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A Comparison of Cobb-Douglas, Translog and Additive Models of the Production Functions of Inpatient Services In Public Hospitals

      Objectives

      To investigate the adequacy of the widely used Cobb-Douglas and translog models of the production functions of hospital in-patient services.

      Methods

      To investigate the adequacy of the widely used Cobb-Douglas and translog models of the production functions of hospital in-patient services, we fitted these and additive models (AMs) to 2002-2007 data for the gynaecology and obstetrics, general and digestive surgery, internal medicine, and traumatology and orthopaedic surgery services of 10 public hospitals in Galicia (NW Spain). Production, measured as admissions weighted in accordance with their diagnosis-related groups (DRGs), was treated as a function of physician full-time equivalents as surrogate labour factor and number of beds as surrogate capital factor.

      Results

      For the General Surgery specialty the findings for the CD model indicate a better fit than those for the Translog and the AM, as it is shown by AIC value while R2 (CD=96.32, Translog=96.30, AM=98.30) prefers the flexible AM. This is a good example of using AM as a tool for checking the behaviour of existing parametric models. In this case we can be confident with Cobb-Douglas estimations.
      Findings for the Internal Medicine specialty indicate responses for the CD (AIC=-17.789) seems to be more “robust” than those based on the AM (AIC=-13.113) and Translog (AIC=-15.939) models, R2 (CD=95.88, Translog=95.80, AM=97.90) shows better fit for the AM regression model.

      Conclusions

      Our Results suggest that while the Cobb-Douglas and translog models suffice to represent the production functions of services with low average DRG weight, the greater flexibility of models such as AMs is required for services with higher average DRG weight.