Micro Theory Reading Group

Title: (When) Can Differential Restrictions be Tested?: A Unification of the Functional and Revealed Preference Approach

Abstract: Historically, testing whether monotonic decision makers (DM) obey certain axioms from choice data has taken 2 rather distinct approaches. The First approach involves observing the entire “Demand Function” and putting restrictions on its derivatives. The second or “revealed preference” approach involves constructing algebraic inequalities which are satisfies if and only if choice data could arise from a DM who obeys the axioms of interest. We show, that under slight tweaks of the notions of revealed preference tests and derivative restrictions the 2 approaches are in fact very similar. This means that any test of derivatives can be used to derive a test of finite data. To do this we define a notion of convergence with certification, which holds under monotone preferences. We then show that monotocity, and therefore certification, is necessary for our results to hold.

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