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Peer-reviewedCC BY 4.0Mathematics

Disagreement Among Firm-Level Productivity Estimators and Its Consequences for Applied Inference

  • Hongsun Qin1,2
  • Bin Gao3
  • Wenwen Wang4
4 affiliations
  1. 1School of Accounting, Guizhou University of Finance and Economics, Guiyang 550025, China
  2. 2School of Mathematical Sciences, Guangxi Minzu University, Nanning 530006, China
  3. 3School of Management, Guangxi Minzu University, Nanning 530006, China
  4. 4School of Economics, Guangxi Minzu University, Nanning 530006, China
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Abstract

Firm-level total factor productivity is not observed: it is estimated, and an applied regression inherits that choice. We give four elementary propositions on the two measurement errors involved. On the left-hand side, the gap between any two residual-based measures in a downstream regression has a closed form in their implied factor elasticities. On the right-hand side, attenuation depends on the reliability of the variation that the estimator uses, and a two-rating design is exactly identified, so its uncorrelated-errors assumption has no testable implication. The propositions are applied to 29,434 firm-years across 4517 Chinese A-share firms (2015–2024) and to eleven measures: six parametric production-function estimators and five nonparametric frontier measures. The closed form predicts the realised gaps among the parametric measures with a correlation of 1.000. Under one specification, the six parametric measures give a positive ESG coefficient, significant at 1 percent, and the five nonparametric measures a coefficient indistinguishable from zero. The nonparametric measures penalise undesirable outputs, so the contrast is not estimator disagreement alone. A conventional slacks-based score on the same inputs and revenue, without those outputs, ranks with the baseline parametric measure at 0.70 rather than 0.23, and its ESG coefficient is positive.

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Cite

BibTeXRIS
BibTeX
@article{qin2026disagreement,
  title = {{Disagreement Among Firm-Level Productivity Estimators and Its Consequences for Applied Inference}},
  author = {Hongsun Qin and Bin Gao and Wenwen Wang},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213900},
  url = {https://www.mdpi.com/2227-7390/14/21/3900},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Disagreement Among Firm-Level Productivity Estimators and Its Consequences for Applied Inference
AU  - Hongsun Qin
AU  - Bin Gao
AU  - Wenwen Wang
PY  - 2026
DA  - 2026/10/26
JO  - Mathematics
DO  - 10.3390/math14213900
UR  - https://www.mdpi.com/2227-7390/14/21/3900
AB  - Firm-level total factor productivity is not observed: it is estimated, and an applied regression inherits that choice. We give four elementary propositions on the two measurement errors involved. On the left-hand side, the gap between any two residual-based measures in a downstream regression has a closed form in their implied factor elasticities. On the right-hand side, attenuation depends on the reliability of the variation that the estimator uses, and a two-rating design is exactly identified, so its uncorrelated-errors assumption has no testable implication. The propositions are applied to 29,434 firm-years across 4517 Chinese A-share firms (2015–2024) and to eleven measures: six parametric production-function estimators and five nonparametric frontier measures. The closed form predicts the realised gaps among the parametric measures with a correlation of 1.000. Under one specification, the six parametric measures give a positive ESG coefficient, significant at 1 percent, and the five nonparametric measures a coefficient indistinguishable from zero. The nonparametric measures penalise undesirable outputs, so the contrast is not estimator disagreement alone. A conventional slacks-based score on the same inputs and revenue, without those outputs, ranks with the baseline parametric measure at 0.70 rather than 0.23, and its ESG coefficient is positive.
SN  - 2227-7390
ER  -