  A long-standing question about consumer behavior is whether individuals'
observed purchase decisions satisfy the revealed preference (RP) axioms of the
utility maximization theory (UMT). Researchers using survey or experimental
panel data sets on prices and consumption to answer this question face the
well-known problem of measurement error. We show that ignoring measurement
error in the RP approach may lead to overrejection of the UMT. To solve this
problem, we propose a new statistical RP framework for consumption panel data
sets that allows for testing the UMT in the presence of measurement error. Our
test is applicable to all consumer models that can be characterized by their
first-order conditions. Our approach is nonparametric, allows for unrestricted
heterogeneity in preferences, and requires only a centering condition on
measurement error. We develop two applications that provide new evidence about
the UMT. First, we find support in a survey data set for the dynamic and
time-consistent UMT in single-individual households, in the presence of
\emph{nonclassical} measurement error in consumption. In the second
application, we cannot reject the static UMT in a widely used experimental data
set in which measurement error in prices is assumed to be the result of price
misperception due to the experimental design. The first finding stands in
contrast to the conclusions drawn from the deterministic RP test of Browning
(1989). The second finding reverses the conclusions drawn from the
deterministic RP test of Afriat (1967) and Varian (1982).
