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Untestability of Average Slutsky Symmetry

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  • Haruki Kono

Abstract

Slutsky symmetry and negative semidefiniteness are necessary and sufficient conditions for the rationality of demand functions. While the empirical implications of Slutsky negative semidefiniteness in repeated cross-sectional demand data are well understood, the empirical content of Slutsky symmetry remains largely unexplored. This paper takes an important first step toward addressing this gap. We demonstrate that the average Slutsky matrix is not identified and that its identified set always contains a symmetric matrix. A key implication of our findings is that the symmetry of the average Slutsky matrix is untestable, and consequently, individual Slutsky symmetry cannot be tested using the average Slutsky matrix.

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  • Haruki Kono, 2025. "Untestability of Average Slutsky Symmetry," Papers 2501.18923, arXiv.org.
    • Handle: RePEc:arx:papers:2501.18923
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    References listed on IDEAS

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    1. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    2. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    3. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
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