A simple back-of-the-envelope calculation can help determine an upper bound on the extent to which these issues
are distorting the comparisons in tables 1 and 2. If all cross-country variation in GDP per capita is assumed permanent and
people are perfect permanent-income consumers, then the coefficients in Table 1 can be interpreted as the response of
well-being to a shock to consumption. Standard estimates for the United States suggest that around half the variation in
annual income in a national cross-section is transitory, and a $1 shock to transitory income typically translates into around
a $0.05 shock to permanent income. Thus, a $1 change in measured income translates to a roughly $0.525 change in
permanent income. In this case the estimates in Table 2 need to be adjusted upward by around 90 percent (1/0.525) to be
interpreted as the relationship between well-being and permanent income or consumption. If, instead of assuming perfect
smoothing, we accept Campbell and Mankiw’s (1990) estimate that 50 percent of income is earned by “rule-of-thumb”
consumers whose propensity to consume from current income is equal to their propensity to consume from permanent
income, the relevant adjustment is closer to 30 percent. This adjustment would make the within- and between-country
estimates roughly similar.
We can also address this issue empirically. In an effort to isolate the response of well-being to permanent income,
the regression reported in the last column of Table 2 instruments for income using educational attainment, entered
separately for each country (Rivers and Vuong, 1988).27 Although we are confident that these instruments isolate variation
in permanent rather than transitory income, we do not hold much faith that the exclusion restriction holds—that education
does not have an effect on well-being beyond that mediated by income.28 Given that these omitted effects are likely
positive, our instrumental variables estimates may overstate the within-country income-well-being gradient. Indeed, in
most cases the instrumental variables estimates are larger than the ordered probit estimates of well-being on income. In
the largest dataset—the Gallup World Poll—the estimated gradient is .6.
The discussion above has been premised on the straightforward view that transitory income shocks yield smaller
impacts on well-being than do permanent shocks. Yet the most direct evidence we have on this point—the movement of
well-being over the business cycle—in fact suggests the opposite. Figure 13 shows that business-cycle variation in the
output gap produces quite large affects on subjective well-being. Indeed, the estimated well-being-transitory income
gradient suggested by these shocks is about five times larger than the well-being-GDP gradient estimated in Table 1. If
this sort of variation is representative of the response of happiness to transitory income, then, paradoxically enough, our
findings in Table 2 may substantially overstate the within-country well-being-permanent income link.
Although our analysis provides a useful measurement of the bivariate relationship between income and well-being
both within and between countries, there are good reasons to doubt that this corresponds to the causal effect of income on
well-being. It seems plausible (perhaps even likely) that the within-country well-being-income gradient may be biased
27 We follow their approach to estimating an instrumental variables ordered probit. Thus, the first stage involves a regression of log
household income on indicator variables for each level of education in each country, controlling for country fixed effects as well as
gender and a quartic in age, entered separately for each gender and indicators for missing age or gender. The second stage involves an
ordered probit regression of well-being on the predicted values and residuals from the second stage, as well as the same controls,
including country fixed effects.
28 For instance, Lleras-Muney (2005) shows positive impacts of compulsory schooling on health.
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