Estimation of cost inefficiency in panel data models with firm specific and sub‐company specific effects

This paper proposes a dual‐level inefficiency model for analysing datasets with a sub‐company structure, which permits firm inefficiency to be decomposed into two parts: a component that varies across different sub‐companies within a firm (internal inefficiency); and a persistent component that applies across all sub‐companies in the same firm (external inefficiency). We adapt the models developed by Kumbhakar and Hjalmarsson (1995) and Kumbhakar and Heshmati (1995), making the same distinction between persistent and residual inefficiency, but in our case across sub‐companies comprising a firm, rather than over time. The proposed model is important in a regulatory context, where datasets with a sub‐company structure are commonplace, and regulators are interested in identifying and eliminating both persistent and sub‐company varying inefficiency. Further, as regulators often have to work with small cross‐sections, the utilisation of sub‐company data can be seen as an additional means of expanding cross‐sectional datasets for efficiency estimation. Using an international dataset of rail infrastructure managers we demonstrate the possibility of separating firm inefficiency into its persistent and sub‐company varying components. The empirical illustration highlights the danger that failure to allow for the dual‐level nature of inefficiency may cause overall firm inefficiency to be underestimated.