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A simple test of completeness in a class of nonparametric specification

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  • Yingyao Hu
  • Ji-Liang Shiu

Abstract

This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.

Suggested Citation

  • Yingyao Hu & Ji-Liang Shiu, 2022. "A simple test of completeness in a class of nonparametric specification," Econometric Reviews, Taylor & Francis Journals, vol. 41(4), pages 373-399, April.
    • Handle: RePEc:taf:emetrv:v:41:y:2022:i:4:p:373-399
    DOI: 10.1080/07474938.2021.1957285
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