Panel Stochastic Frontier Models with Latent Group Structures

2024-12-12

AI Summary

Traditional stochastic frontier models rely on strong distributional assumptions to separate inefficiency from noise, compromising robustness. This paper proposes a panel stochastic frontier model incorporating latent group structures to simultaneously capture heterogeneous technology frontiers and structurally varying inefficiency distributions across firms, thereby relaxing stringent prior distributional requirements. Innovatively, we embed a latent variable-based grouping mechanism into the stochastic frontier framework and develop an EM algorithm-based maximum likelihood estimation procedure, integrated with Monte Carlo simulation and structured mixed-effects estimation. Simulation results demonstrate substantial improvements in both parameter and efficiency estimation accuracy over conventional models. Empirical application to U.S. commercial banks’ cost efficiency successfully identifies distinct efficiency clusters with statistically significant differences and interpretable characteristics.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Structured Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Stochastic frontier models have attracted significant interest over the years due to their unique feature of including a distinct inefficiency term alongside the usual error term. To effectively separate these two components, strong distributional assumptions are often necessary. To overcome this limitation, numerous studies have sought to relax or generalize these models for more robust estimation. In line with these efforts, we introduce a latent group structure that accommodates heterogeneity across firms, addressing not only the stochastic frontiers but also the distribution of the inefficiency term. This framework accounts for the distinctive features of stochastic frontier models, and we propose a practical estimation procedure to implement it. Simulation studies demonstrate the strong performance of our proposed method, which is further illustrated through an application to study the cost efficiency of the U.S. commercial banking sector.

Problem

• Relaxing strong distributional assumptions in stochastic frontier models
• Incorporating latent group structures to address firm heterogeneity
• Estimating cost efficiency in the U.S. commercial banking sector

Innovation

• Introduces latent group structure for firm heterogeneity
• Relaxes distributional assumptions in stochastic frontier models
• Proposes practical estimation procedure for efficiency analysis