The Emerging Equality of Inequality

The common tale of inequality in modern America starts in the 1970s. The disintegration of labor unions, foreign competition, or any melange of factors exert a downward pressure on working-class wages. But in the standard narrative, the last quarter of the 20th century is a good time for women. Rapid female entry into the labor force meant less of Peggy the Secretary and more of Peggy the Copy Chief. Graphs like this certainly corroborate that story:

Image

But that’s only part of the whole picture. The dynamics of inequality within male and female decompositions tell another story. Rather than use the standard Gini as a measure, I’ve created a time-series (from BLS data) with the ratio of the difference between mean and median incomes to the total mean income (call it mean-median, or MM, inequality). This captures “inequality” pretty well. Think about a bar with ten average guys, all earning between $40,000 and $60,000. Let’s say the mean and median are $50,000. Now imagine Steve Jobs enters the room. The median earnings would barely increase, but the mean would skyrocket beyond belief.

That is, the mean is sensitive to large outliers – and we’ve had more of those in America, lately. Take a look:

Image

This gives another context to the first graph. The position of the median female has increased relative to male salaries not necessarily because of more education and entry into the labor force, but the decline of the median man relative to the mean man. (Actually, there is no such thing as the “mean” man, but you get my point).

In the 1960s, the median income was more than 95% of the mean income. Today, it’s a bit less than 70% for males and females. Eyeballing the graph (not a statistically rigorous exercise, I know) there seems to have been a rapid jump in the secular ascent of male inequality around 1994: curiously the year NAFTA came into effect. It’s harder to draw conclusions about female income dynamics. But here’s an interesting correlation:

diffineq

Correlation is not causation, but data seems to suggest that the improved position of female workers today derives in large part from increasing mean-median inequality within male workers. Note that over the time period considered, female inequality shows only a bare increase and the difference rises almost entirely from increasing male inequality. At this point, some of you might be wondering whether my “definition” of inequality is appropriate to begin with. Gini is more statistically sophisticated, and Theil better still. So I checked historical Gini coefficients against what I call an “I-factor”, where

i = (male share of labor force)*(MM-inequality for men) + (female share of labor force)*(MM-inequality for women)

Unsurprisingly, i correlates pretty decently with Gini:

ifactor

Clearly it’s a good fit, so we have good reason to expect that MM inequality represents a decent idea of male and female income discrepancies, at least to the extent that Gini is a sufficient measure. I’ve inserted a linear trendline, though it does seem either some form of an s-curve would be more accurate or there’s a cut at i > 0.20.

There are no big conclusions here. Just some easy, spreadsheet regressions. But it suggests the standard story of inequality deserves another examination. Has the position of the median female worker increased any? As Larry Summers likes to say (in relation to the vaunted debt-to-annual-GDP measure) ratios have the unfortunate habit of needing a denominator. In the female-male income ratio, the emphasis has been too focused on the rise of the numerator, that the deep relative stagnation of the latter is forgotten.

Indeed, a remarkable chunk of the ratio can be explained by increase in male MM-inequality. As a group, females fare a lot better today than during Don Draper’s age. But the inequality within hasn’t fallen, and is only recently comparable to that of men. Yet, despite any of the million factors we believe increased overall inequality, female income discrepancies have at least resisted any upward trend.

But, if nothing else, we’re finally living in a world where inequality is spread equally.

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