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Testing for a Functional Form of Mean Regression in a Fully Parametric Environment

Author

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  • Anatolyev Stanislav

    (CERGE-EI, Politických vězňů 7, 11121 Prague 1, Czech Republic)

Abstract

We develop a test for a restricted functional form of a mean regression when a complex distributional model for all variables is estimated. The test statistic is an average squared deviation from the estimated hypothesized function of the form implied by the estimated parametric model, and is asymptotically distributed as a mixture of χ2 distributions. The test is easy to implement using numerical derivatives, and it performs well in samples of typical size. We illustrate the test using data on labor market characteristics of US young men.

Suggested Citation

  • Anatolyev Stanislav, 2019. "Testing for a Functional Form of Mean Regression in a Fully Parametric Environment," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:bpj:jecome:v:8:y:2019:i:1:p:20:n:4
    DOI: 10.1515/jem-2016-0013
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    References listed on IDEAS

    as
    1. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    2. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
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    More about this item

    Keywords

    mean regression; functional form; specification test; wage regression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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