District hospitals in South Africa are critical for healthcare delivery, particularly in underserved areas. However, their operational efficiency is often underexplored. A systematic literature review was conducted using econometric models, focusing on empirical studies that utilised panel data methods. The analysis aimed at identifying best practices and gaps in current hospital management strategies. Panel-data estimation revealed an average efficiency gain of 15% among district hospitals when employing robust standard errors, indicating a significant improvement in resource utilization. This study underscores the potential of panel data techniques for evaluating healthcare system performance. The identified gains suggest improvements in operational efficiency and resource allocation. District hospital administrators should consider adopting similar econometric models to enhance their understanding of operational efficiencies, thereby improving service delivery. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.