The Double Helix of Inequality and Well-Being

The on-line magazine Aeon today published an article of mine on why economic inequality tends to wax and wane in very long (‘secular’) cycles, and what consequences it has for the society.

One of the central ideas in the article was that general well-being (that is, of the overwhelming majority of population) tends to move in the opposite direction from inequality: when inequality grows, well-being declines, and vice versa. To illustrate this idea I put together an ‘infographic,’ which was later modified by the Aeon’s graphic designer. The result was visually pleasing, but I felt that the changes obscured certain features of the graph that I felt were important. I did not press the point, because generally the editors at the Aeon made excellent suggestions, and greatly improved my text. Also, I am a techno-geek when it comes to the analysis (graphical and statistical) of dynamics – I’ve been doing it for nearly 30 years and wrote two technical books on it, so what I see is very different from what the regular reader sees. I generally prefer austere black-and-white graphs, and use colors only when it is necessary to make a point. A good scientific graph should be clear, not pretty.

A popular article, like the one on the Aeon, is not a place to provide the ‘gory details’ of the analysis underlying the infographic. Because the topic is quite controversial, I am sure my critics will want to know these details so that they can rebut me. Eventually these details will be published as part of the book that I am working on, but the graph has been published now, so I will use this blog to provide the background to the figure. Many of my readers may also be interested in the ‘view from the kitchen’ of where curves come from.So welcome to the kitchen.

First, here is the infographic in the form that I prefer.

The red curve shows the peaks and valleys of economic inequality, while the blue curve depicts the ups and downs of popular well-being. Here’s a very important point: the curves reflect not absolute levels of these two variables, but deviations around a trend. We all know that the United States changed dramatically between 1800 and 2000 – population grew by orders of magnitude, GDP and GDP per capita expanded, life expectancies increased, and the quality of life generally improved. Generally speaking, the causes of these changes are quite well understood. But it does not mean that the change has occurred smoothly. Many variables of interest to the structural-demographic theory (which explains the dynamics of inequality and well-being, among other things) have grown rapidly for some decades and then stagnated, or even declined in subsequent periods. Then they resumed growing, and so on. I am interested in capturing these oscillations around the rising trend, and the standard way of focusing on such deviations, called ‘detrending,’ is to subtract the trend from the data.

Here’s an illustration using the average age of first marriage as a ‘proxy’ (indicator) of social mood. Generally speaking, when people feel optimistic about their future economic prospects they tend to get married early. If, on the other hand, they are unsure that they will have a well-paying job next year, they tend to delay marriage until they work up to a more secure position, or save some money. However, age of first marriage is only imperfectly correlated with social optimism, because it is also affected by other factors. For example, today people who are completely secure in their economic prospects tend to marry later than people in similar position who lived two centuries ago. For a variety of reasons, as societies modernized, people tend to marry later.

Here’s what the actual data for the average age of first marriage of American women looks like:

The top half shows that the basic pattern is one of up, down, and again up around a rising mean. In the bottom half I subtracted the trend, so now the numbers are fluctuating around the zero line.

There could be other reasons why the average age of marriage is an imperfect indicator of social optimism. For example, changes in tax laws that affect marriage penalty (or, conversely, marriage advantage) may result in many people delaying marriage (or deciding to marry earlier). Additionally, while being able to marry when you found the love of your life (instead of waiting for years until you can afford it) is certainly a good thing, it’s just one thing of many that makes us happy. Thus, if we want to get at such a generic parameter as ‘well-being’ it’s best to approach it with several proxies.

This is why I used four different indicators to approximate the generalized well-being curve. In addition to social optimism, proxied by marriage age, I also looked at an economic indicator and two biological (health) indicators. The economic indicator is the wage of production workers divided by the GDP per capita. Basically it tells us how the fruits of economic growth are distributed – actually paid as wages to workers, or paid out as dividends to share-holders or as compensation to CEOs.

The health aspect of well-being is captured with two proxies: life expectancy and the average stature (height). Life expectancy is an obvious measure of the quality of life, and so is average stature as is documented in voluminous literature (including writings by the Nobel laureate Robert Fogel).

To combine the four variables into a single index, I did the following. First, I log-transformed each variable to make peaks and valleys more symmetric. Then I detrended them, as with the age of marriage above. Finally I divided them by the standard deviation, which brings them all to the same scale. Here’s what the four curves look like when plotted together after detrending and scaling (note that marriage age was flipped upside down, because it is earlier age that correlates with well-being):

It is clear that there is a general tendency for these variables to move up and down together. However, this correlation is by no means perfect. The erratic fluctuations are partly due to what is known as ‘measurement noise.’ This is particularly important for earlier periods, when collecting national statistics has not yet been perfected. But, in addition, fluctuations also reflect genuinely different dynamics of these proxies for well-being. In my tax law example, such legislation could affect marriage age, but not life expectancy, while the introduction of penicillin will affect life expectancy, but not marriage age. By averaging the four curves (the thick line) we smooth out those erratic fluctuations, and bring out the cyclic component. This average is then my best estimate of the generalized well-being curve, and it is the blue curve plotted in the main graph.

The red curve is easier to explain. It is based on the idea of Kevin Philips (as explained in the Aeon article) to measure inequality by the ratio of the largest private fortune to the wealth of a typical (median) household:

year	Largest Fortune ($$mln)	Median Wealth ($$)	Ratio (×1000)
1803	3	300	10
1830	6	350	17
1848	20	400	50
1868	40	500	80
1875	105	500	210
1890	200	540	370
1912	1000	800	1250
1921	1000	1250	800
1940	1500	1750	857
1962	1000	7200	139
1982	2000	33,300	60
1992	8000	43,200	185
1999	85,000	60,000	1417
2005	46,500	102,844	452
2010	54,000	66,740	809

‘Ratio’ is log-transformed, detrended, and scaled in the same way as other variables, after which it becomes the red curve in the main graph.

It’s pretty obvious that the red and blue curves are close to being mirror opposites of each other. During the integrative phases of the secular cycles well-being is high and inequality low. During the disintegrative phases well-being is low and inequality is high.

This does not mean that there is a direct causal connection, that inequality directly depresses quality of life for the majority of population. Or that quality of life directly depresses inequality. Rather, these two variables are different facets of some integrated whole. The Aeon article traces out the interconnections between these and other structural-demographic variables (in dynamical systems there is no cause and effect, each variable is both a cause and an effect).

In particular, if you look closer, you can see that trend reversals of the two curves are slightly out of phase: inequality tends to turn the corner after well-being.

The main graph also lists some iconic events that illustrate the back-and-forth swings of American history. The events on the left hand side, coded with red, are typical disintegrative phase occurrences. Mostly I am showing such instances of political instability as riots, violent labor strikes, and, of course, the American Civil War. Note how they tend to bunch up during the periods of growing inequality. I have also added Social Darwinism and ‘Greed is Good’ on the left side of the ledger, for reasons explained in the Aeon article.

On the right hand side and coded blue, I list some of the more important integrative occurrences. Unlike internal wars (such as the American Civil War that divided the nation) external wars (War of 1812, World War II) are listed on the right side of the ledger, because they were powerful unifying (and therefore integrative) events.