The average income in this economy is $16.53. The median income in this economy is $15.90. Suppose you take a snapshot of this economy today, and then revisit it 20 years from now and then in 20 years you find that the median income and average income calculations are exactly the same. Does this imply that individuals in this economy are no better off 20 years from now than they are today?

Not at all. In fact, you learn almost nothing from the summary statistics I presented above. It might be the case that individuals are considerably worse off, better off or somewhere in between. Consider how a typical hierarchy works. College students graduate and elevate into the $10 job that Person 1 has today. In each year the oldest person (assuming salaries are aligned with age here) retires, and this allows each younger worker to move up the income ladder by one spot. So in year two, the original Person 1 now earns $10.50, and Person 19 now occupies the spot of Person 20 and earns $25.27. If the rate of entry of college grads is equal to the rate of exit of retirees, then what you’d see is that every year a person’s living standard increases by 5% and all at the same time the average living standard of the population remains unchanged. So, if we were able to track people over time, a person starting out as Person 1 would end up 153% better off by the end of the period – this is most certainly different than what the aggregate statistics would tell us.

Of course, this could work the other way too! It might be the case that every worker is experiencing a 5% decline in wages each year, but that on average living standards are getting no worse. Further, if the rate of entry into the professions exceeds the rate of exit, it is likely that we’ll see stagnation in wages. On the other hand if the rate of exit exceeds the rate of entry, then we’d likely see increases in wages beyond what I show here.

What is unusual is that so many people seem to confuse aggregate statistics for individual well-being. What is more unusual is that many academic departments actually work this way. Very few faculty members (that I know of) complain about the stagnation in their own wages over time, even as global departmental budgets remain unchanged. So long as retirements and new hires are matched up, every faculty member can enjoy raises year after year after year while the department budget remains unaltered. Is it really so hard to imagine this happening at a larger level? Indeed, the publicly available data that follows people over time provides more evidence for this view than for the “life is no better today” view.

By the end of the book, I am not quite sure what he wants. There are many pages dedicated to the horrific conditions that prevailed (and still do) in some places. But in the next sentence he seems to also denigrate anything that is done to ameliorate such things. For example, in talking about the exercise facilities, hair cuts, massages, dry cleaning and even “sleep pods” that are offered by some employers – the author ends the passage by saying that all of this is a way to induce workers to never have to go home so that they could work all the time.

I’d like to see an author write down simply what they expect the world to look like and whether anything done by a corporation for and to its workers is agreeable. I also find it odd that such tensions arise in a book like this, and at the same time there is a yearning in society among some folks for corporations to do even more for their workers – provide more health insurance, allow them to spend more time at work on volunteer activities, and the like.

I found my head spinning a few times in the book. Here is one passage:

Managers have inclined toward … more benevolent policies when they faced the following … a liberal or progressive national political climate … since they first came here in the 1980s, Japanese automakers with U.S. operations have been keenly aware that they must work hard to be perceived as good neighbors rather than as interlopers who are stealing away American jobs and wealth.

There are way too many quotes like that in the book for my taste, and I’d be blogging it way too much if I focused on them. But it’s nice to know that the 1980s were a time of Progressivism in the US (did someone tell this to Krugman, DeLong, Pelosi, Obama, and the current left?) It’s also nice to know that this simple idea seems to have been refuted by the author with the stroke of a pen.

And here’s another example of the non-charitable, broad-brush view (straw man-ish too) of non-Progressive ideas that I encounter quite a bit:

The bottom line: American conservatives and many businessmen have long maintained that all problems can be solved via the free market and private enterprise.

Really?

You are going to see a lot of apoplexy on the right trying to defend their views of the world by arguing against these data. It is certainly possible to do it, and despite common defenses of the left, it is not a task without merit. However, color me puzzled by the reaction from the right, especially the classically liberal side of it all.

Isn’t it one of “our” core beliefs that the role of the state has been advancing during the last 40 years? Isn’t it our contention that despite a few visible moves toward deregulation that the economy is far more cartelized, credentialized and regulated than 40 years ago? Isn’t it “our” contention that welfare programs have not worked, that the state education system is bloated and inefficient, that the health care system is far from being market oriented (or even market paid for), that the tentacles of governments at all levels are reaching into places no one in their right mind would ever imagine, that immigration policy is a disaster, and so on and on and on?

If that is what we truly believe, then it is completely shocking that the reaction to the current data (and the data coming out for the past decade or so) has not been, “Exactly, what else would you expect?”

But I have not seen such an argument made by many people. Now I have pretty much stopped watching TV with the exception of college football on late Saturdays so it is possible I am missing something here, but even if some people were making this argument I am sure I would be moderately aware of it.

So what we will see for the next 14 horrible months running up the election is a bounty of blathering about whether the data is right or not, rather than an impassioned and reasoned defense of ideas which point to stagnating income and living standards and increased inequality as an outcome. Commercial society has not failed here folks. Not one bit.

Imagine we had twenty people in each of two worlds, call them Sunnyville and Cloudyville. Here is what the list of incomes for people in Sunnyville looks like:

{58 92 45 93 36 28 92 4 23 39 78 31 56 62 99 86 42 34 71 51}

And here is what the list of incomes for the people in Cloudyville looks loke:

{59 96 93 48 45 98 51 31 76 99 75 80 51 35 18 95 73 16 41 44}

Can any of you, upon examining the lists, ascertain which income distribution is in some sense, “better?” Even looking only at twenty numbers is would seem a near impossible task to compare them. But the task may appear easier if y0u use some common statistical metrics to summarize all of these numbers into a few easier to digest bits. (By the way, I used Excel’s random number generator to give me numbers between zero and 100). The average of the Sunnyville incomes is $56 while the average of the Cloudy is $61. Whatever you think of averages, given that you know the population of each place is the same, it is certain that Cloudyville is richer. When it comes to measuring income distributions, these 4 approaches are generally taken:

Approach # 1:  Relative inequality approach

• This approach generally focuses on percentage differences in income between people.
• For example, making the following comparison is using a relative inequality approach:
  • Wintercow earns $80,000 per year
  • Summercow earns $800,000
  • Wintercow’s income is 10% of Summercow’s
  • Similarly, if Wintercow’s income increases to $100,000 and Summercow’s income increases to $1,000,000, the our measure of relative inequality is unchanged – Wintercow’s income is still only 10% of Summercow’s.
• The crude reports of things like, “A Fortune 500 CEO makes 450 times more than a minimum wage worker” is a measure of relative inequality.
• The income inequality measures that you are used to looking at are very likely to be relative inequality measures. For example, if you say something like, “the income share of the poorest 20% of the population is the same today as it was in 1980″ you are making a statement about relative inequality.
  • Here is how this relative inequality measure would change for this countries:
    • Before change: {1,2,2,5,5} the poorest 20% of the people earn 6.7% of the income
    • After change: {1,2,2,5,10} the poorest 20% of the people earn 5.0% of the income
    • Therefore relative inequality has increased (notice I did not apply a normative criterion to this)
• The Gini coefficient that I reported in the two previous posts is also a measure of relative inequality. I’ll describe how it is calculated, in all likelihood, in the next post in the series.

Approach #2: Absolute Inequality Approach

• This approach is generally not reported on very much despite its intuitive appeal to people who dislike any notion of inequality. It is generally measuring inequality not by looking at percentage differences in income between people but rather by raw income differences between people.
• For example, making the following comparison is using an absolute inequality approach:
  • Wintercow’s income is $80,000 per year
  • Summercow’s income is $800,000 per year
  • Wintercow’s income is $720,000 lower than Summercow’s
  • You’ll notice two things about this measure. First, if Wintercow and Summercow each experience the same percentage increase in income next year, then while the first approach above would show no change in inequality, while this measure would.
    • For example, if their income increases by 25% each, as in the first approach, the relative inequality measure would be unchanged (Summercow still earns 10x more than Wintercow), the absolute measure will have increased (noticed I did not say, “worse”). Their incomes will now differ by $900,000.
  • Interestingly, using an absolute inequality approach may lead you to some counterintuitive interpretations of changes.
    • Wintercow’s income is $8 per year (yes, eight dollars)
    • Summercow’s income is $700,000 per year
    • In this case absolute inequality is “better” than it was in the case just above.
    • In short, looking just at raw income differences doesn’t tell us much about the goodness or badness or desirability or anything much about income distributions.
      • One more thought experiment. What if I told you that the absolute inequality between the richest dude and the median dude in Wintercowistan was $100,000 while the absolute inequality between the richest dude and the median dude in Summercowistan was only $80,000, would this mean that Summercowistan was “more equal” or even a better place to live?
      • What if the median income in Wintercowistan was $1,000,000 with the richest dude making $1.1 million and in Summercowistan the median income was $50,000 with the richest dude making $130,000, would that change your opinion of things? There are obvious parallels to real world data and not just farm country data.

Approach #3:  Absolute income approach

• How many people receive how much income? For example, you might ask what share of workers earns above a particular wage.
• A special case of this approach is the absolute poverty approach in which a poverty line is drawn and a poverty measure is calculated (such as the percentage of residents falling below this line)

• Here is how this absolute income measure would change for this country:
  • Before change: {1,2,2,5,5} 40% of the workers earn a high wage
  • After change: {1,2,6,8,10} 60% of the workers earn a high wage
  • Therefore this measure of “inequality” has decreased. Of course, the interpretation of this measure depends on exactly how I frame the measurement.
• The measure is vastly different than the relative inequality measure and absolute inequality measure above and changes in those do not correlate well with changes in this and vice versa – so again, using the metric to report on “inequality” depends on what we care about.
  • For example, one might want to “refute” the notion that income inequality is increasing by referencing a table like this one (Table H-17 from the Census Historical Income tables). In 1967 only 14.4% of the population of households earned $75,000 or more. By 2009, this number had risen to 31.6%. In other words, nearly one in three households earns over $75,000 per year. Or, the share of households earning below $50,000 was 63.6% in 1967. Today that number is 50.1%.
  • Those numbers seem to be telling a different story than the “we are getting poorer” story, or the rich is getting richer at the poor’s expense story. Again, I emphasize there are problems with using this figure to make this point, although it does seem to cause some problems for the conventional wisdom. We’ll dig into the claims and the actual data stories a few posts from now.

Approach #4:  Relative poverty approach

• This approach defines a group that is considered “poor” and then computes an income metric for the group.
• Table H-1 of the Historical Census tables is one way to examine this sort of a metric. For example, that table shows that the households in the poorest 20% of households had a maximum income of $16,845 in 1967 and the maximum income of the households in the poorest 20% today is $20,453.
• A more common approach would be to compute a mean or median for the group under study. Note, too, that it is common to compute income dispersion statistics within various subpopulations of the distribution. This post is already too long to get into details or analysis of these points, for now I just need to show you the various ways of doing measurement.

Approach #5:  Income mobility analysis

• Can only be done when data are available over time.  And this can only be done correctly when we can actually follow the same people and households and families over time. Even if we are able to track the same people, it is not clear what measure is of most interest.
• For me, I would care about things like, “the probability that a given family’s standard of living can increase by ABC% or $ABC over some particular time frame” with ABC changing to suit how much mobility you care about. There are literally dozens of other ways to think about mobility. The general point about mobility is that if there is a single concept that captures the “on the ground” concerns of people, it is some notion of mobility – whether or not the American Dream is achievable for particular persons.
• Two quick points:
  • Commonly presented measures of “income-mobility” do not capture what I would consider “mobility” or what I think you would either. For example, in the Development Economics literature, we often see reported the measure of income mobility that asks what the total change in the difference in the shares of income held by the poor and non-poor is. That looks and sounds much more like one of the first three measures above than it does a true mobility measure.
    • Consider again the following country:
  • • Before change: {1,2,2,5,5} the poorest 20% of the people earn 6.7% of the income; the richest 20% earn 33% of the income.
    • After change: {1,2,2,5,10} the poorest 20% of the people earn 5.0% of the income; the richest 20% earn 50% of the income
      • Therefore, the income share of the poorest fell by 1.7% and the income share of the richest increased by 16.7%. So the total change in the share of income held by the rich versus the poor was 18.4%. I actually have  a hard time conceptualizing this.
  • For all that folks (including myself) celebrate the notion of mobility, I actually am having a hard time convincing myself it is important because the way we think about mobility is framed in a zero-sum manner – we think of our mobility within the distribution of people. This notion totally abstracts from how well off we are, on our own merits. I think some of the same criticisms levied against relative inequality measures (which we will get into) can be thrown out mobility measures as well. It’s probably the best we can do, but it is best if we are cognizant of it.

This post is already massively long, so we’ll leave it for tomorrow’s post to comment on what these all mean, and what we might look for in a desirable income inequality measure.

According to this Gini Measure (which I emphasize we will learn more about in upcoming posts) it appears that the increase in inequality has occurred within all ethnic classes. Inequality among whites increased at 17.8% since 1967 while among blacks inequality actually increased less (by 11.3%) and among hispanics it increased more (by 22.3%). If there is any ethnic trend apparent it seems to be that there is a convergence of inequality across ethnic groups. Whereas in the beginning of the period the Gini for Hispanics was lowest at .373 and highest for blacks at .432 (about a 16% difference between groups, today all ethnic groups seem to be experience “equal inequality” with only a 5% gap between the most unequal distribution (for blacks) and the least (hispanics).

Now to make this claim more rigorous one would have to do much more serious work than this. Does this “convergence” raise any interesting questions? Whatever has been driving inequality changes seems to be doing it for all ethnic classes. What can you NOT deduce from this information? That income differences across ethnicities is shrinking. It could very well be the case that white incomes are increasing faster than black incomes, but that the dispersion in white incomes is also increasing faster than the dispersion in black incomes. We’d have to couple this information with other income data to say more. The reason I bring this up is that income inequality data, particularly focusing on a single metric, are not sufficient statistics (to use the parlance of statisticians) for identifying many underlying social phenomena.

For those of you forgetting what we mean by a sufficient statistic, it is easiest to show you with an example. Suppose I have an underlying population of two numbers. I know that one of them is the number 7. In this case, if I am told that the arithmetic mean, the average, is 9, then this mean is sufficient to tell me everything else about the distribution without actually needing to be given the number. In other words, I know that the other number must be 11.

OK, so in my view this post was really not all that interesting. This promises to change very soon (I listen to too much talk radio, where they constantly promise you that something really interesting will be delivered to you after the next commercial break).

Here are the previous posts in this series:

• Understanding the Genie in the Bottle, Volume I (showing the overall Gini Index and raising some questions about how to think about it)
• These three posts (here, here and here) show the illusory nature of even the most basic agreed upon properly measured measures of inequality, the distinction between actual consumption and potential consumption, and some ethical questions raised by blindly looking at the data
• This post is an outline of my lecture notes on the basics of measuring inequality.