5 ms·

Is the Pareto distribution the way it is because on every time step the tail ends have exponentially more ability to pull away? Is there some sort of statistics

Is the Pareto distribution the way it is because on every time step the tail ends have exponentially more ability to pull away? Is there some sort of statistics concept that models time variation of distributions (first derivative?) or their acceleration (second derivative ?)

hammock 7y ago
No. There is quite a bit of income mobility in the US, and these types of reports never really explore it. Instead, they leave you with the idea that the top 10% today are the same people that were there 10 years ago. Which is false.
- deleted 7y ago
  [deleted]
- FabHK 7y ago
  Social mobility in the US is, by now, smaller than in many other developed countries, IIRC. EDIT to add some sources: > The key observation, based on a growing body of research, is that when it comes to upward social mobility, the U.S. is truly exceptional — that is, it performs exceptionally badly. https://www.nytimes.com/2019/02/28/opinion/ivanka-trump-social-mobility.html https://www.nytimes.com/2019/02/28/opinion/ivanka-trump-soci... > Although the discovery of America’s low mobility, compared to similar countries, is relatively new, it turns out that mobility’s been low for some time. http://www.msnbc.com/msnbc/us-social-mobility-problem http://www.msnbc.com/msnbc/us-social-mobility-problem > A new study indicates that from the 1980s to the 2000s, it became less likely that a worker could move up the income ladder. https://www.theatlantic.com/business/archive/2016/07/social-mobility-america/491240/ https://www.theatlantic.com/business/archive/2016/07/social-...
  - dantheman 7y ago
    It's hard to compare, you have perfect mobility when everyone is dirt poor. In the USA it's possible for people to get really rich, so measuring how many from the very bottom make it to the very top is not a good metric; especially when composing to other countries whose top is in the middle. So if you compare mobility between income ranges you will find the US to be more mobile.
    - jonathankoren 7y ago
      Not only is this shifting the goal posts, it’s also whataboutism. This is a distraction from the problem of wealth concentration and lack of mobility in the United States by saying: Yeah, well, you’re richer than the Haitians, so quit whining. Being part of the largest economy in the world, I would certainly hope the poorest in my country, would be better off than the those in the least developed country in the Western Hemisphere.
    - monocasa 7y ago
      Every country has a rich upper class.
      - dantheman 7y ago
        You need 10 million to be in the top 1% in the US and 700k to be in the top 1% in the UK. There's a big difference between going from 0 net worth to 700k than to 10 million.
- lozenge 7y ago
  Figures like yours usually come from just comparing today's 10% to the 10% from earlier date, and just saying "new entrant" vs "existing entrant". But a new entrant from the bottom 10% would be more interesting than a new entrant from the second 10%. You can get a more holistic view using, say, quintiles: (grabbed off Wikipedia) 42% of children born to parents in the bottom fifth of the income distribution ("quintile") remain in the bottom, while 39% born to parents in the top fifth remain at the top.[5] Only half of the generation studied exceeded their parents economic standing by moving up one or more quintiles.[5] Moving between quintiles is more frequent in the middle quintiles (2-4) than in the lowest and highest quintiles. Of those in one of the quintiles 2-4 in 1996, approximately 35% stayed in the same quintile; and approximately 22% went up one quintile or down one quintile (moves of more than one quintile are rarer). 39% of those who were born into the top quintile as children in 1968 are likely to stay there, and 23% end up in the fourth quintile.[5] Children previously from lower-income families had only a 1% chance of having an income that ranks in the top 5%.[7] On the other hand, the children of wealthy families have a 22% chance of reaching the top 5%.[7]
- jonathankoren 7y ago
  10 years is a pretty big time range, and so you’d expect to see generational effects to show up. (i.e. people fall off the list, because they’re dead.) But this does highlight two important points: intergenerational and intragenerational mobility. https://en.wikipedia.org/wiki/Socioeconomic_mobility_in_the_United_States https://en.wikipedia.org/wiki/Socioeconomic_mobility_in_the_... WRT intergenerational mobility, the US does quite poorly when compared to other modern economies, with a very strong correlation between parental wealth and the child’s wealth. For instance 42% born into the bottom quintile, stay there in the United States, but only 25% remained in Denmark. 8% rose to the top in US, but again, 14% did in Denmark. Intragenerational mobility in my opinion is a bit of a red herring. Often you’ll hear someone trumpet some number about people moving from one group to another in a single year, but you have to look closer to the reasons why. Some people are just on the cusp of the cutoffs and so will bounce around it. Others are experiencing temporary outlays, and will very quickly return to their original levels. Unless the person’s move has some stickiness, along with some large absolute change, it’s meaningless noise.
throwawaymath 7y ago
It's fuzzy, but you can take the probability density function (PDF) of a random variable with a pareto distribution. That sort of matches what you're asking for, with regard to taking a derivative to find the probability of the random variable falling into a range of probabilities over time.

hammock 7y ago

No. There is quite a bit of income mobility in the US, and these types of reports never really explore it. Instead, they leave you with the idea that the top 10% today are the same people that were there 10 years ago. Which is false.

deleted 7y ago
[deleted]
FabHK 7y ago
Social mobility in the US is, by now, smaller than in many other developed countries, IIRC. EDIT to add some sources: > The key observation, based on a growing body of research, is that when it comes to upward social mobility, the U.S. is truly exceptional — that is, it performs exceptionally badly. https://www.nytimes.com/2019/02/28/opinion/ivanka-trump-social-mobility.html https://www.nytimes.com/2019/02/28/opinion/ivanka-trump-soci... > Although the discovery of America’s low mobility, compared to similar countries, is relatively new, it turns out that mobility’s been low for some time. http://www.msnbc.com/msnbc/us-social-mobility-problem http://www.msnbc.com/msnbc/us-social-mobility-problem > A new study indicates that from the 1980s to the 2000s, it became less likely that a worker could move up the income ladder. https://www.theatlantic.com/business/archive/2016/07/social-mobility-america/491240/ https://www.theatlantic.com/business/archive/2016/07/social-...
- dantheman 7y ago
  It's hard to compare, you have perfect mobility when everyone is dirt poor. In the USA it's possible for people to get really rich, so measuring how many from the very bottom make it to the very top is not a good metric; especially when composing to other countries whose top is in the middle. So if you compare mobility between income ranges you will find the US to be more mobile.
  - jonathankoren 7y ago
    Not only is this shifting the goal posts, it’s also whataboutism. This is a distraction from the problem of wealth concentration and lack of mobility in the United States by saying: Yeah, well, you’re richer than the Haitians, so quit whining. Being part of the largest economy in the world, I would certainly hope the poorest in my country, would be better off than the those in the least developed country in the Western Hemisphere.
  - monocasa 7y ago
    Every country has a rich upper class.
    - dantheman 7y ago
      You need 10 million to be in the top 1% in the US and 700k to be in the top 1% in the UK. There's a big difference between going from 0 net worth to 700k than to 10 million.
lozenge 7y ago
Figures like yours usually come from just comparing today's 10% to the 10% from earlier date, and just saying "new entrant" vs "existing entrant". But a new entrant from the bottom 10% would be more interesting than a new entrant from the second 10%. You can get a more holistic view using, say, quintiles: (grabbed off Wikipedia) 42% of children born to parents in the bottom fifth of the income distribution ("quintile") remain in the bottom, while 39% born to parents in the top fifth remain at the top.[5] Only half of the generation studied exceeded their parents economic standing by moving up one or more quintiles.[5] Moving between quintiles is more frequent in the middle quintiles (2-4) than in the lowest and highest quintiles. Of those in one of the quintiles 2-4 in 1996, approximately 35% stayed in the same quintile; and approximately 22% went up one quintile or down one quintile (moves of more than one quintile are rarer). 39% of those who were born into the top quintile as children in 1968 are likely to stay there, and 23% end up in the fourth quintile.[5] Children previously from lower-income families had only a 1% chance of having an income that ranks in the top 5%.[7] On the other hand, the children of wealthy families have a 22% chance of reaching the top 5%.[7]
jonathankoren 7y ago
10 years is a pretty big time range, and so you’d expect to see generational effects to show up. (i.e. people fall off the list, because they’re dead.) But this does highlight two important points: intergenerational and intragenerational mobility. https://en.wikipedia.org/wiki/Socioeconomic_mobility_in_the_United_States https://en.wikipedia.org/wiki/Socioeconomic_mobility_in_the_... WRT intergenerational mobility, the US does quite poorly when compared to other modern economies, with a very strong correlation between parental wealth and the child’s wealth. For instance 42% born into the bottom quintile, stay there in the United States, but only 25% remained in Denmark. 8% rose to the top in US, but again, 14% did in Denmark. Intragenerational mobility in my opinion is a bit of a red herring. Often you’ll hear someone trumpet some number about people moving from one group to another in a single year, but you have to look closer to the reasons why. Some people are just on the cusp of the cutoffs and so will bounce around it. Others are experiencing temporary outlays, and will very quickly return to their original levels. Unless the person’s move has some stickiness, along with some large absolute change, it’s meaningless noise.

throwawaymath 7y ago

It's fuzzy, but you can take the probability density function (PDF) of a random variable with a pareto distribution. That sort of matches what you're asking for, with regard to taking a derivative to find the probability of the random variable falling into a range of probabilities over time.