 6y ago

Here is a short introduction to ergodicity in non-mathematical terms: https://twitter.com/DellAnnaLuca/status/1339621378765537282?s=20 https://twitter.com/DellAnnaLuca/status/1339621378765537282?...

sjg007 6y ago

I see the stock market as an interesting non-linearity that can decouple the value of a company from its monetary performance. Then there is the idea of technology and transformation which can happen in a short amount of time and be bigger than you expect. The market, like the Universe continues to expand and I guess smaller ones go through collapse from time to time but unlike physics we don't have universal forces defining trajectories.

m0rc 6y ago

I remember the first time I heard someone (N. Taleb) expressing a negative opinion about economists because they were not "getting" the concept of ergodicity (in addition to other issues not relevant for this discussion). Initially, I didn't get the idea either. At some later point in time, I read Kelly's and Gellman's papers [1][2] with some effort, and although I was able to follow the arguments I didn't found anything surprising. That is, I didn't get the idea nor the implications. It was during the reading of O. Peters and A. Adamou "Ergodicity Economics" [3] that I better understood the idea. Imagine a basic gamble that repeats indefinitely. In each iteration and with equal probability, the player can win 60% more or lose 40% of the initial capital. For this gamble, the ensemble average (aka expectation) of the player's wealth one step ahead is simply 1/2 x 160% + 1/2 x 60% = 110%. A good gamble, right? However, the time average of the same step (i.e. the average gain of a single individual playing) is sqrt((1.6)x(0.6)) x 100 = 98%. So, the individual looses money with time. This was quite surprising to me although obvious a posteriori given that the multiplicative stochastic process is not ergodic. In other words, this simple gamble shows that the expectation does not have the intuitive meaning we sometimes assign to it specially for some repetitive gambles. In other words. the time and ensemble average differ in general for non-ergodic stochastic processes and in particular for multiplicative stochastic processes (note that for additive processes the expectation of the wealth increment can be used). And here comes the important implication... Given that several economic processes can be modeled as a first approximation as multiplicative random processes (e.g. stock markets, real investments, GDP growth, etc.), it is not a rational strategy to use the ensemble average (aka expectation of wealth increment) to take some economic decisions. There are several implications of the above simple fact including the optimality of the Kelly criterion; the optimal leverage being below 1 in all cases involving multiplicative processes; the incorrect measurement of inequality; or the known inadequacy of the average income, instead of the median, to measure the average well-being to name a few. A possible controversial corollary of the above is that the concept of utility is unnecessary and incorrect as a first approximation to the micro-economic behaviour. Instead an ergodic measurable should be used. In the specific cases of multiplicative stochastic processes the difference of the walth logarithm is ergodic and a rational decision maker should use it to optimize his wealth. This will require further debate within the scientific community because it is not clear that what is an optimal decision is a good model for the people's behavior. In any case, if the expected utility is not optimal, it also does not make much sense as a model for the Homo Economicus. In any case, I really recommend reading instead of rushing to conclusions [3]. [1] J. L. Kelly, A new interpretation of information rate. Bell System Technical Journal, 35 (1956), 917-926. [2] O. Peters and M. Gell-Mann. Evaluating gambles using dynamics. Chaos, 26:23103, February 2016. [3] Peters, Ole, and Alexander Adamou. "Ergodicity economics." London Mathematical Laboratory (2018).