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Nonparametric Testability of Slutsky Symmetry

Florian Gunsilius, Lonjezo Sithole

arXiv 8 May 2025 · Econometrics

arXiv:2505.05603 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Economic theory implies strong limitations on what types of consumption behavior are considered rational. Rationality implies that the Slutsky matrix, which captures the substitution effects of compensated price changes on demand for different goods, is symmetric and negative semi-definite. While empirically informed versions of negative semi-definiteness have been shown to be nonparametrically testable, the analogous question for Slutsky symmetry has remained open. Recently, it has even been shown that the symmetry condition is not testable via the average Slutsky matrix, prompting conjectures about its non-testability. We settle this question by deriving nonparametric conditional quantile restrictions on observable data that permit construction of a fully nonparametric test for Slutsky symmetry in an empirical setting with individual heterogeneity and endogeneity. The theoretical contribution is a multivariate generalization of identification results for partial effects in nonseparable models without monotonicity, which is of independent interest. This result has implications for different areas in econometric theory, including nonparametric welfare analysis with individual heterogeneity for which, in the case of more than two goods, the symmetry condition introduces a nonlinear correction factor.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Holger Dette and Stefan Hoderlein and Natalie Neumeyer (2016) Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness0.94112483%
2Stefan Hoderlein and Enno Mammen (2007) Identification of Marginal Effects in Nonseparable Models without Monotonicity0.90916475%
3Hausman, Jerry A. and Newey, Whitney K (2016) Individual Heterogeneity and Average Welfare0.73732100%
4Maes, Sebastiaan and Malhotra, Raghav (2024) Beyond the Mean: Testing Consumer Rationality through Higher Moments of Demand0.64422100%
5A.K. Bera and R.P. Byron and C.M. Jarque (1981) Further evidence on asymptotic tests for homogeneity and symmetry in large demand systems0.40511100%
6Berthold R. Haag and Stefan Hoderlein and Krishna Pendakur (2009) Testing and imposing Slutsky symmetry in nonparametric demand systems0.40511100%
7Hoderlein, Stefan and Mammen, Enno (2009) Identification and estimation of local average derivatives in non-separable models without monotonicity0.40511100%
8James F. Meisner (1979) The sad fate of the asymptotic Slutsky symmetry test for large systems0.40511100%
9Timothy G. Taylor and J.S. Shonkwiler (1985) A size-corrected Wald test for Slutsky symmetry in systems of demand equations0.40511100%
10Barten, Anton P (1967) Evidence on the Slutsky conditions for demand equations0.40511100%

Showing the top 10 of 22 scored citations.