How much does state population size predict state inequality?

From StatisticalIdeasBlogspot:

Of the top 10 populated states, 5 were also among the top 10 “unequal” states: CA, TX, FL, NY, IL.  Of the 10 least populated states, 4 were also among the 10 least “unequal” states: VT, AK, ME, HI.  So instead of 4 overlapping states, we have a significantly higher 9 (5+4) states overlapping.  Additionally, there are no crossover states (e.g., a highly “unequal” less-populated state, nor a less “unequal” highly-populated state).  The easy math (9>4 with no crossovers) shows something, and it’s not structural inequality.

The only common variable between the selection of the top 10 (and in the selection of the bottom 10) populated states is just population size itself!

There is also a useful map at the link.


Big states = more diversity, so diversity drives inequality. Who wants to share their wealth with people you cannot even identify, much less identify with?

Or, if you like a physics explanation, the bigger the sand pile, the more people, the greater the observed standard deviations from the mean. California has a lot of six sigma events.

If you try to apply that to Europe I am not sure it will work... The highest Gini coef. are Serbia, Latvia, Lithuania, Greece and Portugal... Lowest Norway, Slovakia, Slovenia, Czech Republic and Sweden.

Let's completely ignore wealth when convenient, Morono.

Ray, you have two explanations here:

Big sand pile - more sand the more likely to find grains more standard deviations above the average.

Diversity drives inequalty.

I think you can test the big sand pile theory by creating an artifical state consisting of low population states cobbled together. If that state still shows low inequality it would argue against the sand pile theory.

Looks like they did some experiment of that nature already, Boonton, and here you are responding to it with complete cognitive dissonance.

More populous states are also more developed. More development means more opportunities for specialization.

Spot on.

After thinking about this a little bit, what about looking at states with the largest metropolitan areas against states with the smallest, isnt it a driver of inequality ?

Right, it's metropolis size that more or less drives how rich the rich are in a particular state. Rich people in Illinois are richer than rich people in Iowa on average because Chicago is much a bigger urban center than anywhere in Iowa.

For example, you can make a pretty good apples to apples comparison of "downtown corporate lawyers." Every city in America has business lawyers who work in big office buildings in the middle of town. The ones who work in the biggest cities get paid more on average than the ones who work in smaller cities.

In fact, you could do the same analysis using height of workplace off the ground and get pretty similar results. The average corporate lawyer in Iowa City probably has an office two or three stories off the ground while the average corporate lawyer in Chicago probably has an office ten or twenty stories in the air.

Small population Connecticut is the highest inequality state because it's home to some of the richest suburbs of the biggest metropolis in America.

Assuming I accept that cities are "Engines of Inequality," which doesn't seem unreasonable at first pass, what's the mechanism?

Is it just suppression of family formation? Is it that inequality concentrates in cities, rather than that it's created by them? Is it that status markers are more important in a place where you can't really own more tangible assets and that drives strivers? I'm throwing out theories here rather than arguing for one of them.

Well, there are two sides to inequality, the rich and the poor. Looking at the map, a lot of this inequality is driven by how rich the top 1% are compared to the other 99%. In Connecticut, the top 1% are very, very rich, in part because the hedge fund industry is concentrated in Greenwich, just over the border from New York.

How about: the bigger the metropolis, the more levels of hierarchy.

I think a developer can make more money in an urban area than a rural area. That and you can make bigger business deals in a bigger city so the rich move there and rich who are there can make more also.

I think that works fairly well well. Although political history matters too.

Taking your European data, and look at who is above UK (in 2013). Italy has at least one huge city, Luxemburg is an obvious special case, and all the others have been dictatorships at some time since 1970.

Below the UK, France is nearly has high -- and Paris a very great city like London. Germany is a step behind and it is not so dominated by a single great city. Smaller countries bring up the rear.

Hence the hyperrich in America like policies that create lots of poor servants, unassimilated immigrants, and drone workers even if (or because?) its externalities harm the middle and upper middle class through worse schools, less social cohesion, more crime, etc. in cheaper neighborhoods and outlying areas. Aka New York City, San Francisco, etc. Or more appropriately countries like Brazil or India.

Think about this for a second. You are claiming that rich people prefer their employees less educated, less amiable, and more violent.

Makes sense.

Now, test the hypothesis.

Already did, see: The thread you are responding to. Cognitive dissonance keeps the pain away, Bill.

Exports? You may reach an income plateau selling only to your neighbors, while the ceiling is much higher if you sell to the rest of the world.Texas and California are the top exporters.

For a blog that calls itself "statisticalideas" this post is surprisingly poor on statistics.

"The easy math (9>4 with no crossovers) shows something ". Oh, really? How about backing that up with some statistical analysis?
Couldn't it be just pure coincidence?
(Maybe not. But there are plenty of statistical tools to prove it's no coincidence. And that is completely lacking in this article).

Anyway, the result might also be due to the method.
Note, that the definition of inequality used in this article is somewhat unusual. (The usual method being the gini coefficient).

seconded. it is easy to do significance calculations, and they are as important as the first order results.

What analysis do you need? The easy math, and it is easy if I can do it, tells us that by pure chance we should've observed 2 "top 10 - top 10" overlaps, 2 "bottom 10 - bottom 10" overlaps, 2 "top 10 - bottom 10 overlaps", and 2 "bottom 10 - top 10" overlaps. Instead they observe 5, 4, 0, and 0 respectively. Hmm.

and the significance is ?
"easy math" is not good statistics.

.01 < p < .02

The most unequal area is obviously DC: either you're President, a Congressman or a SCOTUS judge, or you are not. That's on the assumption that it's power that matters, not income.

With the same criteria Moscow is more unequal... or you are Putin or you are not :D

'The most unequal area is obviously DC: either you’re President, a Congressman or a SCOTUS judge, or you are not.'

And if you're not a government official, you can instead be an oppressed nobody like Steve Case with a piddling one and a half billion dollars to your name. Compared to a neighbor like Forrest Mars, Jr., with 20 billion dollars to his name (not that all of his 17 family related billionaires live in the DC area).

Oddly, the DC area, where a large number of residents are still subject in large part to the federal pay scales, tends to be quite flat in terms of income inequality compared to places like NYC or the Bay Area or an oil city like Houston.

"Oddly, the DC area, where a large number of residents are still subject in large part to the federal pay scales, tends to be quite flat in terms of income inequality compared to places like NYC or the Bay Area or an oil city like Houston. "

Washington DC does not tend to be "quite flat in terms of income inequality".

Washington DC is the 5th worst in the nation (out of the top 50 metropolitan areas). It's worse than NYC (ranked 6th) and Houston (11th), but it was better than San Francisco (2nd).

Russians billionaires have provided a contemporary version of an ancient truth: swords > gold. The President has vastly more power than any billionaire.

I'm no statistician, but I do know that wealth is a very strange heavy tailed distribution. I don't know exactly what the distribution looks like, but I suspect that unless you measure inequality in a very clever way, it goes up the more samples you take.

It has a long tailed distribution with an infinite population variance. In other words, the bigger the population, the higher the sample variance. I'm not sure how we're measuring inequality but the answer to the riddle is probably that it's some measure that's positively related to sample variance. That would suffice to give you Tyler's result.

Which, to me at least, implies that inequality is an expected result from population growth and not an intrinsic evil. This idea is anathema to leftists.

Sailer has it right. The US happens to have some rural, homogenous, relatively low population states without even minor metropolitan areas. These have low income inequality (often low incomes overall), but the comparison is not very meaningful. Journalistic and academic articles about the US overall have a bad tendency to do state-by-state comparisons where metropolitan area by metropolitan area comparisons would be more informative.

Funny that you would draw attention to population rather than the blatantly obvious fact that these are blue states. When discussing a loaded political issue, for God's sake.

I guess pointing out that Democrat policies produce inequality won't get you a lot of NYT cocktail party invites.

Hey, it's probably just related to population. Maybe it's the body heat generated by all these people? Maybe more tax money for Planned Parenthood is the answer here?

Is this parody? CA, NY, IL: blue;TX: red; FL: purple; VT, HI: blue, AK: red, ME: purple. Yeah, I see now that you were just kidding.

I don't think you're looking at the same data everyone else is--blue states are pretty clearly more unequal. The ten most unequal states, plus Washington DC, in descending order: CT, NY, NV, FL, CA, MA, TX, DC, IL, NJ, WA. Of those, TX is red, FL is purple, NV is purple. (See table 2 at I would not exactly call 8-1-2 even.

That said, leftward political lean and income inequality both appear to be functions of having large metro areas, so it's not obvious from the data that liberal policies "cause" inequality or vice versa.

(1) Presence of big cities means more wealth.
(2) Higher population density means more likelihood of voting Democratic.

What way does the causality arrow go?

People that have to live in close quarters with lots of people they're not related to value government higher than people whose closest neighbors are two miles away. That shouldn't really surprise anybody.

That's not what's going on.

Urbanization precedes liberalization. Economic development precedes urbanization. Economic development produces inequality.

The blue states became blue only after they became prosperous and unequal.

Yup, this is the best answer. The population size and liberalism variables are distractions, they are correlates rather than the real causal variable: is there a large metropolis in the state?

If the answer is yes, there's going to be higher inequality in the state, and simultaneously said state is not going to be small in population.

The US is an open economy with open immigration suggesting the median income shouldn't vary significantly. The drivers of inequality would be either very high or very low income concentrations.

I suspect low income concentrations are harder to build since a) low income people will be generated at similar rates (due to the open economy), and b) low income populations have low mobility so don't migrate to any district.

High income populations are much more mobile and can accumulate so they are likely the source of the high inequality.

If you look at what high income populations want it's a venue where they have a lot of options for spending their wealth, this would correspond to large urban centres. The accumulation of infrastructure would also afford more opportunities for high leverage/high income jobs.

So large urban centres both attract and produce high income people at a greater rate. Large urban centres predict state size therefore large urban centres predict state inequality.

"Inequality" is a dubious measure to start a discussion with. As noted "inequality" goes up by locating rich people in big cities. However, it might also be interesting to study whether poor populations migrate or locate around the country due to benefit differences.

That study isn't talking about relocation, it's just comparing welfare benefits to entry level jobs. Do you really think poor people are that mobile? Moving states to chase better welfare benefits seems like incredibly hard work.

Does moving to get a 50k job instead of a 20k job seem like incredibly hard work?

For one you're assuming the cost of living doesn't change. Hawaii (I assume the source of the 50k "job") has a far higher cost of living than the state with the 20k figure for benefits, so that move isn't nearly as profitable as you assume.

There's also the fact that one of the major programs they included in their study, TAFN, is temporary for contiguous periods and has a 60 month lifetime cap. The expense of a move could easily cancel out this increase. I'm also unsure how they're handling medicade since the working poor can also access that (and get health care subsidies).

Finally this sentence from the introduction of the study:

"Contrary to stereotypes, there is no evidence that people on welfare are lazy or do not wish to work. Indeed, surveys of welfare recipients consistently show their desire for a job."

This is completely at odds with your hypothetical poor person moving around the country chasing the best welfare benefits.

Sorry, Aaron, but I think you have some faulty reasoning here. First, a fixed percentage of a higher salary earned in the city would result in a larger savings than that same percentage applied to a lower, rural salary. That Manhattan-earned 401k is going to go a long way in Florida. Second, moving can be cheap. 60 months of TANF in NY can amount to over $47,000. You could buy a uhaul for that price. Third, "lazy", and "do not wish to work", are not mutually exclusive to moving for a 150% raise.

Thomas, they're also exposing themselves to a much higher risk of bankruptcy, they have a lot fewer resources to reverse the move if they don't like the new location, and when they TANF runs out they're now left with the task of another relocation back to a less expensive district because they're now in a state with a high cost of living and no job. Also note that the 60 months of TANF is a lifetime cap, the cap for a contiguous period is much shorter (I think 24 months). So you think they'll rip up their lives to move to NY for 2 years to collect TANF, then either risk a higher level of poverty in NY or move back ripping up their lives again and restarting the job search from scratch. And do you really think people on TANF are contributing to their 401k?? You think they're planning to eat up two years of their lifetime cap when they know they might need it again in the future?

Neither of you have supplied any evidence that this supposed migration of poor people chasing benefits is actually happening, just this caricature of poor people expending great effort to avoid work and live off the government in schemes that are completely infeasible.

I suspect that's merely reflecting the degree of urbaniztion within the state rather than really being a function of population size.

"CA, TX, FL, NY, IL" vs "VT, AK, ME, HI"

% of urban population
"95, 85, 91, 88, 85" vs "39, 66, 39, 92"

That's a pretty good fit, with the exception of Hawaii.


The top 5 states all have length to width ratios greater than 1 (CA, 1.85; TX, 1.19; FL, 3.13; NY, 1.17; and IL, 1.86).

Vermont and Maine mess with where I was going with this, but Alaska and Hawaii do have length to width ratios that are less than 1.

Will see if I can do a correlation coefficient on inequality and the length-width ratio, but it is a busy day.

Probably meaningless.

Big-states = higher probability of having at least one large city. Large city = more specialization and economic stratification, more super-rich people, more inequality.

It's real easy to have low inequality in Wyoming since there are no large cities, and real easy to have high inequality in Massachusetts, since it's mostly Boston. The more urbanized a population is, the more inequality there is going to be.

States gain population because the economy is strong. A strong economy makes some very rich. Poor people and those mislabeled as poor because of demographics (young college grads) move to states with strong economies because of opportunities.

I would think that the smallest states would have the biggest and smallest differences in income randomly and the bigger states would be in the middle.

And BTW for you who are willing to give up some wealth for more equality, West Virginia is the place you aught to be.

With Mississippi right behind.

Cost of living differences have an impact here.

There are decent schools all throughout Vermont. California's decent schools are highly concentrated in rich areas.

Being rich in California is far more important than being rich in Vermont and being poor in California yields a much lower real standard of living than being poor in Vermont.

A better measure of living standards would show that inequality is *significantly* worse in places like San Francisco than the basic Census household income data suggest.

Variation in top income measures of inequality* is 100% explained by where rich people choose to live.

*Not actually measures of inequality properly, since they map only onto social welfare functions that are insane.

So basically you're telling me that rich people choose to live in the states the most people like to live? Whodathunkit?

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It looks like some of the written text in your posts are running off the screen. Can someone else
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