Appendix A Cardinalizing Happiness and Life Satisfaction
Our approach to constructing an index of average well-being in a country-year (or country-wave) is to report the
coefficient from an ordered probit regression of subjective well-being on country by year (or country by wave) fixed
effects. This appendix tries to make this approach more transparent, thereby demonstrating how to reconcile our results
with alternative approaches.
A simple approach to aggregating data on subjective well-being involves arbitrarily assigning to qualitative
categories scores equal to their rank order. Thus, in the World Values Survey, a response of “not at all happy” is given a
value of 1, “not very happy” a value of 2, “quite happy” a value of 3, and “very happy” a value of 4. Average well-being
is then calculated as the simple average of these values. This appears to be the most common approach in the literature.
A key difficulty with this approach is that the scaling of well-being measures from different surveys will vary,
depending on whether the question used a three-, four-, five-, seven-, ten-, or eleven-point scale (others also occur). In
turn, this approach yields estimates of the well-being-income gradient that are neither comparable across surveys nor have
an obvious economic interpretation.
Thus, a somewhat more satisfying index might be constructed by normalizing the dependent variable (subtracting
its mean and dividing by its standard deviation), which would yield a common metric. Moreover, this metric would have
an economic interpretation, scaling differences in well-being relative to its cross-sectional standard deviation. (This
approach yields results very close to our approach.)
Even so, the limitation of this approach is that it imposes a linear structure, implying, for example, that the
difference between being “not very happy” and “not at all happy” is equal to the difference between being “quite happy”
and “not very happy.” Although psychologists have often been willing to accept that the subjective distances between
successive points on category scales are similar, we can use data on the proportions of the population who report
themselves as being in each category to relax (or test) this assumption.
To make use of these population proportions, the ordered probit (Figure A1) makes a parametric assumption,
imposing normality on the distribution of the underlying latent “well-being” measure. Two normalizations are also
imposed: that the latent variable has a mean of zero and that it has a standard deviation of one. The country or country by
wave fixed effects we estimate (and interpret as well-being) are simply shifts in the mean of this distribution.
There is a very simple mapping between our results and the simple approach described above: whereas the
“value” of each categorical answer is simply imposed in the simple approach, in our approach it is equal to the expected
value of a standard normal variable, conditional on being between the estimated upper and lower cutoff points. Van Praag
and Ferrer-i-Carbonell (2004) describe this as “probit-adapted OLS.” Table A1 reports the mapping between the
underlying categorical responses, the standardized categorical responses, and our scaling derived from these ordered
probits.
Appendix—1