5 ms·

I've read a bit into econophysics. In stat mech, the exchange of energy between atoms is assumed to be random. When the exchange of energy is random, the result

I've read a bit into econophysics. In stat mech, the exchange of energy between atoms is assumed to be random. When the exchange of energy is random, the resulting distribution of energies is a Gibbs distribution, which means that the probability of atoms with higher energies falls off exponentially. The application is that if you replace energy with money, and atoms with people, then the same equations hold for a model of people who randomly exchange money. Therefore if investments were truly random, you would expect the distribution of investors' wealth to follow an exponential distribution, not a power law! This directly contradicts the article. Interestingly enough, the bottom 99% follows an exponential distribution, while the top 1% follows a power-law, and the transition is very sharp (eg, wealth plots have a "kink" in them). Brief introduction to econophysics for the mathematically inclined: https://arxiv.org/abs/0709.3662 https://arxiv.org/abs/0709.3662

nerdponx 10y ago
I wonder if opportunities follow an exponential distribution. Then it's a matter of having the talent and ambition to capitalize on those opportunities. Although I don't know if a "talent distribution" exists such that its joint distribution with an exponential yields a power law.
lend000 10y ago
Very interesting. I'd be curious to see a subset of this data related to venture capital, where there seems to be a high proportion of 'professional investors' -- although funding from friends, family, and personal savings certainly plays a role in Angel rounds.
throwaway729 10y ago
Is there any reason to believe that econophysics provides a better model of reality than the article's informal model?
- dsacco 10y ago
  Well there are several things that are incoherent about the article's application of this model. 1. Coin flipping is not a fit analogy, despite the fact that it's parroted in financial discussions ad nauseum. Take this quote from the article, for example: Maybe the string of investment and managerial decisions that made one person’s company successful, and that seem so very wise in retrospect, were actually just the entrepreneurial equivalent of flipping a coin 20 times and getting all heads. The chances of that happening are about 1 in 1 million, so if enough people try it, someone is bound to get lucky and look like a coin-flipping genius—purely by chance. What? How do you map the theoretical probabilities of individual entrepreneurial decisions to the chance of a heads or tails on a coin flip? Is the chance of getting into YC 50%? Is the chance of securing venture capital in a Series A round 50%? How about? This is before we even consider that the theoretical chance for each decision will obviously not be the same for everyone, whereas a coin flip is. This is important because it's not falsifiable if we can't map decisions to probabilities. It's also important because the numbers could be wildly different. If each entrepreneurial decision has a 50% chance of success, that might result in a 1 in 1 million chance of getting rich. But what if the actual chances of success for each entrepreneurial decision in lieu of the coin-flip mapping result in a 1 in 4 quadrillion chance of success? One result indicates that essentially all successes could be due to chance, the other suggests the opposite. 2. The author uses very fuzzy measurements with no empirical basis in reality to support the model. For example: To make the game more realistic, assume that if investors’ wealth declines below some level they have to drop out of the game, and are replaced by newly rich players emerging from the middle class. Eventually, the game will reach a kind of equilibrium—one in which the number of players going up is always balanced by the number going down, so that the overall distribution of wealth reaches a steady state and doesn’t change anymore. Wait a second, why are we assuming that this game reaches an equilibrium? We can't just use textbook economics here - there is no reason to assume the "game" won't be weighted towards more players dropping out than moving up or vice versa. 3. The author tries to repair the issues with chance being theoretically equal in my first point with the following: Still, it is possible to get a crude sense of the effect of talent by modifying the investment game to include two types of players. Normal investors are just like those in the first game: They flip a coin with heads yielding a return of 30 percent, and tails producing a loss of 10 percent. But the talented investors are more skilled at playing the market: They earn slightly more than 30 percent when the coin comes up heads, and lose slightly less than 10 percent when the coin comes up tails. Now we set the players loose and ask an empirical question: How big can this “talent differential” be and still stay statistically consistent with the power law wealth distribution we see in the real world? Where are these numbers coming from? How are these a rigorous, empirical model of talent and the subsequent chance differential? By this point in the article the entire game is becoming so "in the clouds" that it doesn't have any basis in reality anymore. It's like I came up with a "law" based on one extremely convoluted thought experiment and attempted to extrapolate it to the entire market in real-world conditions. Basically, the author's model is narrow in some places, vague in others and overall does not empirically prove the premises it attempts to build upon. He hand waves the (extremely common) power law distribution as a sort of magic wand that smooths away all the lack of rigor. There's just not much evidence that the model reflects the real world.
- scottmsul 10y ago
  The equations from physics say "if we have some quantity X distributed among bins Y, and X is randomly exchanged between pairs of Y over and over, then P(bin y has amount x) is proportional to exp(-x)". In physics, X is energy and Y is atoms, while in economics, X is money and Y is people. If the money were truly being exchanged randomly, then the distribution should look exponential, that is, the probability person p has money m is proportional to exp(-m). What we observe is that the probability of having money m is actually m^(-alpha). Therefore the money is not being exchanged randomly, and the richest agents probably aren't lucky.
  - timr 10y ago
    "What we observe is that the probability of having money m is actually m^(-alpha). Therefore the money is not being exchanged randomly, and the richest agents probably aren't lucky." No, it means that you're using the wrong model. There are lots of models of "random" behavior. You can't just pick one out because you like it, and conclude that a system isn't "random" because the model you've chosen doesn't fit the data. The article isn't especially convincing either, but at least they're describing a model that looks somewhat like money, and produces a distribution that matches what's observed in reality. You're describing a model that looks like atoms, and concluding that money isn't random because it doesn't look like atoms.
  - mcguire 10y ago
    Is that a zero sum game? What happens if you add a heat source to the model?
josephdviviano 10y ago
Thanks for the paper, very interesting. All the below is total speculation as I am no 1%er ;). Curious that there's such a sharp change in distributions. It seems like the top 1% participate in a very different sort of financial network than do the remaining 99%. Since the majority's wealth follows such a basic physical theory, their organization must be completely unstructured. For the 1%, then, the question is what the structure is. It might be 'scale free' network [1], or fractal, so it could be due to preferential attachment [2], which would mean those who have lots of money find it easier to make more money (via things like investments or rent-taking), or due to competition between fit nodes [3], which would make sense in that those in the 1% are likely to be merging / acquiring others. I guess what this means isn't too surprising: if you aren't in the 1% now, you need to claw your way in before you can take advantage of these network effects to grow your wealth in any meaningful way. If you aren't in the 1%, you might be successful, but it will be mostly due to luck. But I wonder if the network effects can be taken advantage of without the wealth to start. Following this line of thinking [4], the wealth flows due to social networking, not due to financial networking. If you can connect with the 1%'s social sphere, you stand a much better chance at becoming a part of that financial class. [1] https://en.wikipedia.org/wiki/Scale-free_network https://en.wikipedia.org/wiki/Scale-free_network [2] https://en.wikipedia.org/wiki/Preferential_attachment https://en.wikipedia.org/wiki/Preferential_attachment [3] https://en.wikipedia.org/wiki/Fitness_model_(network_theory) https://en.wikipedia.org/wiki/Fitness_model_(network_theory) [4] https://www.quora.com/What-is-the-most-effective-yet-efficient-way-to-get-rich-2 https://www.quora.com/What-is-the-most-effective-yet-efficie...
- scottmsul 10y ago
  Right, power laws are extremely common, and all it says is that some aspect of the distribution is scale-invariant, but without saying why. For example, most companies are scalable, so it's no surprise that company valuations follow a power law. And since investors/founders own such large shares of companies, that would help explain why the 1% follows a power law. But as this article claims, if people gamble on log-scales, that would also create a power law. Power laws are so common and general, I find it difficult to believe that a power law is evidence of one way or the other.
dsacco 10y ago
Thanks for the paper. Do you have suggestions for other reading on econophysics at a similarly accessible level?
beefield 10y ago
I would assume that the exchange of energy between atoms is assumed to be independent in addition to being random. And by independent I mean that how much other atoms have exchanged energy with a particular atom does not have effect in how many atoms are likely to exchange energy with this particular atom. (Or, to be more precise, atom that has received energy from other atoms is not more, but _less_ likely to get energy from next encounters with other atoms) But that does not hold in society. Preferences of people are highly dependent. If a singer has gotten praise from one person, it is more likely that s/he is getting praise from the next one as well (assuming these can share their preferences), and by more I mean more than what would be expected from singing talent alone. I am quite sure there was a social psychology research on specifically this example, how people rank music in groups, but for some reason I can't find it from google just now. From the investment point of view, I think Piketty showed that larger investors seem to get better returns on their investments. You can debate causality, correlation and luck here probably endlessly, though.
- gizmo 10y ago
  I'm pretty sure this is the research report about how social influence determines which songs are likely to become hits: https://www.princeton.edu/~mjs3/salganik_dodds_watts06_full.pdf https://www.princeton.edu/~mjs3/salganik_dodds_watts06_full....
  - beefield 10y ago
    Yes. Thank you.
- beefield 10y ago
  Now, I am quite confident I have not uttered word "Piketty" anywhere else in any way (not from my mouth nor keyboard) in a long time. But now my Facebook feed is filled with advertisements to buy piketty's book. If this is not an anecdote, how do they do that?
Jorenby 10y ago
Explaining the top 1% is exactly the goal of the article: "Could the differences between the very rich and the hugely rich [...] be the result of pure, dumb luck?" So if the model you're looking at indicates power law distribution at the top, that seems to lend further support to the author's thesis.
pdog 10y ago
It's almost as if human interaction can't be reduced to a Gaussian distribution... How strange.
Nomentatus 10y ago
I'm going to guess that insider trading is that top 1%, then, or most of it. Some trading on insider knowledge (such as when you sell a stock, depending) is perfectly legal, or at least wholly unpreventable or unprosecutable, of course. Those in the bottom 99% of investors may still be capturing at least some of the increase in world wealth over time. Then again, maybe not: or not much. I'd have to read the article to know if the answer to that question is there, and I can't afford the extra time, alas.
fallingfrog 10y ago
My understanding is that the "kink" represents the transition point where people are making money from ownership of things (investing) rather than labor. In the investing world, the more money you have, the more money you can make, which gives a different kind of law than one in which money is just transferred randomly.
iklos55 10y ago
very good paper from first looks! thank you
RugnirViking 10y ago
Regarding your penultimate paragraph, isn't this just saying that for the most part, to make good money, you have to be lucky, whereas to be extremely rich, you need to be lucky and good at what you do?

nerdponx 10y ago

I wonder if opportunities follow an exponential distribution. Then it's a matter of having the talent and ambition to capitalize on those opportunities. Although I don't know if a "talent distribution" exists such that its joint distribution with an exponential yields a power law.

lend000 10y ago

Very interesting. I'd be curious to see a subset of this data related to venture capital, where there seems to be a high proportion of 'professional investors' -- although funding from friends, family, and personal savings certainly plays a role in Angel rounds.

throwaway729 10y ago

Is there any reason to believe that econophysics provides a better model of reality than the article's informal model?

dsacco 10y ago
Well there are several things that are incoherent about the article's application of this model. 1. Coin flipping is not a fit analogy, despite the fact that it's parroted in financial discussions ad nauseum. Take this quote from the article, for example: Maybe the string of investment and managerial decisions that made one person’s company successful, and that seem so very wise in retrospect, were actually just the entrepreneurial equivalent of flipping a coin 20 times and getting all heads. The chances of that happening are about 1 in 1 million, so if enough people try it, someone is bound to get lucky and look like a coin-flipping genius—purely by chance. What? How do you map the theoretical probabilities of individual entrepreneurial decisions to the chance of a heads or tails on a coin flip? Is the chance of getting into YC 50%? Is the chance of securing venture capital in a Series A round 50%? How about? This is before we even consider that the theoretical chance for each decision will obviously not be the same for everyone, whereas a coin flip is. This is important because it's not falsifiable if we can't map decisions to probabilities. It's also important because the numbers could be wildly different. If each entrepreneurial decision has a 50% chance of success, that might result in a 1 in 1 million chance of getting rich. But what if the actual chances of success for each entrepreneurial decision in lieu of the coin-flip mapping result in a 1 in 4 quadrillion chance of success? One result indicates that essentially all successes could be due to chance, the other suggests the opposite. 2. The author uses very fuzzy measurements with no empirical basis in reality to support the model. For example: To make the game more realistic, assume that if investors’ wealth declines below some level they have to drop out of the game, and are replaced by newly rich players emerging from the middle class. Eventually, the game will reach a kind of equilibrium—one in which the number of players going up is always balanced by the number going down, so that the overall distribution of wealth reaches a steady state and doesn’t change anymore. Wait a second, why are we assuming that this game reaches an equilibrium? We can't just use textbook economics here - there is no reason to assume the "game" won't be weighted towards more players dropping out than moving up or vice versa. 3. The author tries to repair the issues with chance being theoretically equal in my first point with the following: Still, it is possible to get a crude sense of the effect of talent by modifying the investment game to include two types of players. Normal investors are just like those in the first game: They flip a coin with heads yielding a return of 30 percent, and tails producing a loss of 10 percent. But the talented investors are more skilled at playing the market: They earn slightly more than 30 percent when the coin comes up heads, and lose slightly less than 10 percent when the coin comes up tails. Now we set the players loose and ask an empirical question: How big can this “talent differential” be and still stay statistically consistent with the power law wealth distribution we see in the real world? Where are these numbers coming from? How are these a rigorous, empirical model of talent and the subsequent chance differential? By this point in the article the entire game is becoming so "in the clouds" that it doesn't have any basis in reality anymore. It's like I came up with a "law" based on one extremely convoluted thought experiment and attempted to extrapolate it to the entire market in real-world conditions. Basically, the author's model is narrow in some places, vague in others and overall does not empirically prove the premises it attempts to build upon. He hand waves the (extremely common) power law distribution as a sort of magic wand that smooths away all the lack of rigor. There's just not much evidence that the model reflects the real world.
scottmsul 10y ago
The equations from physics say "if we have some quantity X distributed among bins Y, and X is randomly exchanged between pairs of Y over and over, then P(bin y has amount x) is proportional to exp(-x)". In physics, X is energy and Y is atoms, while in economics, X is money and Y is people. If the money were truly being exchanged randomly, then the distribution should look exponential, that is, the probability person p has money m is proportional to exp(-m). What we observe is that the probability of having money m is actually m^(-alpha). Therefore the money is not being exchanged randomly, and the richest agents probably aren't lucky.
- timr 10y ago
  "What we observe is that the probability of having money m is actually m^(-alpha). Therefore the money is not being exchanged randomly, and the richest agents probably aren't lucky." No, it means that you're using the wrong model. There are lots of models of "random" behavior. You can't just pick one out because you like it, and conclude that a system isn't "random" because the model you've chosen doesn't fit the data. The article isn't especially convincing either, but at least they're describing a model that looks somewhat like money, and produces a distribution that matches what's observed in reality. You're describing a model that looks like atoms, and concluding that money isn't random because it doesn't look like atoms.
- mcguire 10y ago
  Is that a zero sum game? What happens if you add a heat source to the model?

josephdviviano 10y ago

Thanks for the paper, very interesting. All the below is total speculation as I am no 1%er ;). Curious that there's such a sharp change in distributions. It seems like the top 1% participate in a very different sort of financial network than do the remaining 99%. Since the majority's wealth follows such a basic physical theory, their organization must be completely unstructured. For the 1%, then, the question is what the structure is. It might be 'scale free' network [1], or fractal, so it could be due to preferential attachment [2], which would mean those who have lots of money find it easier to make more money (via things like investments or rent-taking), or due to competition between fit nodes [3], which would make sense in that those in the 1% are likely to be merging / acquiring others. I guess what this means isn't too surprising: if you aren't in the 1% now, you need to claw your way in before you can take advantage of these network effects to grow your wealth in any meaningful way. If you aren't in the 1%, you might be successful, but it will be mostly due to luck. But I wonder if the network effects can be taken advantage of without the wealth to start. Following this line of thinking [4], the wealth flows due to social networking, not due to financial networking. If you can connect with the 1%'s social sphere, you stand a much better chance at becoming a part of that financial class. [1] https://en.wikipedia.org/wiki/Scale-free_network https://en.wikipedia.org/wiki/Scale-free_network [2] https://en.wikipedia.org/wiki/Preferential_attachment https://en.wikipedia.org/wiki/Preferential_attachment [3] https://en.wikipedia.org/wiki/Fitness_model_(network_theory) https://en.wikipedia.org/wiki/Fitness_model_(network_theory) [4] https://www.quora.com/What-is-the-most-effective-yet-efficient-way-to-get-rich-2 https://www.quora.com/What-is-the-most-effective-yet-efficie...

scottmsul 10y ago
Right, power laws are extremely common, and all it says is that some aspect of the distribution is scale-invariant, but without saying why. For example, most companies are scalable, so it's no surprise that company valuations follow a power law. And since investors/founders own such large shares of companies, that would help explain why the 1% follows a power law. But as this article claims, if people gamble on log-scales, that would also create a power law. Power laws are so common and general, I find it difficult to believe that a power law is evidence of one way or the other.

dsacco 10y ago

Thanks for the paper. Do you have suggestions for other reading on econophysics at a similarly accessible level?

beefield 10y ago

I would assume that the exchange of energy between atoms is assumed to be independent in addition to being random. And by independent I mean that how much other atoms have exchanged energy with a particular atom does not have effect in how many atoms are likely to exchange energy with this particular atom. (Or, to be more precise, atom that has received energy from other atoms is not more, but _less_ likely to get energy from next encounters with other atoms) But that does not hold in society. Preferences of people are highly dependent. If a singer has gotten praise from one person, it is more likely that s/he is getting praise from the next one as well (assuming these can share their preferences), and by more I mean more than what would be expected from singing talent alone. I am quite sure there was a social psychology research on specifically this example, how people rank music in groups, but for some reason I can't find it from google just now. From the investment point of view, I think Piketty showed that larger investors seem to get better returns on their investments. You can debate causality, correlation and luck here probably endlessly, though.

gizmo 10y ago
I'm pretty sure this is the research report about how social influence determines which songs are likely to become hits: https://www.princeton.edu/~mjs3/salganik_dodds_watts06_full.pdf https://www.princeton.edu/~mjs3/salganik_dodds_watts06_full....
- beefield 10y ago
  Yes. Thank you.
beefield 10y ago
Now, I am quite confident I have not uttered word "Piketty" anywhere else in any way (not from my mouth nor keyboard) in a long time. But now my Facebook feed is filled with advertisements to buy piketty's book. If this is not an anecdote, how do they do that?

Jorenby 10y ago

Explaining the top 1% is exactly the goal of the article: "Could the differences between the very rich and the hugely rich [...] be the result of pure, dumb luck?" So if the model you're looking at indicates power law distribution at the top, that seems to lend further support to the author's thesis.

pdog 10y ago

It's almost as if human interaction can't be reduced to a Gaussian distribution... How strange.

Nomentatus 10y ago

I'm going to guess that insider trading is that top 1%, then, or most of it. Some trading on insider knowledge (such as when you sell a stock, depending) is perfectly legal, or at least wholly unpreventable or unprosecutable, of course. Those in the bottom 99% of investors may still be capturing at least some of the increase in world wealth over time. Then again, maybe not: or not much. I'd have to read the article to know if the answer to that question is there, and I can't afford the extra time, alas.

fallingfrog 10y ago

My understanding is that the "kink" represents the transition point where people are making money from ownership of things (investing) rather than labor. In the investing world, the more money you have, the more money you can make, which gives a different kind of law than one in which money is just transferred randomly.

iklos55 10y ago

very good paper from first looks! thank you

RugnirViking 10y ago

Regarding your penultimate paragraph, isn't this just saying that for the most part, to make good money, you have to be lucky, whereas to be extremely rich, you need to be lucky and good at what you do?