Thursday, May 23, 2024

A Simple Statistic for Measuring Income Inequality

The traditional macroeconomic measures of economy-wide  performance are the unemployment rate and the inflation rate.  When both are low the economy is thought to be performing well.  When one or both are high, there are economy-wide problems of some sort.  But even when both of these measures are low, might it be that a significant fraction of the population is not benefiting from that overall good performance and, indeed, could it be that many are struggling?  While most can readily admit to that possibility, out of sight is out of mind, or if you prefer Daniel Kahneman's acronym from Thinking, Fast and Slow, there is WYSIATI.  In other words, unless there is a third statistic to go along with the unemployment rate and inflation rate, one for measuring income inequality, the income distribution issues become a tertiary matter only in thinking about economy-wide performance, so we don't really discuss those who are hurting economically in spite of the strong indicators. 

But the statistic that economists are likely to want to play this role, the Gini coefficient, hasn't caught on in popular discussions of income inequality.  It is my view that the Gini coefficient is too complex for most people to understand and thus a simple-to-understand statistic is needed to play this role. Admittedly, such a statistic will have its limitations.  I don't want to deny this.  But as politicians discuss the issue, the usual focus is on the middle class.  For that reason I think the statistic I suggest is compelling.  It is the ratio of median income to mean income.  (On the Fred Blog, the reciprocal ratio is graphed, though their data only goes through 2013.  They draw a similar conclusion to what I concluded below about this as an indicator that income inequality has been increasing, though they don't hazard an explanation for these results.)  I will illustrate this measure with a simple Excel workbook I put together from readily available data. Below is a brief discussion of how this workbook was constructed. 

I did a Google search on - mean household income U.S. - and soon found what I wanted.  The first hit was the U.S. Census; but that didn't have what I needed. At the second hit I found this page from the St. Louis Federal Reserve Bank.  Note that the graph says family income rather than household income.  With the aide of a friend, I found this definition of household at the Census.gov Website. From there, households are divided into two categories, family or nonfamily.  From what I know about the income data, family households must, on average, have higher income than nonfamily households.  Further, from elsewhere on the Website there is an issue of non-reporting.  I suspect the issue is more serious with nonfamily households.  Taken together, this may explain why the St. Louis Fed seemed to prefer family income to household income.  

I really liked the page I found because if you scroll down from the graph it provides links to a host of other graphs for related searches, median income distribution for example. And with a bit of further exploration I learned that each graph gives you the ability to download the data that generates the graph.  Initially I downloaded two worksheets, one for real median family income, the other for real mean family income.  They cover the same years, from 1953 to 2022.  I copied and pasted the data into a blank Excel workbook on the same worksheet.  So, the first four columns of my Excel (columns A and B and then columns D and E) are simply reposts of the St. Louis Fed data.  My contribution, meager though it is, can be found in column G, where the entry in column B is divided by the entry in the same row that's in column E, with the result expressed in percentage terms.  I don't believe the ratio of median to mean income to be very compelling on strictly theoretical grounds.  But I found the downward trend extremely interesting, something worthy of further discussion. 

To make sure I was on terra firma, I repeated the exercise, this time with nominal data.  There is a series of median family income that is not inflation adjusted and another series of mean family income not inflation adjusted.  The latter actually has two different series, either Vintage 2022-09-13 or Vintage 2023-09-12.  I chose the latter as it had data for 2022.  The former only goes as far as 2021.   I then did essentially the same thing as before in computing the ratios.   I compared the real and nominal results side by side (that is not shown in the Excel) and learned that while the results are not identical, they are quite close, within a few hundredths of a per cent in each case.  And the downward trend is still there.

Some Mechanics of Income Distribution and of the Trend in Question

I mean this essay to be available to non-economists and non-statisticians.  Anyone who has an interest in economics as it speaks to our national politics should find this essay accessible.  So here I'd like to explain a little about what's going on behind the scene to drive the results.  For those readers who don't need this type of hand holding, you can skip this section, puzzle for a bit over what explains the downward trend, and then resume reading the next section. 

If the income distribution were a bell curve, the median and the mean would coincide, so their ratio would equal 1 or 100%.  If you held all incomes below the median constant but added a fixed amount to each income above the median, then the median itself would remain unchanged but the mean would go up by half the fixed amount (as half the population received that income increase).  More generally, symmetric distributions, such as one that yields a bell curve, will produce an equal median and mean, while distributions that are skewed to the right will have the median less than the mean.  The greater the skewness the more the disparity between median and mean.  The U.S. income distribution is skewed in this way.  Evidently, the distribution was closer to a bell curve in 1953 than it was in 2022.  

Income in the U.S. has mainly been growing; both median and mean family income have been growing, the data say as much.  If median income grows at the same rate as mean income, then their ratio will remain unchanged.  For this ratio to fall requires mean income to grow faster than median income.  The reader should interpret this as incomes higher in the income distribution growing faster than incomes lower in the distribution.  That this has been the pattern for some time suggests that those who are lower in the distribution may have distinctly different views of the overall economy than those who are higher in the distribution. 

What Caused the Downward Trend?  Will the Trend Continue?

Here is some speculation on my part, which might be thought of as the start of an argument on these questions.  Post World War II, the U.S. economy really embodied the notions we associate with a "middle class society."  The GI Bill, in particular, repaid, in part, those who served in the military by helping them start on a middle class lifestyle, which I will note was far more modest than its equivalent today.  For example, the square footage of the family house or apartment was comparatively small and there might have been a single vehicle for the family car.  So, part of this is about attainment level.  Another part of this is about institutions that supported this attainment.  Unions were much stronger then and many more people were union members.  Unions helped their members lead a middle class lifestyle.

Now let's make a little conjecture that I deem likely - voting participation correlates with income.  The downward trend in the median to mean income ratio can be thought of as the system rewarding those with higher incomes, who in turn tend to vote their pocketbook.  In this view the surprise might be that the trend wasn't steeper earlier.  I do want to note that in my eyeballing of the data the trend happened under both Democratic and Republican Presidents, though it was somewhat steeper when Reagan was President.  

It can be argued that high marginal tax rates at upper incomes, which existed through the Carter administration, and have kept coming down for the most part since, inhibited the taking of very high income.  That inhibition lessened as the tax code changed.  The rich could then be more greedy and without shame.

Still a different way of looking at this, economic theory explains that a factor of production must be paid at least its opportunity cost (what that factor could earn at its next best opportunity) in order to elicit the factor's participation.  Payment in excess of the opportunity cost is called an economic rent.  Economic rents tend to exist where the factor is supplying something scarce.  And when there is excess demand for the product produced, those economic rents can skyrocket.  Earnings for those people will grow much faster than for those who merely earn their opportunity cost.  Parallel to this, certain sectors of the economy have experienced hyperinflation - health care and higher education are two such areas.  I believe that accounting and finance are also in this category.  These are just examples and are not meant to be an exhaustive list. The areas experiencing hyperinflation are likely the same areas where earnings have grown much faster than median income.

Is this slowing down now?  I'm not seeing it.

Naming the Median/Mean Income Ratio

Coming up with an idea is one thing.  Marketing it is quite another.  I'm including this cutesy section because I think the marketing calls for a compelling name, yet I couldn't come up with any that weren't too convoluted.  So I encourage those readers who want to make a go of if to suggest a name and then either do so in a comment or send me an email with it.  I'll post those and see if readers can identify a favorite.  

The Frequency in Updating the Measure

I believe that both the CPI and the unemployment rate are updated monthly.  Further, seasonal adjustments in CPI measures allow them to reconsider the earlier numbers in light of new information, going back at most 5 years to make such adjustments.  (Beyond 5 years the numbers are fixed.)  The data I used for computing the Median/Mean Family Income Ratio were annual.  Can a measure that only changes annually compete for importance with these other traditional measures of the macro economy?  Alternatively, might it be possible to get more frequent income measures so the numbers would be more timely?

I don't know the answers to these questions.  My thought is that if this remains just an idle curiosity then we're stuck with annual measures, which might then reinforce why the measure isn't taken more seriously.  Alternatively, if interest in the measure spiked, then perhaps there would be data forthcoming to support a more frequent adjustment of the numbers.  But that's just speculation on my part.  

Wrap Up

In the previous decade I wrote a fair amount about income redistribution, as a policy matter.   This post is probably the last one I wrote of that sort.  It was written while Trump was President and before Covid had manifest.  

I view the current post as several steps back from policy.  It's about how people perceive the economy.  It is not an unusual proposition to say that people will see the same thing differently depending on where they are standing at the time they make the observation.  Yet somehow when we talk about the macro economy, we lose this thought except for saying that Democrats will see it differently than Republicans.  I do think where people are in the income distribution matters for this perception.  It matters a lot.  Indeed, it matters much more now than it did in 1953, when the U.S. really was a middle class society.  We need a way to talk about that and I hope that the simple statistic I suggest in this post offers a vehicle for doing so. 

And, to be clear, I view income inequality itself as a proxy for wealth inequality.  Those who have a large debt burden relative to their income and "live paycheck to paycheck" have to endure every bump that the economy dishes out whereas those with enough savings and access to credit have buffers to allow them to be comfortable in spite of the economy's vicissitudes.  But getting direct measures on wealth and access to credit is much harder.  So proxy measures will have to do.  And the one I suggest is both readily available and easy to understand.

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