Nonparametric Testability of Slutsky Symmetry

TL;DR

This paper develops a nonparametric testing method for Slutsky symmetry, a key rationality condition in consumer demand theory, accounting for heterogeneity and endogeneity, with broad implications for econometric analysis.

Contribution

It derives the first nonparametric conditional quantile restrictions that test Slutsky symmetry in complex settings with heterogeneity and endogeneity, extending identification theory.

Findings

Established nonparametric testable implications of Slutsky symmetry.

Provided a multivariate generalization of identification in nonseparable models.

Implications for nonparametric welfare analysis with multiple goods.

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 constitute a testable implication of 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 nonlinear correction factors.