Crude Materialism versus the Wolfers Equation

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 .35/1.44=.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.

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