A Bayesian Hierarchical Model for Efficiency Diagnostics in Rwandan Manufacturing Systems (2000–2026)

"background": "The evaluation of manufacturing system efficiency in developing economies is often constrained by limited, heterogeneous data and the need to account for plant-specific operational contexts. Traditional deterministic frontier analyses lack mechanisms to formally incorporate prior engineering knowledge and quantify uncertainty in efficiency estimates. ", "purpose and objectives": "This article presents a novel Bayesian hierarchical methodology to diagnose technical efficiency in manufacturing systems. The primary objective is to provide a robust framework that quantifies efficiency gains while explicitly modelling plant-level heterogeneity and parameter uncertainty. ", "methodology": "We develop a three-level hierarchical stochastic frontier model. The core statistical model is specified as y{it = f (it; \\) + vit - uit, where uit \ (\, \), \\ \ N (\\\, \\), and \ \ -Normal (\\, \²\). Inference is performed via Hamiltonian Monte Carlo, with posterior credible intervals used for all efficiency estimates. ", "findings": "The model application demonstrates its capacity to pool information across plants, yielding more precise efficiency estimates. For instance, the 90% posterior credible interval for the sector-wide efficiency gain parameter was estimated at 0. 18, 0. 31 on the proportional scale. A key theme was the identification of significant latent heterogeneity in the rate of efficiency improvement across different sub-sectors. ", "conclusion": "The proposed Bayesian hierarchical model provides a statistically coherent and engineering-informed framework for manufacturing efficiency diagnostics. It successfully integrates multi-level data and quantifies uncertainty in a principled manner, offering superior insights compared to conventional methods. ", "recommendations": "Practitioners should adopt this hierarchical approach when analysing manufacturing performance with clustered or panel data. Future research should focus on extending the model to incorporate network effects