As the table shows, our method yields a cardinalization that is very similar to that obtained simply by
standardizing the variables used in the usual approach. This provides a useful approximation: to map results in other
studies to ours, one can simply divide the estimates of the well-being-income gradient estimated in those studies by the
standard deviation of well-being. These results are graphed in Figure A2, which shows the cardinalization imposed by our
ordered probit procedure in each of three key datasets. As should be clear, our procedure is well approximated by a linear
transformation of the simpler approach, which simply analyzes the ordered categories directly.
Next, it is worth assessing this approach relative to four alternative metrics, of which three are typically used in
the literature; the fourth is an interesting extension of our approach.
Means: Continuing with the most common approach in the literature, the simplest (and most transparent) approach is to
take the ordinal ranking of alternatives as cardinal measures of happiness. This approach may make more sense when
analyzing questions that ask respondents to give a cardinal response (such as the World Values Survey life satisfaction
question, which asks for a response on a scale of 1 to 10).
Population proportions: An alternative involves reporting the proportion of the population reporting themselves as, say,
“quite happy” or “very happy.” This approach has the advantage that it yields a natural scaling (from 0 to 1) and is
directly interpretable. One difficulty is that this approach may lead changes in the dispersion of happiness to be interpreted
as changes in the average level of happiness. To minimize this possible confound, one typically chooses a cutoff near the
median response. However, the median response in poor countries can turn out to be a far more common response in rich
countries.
Ordered logits: The ordered logit is similar to our ordered probit approach but assumes a slightly different (fatter-tailed)
distribution of the latent “happiness” in the population. The logistic function also imposes a standard deviation on the
latent variable of πZ√3, which makes the coefficients somewhat differently scaled than with the ordered probit.
Heteroscedastic ordered probit: The ordered probit imposes an equal variance in residual happiness, whereas the
heteroscedastic ordered probit allows both the mean and the variance of happiness to vary by country-year. Alternatively
phrased, this approach relaxes the assumption of similar cutoff points for each country and year, allowing proportional
shifts in these cutoff points, by country-year.43
Figures A3 through A5 compare these alternative aggregators with our ordered probit approach, analyzing
separately the satisfaction ladder from the Gallup World Poll and the life satisfaction and happiness data, by country and
wave, in the World Values Survey. Thesfigures suggest that alternative methods of aggregating subjective well-being all
tend to yield highly correlated estimates.
43 Stevenson and Wolfers (2008) provide greater detail on this method.
Appendix—2