In an earlier post, I promised to return to trying to understand whether The Paradox of Declining Female Happiness is quantitatively important. As Deidre McCloskey has argued, we shouldn't be in the business of "asterisk econometrics", but instead, figuring out what effects have "oomph". Given that we are analyzing changes in happiness - a qualitative variable - this is no easy task. I want to provide both a fun way of explaining these difficulties, and a response to some critical commentary about "The Happiness Gap and the Rhetoric of Statistics", arguing that:
these effects, whatever they are, are quite small, requiring clever statistical analysis over very large amounts to [sic] data to be seen at all.
This sentence is for the Stata-philiacs: Our ordered probit regression suggests that between 1972 and 2006, the relative wellbeing of women, relative to men, declined by ΔβΔt=0.399*(2006-1972)=0.13 points. (See Table 1 of the paper.)
Our task now is to understand what this means. And for the non-gearheads, you can now tune back in. Her are a few ways of thinking about the magnitude or "oomph" of the change we document:
- Effect Sizes: The coefficient in an ordered probit can be thought of as an "effect size", and hence the relative decline in the happiness of women is roughly one-eight of one standard deviation of the distribution of happiness in the population. If you think there is a lot of variation in happiness in the population, this is big; if not, it is small.
- Changing Positions: Let's think of lining up all the men in 1972, in order of their happiness. In 1972, the median woman ranked between the 53rd and 54th man, happier than a slight majority of men. By 2006, the median woman is somewhat less happy, ranking between the 48th and 49th man. (A point of comparison: Moving from the 53rd to the 48th percentile of the household income distribution involves a difference of about $6,000 per year.)
- Compared to Other Shifters of Happiness: We know from prior studies that unemployment lowers average levels of happiness. Comparing estimates across studies, we can say that the relative declien in women's happiness that we document is equivalent to the decline in average happiness that would occur in a state if its unemployment rate rose by 8-1/2 percentage points (from, say, today's 4-1/2% to 13%). Alternatively, there are data linking happiness to the level of economic development. Over the period we examine, real GDP per capita nearly doubled, and by this metric, such an increase should have led to an average increase in happiness of about one-eighth of the cross-sectional standard deviation of happiness. Thus, our finding is that the relative decline in women's happiness is as large as if women had enjoyed none of the accumulated gains due to economic growth.
- Compared to Other Changes in the Gender Happiness Gap: Our estimates are aggregate, or on-average effects. What do we know about other aggregate shocks to the gender happiness gap? We estimated the gender happiness gap year-by-year, and found that its long-run reversal is 1-1/2 times as large as the year-to-year standard deviation of the measured happiness gap. (We would guess that sampling errors lead us to overstate the standard deviation of the gap, and hence this metric likely understates the relevant magnitudes.)
A qualifier: None of these comparisons are entirely satisfactory. For instance, if you believe that there is very little variation in happiness across people, time, or states of the economy, then you would interpret the above comparisons as suggesting that the change in the female happiness gap is big, only when compared with small things.
Another qualifier: We only document changes in the measured gender happiness gap.
Any other ideas on how to describe the "oomph" (or economic significance) of changes in qualitative variables like happiness?
[Thanks to Betsey Stevenson for coauthoring this post.]
UPDATE 1: Steve Levitt chimes in.
UPDATE 2: Jezebel adds some perspective.
The household income distribution is not a normal distribution. (e.g. I strongly doubt that anyone is as much happier than the median as Gates and Ellison are richer than the median.)
Height is normally distributed. How much height difference would it make to move from the 54th to the 48th percentile? Not much.
Over the period we examine, real GDP per capita nearly doubled, and by this metric, such an increase should have led to an average increase in happiness of about one-eighth of the cross-sectional standard deviation of happiness.
Maybe men’s happiness benefits more from rising GDP than women’s. If I may crudely stereotype for a moment, the gadgets today are much cooler and cheaper than they were in 1972, but “relationships” and other emotional bellwethers are (the current discussion on divorces notwithstanding) more or less the same.
The shift from the woman advantage in “very happy” seems to hit relatively abruptly around 1984. Before that year, there’s a moderately consistent (but noisy) advantage for women. From there on out, there’s no difference.
You’d need a different statistical model to try to capture the idea of a discrete shift (rather than the regression model that captures the overall shape of the trend). But the idea that the shift might have been somewhat discrete would lead to different interpretations of the effect.
A good question is why was there a happiness gap favoring women in the 70s? Has there been a historical happiness gap or did that reflect events of that time?
For example, you could suggest that the 1972-1984 period reflects a period of raised awareness for women just coming out of the gender stereotypes of the 50s (and into the 60s) that gave them a temporary relative lift in happiness. This interpretation would suggest there was a transient advantage in women’s happiness that faded over time (which only looks like a reduction because the data don’t go back far enough).
Also of note is that if you look at the income inequality graph Brad DeLong had up awhile back, right around 1985 inequality starts to shoot up:
http://delong.typepad.com/photos/brad_delongs_images/20070314_ps_top1percent19172005.png
But if the effect were inequality-driven, I’d expect the gap would go away by men catching up to the women in rated happiness (since they are likely to get slightly more of the boost to the richest) rather than women coming down to the male level.
I’d be tempted to speculate about the mid-80s being the beginning of the establishment of the current political party positions. But if that were the case, I’d think you’d see more relative effects in the 90s and 00s as the parties traded (presidental) power.
I know some worry about some interpretations of these data, but there are lots of possible reasons for the data to be this way (probably enough to offend everybody with a little work).
Let’s compare your finding to something we understand fairly well. One eighth of a standard deviation is like two points on the IQ scale (where the standard deviation is set to equal 15). Two point differences in IQ generally aren’t worth worrying about.
We have a century of data validating what IQ is useful for. So, unless you can show that your happiness measurement is more valid and more important than IQ, I’d say your finding is too trivial to worry about.
Let’s compare your finding to something we understand fairly well. One eighth of a standard deviation is like two points on the IQ scale (where the standard deviation is set to equal 15). Two point differences in IQ generally aren’t worth worrying about.
We have a century of data validating what IQ is useful for. So, unless you can show that your happiness measurement is more valid and more important than IQ, I’d say your finding is too trivial to worry about.
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If you think there is a lot of variation in happiness in the population, this is big; if not, it is small.
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