Analysis of the translog production function with constant returns-to-scale: implications for synthetic data generation in DEA

The transcendental logarithmic (translog) production function is recognised as a flexible functional form for modelling production processes. It accommodates varying elasticities of input substitution and diverse types of returns-to-scale, thus outperforming the Cobb-Douglas production function in empirical accuracy. However, the translog function qualifies as a valid production function only under specific parameter conditions. In this paper, we analyse the properties of the translog function and derive parameter conditions that ensure key properties such as monotonicity, concavity, weak essentiality, and constant returns-to-scale. Leveraging these results, we propose a systematic procedure for generating synthetic production data suitable for Monte Carlo simulations. This data can be employed to assess various features of Data Envelopment Analysis (DEA) models and to facilitate the numerical analysis of algorithms for large-scale DEA. The applicability of the proposed approach is illustrated through a case study, in which several DEA models are evaluated based on the Monte Carlo simulations.