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Sieve Instrumental Variable Quantile Regression Estimation of Functional Coefficient Models

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  • Su Liangjun

    () (Singapore Management University)

  • Tadao Hoshino

    () (Waseda University)

Abstract

In this paper, we consider sieve instrumental variable quantile regression (IVQR) estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates. We approximate the unknown functional coefficients by some basis functions and estimate them by the IVQR technique. We establish the uniform consistency and asymptotic normality of the estimators of the functional coefficients. Based on the sieve estimates, we propose a nonparametric specification test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis, a sequence of local alternatives and global alternatives, and propose a wild-bootstrap procedure to obtain the bootstrap p-values. A set of Monte Carlo simulations are conducted to evaluate the finite sample behavior of both the estimator and test statistic. As an empirical illustration of our theoretical results, we present the estimation of quantile Engel curves.

Suggested Citation

  • Su Liangjun & Tadao Hoshino, 2015. "Sieve Instrumental Variable Quantile Regression Estimation of Functional Coefficient Models," Working Papers 01-2015, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:01-2015
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    Cited by:

    1. Tadao Hoshino, 2014. "Quantile regression estimation of partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 509-536, September.
    2. Liang Chen, 2019. "Nonparametric Quantile Regressions for Panel Data Models with Large T," Papers 1911.01824, arXiv.org, revised Sep 2020.
    3. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    4. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    5. Antonio F. Galvao & Jiaying Gu & Stanislav Volgushev, 2018. "On the Unbiased Asymptotic Normality of Quantile Regression with Fixed Effects," Papers 1807.11863, arXiv.org, revised Feb 2020.
    6. Miao, Ke & Li, Kunpeng & Su, Liangjun, 2020. "Panel threshold models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 219(1), pages 137-170.
    7. Tadao Hoshino, 2018. "Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 160-172, January.
    8. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    Endogeneity; Functional coefficient; Heterogeneity; Instrumental variable; Panel data; Sieve estimation; Specification test; Structural quantile function;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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