Efficiency as a Quantile Process: Functional Profiles and Panel Heterogeneity in Firm Data; Contemporary Mathematics; Vol. 7, iss. 5

Bibliographic Details
Parent link:	Contemporary Mathematics.— .— Singapore: Universal Wiser Publisher Vol. 7, iss. 5.— 2026.— 46 p.
Corporate Author:	Томский политехнический университет Бизнес-школа
Other Authors:	Spitsin V. V. Vladislav Vladimirovich, Spitsina (Spitsyna) L. Yu. Lubov Yurievna, Gasanov M. A. Magerram Ali Ogly, Leonova V. A. Victoria Aleksandrovna
Summary:	Title screen This paper develops a functional extension of quantile-based frontier efficiency analysis for firm-level panel data. Instead of representing technical efficiency by a single benchmark-specific score, it defines a quantile-indexed efficiency profile that tracks how a firm-year observation changes as the benchmark moves across an ordered family of upper conditional quantiles. The framework is formulated in a log-log quantile frontier model with non-crossing benchmark curves, making it possible to study efficiency as a structured profile rather than an isolated scalar. Three interpretable profile summaries are introduced: the average profile level, measuring overall proximity to the frontier over the selected quantile interval; the tail fragility index, capturing the deterioration of relative performance under the most demanding upper-tail benchmarks; and the decline rate, summarizing profile steepness. The paper establishes key theoretical properties of the profile and its summaries, including boundedness,monotonicity with respect to benchmark strictness, dominance ordering, continuity, endpoint and approximation results, curvature-based shape interpretation, local classification stability, and plug-in consistency under uniform convergence of the estimated frontier. Empirically, the framework is applied to 2,464 Russian firms observed over 2019-2023. The estimated profiles are nondegenerate, heterogeneous in shape, and support an economically interpretable classification into frontier-near, intermediate,tailfragile, and uniformly lagging types. Comparisons with endpoint benchmarking and Data Envelopment Analysis (DEA)-based scalar efficiency scores show that the profile contains information not recoverable from standard one-number or discrete quantile-specific measures. Fixed-effects regressions indicate that the average profile level behaves as a level-type efficiency measure, whereas tail fragility captures a distinct shape-related dimension. Robustness checks based on alternative quantile ranges, classification thresholds, model specifications, bootstrap confidence intervals, and lagged performance regressions support the empirical relevance of the proposed representation. Overall, replacing one-number efficiency measures with quantile efficiency profiles yields a richer and more informative representation of firm heterogeneity Текстовый файл AM_Agreement
Language:	English
Published:	2026
Subjects:	quantile frontier technical efficiency efficiency profile non-crossing quantile process functional data analysis firm heterogeneity электронный ресурс труды учёных ТПУ
Online Access:	https://doi.org/10.37256/cm.75202610170
Format:	Electronic Book Chapter
KOHA link:	https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=688599