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A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics

Author

Listed:
  • Francisco J. A. Cysneiros

    (Universidade Federal de Pernambuco)

  • Víctor Leiva

    (Pontificia Universidad Católica de Valparaíso)

  • Shuangzhe Liu

    (University of Canberra)

  • Carolina Marchant

    (Universidad Católica del Maule)

  • Paulo Scalco

    (Universidade Federal de Goiás)

Abstract

We propose a methodology for modelling and influence diagnostics in a Cobb–Douglas type setting. This methodology is useful for describing case-studies from economics. We consider stochastic restrictions for the model based on auxiliary information in order to improve its predictive ability. Model errors are assumed to follow the family of symmetric distributions and particularly its normal and Student-t members. We estimate the model parameters with the maximum likelihood method, which allows us to compare the normal case with a flexible framework that provides robust estimation of parameters based on the Student-t case. To conduct diagnostics in the model, we use two approaches for studying how a perturbation may affect on the mixed estimation procedure of its parameters due to the usage of sample data and non-sample auxiliary information. Curvatures and slopes used to detect local influence with both approaches are derived, considering perturbation schemes of case-weight, response and explanatory variables. Numerical evaluation of the proposed methodology is performed by Monte Carlo simulations and by applications with two data sets from economics, all of which show its good performance and its further applications. Particularly, the real data analyses confirm the importance of statistical diagnostics in the data modelling.

Suggested Citation

  • Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    • Handle: RePEc:spr:qualqt:v:53:y:2019:i:4:d:10.1007_s11135-018-00834-w
    DOI: 10.1007/s11135-018-00834-w
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    References listed on IDEAS

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    1. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
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    8. Marco Riquelme & V�ctor Leiva & Manuel Galea & Antonio Sanhueza, 2011. "Influence diagnostics on the coefficient of variation of elliptically contoured distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 513-532, November.
    9. Víctor Leiva & Shuangzhe Liu & Lei Shi & Francisco José A. Cysneiros, 2016. "Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 627-642, March.
    10. Khalid Mahmood & Shehla Munir, 2018. "Agricultural exports and economic growth in Pakistan: an econometric reassessment," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1561-1574, July.
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    12. Astrid Cullmann & Petra Zloczysti, 2014. "R&D efficiency and heterogeneity - a latent class application for the OECD," Applied Economics, Taylor & Francis Journals, vol. 46(30), pages 3750-3762, October.
    13. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
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    Cited by:

    1. Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    2. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    3. Martina Novotná & Ivana Faltová Leitmanová & Jiří Alina & Tomáš Volek, 2020. "Capital Intensity and Labour Productivity in Waste Companies," Sustainability, MDPI, vol. 12(24), pages 1-15, December.
    4. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2021. "Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 53-73, January.
    5. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Helton Saulo & Roberto Vila & Giovanna V. Borges & Marcelo Bourguignon & Víctor Leiva & Carolina Marchant, 2023. "Modeling Income Data via New Parametric Quantile Regressions: Formulation, Computational Statistics, and Application," Mathematics, MDPI, vol. 11(2), pages 1-25, January.

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