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Gradient estimation of the local-constant semiparametric smooth coefficient model

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  • Geng, Xin
  • Sun, Kai

Abstract

This paper studies the analytic gradient of the local-constant estimator for the semiparametric smooth coefficient (SPSC) model. This gradient estimator is shown to be consistent and asymptotically normal. A gradient-based cross-validation method for bandwidth selection is proposed for the SPSC model. Simulation suggests that the analytic gradient of the local-constant estimator outperforms the local-linear counterpart with a relatively large sample size. The gradient estimators are then applied to estimate the marginal effects of research and development on capital and labor productivity in China’s high-technology industry.

Suggested Citation

  • Geng, Xin & Sun, Kai, 2019. "Gradient estimation of the local-constant semiparametric smooth coefficient model," Economics Letters, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:ecolet:v:185:y:2019:i:c:s0165176519303416
    DOI: 10.1016/j.econlet.2019.108684
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    References listed on IDEAS

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    1. Zhang, Rui & Sun, Kai & Delgado, Michael S. & Kumbhakar, Subal C., 2012. "Productivity in China's high technology industry: Regional heterogeneity and R&D," Technological Forecasting and Social Change, Elsevier, vol. 79(1), pages 127-141.
    2. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
    3. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    4. Yin‐fang Zhang & Kai Sun, 2019. "How Does Infrastructure Affect Economic Growth? Insights From A Semiparametric Smooth Coefficient Approach And The Case Of Telecommunications In China," Economic Inquiry, Western Economic Association International, vol. 57(3), pages 1239-1255, July.
    5. Stevenson, Rodney, 1980. "Measuring Technological Bias," American Economic Review, American Economic Association, vol. 70(1), pages 162-173, March.
    6. Henderson, Daniel J. & Li, Qi & Parmeter, Christopher F. & Yao, Shuang, 2015. "Gradient-based smoothing parameter selection for nonparametric regression estimation," Journal of Econometrics, Elsevier, vol. 184(2), pages 233-241.
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    Cited by:

    1. Kai Sun & Ruhul Salim, 2020. "A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry," Journal of Productivity Analysis, Springer, vol. 54(2), pages 139-156, December.

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    More about this item

    Keywords

    Semiparametric smooth coefficient model; Partial derivative;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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