On Inequality

When we talk about income over time, we recognize that it has two components. First, how much do people earn today compared to the past? Second, how much is that money worth in material (“utility”) terms? In other words, if my income goes from $20K a year to $40K a year, but the prices of everything I buy also double, my “real” income has stayed exactly the same, because my material well-being is unchanged.


Now turn to income inequality. On its face, income inequality seems much, much simpler. If a rich person earns 100 times what a poor person earns in 1950, and 1000 times a poor income in 2011, then inequality of income has increased tenfold. After all, inflation acts on both the “rich” money and the “poor” money, so the effect cancels out when we get the ratio. Right?


That’s a very common assumption, and it’s the one used in official statistics, but it’s not quite right. Let’s look at a hypothetical economy in two years, 1950 and 2011.


There are two products: food and air conditioning, with two quality levels.


Year    Product    Quality    Price

1950   Food        Low         $5

1950   Food        High        $10

1950   A/C         Low         $10

1950   A/C          High        $50


2011   Food       Low          $1

2011   Food       High         $200

2011   A/C         Low          $10

2011   A/C          High         $1000


There are two income classes:


Year     Class     Income

1950    Poor      $5

1950    Rich      $60


2011    Poor      $11

2011    Rich      $1200


In 1950, the poor people get food and no A/C. The rich people buy A/C and high quality food.

In 2011, everyone buys food and A/C, both either low or high quality based on your income.


What’s the inflation rate? Remember, the inflation rate is just a way to convert one year’s income to another’s such that you’ll get equal utility from both incomes. Since there’s no such thing as a “typical” consumer in this hypothetical society, we’ll do this twice, once for each income class.


Look at the rich first. Since the rich are buying exactly the same products in 2011 as in 1950 (high quality food and A/C), we know that $1200 dollars in 2011 is the equivalent, in terms of material well-being, of $60 in 1950. So that’s a 2,000% increase in all prices (including the price of rich labor), with 0% real growth.


Now look at the poor. A poor person in 2011 has low quality food and low quality A/C, and earns $11 a year. To have the same material well-being in 1950–to purchase low-quality food and A/C in that year–they would need $15. Whoah. $15 in 1950 is the utility equivalent of $11 in 2011. That’s deflation–prices have gone down by over 25%. And incomes have tripled in “real” terms.


On to inequality. First, the way everyone actually does it: look at the ratio of poor/rich incomes in both years, and compare them. In 1950, poor incomes were 7% of rich incomes. In 2011, poor incomes are only 1% of rich incomes. It’s a new gilded age!


Next we’ll control for the weird, distinct inflation rates. 1950 stays the same–poor people make 7% of the rich income. But now let’s look at 2011, but use 1950 prices. Easy. $11 in 2011 is the same as $15 in 1950. $1200 in 2011 is the same as $60 in 1950. So, in 2011, poor incomes are $15/$60, or 25% of rich incomes. Inequality, it turns out, has gone down quite a bit.


Which vision of inequality is “correct”? Both, and neither. Materially, the poor are better off compared to the rich than they were before. But if there were, say, an expensive educational prerequisite for earning the rich salary, it’ll clearly be tougher for poor people to afford. In other words, life will be harder for poor people where they’re directly competing with rich people, but easier everywhere else.




It’s easy to construct a hypothetical world that fits your preconceptions. Do we really live in a world where material inequality has decreased? Well, maybe. Walk into a poor person’s house, and then a rich person’s house. You’ll see many of the same appliances, entertainment devices, etc. Yes, the quality will be much different, but we no longer have many poor people unable to keep their food cold because they lack refrigeration. That’s a big change since 1920, when fewer than 10% of households had a refrigerator, around 1% had a dishwasher, and under 50% had a flush toilet. Or 1960, when the bottom 20% still didn’t have refrigerators, 25% didn’t have flush toilets, 30% didn’t have washing machines, and only 5% of households had dishwashers. In 1920, the rich could dramatically increase their mobility by buying a car. Today, everyone flies–the rich go first class, or in a private jet, but the difference in capabilities between a private jet and coach is much, much less than the difference between driving and walking. Those sorts of things have a pretty powerful effect on quality of life.


In reality, material inequality has probably increased–but not by nearly as much as income inequality. Two U Chicago researchers recently found that controlling for distinct inflation rates for the poor and the rich (due to them buying different “baskets” of goods) eliminated half of the increase in inequality from 1994-2005 (Broda and Romalis 2009). They also concluded that this pattern was not limited to that recent period (the only one for which they had sufficient data). Just to reality-check, let’s look at some other trends.


If they’re right, and if utility has anything to do with happiness, there should be a disconnect between the trends in happiness inequality and income inequality. In fact, self-reported happiness inequality has decreased dramatically over the past four decades, the black-white happiness gap is 2/3 gone, and the gender happiness gap has disappeared entirely (here: http://isites.harvard.edu/fs/docs/icb.topic457678.files//HappinessInequality.pdf).


Declining marginal utility for spending at the top of the distribution would also lead to lower consumption inequality (since you get relatively less out of your 1 millionth dollar relative to the past, and more from your 1000th dollar relative to the past, you’ll be less likely to spend your 1 millionth dollar and more likely to spend your 1000th dollar). And indeed, consumption inequality has also increased much slower than income inequality (here: http://www.aeaweb.org/annual_mtg_papers/2007/0105_1430_0603.pdf).




The takeaway: there are many types of inequality. Nominal income inequality has increased dramatically, and certain types of inequality have increased even more (some goods, like admittance to a top-tier college or a house in a great location, necessarily create direct competition for a limited number of top slots). This explains why we’re increasingly concerned about unequal access to education and healthcare. On the other hand, growth in the material difference between the lives of the rich and the poor has been much slower, as has the growth in consumption inequality.


Most pundits, protestors, and economists focus solely on inequality in nominal incomes. But it isn’t clear to me that this variety of inequality is so obviously more important than, say, happiness inequality, which has declined. Or inequality of material well-being, or consumption inequality, which have both increased far less. (E.g., focusing on consumption inequality allows us to worry less about fairly wealthy, low-income elderly and more about, say, low-income parents.) Or liberty inequality, which has probably increased dramatically (the number of people imprisoned for drug crimes has gone up twelve times since 1980, and the total incarceration rate has gone up fivefold) but won’t be solved through income redistribution. Or inequality between citizens and non-citizens (in social, economic, and legal status) which is hugely influenced/determined by government policy–and therefore much easier to influence through politics.


Next time you hear someone say that inequality has increased, ask yourself which type(s) of inequality they’re actually thinking about. They may assume that it’s the only type, or the obviously most important type, but you shouldn’t make the same mistake.

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