Slutsky Matrix Norms and Revealed Preference Tests of Consumer Behaviour

Abstract

Given any observed finite sequence of prices, wealth and demand choices, we characterize the relation between its underlying Slutsky matrix norm (SMN) and some popular discrete revealed preference (RP) measures of departures from rationality, such as the Afriat index. We show that testing rationality in the SMN aproach with finite data is equivalent to testing it under the RP approach. We propose a way to “summarize” the departures from rationality in a systematic fashion in finite datasets. Finally, these ideas are extended to an observed demand with noise due to measurement error; we formulate an appropriate modification of the SMN approach in this case and derive closed-form asymptotic results under standard regularity conditions.

Keywords: consumer theory; rationality; Slutsky matrix function; revealed preference approach; bounded rationality.

JEL Classification: C60, D10