What do revealed preference axioms reveal about elasticities of demand?

It is well-known that observed data on prices and quantities of a set of goods is consistent with rational choice if the data satisfy revealed preference. In this paper, we derive estimators for demand and substitution elasticities at the observed data points for datasets satisfying the Strong version of the Strong Axiom of Revealed Preference (SSARP) from Chiappori and Rochet (1987). We find that these estimators are identified only up to a strictly positive parameter, which must be small enough that the utility function rationalizing the dataset satisfies certain properties. We show that the estimated elasticities of substitution approach zero in the limit as this parameter approaches zero. Thus, if the dataset satisfies SSARP, then it is consistent with negligible substitutability between any pair of goods at all observed data points. Our estimators are derived directly from results in Brown and Shannon (2000) and Brown and Kannan (2005).