Quality & Quantity

, Volume 53, Issue 4, pp 1693–1719 | Cite as

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

  • Francisco J. A. Cysneiros
  • Víctor LeivaEmail author
  • Shuangzhe Liu
  • Carolina Marchant
  • Paulo Scalco


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.


Likelihood-based methods Local influence Mixed estimation Monte Carlo simulations Regression models R software Symmetric distributions 



The authors thank the editors and reviewers for their constructive comments on an earlier version of this manuscript. This research was supported by: CNPq from the Brazilian government and the National Commission for Scientific and Technological Research of Chile—Fondecyt Grant No. 1160868.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversidade Federal de PernambucoRecifeBrazil
  2. 2.School of Industrial EngineeringPontificia Universidad Católica de ValparaísoValparaísoChile
  3. 3.Faculty of Science and TechnologyUniversity of CanberraCanberraAustralia
  4. 4.Faculty of Basic SciencesUniversidad Católica del MauleTalcaChile
  5. 5.Faculty of Administration, Accounting and EconomicsUniversidade Federal de GoiásGoiâniaBrazil

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