Urban public libraries: Performance analysis using dynamic-network-DEA

The aim of this work is to posit a model to evaluate the efficiency of a system of urban public libraries and to examine the impact of certain contextual variables on the level of performance. We take the System of Public Libraries in the city of Medellin (Colombia) as a case study and consider a production function which displays three main characteristics. First, it is a complete production function which spans the different activities undertaken by these institutions, not only the one that identifies it with its function as a repository of knowledge. Second, there is the production function in stages, which allows us to distinguish between the various activities controlled by management from those coproduced with users, together with the link between the two. The third is a production function which takes into account temporal interdependence relations by identifying quasi-fixed inputs that remain for the provision of the service over time. This then allows us to analyse how efficiency evolves during the period in question. Efficiency evaluation is carried out by employing a dynamic-network-DEA model and we also apply truncated bootstrap regression to estimate the effect of certain contextual variables on library efficiency. The results evidence a growing trend in the efficiency indices, with values that are slightly more favourable in the second stage of service provision than in the stage focusing on managing the cultural programme. Factors such as the level of education, population density, youthfulness, and safety are seen to positively affect library performance, particularly in the second stage vis-à-vis the public.