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Semiparametric models with single-index nuisance parameters

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  • Song, Kyungchul

Abstract

In many semiparametric models, the parameter of interest is identified through conditional expectations, where the conditioning variable involves a single-index that is estimated in the first step. Among the examples are sample selection models and propensity score matching estimators. When the first-step estimator follows cube-root asymptotics, no method of analyzing the asymptotic variance of the second step estimator exists in the literature. This paper provides nontrivial sufficient conditions under which the asymptotic variance is not affected by the first step single-index estimator regardless of whether it is root-n or cube-root consistent. The finding opens a way to simple inference procedures in these models. Results from Monte Carlo simulations show that the procedures perform well in finite samples.

Suggested Citation

  • Song, Kyungchul, 2014. "Semiparametric models with single-index nuisance parameters," Journal of Econometrics, Elsevier, vol. 178(P3), pages 471-483.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:471-483
    DOI: 10.1016/j.jeconom.2013.07.004
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    Cited by:

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    3. Ardakani, Omid M. & Kishor, N. Kundan & Song, Suyong, 2018. "Re-evaluating the effectiveness of inflation targeting," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 76-97.
    4. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Sample selection model; Conditional median restrictions; Matching estimators; Maximum score estimation; Cube-root asymptotics; Generated regressors;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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