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Wednesday, July 12, 2006

On the Happy Planet Index

I'm going to jump out in front of this one as I am sure the Happy Planet Index will make a splash with a lot of the Greens. The idea behind the index is that it is possible to be happy with your life even if you don't have a lot of income and if you live in a country that doesn't use a lot of environmental resources.

All of this is true, and if the folks who made this claim stopped there, then I wouldn't have a problem. Instead, the New Economics Foundation, a group that claims the goal of a "new economy centered on people and the environment," puts some "scientific" trappings on their claim. Unfortunately, about five minutes of working with their data to show that the claim that people are happier with less is not supported.

Moreover, the group attempts to make interpersonal utility comparisons which are fraught with problems (more on this at the end of this post).

The Happiness index suggests that the United States is ranked 150 out of 178, just ahead of the Ivory Coast and just behind Lithuania. This does not pass the smell test and it flies in the face of revealed preference: there are a lot more people trying to come to live in the United States than in any other country in the world. Which is more correct - the revealed happiness of people as evidenced by their relocation or the calculated happiness by the NEF?

Anyway, the Happiness index ostensibly takes into account life expectancy, life satisfaction, and then deflates these positives by an estimation of how much of the earth's resources are used per-capita in a country. Therefore happiness is calculated as

HI = (satisfaction x life expectancy)/(ecological footprint)

The happiest place on earth, according to this formula is Vanuatu, followed by Colombia and Costa Rica. The least happiest places on earth include Burundi, Swaziland, and Zimbabwe. In the lowest ranks, I think there would be general agreement.

The press release suggests that it is possible, and indeed rather practical, for us to be happy without all the gadgets, cars, airplanes, etc. that suck up the world's resources. The "get more with less" philosophy is not new (read Thoreau’s Waldon Pond), yet the NEF can only suggest that those parts of the world that consume more of the world's resources are the least happy because that is how their formula works.

The NEF was nice enough to publish the raw data with which they calculated the happiness index (I'll give them that). The suggestion that the most wealthy countries of the world are also the least happy has little statistical support. I grabbed the data and threw it into STATA.

Here is the relationship between life satisfaction and per-capita GDP:

The correlation is 0.58 and is statistically significant.

Here is the relationship between life expectancy and per-capita GDP:

The relationship between life expectancy and GDP is non-linear and is approximated by a hyperbola of the following form: Life expectancy = 74.008 - 23,730/GDP. The estimated parameters are statistically significant. In other words, as income increases, life expectancy climbs but at a decreasing rate.

Here is the relationship between ecological footprint and per-capita GDP:

Naturally, as per-capita income increases the economic footprint increases.

The happiness index therefore takes two variables that are positively correlated with income (life satisfaction and life expectancy) and divides this product by another variable that is positively correlated with income (ecological footprint).

If we re-write the happiness index as

HI(GDP) = [SAT(GDP)xLIFE(GDP)]/FOOT(GDP), where SAT (satisfaction), LIFE (life expectancy) and FOOT (footprint) are functions of per-capita GDP, then the marginal impact of income on the happiness index is ambiguous.

Indeed, with some algebraic manipulation it is possible to show that the happiness index will increase with income if

ELG + ESG > EFG, where the E's indicate elasticities.

This may seem confusing, but it is relatively easy. The income elasticity of life expectancy is positive but decreasing with income. The income elasticity of life satisfaction is likewise positive but decreasing with income. The income elasticity of ecological footprint is likely positive but may also be decreasing as wealthier countries use cleaner technologies. Therefore, if the sum of the income elasticities of life and satisfaction outweigh the income elasticity of footprint, the Happiness index will increase with income. On the other hand, if the income elasticity of the footprint outweighs the combined income elasticities of satisfaction and life expectancy, the happiness index will decline with an increase in income.

Therefore, the way the HI is calculated and the relationships between its components and income just about ensure that the HI will be lower for the wealthier countries while not providing much information about what will happen to happiness if, say, Vanuatu experienced a thirty percent increase in per-capita income.

To further investigate the relationship between income and happiness, I took the Happiness Index, as calculated, and regressed it against per-capita GDP:

. reg happiness percap,r

Regression with robust standard errors Number of obs = 178
F( 1, 176) = 1.57
Prob > F = 0.2125
R-squared = 0.0047
Root MSE = 11.748

| Robust
happiness | Coef. Std. Err. t P>|t| [95% Conf. Interval]
percapgdp | -.0000842 .0000673 -1.25 0.212 -.0002169 .0000486
_cons | 43.96931 1.296957 33.90 0.000 41.40972 46.5289

The regression above suggests that there is no statistically significant linear relationship between per-capita GDP and the happiness index, although the parameter estimate is positive.

The next model regresses happiness against the log of per-capita income. This model reflects the change in happiness after a percentage change in income (using robust standard errors to help correct for heteroscedasticity):
. reg happiness lnper,r

Regression with robust standard errors Number of obs = 178
F( 1, 176) = 1.53
Prob > F = 0.2181
R-squared = 0.0070
Root MSE = 11.735

| Robust
happiness | Coef. Std. Err. t P>|t| [95% Conf. Interval]
lnpercap | .8659363 .7005443 1.24 0.218 -.516612 2.248485
_cons | 35.76009 6.252709 5.72 0.000 23.42015 48.10003
Still nothing as the p-value is well above 0.05, but once again the parameter estimate is positive.

The next model regresses the log of the happiness measure against the log of per-capita GDP. Notice that the log of the happiness index is

ln(HI) = ln([SATxLIFE]/FOOTPRINT) = ln(SAT) + ln(LIFE) - ln(FOOT)

In this case, the the happiness index is still penalized by the ecological footprint but in a log-linear fashion. Regressing the log of the HI against the log of per-capita income provides an income elasticity of happiness which is the relationship that the original article claimed to measure.

Here's what we get:
. reg lnhap lnper,r

Regression with robust standard errors Number of obs = 178
F( 1, 176) = 2.86
Prob > F = 0.0927
R-squared = 0.0140
Root MSE = .2949

| Robust
lnhap | Coef. Std. Err. t P>|t| [95% Conf. Interval]
lnpercap | .0309064 .018282 1.69 0.093 -.0051738 .0669867
_cons | 3.459669 .1634108 21.17 0.000 3.137172 3.782166

What do we find? At the ten percent significance level (granted not a great level of confidence), the income elasticity of happiness is statistically different from zero and at the five percent level of significance (using a one-tailed test) the income elasticity of happiness is POSITIVE - the exact opposite of what the NEF claims.

These estimations are obviously very naive - there are a lot of elements that haven't been included to explain happiness. Indeed, it is possible that these omitted elements can introduce sufficient bias into the estimation that we see a positive income elasticity of happiness when it is actually negative.

However, my main point is that the relationship between income and happiness is not nearly as simplistic as the NEF portrays, and if we believe economic theory, more income allows you to obtain higher levels of satisfaction.

My other concern with the NEF measure is the use of the ecological footprint to deflate my life satisfaction and life expectancy. However flawed the life satisfaction measure, it is still a measure. The life expectancy measure is fairly objectively obtained. Even the footprint seems objectively measured. The problem is using the footprint to adjust downward the satisfaction of those who live in a country that has a big ecological footprint.

It is entirely possible that those who live in the U.S. not only consume a lot of the world's resources, they like consuming more of the world's resources than the rest of the world. This might not be in good taste, but there is no accounting for taste. The NEF projects its preferences for smaller ecological footprints on the happiness (utility) of others. This is like me projecting my taste for bourbon on another person who doesn't and won't like bourbon - ever. I can claim the person would be happier if they consumed more bourbon, but the other person might still disagree. In such an exchange, I would wager that most would suggest that I mind my own business and quit trying to project my preferences onto others. Those people would be correct in giving such advice, but are also unlikely to follow it.

Perhaps consuming the earth's resources contributes negative externalities on others, but this would suggest that the countries that don't have a lot of income and that don't have large ecological footprints would be less happy - because they bore the externalities caused by those of us busy consuming the earth's resources. This doesn't seem to be the case.

My take is that while it is possible to be happy with less, it is far easier to be happy with more.

Here's my personal Happiness Index in Adobe format. I was shocked that I was less happy than the average Joe - folks who know me probably know that I have my burdens to bear but that I laugh and have a great time with life for the most part. Evidently the real cause of my lack of happiness is the amount of time I spend flying each year. From the report provided that this survey :
You are using over five times your share of the world's resources. This is well above the average for most nations - the only nations that can match you or come close for resource consumption are the USA and a few Gulf States. Of course, that is not to say that there aren't hundreds of millions of individuals living at your level of consumption, even including a few in the poorest countries in the world.

To be honest, pretty much any change in your lifestyle would reduce your footprint a bit. However, we would prescribe three urgent steps to get you on the right road:

  • Get off the road! Car use has a huge impact on ecological footprint. Obviously it's harder for people in certain circumstances, but where possible, try to use public transport more. Or, even better, get a bike!

  • You don't have to become vegetarian, but cutting down on meat, particularly beef, and particularly from animals fed by imported soya feed, is an effective step to reducing your footprint.

  • No doubt the biggest chunk of your footprint is coming from air travel. For example, flying direct from London to Sydney and back would add 5.44 g ha to your footprint - that's the average Briton's footprint for an entire year. And, of course, flying indirect adds even more polluting air miles.
  • So, I am supposed to walk to work (no mass transit in Arlington and riding a bike is dangerous on our roads), I am supposed to eat less meat, and not fly - and this will somehow make me happier? I fly to be with my family and friends because they live so far from me. For example, I will fly to Atlanta this fall to see a UGA football game with my best friends. This will make me very, very happy (win or lose) and if I chose not to do this I would be considerably less happy. Oh well, just another example of how it is hard to make interpersonal utility comparison.

    STATA data file

    New Economics Foundation, et. al., would be much happier if everyone would just live the way they are told. If you would do that then you happy little natives would be just the happiest little natives.
    Hello Craig

    I'm one of the authors of the NEF report and recently came across your piece.

    We've been resolutely not responding to blog articles, largely because they either agree with us (in which case, great), or think we're idiots and slag off our work (in which case, not much point trying to reason with them). And, frankly, it would be a lot of effort for not much gain.

    However, I thought your piece was thoughtful and interesting, so I just wanted to make one point, which is that we don't claim that the index measures happiness (we emphasise several times, in fact, that it doesn't). Rather, we claim that it measures well-being efficiency: that is, the relative 'price paid' for experienced well-being by countries as a function of their resource consumption.

    Of course it's quite possible to argue that this is a silly premise in the first place - that's a reasonable view (although we wouldn't share it). The point, though, is that we don't disagree about whose experienced well-being is highest - obviously, it's the Western nations. Our contention is just that, given the huge disparity in resource use, well-being in the West should be a lot higher than in most other countries, whereas in fact it is only just above that of quite a few 'medium development' countries. To us, the key message is about drastically diminishing returns and their associated environmental cost.

    A second point is that all countries could perform better on the index - being near the top doesn't necessarily mean doing well relative to reasonable expectations. We tried to argue this throughout the report, but obviously it's a more subtle message that the press have generally ignored.

    To an extent we asked for this kind of (mis)interpretation by using the word 'happy' in the title of the report - we have wondered, with hindsight, whether this was such a good idea. The trade off is that we got a huge (and 95% positive) press hit - and that's all part of the game too..

    Doubtless we still disagree about the value of the whole exercise, the relibility of the data sources, and so on, so I'm going to leave it there. But thanks for taking the time to think about it properly!

    Best wishes
    Sam Thompson

    They also bias the results by their choice of units. The dynamic range of life expectancy is about 2.5 (82 max/33 min), that of life satisfaction is also about 2.5 (7.5 max/3.3 min) and the dynamic range of Environmental Footprint is 16 (9.9 max/0.6 min)! Thus, the footprint has over twice the weight of the other two factors combined. Sheesh.

    Virginia Beach

    It's not simply about making you happier. It may or may not make you happier riding a bike or flying less, but it will certainly make those living in 100 years time happier if you and others didn't fly and drive so much. The Happy Planet Index is not about individual happiness, it's about the sustainability and equity of your happiness.
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