These question-order changes make direct comparisons of country’s well-being levels across successive waves
problematic. However, to the extent that these influences are common across countries, first differencing will yield useful
estimates. Thus, in Figure 15, we analyze changes in life satisfaction and log GDP between each wave of the panel. The
first row shows differences between adjacent waves, while the second row shows longer differences, with the last panel
showing differences between the first and last wave. (Because of the uneven participation through time of many countries,
these longer difference panels contain information not shown in the first row). In each comparison of pairs of waves, we
find that larger rises in per capita GDP are associated with larger rises in life satisfaction, and the magnitude of these
gradients tends to be centered around 0.4. A parallel analysis of the happiness data (not shown) yielded roughly similar
results (the slope was positive in five of six panels and statistically significant in only one case).
Panel regressions provide an alternative and statistically more efficient way to combine this information, and so in
Table 3 we turn to analyzing both life satisfaction and happiness measures in the World Values Survey as a country-wave
panel dataset. The first column reports the results of respondent-level ordered probit regressions of well-being on log GDP
per capita, while the second column aggregates the data to the country-wave level; these are ordinary least squares
regressions of our well-being index on log GDP per capita. The first row reports results for the simple bivariate well-
being-GDP relationship and hence pools both within-country and between-country variation. The estimated coefficients
are 0.4 for life satisfaction and 0.2 for happiness. To isolate the within-country time-series variation, the second row adds
controls for country fixed effects. Consistent with Figure 14, the well-being-GDP gradient estimated from this time-series
variation is similar to that estimated from the point-in-time between-country comparisons.
The next row adds controls for each wave of the World Values Survey, these controls partial out the changes in
well-being that reflect differences in surveys across waves. As might be expected, in light of the previous discussion of
question order effects, the inclusion of these controls increases the estimate of the time-series life satisfaction-GDP
gradient to nearly 0.6, and lowers the estimate of the time-series happiness-GDP gradient to a bit more than 0.2.
In subsequent rows we take first differences of consecutive country-wave observations, as well as long differences
(subtracting the first from the last observation for each country). Consistent with the analysis in Figure 15, there is a clear,
and statistically significant, relationship between changes in life satisfaction and log GDP per capita over time in these
countries. The estimates for happiness are similar, albeit smaller and less precisely estimated. These repeated international
cross-sections yield estimates of the time series well-being-income gradient centered roughly around 0.4, with larger
estimates for life satisfaction than happiness.
Equally, it is worth emphasizing that these estimates are both somewhat imprecisely estimated, and fragile.
Although the large cross-country datasets allow for useful comparisons between populations in abject poverty with those
in industrialized powerhouses, the within-country time series variation is simply less impressive. Indeed, it is worth noting
that the standard deviation of log GDP per capita across countries (in the 1999-2004 wave) is 1.0, whereas the standard
deviation of between-wave first differences in log GDP per capita (across all waves) is only 0.2, and hence strong
inferences are difficult to draw. Moreover, the inferences one draws from these data are particularly sensitive to the quite
18