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Orthogonality conditions for convex regression

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  • Sheng Dai
  • Timo Kuosmanen
  • Xun Zhou

Abstract

Econometric identification generally relies on orthogonality conditions, which usually state that the random error term is uncorrelated with the explanatory variables. In convex regression, the orthogonality conditions for identification are unknown. Applying Lagrangian duality theory, we establish the sample orthogonality conditions for convex regression, including additive and multiplicative formulations of the regression model, with and without monotonicity and homogeneity constraints. We then propose a hybrid instrumental variable control function approach to mitigate the impact of potential endogeneity in convex regression. The superiority of the proposed approach is shown in a Monte Carlo study and examined in an empirical application to Chilean manufacturing data.

Suggested Citation

  • Sheng Dai & Timo Kuosmanen & Xun Zhou, 2025. "Orthogonality conditions for convex regression," Papers 2506.21110, arXiv.org.
    • Handle: RePEc:arx:papers:2506.21110
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    References listed on IDEAS

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    1. Andrew Johnson & Timo Kuosmanen, 2011. "One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method," Journal of Productivity Analysis, Springer, vol. 36(2), pages 219-230, October.
    2. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 317-341.
    3. Cordero, José Manuel & Santín, Daniel & Sicilia, Gabriela, 2015. "Testing the accuracy of DEA estimates under endogeneity through a Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 244(2), pages 511-518.
    4. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521012263, January.
    5. Rahul Mazumder & Arkopal Choudhury & Garud Iyengar & Bodhisattva Sen, 2019. "A Computational Framework for Multivariate Convex Regression and Its Variants," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 318-331, January.
    6. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, August.
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    1. Kuosmanen, Natalia & Kuosmanen, Timo & Pajarinen, Mika, 2025. "Are Firms Hiring Enough Workers? Firm-level Evidence from Finland’s Manufacturing and Service Industries," ETLA Working Papers 133, The Research Institute of the Finnish Economy.

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