Modelling efficiency with farm-produced inputs: dairying in KwaZulu-Natal, South Africa

This paper models dairy farms in KwaZulu-Natal, South Africa, emphasising the complexities unique to this multi-product industry. Net and gross output approaches to measuring production are discussed and then tested using panel data from 37 dairy farms in KwaZulu-Natal from 1999 and 2007. Production functions for the three outputs: milk production, animals and farm-produced feed, are fitted as a simultaneous system to model the farms' production activities. This simultaneous model is complemented by a single equation reduced form that is fitted as a frontier, which allows estimation of the relative efficiencies of the individual farms. The results show that, with data this detailed, it is possible to refine the model until it fits very tightly. Indeed, in the gross output model that includes cows there is nothing left to call inefficiency and what was clearly a frontier becomes a mean response function.