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# Crude Materialism versus the Wolfers Equation

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Suppose you're a crude materialist who believes that money is the secret to happiness.  You're estimating an equation of the form:

Happiness (in Standard Deviations) = a + b * ln(income)

How big should you expect b to be?  Well, you'd probably think that increasing income by 100% would increase happiness by at least a full standard deviation.  Since ln(2)=.69, doubling income corresponds to a .69 log-dollar increase.  So you should expect to see something like:

Happiness (in Standard Deviations) = a + 1.44 * ln(income)

At the other extreme,  suppose you're a hard-line Epicurean who believes that human beings instantly acclimate to their financial circumstances.  Then you'd expect to find something like:

Happiness (in Standard Deviations) = a + 0 * ln(income)

Last week Justin Wolfers came to GMU to present the best available individual, cross-national, and over-time evidence on income and happiness.  After exploring a wide range of data sets, he gleefully presented the answer:

Happiness (in Standard Deviations) = a + .35 * ln(income)

As usual, Wolfers' work was both careful and thorough.  But what does it mean?  Most people interpret Wolfers' findings as a shocking refutation of everyone who thinks that money has little effect on happiness.  Wolfers largely embraced this take.  But should he?

I think not.  If you picture a continuum with Epicureanism at 0, and crude materialism at 1, Wolfers stands at .24.  According to his results, the effect of income on happiness, though positive, is small.

Not convinced?  Consider: Wolfers' result implies that to raise happiness by one standard deviation, you have to raise income by 1/.35=2.86 log points.  How much is that exactly?  In percentage terms, that's (e^2.86)-1 - an increase of  1,640%.  So if you currently earn \$50,000, Wolfers' coefficient implies you'd need an extra \$820,585 per year to durably increase your happiness by one lousy standard deviation.  In math, that's not "zero effect of income on happiness."  But in English, it basically is.

Still not convinced?  Remember that Wolfers deliberately refrains from controlling for confounding variables, so the true effect of income on happiness is almost certainly even smaller than it looks.

The view that money has a major effect on happiness is ideologically convenient for me.  But it goes against first-hand experience, the wisdom of the ages, and the rightly interpreted empirical evidence.  So to hell with ideological convenience.

Eric Falkenstein writes:

The lines in some those scatter plots are pretty weak. His time series data neglects the US, China, and Japan, which he implies don't have data. They do, it just doesn't fit his hypothesis. Selective, not thorough.

writes:

Why is the standard deviation the relevant figure of merit here? Does my happiness relative to most if the population matter?

[broken link fixed. Watch those doubled http's--Econlib Ed.]

honeyoak writes:

My issue with the happiness research is that a one standard deviation on the average response to a 10 point scale is not a meaningful measure.

writes:

So, whether you earned 100 billion dollars per year your whole life, or 1 peso per century your whole life, taking a 1 year vacation at zero income makes you pretty much just as (infinitely) unhappy. Any sensitivity analysis to determine how close to the domain bounds you have to get before things get patently absurd?

Prof writes:

You are calibrating wrong. Assuming you are at average happiness today, a 1 std deviation would shift you to the 84%ile of income. In the US, this would require a 400% increase in income IF we assume no skew in incomes.

However we know there is HUGE skew, so the 16x figure doesn't surprise me in the least and actually adds credibility.

Dylan writes:

Awesome post, Bryan. It shows, besides what is evident (aka, that money alone doesn't bring happiness) how clueless is science alone, and how important is philosophy in order to interpret properly the data and results obtained.

It also shows one of the very few things I'm absolutely convinced of: that science won't be able to say anything new about how to acquire wisdom and make yourself happier that ancient philosophers haven't said before. Science may prove it empirically at best, but the wisdom was already there for centuries.

Dylan writes:

Awesome post, Bryan. It shows, besides what is evident (aka, that money alone doesn't bring happiness) how clueless is science alone, and how important is philosophy in order to interpret properly the data and results obtained.

It also shows one of the very few things I'm absolutely convinced of: that science won't be able to say anything new about how to acquire wisdom and make yourself happier that ancient philosophers haven't said before. Science may prove it empirically at best, but the wisdom was already there for centuries.

Bill writes:

Consumer theory does not equate happiness with utility. Furthermore, utility is ordinal, not cardinal. Finally, economic theory does not require interpersonal comparisons of utility. It appears that Wulfers has violated these axioms.

Glen Smith writes:

Several huge variables seem to be missing here. While income is obviously a major player in happiness, I would suspect it might begin to have a negative effect at some point.

writes:

I think ln(income) is the wrong way to go. I would guess this function would look more like U = a + b[x + sin(x)].

It makes sense that happiness follows an ln(income) pattern at low levels of income, then tapers off as diminishing marginal U kicks in. But then I would expect that critical additional increases to income start to matter more and more as a person gets used to luxury consumption. Then I would guess it would start to taper off again.

Perhaps restricting the model to ln(income) is masking the real action.

Finch writes:

1640% growth is 142 years at 2% per year. 96 at 3% growth. It doesn't seem crazy to me that we might be twice as happy as people living in the late 1800s, in an era of war, disease, and commonplace childhood death.

It certainly sounds like a good reason to emphasize pro-growth policies in any long-term view, even if you might only see a fraction of this over an individual working career.

writes:

Like Keynes' consumption function, the thinking here is somewhat limited in that it only considers income, not wealth.

Does wealth make us happy? Did Wolfers review any evidence on that?

Also consider that guaranteed government benefits in a very real sense constitute wealth, or at least deliver a similar effect.

A guaranteed basic income, for instance, is essentially the same as owning an annuity.

Guaranteed free health care and education are like having wealth -- you know you can buy those things if you want or need to.

Basically as a citizen (or resident) you own equity in the country, and you earn dividends.

The economic security that these programs provide *has utility.* Likewise, those programs give people choices that they wouldn't have otherwise -- "freedom!" Different choice sets have different utilities, and individuals largely don't control the big-picture choice sets available to them. They're fish in the swirling sea. We determine those choice sets collectively, through democracy.

A simplistic summation, with apologies to Chris Christoferson: Freedom's just another word for...having money.

writes:

Does this research hold other variables constant, or does it ignore what usually has to be given up for more income?

If I have to give up time with my family and doing the things I really enjoy doing to double my income, I'm probably not happier. But if an extra hundred grand a year magically appears in my bank account, I can guarantee my happiness will increase.

writes:

@Dan Hill:

Very good point. Shouldn't we add hours *not worked,* at some hourly rate, to GDP to achieve some measure of Gross Domestic Prosperity?

Would you rather live in a country where everyone works 30 instead of 40 hours a week, while earning the same \$50K (mean) a year? Which country's more "prosperous"?

Daniel Molling writes:

My initial reaction was that those results can still be extremely significant, depending on how large or important you think a standard deviation is. I'd think there could be a significant change in actual happiness from moving even 1/2 (or less) of a standard deviation. Does that seem reasonable?

Thomas Boyle writes:

As an engineer, I recognize happiness as part of a control system. It does not result from arriving at the goal; it is part of the system that steers people toward their goals.

People become dissatisfied when they become aware that their situation could be improved. Active unhappiness is a signal, that something needs to be improved.

Once the person discovers an effective path to improvement, the brain encourages them to do whatever it takes to keep moving on that path, rewarding their effort with "happiness".

Once no further improvement is possible, there is no need for the continued reward, and the person reverts to their "normal" level of contentedness, being neither happy nor unhappy.

Happiness is not a function of income (or anything else). It is a function of finding ways to increase income (or any other good thing). The wealthiest people may not be happier than everyone else, but ask people who are rapidly getting wealthier how they feel about it.

Lawrence H. White writes:

@Bill (who posted February 27, 2014 8:31 A)

Nobody said that Wolfers and other people studying reported happiness are using any microeconomic theory, or the choice-theoretic concept of utility. Because what you say about utility theory is right, it's in fact pretty obvious that they aren't.

David Barry writes:

Average incomes across the world span about two orders of magnitude. If you're somewhere near the bottom of that distribution, then doubling your income doesn't get you anywhere near a low typical income in an affluent country. So I am not surprised that it corresponds to much less than a standard deviation's worth of happiness, if that standard deviation is measured across many countries or across suitably large timescales.

Mark V Anderson writes:

Even if the equation is anywhere near correct, it says nothing about causality. I suspect that the positive correlation of income to happiness has more to do with effective people causing both riches and happiness.

Jason Dana writes:

Bryan, your argument that the coefficient should be 1.44 for a materialist implicitly assumes perfect measurement of happiness. What should the coefficient be when we regress very crude measures, both psychometrically and philosophically, on log income? I think .35 is impressive, given how crudely measured happiness it.

Sean writes:
"Well, you'd probably think that increasing income by 100% would increase happiness by at least a full standard deviation."

I feel like I might be missing something obvious, but where does the 100% increase = 1 sd thing come from? Why not more? Or less? Was that just a ballpark figure? If so, I feel like the bits below become a bit shakier.

writes:

The Wolfers equation would seem to be more relevant in developing countries, where 1,640% differences in income do exist, and smaller-but-still-large differences are ubiquitous.

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