EconBase
← All papers

Orthogonality conditions for convex regression

Sheng Dai, Timo Kuosmanen, Xun Zhou

arXiv 26 Jun 2025 · Statistics — Methodology

arXiv:2506.21110 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

40
references
74
in-text mentions
41
distinct cited
4
self-citations
9,214
main-text words

appendix boundary found by appendix_titled_section at “Appendix” · 90% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Kuosmanen (2008) Representation theorem for convex nonparametric least squares self1.00063100%
2Seijo and Sen (2011) Nonparametric least squares estimation of a multivariate convex regression function0.9416483%
3Collard-Wexler and De Loecker (2016) Production function estimation with measurement error in inputs0.84333100%
4Olley and Pakes (1996) The dynamics of productivity in the telecommunications equipment industry0.84333100%
5Afriat (1967) The construction of utility functions from expenditure data0.81142100%
6Afriat (1972) Efficiency estimation of production functions0.73732100%
7Levinsohn and Petrin (2003) Estimating production functions using inputs to control for unobservables0.73732100%
8Yatchew (2003) Semiparametric regression for the applied econometrician0.73732100%
9Ackerberg, Caves and Frazer (2015) Identification properties of recent production function estimators0.64422100%
10Chetverikov and Wilhelm (2017) Nonparametric instrumental variable estimation under monotonicity0.64422100%

Showing the top 10 of 41 scored citations.