Rising Inequality as a Statistical Mirage?

I don't much care about rising inequality, but for a lot of people, it's a very important issue. And even if people disagree on the causes or the necessary policy responses (if any), everyone knows that inequality has exploded over the last 25 years or so, right?

Well, maybe not. Here's a fascinating new paper about inequality in America. From the abstract:

I show that from 1980 to 2000, college graduates have increasingly concentrated in metropolitan areas that are characterized by a high cost of housing. This implies that college graduates are increasingly exposed to a high cost of living and that the relative increase in their real wage may be smaller than the relative increase in their nominal wage. [. . .] I find that half of the documented increase in the return to college between 1980 and 2000 disappears when I use real wages. [. . . ]The empirical evidence indicates that relative demand shifts are more important than relative supply shifts, suggesting that the increase in well-being inequality between 1980 and 2000 is smaller than the increase in nominal wage inequality.

What's going on here? Well, it turns out that while it is true that the rich have been getting richer in nominal terms at a faster rate, much of that extra income is eaten up in higher rent.

This is not the only paper arguing that inequality may not have increased all that much. They are only looking at housing costs, but other goods show the same property. From a recent working paper:

We revisit the distributional consequences of increased imports from China by looking at the compositional differences in the basket of goods consumed by the poor and the rich in America. Using household data on non-durable consumption between 1994 and 2005 we document that much of the rise of income inequality has been offset by a relative decline in the price index of the poor.

Both papers are worth a read. I'm not claiming they are the end-all of the discussion on inequality, or that the issue is now settled. But it may very well have been the case that much of the increase in inequality is a statistical fiction, an artifact of how we collect and aggregate data.

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Thomas Sowell talks about

Thomas Sowell talks about the dangers of using household measures to determine inequality in his book "Economic Facts and Fallacies". When you account for changes in household composition much of the rising inequality in recent decades disappears.


Inequality is intrinsically a statistical artifact. It is, after all, not a property of the universe that can be directly measured. In order to attempt to measure it we cook up various techniques like income quintiles and Gini coefficients and all that rot, but the results are always implicit in the process.

You could analogize it to the mean of a normal distribution, but that would be an insult to means. There are actually natural processes that follow the normal distribution (or other distributions) that have means and variances that can be estimated. But when we purport to measure inequality we are not doing the same thing, for there is no underlying process with mathematical properties that allow us to model it with a distribution. We are basically just Making Shit Up.

Isn't "inequality" just

Isn't "inequality" just another word for the variance of a distribution? Suppose that income has a log-normal distribution. If the standard deviation increases, isn't it reasonable to say that income inequality is increasing?

The nature of big cities has changed

After the Civil Rights Acts of 1964 were implemented the public school systems of most large cities were trashed thus white flight flew. In the last 10 or 20 years most of the residential construction in the cities, at least on the Left Coast, have been high rise apartments and condos which attract young professional people and older people who want to escape their children. The majority of family people who move into the city are those who can afford private schools for their children. Most of the city school system children come from low income families. I suggest that most of the new young people in the cities are childless and/or sharing living space . . . unmarried.

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Inequality vs. Inequality

My perception is that when leftists whine about inequality, they aren't talking about the difference between people at the 10th percentile and people at the 90th percentile. There really isn't a lot of political hay to be made by attacking college-educated people with upper-middle-class incomes (except finance professionals). They're talking mostly about the difference between people in the top 1%, or even the top 0.1%, and everyone else.

So while this may be true, it's kind of beside the point, unless you can demonstrate that it's also true for those at the very top.

Depends on the context

They're talking mostly about the difference between people in the top 1%, or even the top 0.1%, and everyone else.

Democrats talk that way in the context of an election in order to reassure 99% of the electorate that they are not coming after their money. (It's a lie.)

Apart from elections, people on the left side of the spectrum engage in a contest of holiness by claiming to care about the difference between the bottom X % and everyone else.

Apart from elections and apart from competition in saintliness, there are many more attacks on people who have wealth encompassing not the top 1% but the top 80% or more. Leftists who decry "consumerism" are criticizing the vast majority and not merely the top 1%. Leftists who decry pollution, global warming, deforestation, and Walmart are in effect attacking everybody richer than the bottom fifth of Zimbabwe. While inequality is not explicitly the target here - the explicit target is various sins of the top 80%+ - my sense is that a lot of it is motivated by outrage at and resentment of inequalities large and small.

There is also the purported inequality, not purely financial, between the races and between the genders.

Exponential curve, not a bell curve.

Compare with the IQ curve. The bottom 1% have an average IQ of maybe 60 and the top 1% maybe an average of 160, can't remember the exact numbers. If the median was IQ was around 100-110 but the top 2% started at 500 and the top 1% range was 1,000-10,000 the curve would be very skewed. The income curve IS very skewed. If "rich" starts at $250K/year and very rich, $100 million a year . . . .

But there is a fundamental long term economic difference between the working class and the very rich. The working spends 80% of his annual income and when he dies he is lucky to pass on a house and a couple of cars free and clear to the next generation. The very rich doesn't know how to spend 10% of his annual increase and when he dies he leaves a a billion dollars to a tax exempt charity.

Gates' charity, for example. Recently people have noted that while the charity might be trying to cure malaria, his money is invested in un green and off shore American worker screwing international companies. It doesn't mean squat who is elected president, does it? Rule by billionaire, rule by tax exempt charity, same thing because the charity boards are controlled by our owners.

Bell Curve not Exponential Curve

Not sure what you are on about here. Be careful what you ask for.

IQ isn't truly a bell curve either. The tail on the left is limited to an IQ of zero. Once you are a vegetable there is no going lower. Ones IQ on the upside is unbounded. It's a kind of asymmetrical bell, with X axis as IQ and Y as number of people. Of course the mean still sits at 100.

The IQ curve is defined not merely by IQ but the quantities of people that have the higher IQs. It not an exponential curve because the Y axis measures the number of people with a particular IQ. As you move to higher IQs you get less people having those IQs. So the graph turns down, not up. Even if you plotted IQ on both the X and Y axis it would be a straight line not a exponential.

Same is true for income distribution. It too is bell shaped. It is definitely not exponentially shaped.

Here's an example: Pareto's wealth curve.

It's sideways but you get the picture. It looks like a lopsided bell, and not an exponential curve. Heck, and exponential curve would be a great thing. Most everyone rich and very few poor people.

What's funny is that the guy at the site doesn't realize that the curve is drawn incorrectly. It must be since there is nobody with zero, or negative wealth. No one earns (or has less than) a on that chart.

For a while there back int he 1980's Donald Trump was in negative territory on wealth, even though he was living a much richer lifestyle than me. If liquidated he would have still owed on all his loans. So if this is a chart of "net wealth" (not income) then many of the rich should be on the negative side.

Likewise if the chart was suppose to be about income. There are plenty of people who make nothing or next to nothing and live on charity, or on the dole. Even in Pareto's time. If they are alive then they are consuming something, and must either be earning a portion of that or not. If the are even partially self reliant then they must be somewhere between zero and his lowest number. If completely on the dole these people are in negative territory.

There are loads of people in NYC that are below negative, being totally on the dole. In fact, I betcha there are way more people earning negative income than super rich in NY.

Besides do you want to live in a country where the bell curve is skewed to large quantities of poor people? The whole idea that having a bell curve somehow proves that things are fair is nonsense in the first place. In a fair system there is no predetermined outcome on this.

If everyone is of equal capability, is equally prudent, has equal luck, has equally generous and frugal parent, lives on equally bountiful land, etc. then maybe you'd expect a straight vertical line curve on the income that everyone shared in common. The world isn't like this so all portions of the curve doesn't get an equal share.

My math isn't so good

9 guys drinking beer in a tavern. Their median net worth is $20K and their mean net worth is $40k. Bill gates walks in. The median net worth of 10 becomes $22K and their mean net worth is $20 billion?

Seems to me the difference between the mean and median is more important than the actual numbers. When 10% of the people own 90% of the assets . . . .

Along the same lines as billwald....

What's going on here? Well, it turns out that while it is true that the rich have been getting richer in nominal terms at a faster rate, much of that extra income is eaten up in higher rent.

Ok. And to whom are these increased rents being paid?

I can’t get the article to open, which is a shame ‘cuz I’m really curious about what it actually demonstrates. Does this article debunk the idea that there is a growth in either income disparity or well-being disparity? Or does it merely debunk the idea that we can account for the growth of either disparity by looking at the growth of education disparity?

I suspect the article demonstrates that people getting college educations tend to work in urban areas where they are highly productive, but the value of the productivity is in fact not accruing to them. It is, instead, accruing largely to their employers and to people providing urban services (including landlords).

That message would hardly mollify people concerned with social inequality. To the contrary, politicians and pundits try to quiet populist unrest over inequality by telling people to pick themselves up by their bootstraps and go get more education. I suspect this study demonstrates that quite a bit of the growth of wealth disparity cannot be explained by the increase in educational disparity. After all, it’s not by and large the PhDs who have gotten fabulously wealthy since 1980. Rather, people getting educations today are like gold prospectors in the 1890s; they slave away while the railroad companies and pick-vendors get rich off their labor.

I don’t mean to impugn railroad companies, pick-vendors, or urban service providers. But let’s not be confused about the real dynamics at work here.

Ok. And to whom are these

Ok. And to whom are these increased rents being paid?

Good question. I'll have to read the paper again to answer it better. I think it might be related to Brandon's point above, about "upper-middle-class" inequality vs. "super rich" inequality.