Using flexible regression models for calculating hospital's production functions

The relative lack of flexibility of parametric models has led to the development of nonparametric regression techniques based on the family of generalized additive models. However, despite the potential advantages of using Generalized Additive Model (GAM) in practice many models have, until now, not been sufficiently explored in health economics problems. It could be interesting to calculate a new flexible hospital production function by means of a GAM including interactions and to compare it with the classic model Cobb-Douglas in the prediction of the behavior of productive factors.

The flexible model considered has been the AM including the beds-facultative interaction. The covariates "Hospital", being a categorical variable and "Year" being a continuous variable, have also been included in the model. Based on the estimation of the model penalized thin plate splines will be used to represent smoothed functions. In this configuration, the smoothed parameters will be estimated via REML.

Cobb-douglas model fits well for the production functions of the more general clinical and surgical services, while the GAM adjusts better in the case of more specialized medical services.

Generalized Additive Models are more flexible than parametric models, providing a better fit in the presence of non-linear relationships and thus allowing more accurate prediction values. The results of this study suggest that AM is a promising technique for the areas of research and application in health economics.