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Shape-Constrained Kernel-Weighted Least Squares: Estimating Production Functions for Chilean Manufacturing Industries

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  • Daisuke Yagi
  • Yining Chen
  • Andrew L. Johnson
  • Timo Kuosmanen

Abstract

In this article, we examine a novel way of imposing shape constraints on a local polynomial kernel estimator. The proposed approach is referred to as shape constrained kernel-weighted least squares (SCKLS). We prove uniform consistency of the SCKLS estimator with monotonicity and convexity/concavity constraints and establish its convergence rate. In addition, we propose a test to validate whether shape constraints are correctly specified. The competitiveness of SCKLS is shown in a comprehensive simulation study. Finally, we analyze Chilean manufacturing data using the SCKLS estimator and quantify production in the plastics and wood industries. The results show that exporting firms have significantly higher productivity.

Suggested Citation

  • Daisuke Yagi & Yining Chen & Andrew L. Johnson & Timo Kuosmanen, 2020. "Shape-Constrained Kernel-Weighted Least Squares: Estimating Production Functions for Chilean Manufacturing Industries," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 43-54, January.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:1:p:43-54
    DOI: 10.1080/07350015.2018.1431128
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    Cited by:

    1. Cristina Polo & Julián Ramajo & Alejandro Ricci‐Risquete, 2021. "A stochastic semi‐non‐parametric analysis of regional efficiency in the European Union," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(1), pages 7-24, February.
    2. Jose Manuel Cordero & Cristina Polo & Javier Salinas-Jiménez, 2021. "Subjective Well-Being and Heterogeneous Contexts: A Cross-National Study Using Semi-Nonparametric Frontier Methods," Journal of Happiness Studies, Springer, vol. 22(2), pages 867-886, February.
    3. Jose M. Cordero & Cristina Polo & Daniel Santín, 2020. "Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation," Operational Research, Springer, vol. 20(4), pages 2245-2265, December.
    4. Layer, Kevin & Johnson, Andrew L. & Sickles, Robin C. & Ferrier, Gary D., 2020. "Direction selection in stochastic directional distance functions," European Journal of Operational Research, Elsevier, vol. 280(1), pages 351-364.
    5. Lee, Chia-Yen & Wang, Ke, 2019. "Nash marginal abatement cost estimation of air pollutant emissions using the stochastic semi-nonparametric frontier," European Journal of Operational Research, Elsevier, vol. 273(1), pages 390-400.
    6. Oliver Y. Feng & Yining Chen & Qiyang Han & Raymond J. Carroll & Richard J. Samworth, 2022. "Nonparametric, tuning‐free estimation of S‐shaped functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1324-1352, September.
    7. Tsionas, Mike, 2022. "Efficiency estimation using probabilistic regression trees with an application to Chilean manufacturing industries," International Journal of Production Economics, Elsevier, vol. 249(C).
    8. Feng, Oliver Y. & Chen, Yining & Han, Qiyang & Carroll, Raymond J & Samworth, Richard J., 2022. "Nonparametric, tuning-free estimation of S-shaped functions," LSE Research Online Documents on Economics 111889, London School of Economics and Political Science, LSE Library.
    9. Dai, Sheng & Kuosmanen, Timo & Zhou, Xun, 2023. "Generalized quantile and expectile properties for shape constrained nonparametric estimation," European Journal of Operational Research, Elsevier, vol. 310(2), pages 914-927.
    10. Eunji Lim & Kihwan Kim, 2020. "Estimating Smooth and Convex Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(5), pages 1-40, September.
    11. Ghosal, Rahul & Ghosh, Sujit & Urbanek, Jacek & Schrack, Jennifer A. & Zipunnikov, Vadim, 2023. "Shape-constrained estimation in functional regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    12. Mike G. Tsionas & Valentin Zelenyuk, 2022. "Testing for Optimization Behavior in Production when Data is with Measurement Errors: A Bayesian Approach," CEPA Working Papers Series WP012022, School of Economics, University of Queensland, Australia.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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