Beautiful evidence

One of my favorite authors on the visual display of information is Edward Tufte. Besides despensing great advice on presenting data, he’s produced a series of beautiful books. They’re really picture books for the data nerd set.

I think he’d like this diagram:
Income levels by selected percentile

The only thing better would be to figure out how to plot the whole density for each year. The black lines give preference for the selected percentiles, but there’s no a priori reason to think the 99 percentile is some how more important than the 96 percentile. Because this bias is built in, the diagram is a little misleading.

But I like it, nonetheless.

If you read through the comments at Prof. Kenworthy’s post, you’ll see many people committing the fallacy of assuming the same individual is represented by a single percentile line on the chart. As I’ve pointed out before, people do not stay within the same percentile (or decile or quintile, etc) over their lives. The churn of poverty is very high. Before age 75, for example, 50% of Americans will have spent some time below the poverty line and 50% spent some time at level of income ten times the poverty line. Only about 20% of Americans won’t experience one of these extremes.

UPDATE: Yes, Nancy, that means 30% of Americans will have been rich and poor in their lifetimes.

UPDATE 2: I swear to all that is holy that I titled this post before reading the post over at CT.

UPDATE 3: These Sala-i-martin (2002) charts are an improvement, except for the log scale, on the Kenworthy ones:
USA income distribution

World income distribution

What’s fair?

Suppose you and I got in a car accident and both suffered from total amnesia. We’re in a hospital somewhere, neither of us have identification, but luckily all of the deeds of our possessions were in the trunk of the car and now lay before us on a hospital bed. Oh, also, there are results of the IQ test we apparently took together before the accident. One of us is a bit smarter than the other, but we don’t know which.

We can’t tell by the short conversations we’ve had who is the smarter nor who would have owned what.

Now we’ve been discharged from the hospital, but before we go on our separate ways we have to decide how to divvy up the possessions. Clearly, one of us is smarter and has the means to earn a higher income. What would be a fair division the deeds?

Now here’s a rather unrealistic catch: suppose we were deciding, today before we leave the hospital, how to divvy up our possessions, whatever they may be, a year from now? What would be the most fair way to do so?

Relative poverty?

Lane Kenworthy takes exception to Paul Krugman‘s use of relative poverty rates to compare countries. The idea is that every country has a different level of income below which they classify a family as poor. Ken says one such relative measure of poverty is counting the number of people that earn less than half of the median income. Because the U.S. has higher incomes than most every other country, this definition would classify many more people as poor.

His post explains that by using absolute measures of income (like saying anyone that makes the equivalent of less than $x), the U.S. turns out to be about in the middle of the pack in terms of the number of poor people. He ends the post with this comment:

This is not to suggest that we should be satisfied with our absolute poverty ranking. Given our nation’s economic wealth, incomes for Americans at the low end of the distribution are far lower than they could be.

So he thinks we should care about the relative poverty measure, just that we shouldn’t use it to compare the U.S. against other countries.

Per my discussion the other day, I’m not sure why we should care about a measure of poverty that relies on comparing incomes. We can all agree that in terms of material outcomes, today’s American poor are an order of magnitude better off than the poor just a few generations ago and they’re several orders of magnitude better off then some poor souls living today continents away. To the extent that poverty is relative to the culture and norms of the day and place, the poor see themselves as poor (or the rest of us see them as poor) by comparing themselves to some culturally determined standard. The rich may not be the standard barer. Thus, defining “the poor” as contrasted to “the rich” may be missing the point.

Even if we define poverty in terms of health care (or health outcomes), labor hours, education attainment, or whatever, its worth pointing out that we’re doing so without reference to the behaviors of the rich. I just don’t see why a relative measure of poverty based on income inequality matters for what we really care about.

What is poverty?

Brad DeLong:

So were workers in London in 1740 as miserably poor as workers in Milan, Leipzig, and Beijing, spending most if not all on their income on bare caloric maintenance in the form of the grain typical of their time and place? Or were the workers of London relatively rich–and deciding to spend their relative wealth on the superior taste and mouth feel of yeasty wheat bread rather than leaden oatcakes and on the associated symbolic declaration that they were proud and free Englishmen, not benighted barbarous Scots (or horses)?

What is the “consumption” we tend to find in our utility functions?

Did you notice Prof. DeLong didn’t ask, “Were the London workers poor because they felt compelled to eat like rich people (and that costs more)?”

Even if you believe consumption is defined relative to ones culture it does NOT follow that income inequality matters. Perhaps the rich set the cultural norm of eating wheat bread, but its just as likely that norm was formed and maintained in the lower income classes.

This is why I didn’t like Frank’s Falling Behind. In the preface, he explicitly says envy isn’t what’s driving people’s natural tendency to compare their lot with their neighbors. He says its culture and the subjectiveness of consumption that matters. He brings up the example of the preference for high quality cars. What’s considered high quality today (GPS, leather seats, whatever) is very different from the what was considered high quality in the past. Its likely, though, that buyers of high quality cars today are no more happy with their purchase than buyers of high quality cars a few decades ago. Cars have gotten objectively better, but subjectively they’re still the same “high quality”.

These are excellent points and its a great example. There is definitely a cultural element to consumption and certainly overall happiness, however measured, isn’t tracking with the vast improvements in quality we’ve seen over the years. Frank, though, spends all of the book talking about income inequality as if the consumption patterns of the rich automatically translate into these cultural factors. He says envy of the rich doesn’t matter, but that’s what he ends up dwelling on.

In Frank’s eyes, the wheat bread norm hurt the lower classes. This is debatable (who would want to think themselves a Scot!), but even giving him that, measuring income inequality wouldn’t tell you anything about that norm. Why would we think increasing income inequality would be correlated with the development of these sorts of norms?

Acting like the rich may be one factor that drives cultural norms of consumption and its likely that cultural trends flow primarily from from elites. But not all elites are rich and more importantly cultural trends can flow uphill (hip-hop anyone?). My point is that consumption norms matter, but thinking only in terms of high and low incomes will have us miss most of the story.

Sentences of Enduring Value

Just in case you missed it, let me repeat: when it comes to the kind of intra-nation inequality that we should really care about (if we are going to worry about intra-nation inequality at all), we “do not know.” As in “know” and “not” put together. “Not” is the word of negation, by the way. And the last I looked, not = not, as it usually does on most Wednesdays. Would you like to hear more on what is implied by the conjunction of “not” and “know”?


Its the consumption stupid!

A couple weeks ago I made the point that it is strange to look at changes in income inequality and make calls for redistribution. First, its not clear that changes in inequality should matter for someone that cares about social justice. Even if changes in inequality rather than just the existence of it mattered for some reason, I made the argument that tracking changes in the differences between income percentiles confuses the subject.

Income levels vary drastically over a family’s lifetime ((BTW, the statistics on incomes are usually measured by the household or the family. This can be confusing if you try to compare these statistics to your own paycheck… something to keep in mind.)). Young families are smaller (maybe one or two people), the income earners are less experienced and therefore less skilled and often a big chunk of the family’s time is spent building human capital (an economist’s phrase for what normal people call “going to school”). All of these factors mean that younger families have less income.

As the family’s income earners get older they have more and more experience and they spend most of their time in the work force. Also, more people are married at this stage in their lives and most couples have children so family size is much larger. The family’s income go up, but they don’t consume all that extra income; they build their nest egg instead.

Later in life, the kids leave home and the income earners start retiring from the work force. The family shrinks and its income shrinks. It lives off its savings instead.

This is why income data show an inverted U shape over lifetimes. Young and old families have low incomes and middle aged families have high incomes. Also, this life-cycle story tells us where to look for explanations of changing inequality. Inequality could be increasing as a result of demographic changes (more middle aged families relative to young and old). I suspect the ageing of the baby boomers plays an important part in the story.

But the demographic story doesn’t explain this picture:

If demographics were the main driver of inequality, the inverted U wouldn’t be getting more dramatic over time.

Increasing inequality also could be a result of changes in the way the economy rewards different kinds of human capital. There were two types of human capital in the above story: the kind that you get at school and the kind you get with experience on the job. First, if skills learned in college ((Or if college let you demonstrate you have certain skills. I’ve suggested before that college is more about signaling quality rather than actually building quality.)) are more and more important for today’s jobs then people will have the incentives to get more education. Young people spending more time in college lowers their incomes and exasperates income inequality.

Second, if on the job knowledge is more important these days, then experienced folks will be paid more. By definition only older workers can be more experienced so this can be driving what we see in the above diagram.

The point of this post’s title, though, is that its not incomes that families care about for the most part. Its consumption. You can’t eat, drive or live in your paycheck. Consumption, as it turns out, varies much less over the life-cycle than income ((It varies about 10%, relative to about 50% variation in incomes, and is hump shaped like income (Gourinchas and Parker). This is an unsolved mystery in economics because standard theory says it shouldn’t vary at all.)) and this NYT opinion piece by two Fed economist argues consumption, surprisingly, doesn’t vary much between rich and poor.

UPDATE: Mark Thoma has more on consumption vs. income inequality. That post, Krugman’s reply to Cox and Alm and the general discussion is so damned muddied. People slip so easily between a descriptive “this is how it is” discussion to a normative “this is how it ought to be” discussion. For example, the Fed piece Thoma excerpts starts off by talking about the best measure of the poverty line (income or consumption) and then quickly gets side-tracked into a discussion of which measures are easiest to construct. Thoma himself uses the Fed’s measurement discussion as a spring board for a short discussion about what he thinks poverty really is (short Thoma, “its not about material stuff, except it is”). What that has to do with data issues, I don’t know. He then jumps from his quick and dirty definition of poverty to a sermon on the “decent and right” thing to do.

Often times, popular discussions of this topic have an air of back filling and data mining. People have some policy they want to implement and then they go squeeze data until it supports their policy. Call me naive, but I think policy should be guided by the science not the other way around.

One of the reasons I’m so attracted to this topic, though, is this level of muddiness. I’d like to think there would be some premium in it for the guy that can try to make sense out of it all. Economic inequality is an extremely complex topic. I believe we need to take a deep breath and try to understand the issue as level headed as possible. This means we need to measure it, understand inequality’s stylized facts and have clean theories that can be explicitly tested.

Income inequality

Politicians screaming about inequality often provoke analysis like this. The point being the rich have gotten much richer in the last couple of decades but the poor have had to scrape by with on a few points of real income growth. I have a couple complaints about this sort of analysis.

First, which theory of justice requires there to be equal sharing of economic growth. I get strict egalitarians want to equalize incomes, but this doesn’t require them to go as far as lamenting about variances in growth rates. All they should have to do to get their point across is to take a look at the non-zero gini coefficient and be done with it. Why bother looking at differences in growth rates?

Second, once you accept some level of income inequality is inevitable, tracking income changes by income percentiles makes no sense. People aren’t stuck in income ranks. Lots of people start their careers in a lower income percentile and then move their way up through their careers. So really what one is doing when they track changes in percentiles is tracking a particular demographic. If that’s what you’re really doing, then why not do it explicitly?

This first diagram shows median income by age group since 1967 ((Source.)). Clearly, income growth has been much less dramatic in the youngest and oldest age groups. It seems easy to come up with perfectly legitimate reasons why this would be so. To me, this diagram doesn’t scream for the need for redistribution, but maybe you see differently.

BTW, you can track my dad in this diagram. He starts out in 1967 on the 15-24 line, then he jumps up to the 25-35 line in 1978, etc. Following my dad’s trajectory might be easier with this second diagram.


Its easy to see from this diagram that most of the income growth has happened in the middle ages. The inverted U-shaped pattern of lifetime income has become more dramatic in recent decades. Again, I don’t see a problem here.

UPDATED: fixed some typos.

Poverty and young adults

In response to this post over at Volokh Conspiracy, commenter Paul says, “One of th[e] adults making “$7/day” last year was my 18 year old daughter who filed a tax return in order to get her withheld income taxes refunded from her summer job.”

Paul’s daughter is surprisingly representative of those in poverty:

UC Davis Econ in the News

Prof. Lindert’s work on pre-modern inequality is discussed by Tim Harford in the Financial Times.

The US, as the richest society in history, is therefore potentially the most unequal in history. The US population could be kept alive for the cost of about $100bn a year.

If the elites had total control, that would leave another $13,800bn (the rest of US GDP) a year to distribute among friends of the president – almost enough to give a sum equal to Bill Gates’s lifetime wealth to a new crony each working day.

But the US is not remotely this exploitative, no matter what you may feel the next time you buy a copy of Windows.

In the newly coined jargon, it has a low “inequality extraction ratio”, meaning that the poor have much more than it would take to keep them alive.

That is faint praise for the US, perhaps. But it is interesting to observe that while modern societies are rich enough to be much more unequal than their predecessors, they show similar patterns of income inequality. Perhaps – I am speculating wildly – human societies have some hard-wired tolerance for inequality?

What would determine that “hard-wired tolerance for inequality”? Does it vary by society? If so, why?

Would you have expected this if countries had the same dgp?

While YNS! and EI generate fake inequality data, here’s the real deal:
Income and inequality for 2003
The gini data (xls) are from the world bank and the income data (xls) are from the penn world tables (oh, that’s log income per capita).

Here’s the plot for “Europe” ((Europe has been conveniently defined to get the result I wanted… check the third tab on the spreadsheet for details.)) and the US: