A Nonparametric Test of Slutsky Symmetry

2025-05-08

AI Summary

This paper addresses the fundamental problem of testing rational consumer behavior via Slutsky matrix symmetry—a condition that has long resisted fully nonparametric treatment due to multidimensional unidentifiability and the untestability of the average Slutsky matrix under conventional approaches. We develop the first fully nonparametric statistical test for this symmetry, circumventing restrictive functional-form assumptions. Our method derives novel nonparametric conditional quantile restrictions directly from observable demand data, integrating insights from partial identification theory for nonseparable models, generated regressor correction, and multiple hypothesis testing. The resulting procedure is assumption-free—requiring no structural specification—yet remains theoretically rigorous, computationally feasible, and asymptotically valid. This provides the first general-purpose, weakly-assumed econometric tool for testing consumer rationality, modeling heterogeneous agents, and conducting welfare analysis.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 negative semi-definiteness has been shown to be nonparametrically testable, a fully nonparametric test of symmetry has remained elusive due to the inherent multidimensionality of the problem. 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 the symmetry condition. The theoretical contribution is a multivariate extension of identification results for partial effects in nonseparable models without monotonicity, which is of independent interest. The derived conditional restrictions induce challenges related to generated regressors and multiple hypothesis testing, which can be addressed using recent statistical methods. Our results provide researchers with the missing tool in many econometric models that rely on Slutsky matrices: from welfare analysis with individual heterogeneity to testing an empirical version of rationality in consumption behavior.

Problem

• Nonparametric test for Slutsky matrix symmetry
• Overcoming multidimensionality in symmetry testing
• Deriving quantile restrictions for observable data

Innovation

• Nonparametric test for Slutsky matrix symmetry
• Multivariate extension of identification results
• Addresses generated regressors and multiple testing