Welfare Adjusted Scale Score: Method Toward the Development of an Equal-Interval Welfare Scale

It is common to question the equal-interval assumptions of most academic scale scores. Even if interval assumptions hold, it is problematic to assume equal-interval distances with respect to benefits. For example, equivalent gains at the top and bottom of the distribution are unlikely to yield equivalent welfare returns. I develop a method to estimate the welfare returns to academic achievement directly, by making use of established methodologies in health economics. Using performance level descriptors and achievement data from the National Assessment of of Educational Progress LongTerm Trends, I estimate a random utility model to construct a welfare-adjusted equalinterval scale. I then show that welfare returns to achievement are non-linear, convex and lead to different inferences regarding achievement gap trends.