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On testing conditional moment restrictions: The canonical case

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  • Tripathi, Gautam
  • Kitamura, Yuichi

Abstract

Let (x, z) be a pair of random vectors. We construct a new smoothed empirical likelihood based test for the hypothesis that E(z|x) a.s. = 0, and show that the test statistic is asymptotically normal under the null. An expression for the asymptotic power of this test under a sequence of local alternatives is also obtained. The test is shown to possess an optimality property in large samples. Simulation evidence suggests that it also behaves well in small samples.

Suggested Citation

  • Tripathi, Gautam & Kitamura, Yuichi, 2000. "On testing conditional moment restrictions: The canonical case," SFB 373 Discussion Papers 2000,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200088
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    References listed on IDEAS

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    1. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(4), pages 452-475, December.
    2. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    3. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Working Papers 99-02, University of Iowa, Department of Economics.
    4. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    5. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    6. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(4), pages 435-451, December.
    7. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An adaptive, rate-optimal test of a parametric model against a nonparametric alternative," SFB 373 Discussion Papers 1999,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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    Cited by:

    1. Chen, Song Xi & Gao, Jiti, 2007. "An adaptive empirical likelihood test for parametric time series regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 950-972, December.
    2. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    3. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.

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