Relationship and factors of technical efficiency and quality of hospital care: the federal state system of Germany

Healthcare is one of the most important segments of the public sector. The health services segment affects every individual and everyone should care about it. The healthcare system utilises parameters like quality, efficiency, and equality (availability), creating a flexible system in which one parameter reacts to another to a certain extent. This research reacts to these facts, often discussed by experts as well as the general public. It aims to determine the relationship between technical efficiency and quality of hospital care in the context of the federal states of Germany and approximate the influence of selected external factors on their results. The inquiry involves 64 homogeneous production units, i.e., 16 federal states, in 2018–2021. It is therefore a macroeconomic view of the technical efficiency of the units examined and the quality of hospital care within the context of external conditions. Four variables were selected for the evaluation of the DEA input-oriented model (CRS, VRS)—2 inputs (number of patients per 1 physician, number of patients per 1 nurse) and 2 outputs (number of hospitalised patients per 1 bed, number of days of treatment per 1 bed). The quality of hospital care was analysed based on the results of the nationwide survey of satisfaction of hospital patients. The following factors were selected to investigate the influence of the factors on the results of technical efficiency and quality: number of public hospitals, number of non-profit hospitals, number of private hospitals, number of persons up to the age of 15, number of persons aged over 65. The results showed that the relationship between technical efficiency and quality is inverse in most DMUs. Different results were observed in the city states of Berlin, Bremen, and Hamburg. The results of the tobit model showed that 84% of the net technical efficiency of the hospitals depends on the proportion of limit population groups within the population of the state in question. The results of the influence of external factors on patient satisfaction scores can be explained at the rate of 32%.