Florian Gunsilius, Lonjezo Sithole
arXiv 8 May 2025 · Econometrics
arXiv:2505.05603 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Holger Dette and Stefan Hoderlein and Natalie Neumeyer (2016) Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness | 0.941 | 12 | 4 | 83% |
| 2 | Stefan Hoderlein and Enno Mammen (2007) Identification of Marginal Effects in Nonseparable Models without Monotonicity | 0.909 | 16 | 4 | 75% |
| 3 | Hausman, Jerry A. and Newey, Whitney K (2016) Individual Heterogeneity and Average Welfare | 0.737 | 3 | 2 | 100% |
| 4 | Maes, Sebastiaan and Malhotra, Raghav (2024) Beyond the Mean: Testing Consumer Rationality through Higher Moments of Demand | 0.644 | 2 | 2 | 100% |
| 5 | A.K. Bera and R.P. Byron and C.M. Jarque (1981) Further evidence on asymptotic tests for homogeneity and symmetry in large demand systems | 0.405 | 1 | 1 | 100% |
| 6 | Berthold R. Haag and Stefan Hoderlein and Krishna Pendakur (2009) Testing and imposing Slutsky symmetry in nonparametric demand systems | 0.405 | 1 | 1 | 100% |
| 7 | Hoderlein, Stefan and Mammen, Enno (2009) Identification and estimation of local average derivatives in non-separable models without monotonicity | 0.405 | 1 | 1 | 100% |
| 8 | James F. Meisner (1979) The sad fate of the asymptotic Slutsky symmetry test for large systems | 0.405 | 1 | 1 | 100% |
| 9 | Timothy G. Taylor and J.S. Shonkwiler (1985) A size-corrected Wald test for Slutsky symmetry in systems of demand equations | 0.405 | 1 | 1 | 100% |
| 10 | Barten, Anton P (1967) Evidence on the Slutsky conditions for demand equations | 0.405 | 1 | 1 | 100% |
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