A Comparative Application of Data Envelopment Analysis and Translog Methods: An Illustrative Study of Hospital Production

TLDR

Numerous studies apply either translog cost modeling or DEA to hospital data, but few compare the two on the same dataset to assess their relative strengths. This study aims to compare hospital cost and production inferences derived from translog cost modeling and DEA by applying both methods to the same data. The authors estimate a translog cost function and conduct DEA on the same hospital dataset to evaluate technical efficiencies and returns to scale. The translog model indicates constant returns to scale, whereas DEA reveals both increasing and decreasing returns across segments, and both methods agree that child patient days are more resource intensive; additionally, DEA efficiencies correlate with capacity utilization while translog efficiencies do not, highlighting the differing insights each approach provides.

Abstract

This paper compares inferences about hospital cost and production correspondences from two different estimation models: (1) the econometric modeling of the translog cost function, and (2) the application of Data Envelopment Analysis (DEA). While there are numerous examples of the application of each approach to empirical data, this paper provides insights into the relative strengths of the estimation methods by applying both models to the same data. The translog results suggest that constant reruns are operant, whereas the DEA results suggest that both increasing and decreasing returns to scale may be observed in different segments of the production correspondence, in turn suggesting that the translog model may be ‘averaging’ diametrically opposite behavior. On the other hand, by examining the rate of output transformation, both models agree that patient days devoted to care of children are more resource intensive than those devoted to adults or to the elderly. In addition, we compare estimates of technical efficiencies of individual hospitals obtained from the two methods. The DEA estimates are found to be highly related to the capacity utilization, but no such relationship was found for the translog estimates. This comparative application of different estimation models to the same data to obtain inferences about the nature of underlying cost and production correspondences sheds interesting light on the strengths of each approach, and suggests the need for additional research comparing estimation models using real as well as simulated data.