Bounded vs. Unbounded
Lately I’ve been noticing a general phenomenon that strikes me as shady… comparing something unbounded against something bounded. The top quintile, decile, percentile, or whatever on, say, the income distribution is going to have no limit on the number. Which is why it is possible to have such a huge gap between the median and the mean when it comes to the top 1% in the income distribution, but unlikely at an n-tile beneath the top.
Or… The fact that happiness surveys lay a 1 to 4 or 1 to 10 scale on top of an in-principle unbounded income distribution, or in-priniciple unbounded growth in income over time, seems to me as a reason not to make a huge deal out of the fact that the average score on a bounded scale doesn’t necessarily rise with an essentially open-ended thing like economic growth. If growth is ongoing, and self-reported happiness rises with growth — even excruciatingly slowly — then it is just a logical necessity that there is some time in the future when everybody hits the ceiling of the scale. Even if income and happiness continues to grow, the scale will HAVE to report a flat average, and will HAVE to stop being fully informative. Now, if — as seems to be the case — people have a kind of aversion to putting themselves at or near the top of the scale (if I don’t know how happy I can get, I may not want to say that I’m already there, or even almost there), then you’ve got a case for totally banal scale re-norming that will also produce a flat trend over time, below the top of the scale — again, even if the effect of growth on happiness is ongoing. Perhaps someone can explain to me why this is not considered a huge problem.
February 2nd, 2007 11:51
It strikes me that there are at least reasons why you might not think this is a huge problem (as opposed to merely a problem). Haven’t entirely decided what I think of them yet.
(1) You’re willing to assume that happiness is in fact bounded, or that we can be “fully satisfied” with our lives. Clearly that’s not a testable assumption from the data, but it’s not a hugely implausible one either. (And people certainly seem to make sense of the “fully satisfied” category when it’s presented.) I think van Praag has argued for this explicitly, though perhaps not especially convincingly.
(2) As a matter of empirical fact, you think the distribution of responses is sufficiently far from the flatline that you don’t think it’s really making that much of a difference to your conclusions at this point in time. If there are people whose happiness flatlines below the highest category/ies, despite large increases in income, for example, this would suggest that it’s not boundedness driving the “money doesn’t buy happiness” result.
(3) You have sufficiently strong prioritarian tendencies that, even if there are people who are flatlining, you attitude to any particular distribution of happiness isn’t going to be much affected by it. (Though this is clearly a limited defence, and wouldn’t apply to other attempted uses of the survey data.)
P.S. “If growth is ongoing, and self-reported happiness rises with growth — even excruciatingly slowly — then it is just a logical necessity that there is some time in the future when everybody hits the ceiling of the scale.” This is being pedantic (and is irrelevant to the issue with happiness surveys) but with a continuous scale, it’s entirely possible to asymptote to the upper bound without ever reaching it.
February 4th, 2007 15:34
I’ve read that happiness increases with income only up to a certain point (say, around $200 k per year). After that, the thinking goes that you’ve generally got enough of what actually makes you happy that any more won’t make you happier. For instance, you probably have a good deal of control over your employment, have a fair bit of job security and peace of mind for when you retire, enough vacation time to be relaxed (any more would probably just make you feel bored).
But what, I think, will prevent everyone from ever reaching that happiness ceiling is that many of those things that seem to contribute to our happiness are what you could call scarce goods: e.g. not everyone will be able to be their own boss. Also, if the happiness that seems to be correlated to increased income is related to the possession and display of luxury/status goods (fancy cars, etc.) then that prestige would disappear if everyone had them: the happiness-benefit that they confer (if any) is reliant upon the fact that many other people will not possess them.
Just some thoughts.
February 6th, 2007 12:04
I guess it depends on the argument you wish to make. If there were no significant variance in the happiness data at all, at any level of income, then I think that would spell a large problem indeed.
But if you look at a cross-section, either intra- or inter-nationally, there’s plenty of variation (albeit also some negative skew, at least on a 1-10 scale). And comparing this to income shows that people at the bottom, in both cases, are clearly less satisfied than those at the top, and by some margin.
But because the relationship isn’t usually found to be linear (I know Layard’s team, for instance, are currently testing the idea that it is logarithhmic), many authors make the comparison as a means of asking two questions: at what point do diminishing returns start to bite? And then: why THAT point and not at some higher (or lower) income level?
As long as these are the questions being posed, the boundedness or otherwise of the happiness scale doesn’t seem to be a huge problem. Even making the strong assumption that the functional shape of the relationship is wholly the artefact of a methodological ceiling effect (and that happiness is, in fact, unbounded), that doesn’t explain where along the x-axis the change occurs - and in policy terms, at least, that’s the interesting bit.
February 6th, 2007 12:37
Sam, Yes. Layards’ team needs to think harder about whether the possible log relationship reflects a shift in reporting biases along the income scale. The issue may be that, up to a certain threshold, reporting improves as a function of income, since income up to that threshold, affects more immediately salient and available dimensions of affect. After the income threshold, income continues to be converted into improvements in the quality of various dimensions of affect, but levels and changes in these dimensions are less available to consciousness. It could also be simpler than that, and people simply have a ceiling aversion, so once they’ve got enough money to say “pretty happy,” things flatten out, even as people feel better. I don’t know how big these effects are, but I’d put good money on their existence. I suspect the effect is large. However, we know in advance that Layard will clumsily interpret the curve in verbal self-reports as a function of incomme in a simplistic methodological manner, unless of course it is ideologically convenient to be careful. Maybe he can try to say something fancy about the Weber-Fechner law, but that probably describes attentional adaptation as well actual hedonic adaptation.
February 6th, 2007 17:15
Yes, I think you’re right — it is begging the question to claim that happiness does not keep rising with income while using a scale that guarantees it cannot possibly keep rising with income.
What would happen if, instead, you asked people to rate their happiness on a scale of 0 to 100 billion where:
0 = the most miserable person in the world
100 billion = the happiest person in the world
February 8th, 2007 13:51
Will –
I’m not sure I fully understand your concern, but I think that one of your assumptions — that people have a kind of “aversion” to reporting their happiness accurately/truthfully at the extremes of the scale — does most of the work for your argument. If we don’t trust the self-reports from the surveys (and there are many reasons to be skeptical, not only at the extremes of the happiness scale, but at any point therein) then the survey measure is largely useless anyways. This is why such surveys are most helpful and robust when combined with other methods to triangulate on SWB (maybe more in depth interviews, brainscans, congruence with other behaviors, etc.).
However, if we are willing to take people at their word when they say, for example, that they are a “1″ on a SWB scale of 1-4, or an “8″ on a 1-10 scale, then your argument seems to lose force until the distribution becomes so skewed that everyone is (truthfully, by my assumption) at or around the maximum happiness levels. At that point, the inquiry either becomes uninformative or we are all just very happy!
To alleviate the problem, we could construct a scale with finer gradients — like 1.0, 1.1, 1.2….9.8, 9.9, 10 — to distinguish among the people even when we begin to approach the top (or bottom) portion of the scale. I know that this compounds the problem of quantifying happiness in a survey (and complicates comparisons across years, with less exacting scales), but it demonstrates, I think, that your concern is fundamentally about truth in reporting rather than anything else. After all, it would be even less informative if we constructed an unbounded happiness metric to match the unbounded income dimension — “Survey question 1: Report a number in between 0 and infinity that reflects your happiness…”
Does this make sense?
DED