Using flexible regression models for calculating hospital’s production functions

Abstract

Background 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. Method 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. Results 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. Conclusions 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.

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“…Our choice of the Cobb-Douglas function as a parametric estimate of the production function is motivated by our empirical analyses in Section 5 . Our consideration is also more in line with several studies that argue that the Cobb-Douglas function is a standard parameterization of production functions in the literature (Douglas 1976 ), especially in the context of primary care (Wichmann and Wichmann 2020 ), and nursing homes (Reyes-Santías et al 2020 ). Using the recent data collected by Chen et al ( 2021 ) on US nursing homes, we approximate a typical nursing home’s production function as , where y i is the total number of residents (proxies the nursing home’s output) who receive care, k i is the total number of beds (proxies the capital), and h i is the number of occupied beds (proxies the labor supply).…”

Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States

“…Our choice of the Cobb-Douglas function as a parametric estimate of the production function is motivated by our empirical analyses in Section 5. Our consideration is also more in line with several studies that argue that the Cobb-Douglas function is a standard parameterization of production function in the literature (Douglas, 1976), and especially in primary care (Wichmann & Wichmann, 2020), and nursing homes (Reyes-Santías et al, 2020). Using the recent data collected by Chen et al ( 2021) on U.S. nursing homes, we approximate a typical nursing home's production function as…”

Production function for modeling hospital activities. The case of Polish county hospitals

“…The Random Effect Zero-Inflated Poisson model incorporating a first order autoregressive structure was used for this purpose. The problem of choosing the right analytical tools was also addressed in the next article [ 12 ]. The authors focused on creating a new flexible hospital production function using the Generalized Additive Model (GAM) and on the comparison of the results obtained with those provided by the classic Cobb-Douglas model.…”