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 (J Appl Econom 10:33–47, 1995) and Kumbhakar and Heshmati (Am J Agric Econ 77:660–674, 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.