  This paper describes a fundamental and empirically conspicuous problem
inherent to surveys of human feelings and opinions in which subjective
responses are elicited on numerical scales. The paper also proposes a solution.
The problem is a tendency by some individuals -- particularly those with low
levels of education -- to simplify the response scale by considering only a
subset of possible responses such as the lowest, middle, and highest. In
principle, this ``focal value rounding'' (FVR) behavior renders invalid even
the weak ordinality assumption often used in analysis of such data. With
``happiness'' or life satisfaction data as an example, descriptive methods and
a multinomial logit model both show that the effect is large and that education
and, to a lesser extent, income level are predictors of FVR behavior.
  A model simultaneously accounting for the underlying wellbeing and for the
degree of FVR is able to estimate the latent subjective wellbeing, i.e.~the
counterfactual full-scale responses for all respondents, the biases associated
with traditional estimates, and the fraction of respondents who exhibit FVR.
Addressing this problem helps to resolve a longstanding puzzle in the life
satisfaction literature, namely that the returns to education, after adjusting
for income, appear to be small or negative. Due to the same econometric
problem, the marginal utility of income in a subjective wellbeing sense has
been consistently underestimated.
