Taisuke Otsu and Luke Taylor

Published 15 August 2016

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This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the method proposed by Hall and Ma (2007), our test allows general nonlinear regression models. Since our test employs the smoothing approach, it complements the nonsmoothing one by Hall and Main terms of local power properties. The other existing method, by Song (2008), is shown to possess trivial power under certain alternatives. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities and develop a bootstrap method to approximate the critical value. We apply the test to the specification of Engel curves in the US. Finally, some simulation results endorse our theoretical findings: our test has advantages in detecting high frequency alternatives and dominates the existing tests under certain specifications.