Universität Bonn

Department of Economics

Mauricio Olivares Gonzalez - LMU Munich

"Testing for Classical Measurement Error"

Abstract

Empirical work that accounts for measurement error typically combines functional form assumptions on equations of interest with a tightly parameterized measurement error process. In this paper, we provide conditions under which the assumption of classical measurement error (CME) is equivalent to a condition in terms of three observable measures for the latent variable of interest. The equivalence holds under weak conditions, in particular allowing measurement errors to depend on each other. This observable restriction can then directly be tested without solving for the distribution of unobservables and without making functional form or distributional assumptions.

However, researchers commonly have many measurements of the latent variable of interest. The abundance of measurements renders our characterization into a multiple testing problem, where the number of comparisons could be (potentially much) higher than the sample size in some applications. To overcome this problem, we propose a max-type test using high-dimensional Gaussian and block-multiplier bootstrap methods. Our proposed test has several advantages. First, it is asymptotically valid and consistent under weak assumptions. Second, it allows the number of comparisons to be exponentially larger than the sample size. Third, it enables the researcher to identify those measurements for which one has evidence in favor of CME via the step-down method à la Romano–Wolf.

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