How many consumers are rational?

Abstract

Rationality places strong restrictions on individual consumer behavior. This paper is concerned with assessing the validity of the integrability constraints imposed by standard utility maximization, arising in classical consumer demand analysis. More specifically, we characterize the testable implications of negative semidefiniteness and symmetry of the Slutsky matrix across a heterogeneous population without assuming anything on the functional form of individual preferences. In the same spirit, homogeneity of degree zero is being considered. Our approach employs nonseparable models and is centered around a conditional independence assumption, which is sufficiently general to allow for endogenous regressors. It is the only substantial assumption a researcher has to specify in this model, and has to be evaluated with particular care. Finally, we apply all concepts to British household data: We show that rationality is an acceptable description for large parts of the population, regardless of whether we test on single or composite households.

Nonparametric Estimation of a Nonseparable Demand Function under the Slutsky Inequality Restriction

“…Hoderlein (2011) studies the testable implications of negative semidefiniteness as well as symmetry of the Slutsky matrix in a heterogeneous population. Hoderlein and Stoye (2014) investigate how violations of the weak axiom of revealed preference (WARP) can be detected in a heterogeneous population based on repeated cross-sectional data.…”

Local indirect least squares and average marginal effects in nonseparable structural systems

“…When X is input and Y is output, the system corresponds to models for the estimation of production functions (see Imbens and Newey, 2009). When Y is a budget share and X represents total expenditures, the system corresponds to a nonparametric demand system with a heterogeneous population, as in Hoderlein (2005Hoderlein ( , 2007. In all these examples, Z serves as a driver of X excluded from the structural equation for Y .…”

“…This is the "monotonicity of the endogenous regressor in the unobserved component" assumed in Imbens and Newey (2009) (see also Chesher (2003) and Matzkin (2003), for example); this always holds when X is separably determined. With index monotonicity, an explicit expression for q 1 can be given along the lines of Hoderlein (2005Hoderlein ( , 2007 …”

“…Hoderlein (2005Hoderlein ( , 2007 and Imbens and Newey (2009) derive useful control variables in nonlinear structures where the cause of interest is determined by exogenous instruments and a scalar unobserved term and is strictly monotonic (or even additively separable) in this scalar. Chalak and White (2007) and White and Chalak (2008) discuss identifying and estimating causal e¤ects in structures nonseparable between observables and multiple unobservables, providing structural conditions ensuring the availability of useful conditioning instruments more generally.…”

Bounding Counterfactual Demand with Unobserved Heterogeneity and Endogenous Expenditures

“…Kitamura and Stoye (2016) address the same question but use SARP as a rationality condition, and Kawaguchi (2017) develops tests to verify various other stochastic axioms of revealed preference. In a similar vein, Hoderlein (2011) and Dette, Hoderlein, and Neumeyer (2016) check whether a population of heterogeneous consumers satisfies the differential Slutsky symmetry or negativity restrictions. None of these studies imposes restrictions on the unobserved heterogeneity component.…”