Testing for the Presence of Measurement Error

This paper proposes a simple nonparametric test of the hypothesis of no measurement error in explanatory variables and of the hypothesis that measurement error, if there is any, does not distort a given object of interest. We show that, under weak assumptions, both of these hypotheses are equivalent to certain restrictions on the joint distribution of an observable outcome and two observable variables that are related to the latent explanatory variable. Existing nonparametric tests for conditional independence can be used to directly test these restrictions without having to solve for the distribution of unobservables. In consequence, the test controls size under weak conditions and possesses power against a large class of nonclassical measurement error models, including many that are not identified. If the test detects measurement error, a multiple hypothesis testing procedure allows the researcher to recover subpopulations that are free from measurement error. Finally, we use the proposed methodology to study the reliability of administrative earnings records in the U.S., finding evidence for the presence of measurement error originating from young individuals with high earnings growth (in absolute terms).