Political scientists have long been concerned about the validity of
survey measurements. Indeed, given the increasing use of survey
experiments, measurement error represents a threat to causal
inference. Although many have studied classical measurement
error
in linear regression models where the error is assumed to arise
completely at random, in a number of situations the error may be
correlated with the outcome. Such differential measurement
error
often arises in retrospective studies where the treatment is
measured after the outcome is realized. We analyze the impact
of
differential measurement error on causal estimation by deriving
the
sharp bounds of the average treatment effect. The proposed
nonparametric identification analysis avoids arbitrary modeling
decisions and formally characterizes the roles of additional
assumptions. We show the serious consequences of differential
misclassification and offer a new sensitivity analysis that
allows
researchers to evaluate the robustness of their conclusions.
Our
methods are motivated by a field experiment on democratic
deliberations, in which one set of estimates potentially suffers
from differential misclassification. We show that an analysis
ignoring differential measurement error may considerably
overestimate the causal effects. The finding contrasts with the
case of classical measurement error which always yields
attenuation
bias.
(Last Revised June, 2008)
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