Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: Convexity of preferences is a pervasive assumption in economic analysis, so it is important to understand precisely how this property is revealed in data. In this paper, we develop a method to test for convexity given partial preference information in the form of a pair of weak and strict (incomplete) orders. We characterize the pairs that can be extended to convex preferences and provide an efficient algorithm to verify this property. Requiring the convex preference to align with an order that satisfies independence (e.g., the Euclidean order or first-order stochastic dominance) does not complicate the test. We apply our results to choices over risky or uncertain prospects and to consumer demand with linear or nonlinear budget sets, with either finitely or infinitely many observations (as in Afriat(1967), Matzkin (1991), Forges and Minelli (2009), and Reny (2015)), among others; in this setting, we identify precisely when demand data are rationalizable by a convex and increasing preference.