DEA-Inspired Constrained Log-Log Quantile Frontier: Smooth Bench-marking, Calibration, and Dynamic Interpretation; Contemporary Mathematics; Vol. 7, iss. 3
| Parent link: | Contemporary Mathematics.— .— Singapore: Universal Wiser Publisher Vol. 7, iss. 3.— 2026.— 32 p. |
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| Other Authors: | , , , , |
| Summary: | Title screen This paper proposes a Data Envelopment Analysis (DEA)-inspired smooth benchmarking approach based ona constrained log-log quantile production frontier. The frontier is estimated by quantile regression under economicallymotivated inequality restrictions—monotonicity in inputs and a non-increasing-returns (concavity-compatible) restrictionwithin the Cobb-Douglas class—yielding a continuously differentiable benchmark with elasticity-based interpretationand tractable inference via constrained quantile regression theory. Our contribution is threefold: we (i) formalize large-sample inference for constrained quantile frontiers under economically interpretable inequality restrictions, (ii) introducea calibration perspective for probabilistic frontiers via exceedance/coverage diagnostics (and a simple non-crossingadjustment for multiple quantiles), and (iii) derive closed-form links between output- and input-oriented quantile efficiencyindices through the returns-to-scale parameter, together with a high-quantile interpretation within a one-sided stochasticproduction model. We emphasize the probabilistic nature of quantile frontiers: for any fixed quantile levelτ∈(0,1),the fitted frontier is a coverage benchmark rather than a deterministic envelopment surface, so a non-negligible share ofobservations may lie above it. Empirically, we apply the framework to firm-level panel data from the SPARK-Interfaxinformation system covering 1,035 Russian manufacturing firms over 2019–2023 (5,175 firm-year observations). Webenchmark the proposed smooth quantile frontier against classical DEA and a parametric Stochastic Frontier Analysis(SFA), and we report internal validation (pinball loss, coverage) together with sensitivity diagnostics acrossτ. The resultingefficiency measures exhibit significant associations with profitability (net Return onAssets (ROA)), changes in profitability,and sales growth, indicating economic relevance. Overall, the proposed approach complements deterministic envelopmentby providing smooth differentiability, robustness to noise, and calibration-driven interpretability for heterogeneous datasets,while retaining economically meaningful shape discipline and enabling a dynamic decomposition of frontier shifts andrelative performance Текстовый файл AM_Agreement |
| Language: | English |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.37256/cm.7320269045 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=686426 |
| Summary: | Title screen This paper proposes a Data Envelopment Analysis (DEA)-inspired smooth benchmarking approach based ona constrained log-log quantile production frontier. The frontier is estimated by quantile regression under economicallymotivated inequality restrictions—monotonicity in inputs and a non-increasing-returns (concavity-compatible) restrictionwithin the Cobb-Douglas class—yielding a continuously differentiable benchmark with elasticity-based interpretationand tractable inference via constrained quantile regression theory. Our contribution is threefold: we (i) formalize large-sample inference for constrained quantile frontiers under economically interpretable inequality restrictions, (ii) introducea calibration perspective for probabilistic frontiers via exceedance/coverage diagnostics (and a simple non-crossingadjustment for multiple quantiles), and (iii) derive closed-form links between output- and input-oriented quantile efficiencyindices through the returns-to-scale parameter, together with a high-quantile interpretation within a one-sided stochasticproduction model. We emphasize the probabilistic nature of quantile frontiers: for any fixed quantile levelτ∈(0,1),the fitted frontier is a coverage benchmark rather than a deterministic envelopment surface, so a non-negligible share ofobservations may lie above it. Empirically, we apply the framework to firm-level panel data from the SPARK-Interfaxinformation system covering 1,035 Russian manufacturing firms over 2019–2023 (5,175 firm-year observations). Webenchmark the proposed smooth quantile frontier against classical DEA and a parametric Stochastic Frontier Analysis(SFA), and we report internal validation (pinball loss, coverage) together with sensitivity diagnostics acrossτ. The resultingefficiency measures exhibit significant associations with profitability (net Return onAssets (ROA)), changes in profitability,and sales growth, indicating economic relevance. Overall, the proposed approach complements deterministic envelopmentby providing smooth differentiability, robustness to noise, and calibration-driven interpretability for heterogeneous datasets,while retaining economically meaningful shape discipline and enabling a dynamic decomposition of frontier shifts andrelative performance Текстовый файл AM_Agreement |
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| DOI: | 10.37256/cm.7320269045 |