Sharp for SARP: Nonparametric Bounds on Counterfactual Demands

Sharp nonparametric bounds are derived for counterfactual demands and Hicksian compensating and equivalent variations. These “i-bounds” refine and extend earlier results of Blundell, Browning, and Crawford (2008). We show that their bounds are sharp under the Weak Axiom of Revealed Preference (WARP) since they do not require transitivity. The new bounds are sharp under the Strong Axiom of Revealed Preference (SARP). By requiring transitivity they can be used to bound welfare measures. The new bounds on welfare measures are shown to be operationalized through algorithms that are easy to implement. (JEL D04, D11)