Approximating the influence of external factors on the technical efficiency score of hospital care: evidence from the federal states of Germany

Abstract

Background: A good health care system and, especially, the provision of efficient hospital care are the goals of national and regional health policies. However, the scope of general hospital care in the 16 federal states in Germany varies considerably from region to region. The objectives of this paper are to evaluate the technical efficiencies of all general hospitals of the 16 federal states for the period from 2015 to 2020, to find out the relation between the exogenous factors and score of efficiency, and also the influence of the COVID-19 pandemic on the results of the technical efficiency of hospital care in the German states.

Methods: A two-step approach was used. First, an input-oriented Data Envelopment Analysis model with constant returns to scale and variable returns to scale was applied for the 6-year period from 2015 to 2020. The calculation of technical efficiency according to the input-oriented DEA model contains the three components-total technical efficiency (TTE), pure technical efficiency (PTE) and scale efficiency (SE). In the second stage, the influence of exogenous variables on the previously determined technical efficiency was evaluated by applying the tobit regression analysis.

Results: Although the level of average technical efficiency of about 90% is high, total technical efficiency deteriorated steadily from 2015 to 2020. Its lowest point at around 78%, was in the year 2020. The deterioration of the average technical efficiency is notably influenced by the lower results in the years 2019 and 2020. The decomposition of technical efficiency also revealed that the deterioration of overall average efficiency was influenced by both pure technical efficiency (PTE) and scale efficiency (SE). Based on the tobit regression analysis performed, it was possible to conclude that the change in the efficiency score can be explained by the influence of exogenous factors only from 6.4% for overall efficiency and from 7.1% for scale efficiency.

Conclusions: The results of the analysis of the overall technical efficiency reveal that the aggregated data of all general hospitals of all 16 federal states show a steadily worsening total technical efficiency every year since 2015. Although, especially, the deterioration of the year 2020 with the occurrence of COVID-19 pandemic, contributes to a deteriorated efficiency average, the deterioration of the efficiency values, based on the analysis performed, is also observable between the years 2016 and 2019. Considering the output generated, for inefficient units and the relevant policy authorities in the hospital sector, it can be recommended that the number of beds and in particular the number of physicians, should be reduced as inputs. Based on this study, it is also recommended that decisions to increase the efficiency of general hospitals should be made with consideration of exogenous factors such as the change in the number of general hospitals or the population density in the respective state, as these had explanatory value in connection with the increase in efficiency values. Due to the wide variation in the size of the federal states, the recommendation is more appropriate for federal states with low population density.

Keywords: Data Envelopment Analysis; Efficiency; Federal states; General hospitals; Germany; Tobit regression.

Fig. 1

Scheme of two-phase analysis

Fig. 2

Inverse Normal Analysis and Boxplot Y1, Y2 and Y3, n = 96