Grantmaking, Grading on a Curve, and the Paradox of Relative Evaluation in Nonmarkets

Abstract The paper develops a model of nonmarket allocation of resources such as the awarding of grants to meritorious projects, honors to outstanding students, or journal slots to quality publications. On the supply side, the available budget of grants is awarded to applicants who are evaluated most favorably according to the noisy information available to reviewers. On the demand side, stronger candidates are more likely to obtain grants and thus self-select into applying, given that applications are costly. We establish that if evaluation is perfect, grading on a curve inefficiently discourages even the very best candidates from applying. More generally, when the budget is insufficient to award grants to all applicants, the equilibrium unravels if information is symmetric enough—the paradox of relative evaluation. Leveraging a technique based on the quantile function pioneered by Lehmann, we characterize a broad set of nonmarket allocation rules under which an increase in evaluation noise in a field (or course) raises equilibrium applications in that field, and reduces applications in all other fields. We empirically confirm these comparative statics by exploiting a change in the rule for apportioning the total budget to applications in different fields at the European Research Council, showing that a one standard deviation increase in own evaluation noise leads to a 0.4 standard deviation increase in the number of applications and budget share. Moreover, we derive insights for the design of evaluation institutions, particularly regarding the endogenous choice of noise by fields or courses and the optimal aggregation of fields into panels.