Semi-Parametric Regression Models and Connecticut's Hospital Costs

The application of spatial analysis in assessing hospital costs has been largely ignored but is deserving of attention. Proximity to other hospitals can lead to spatial spillovers, and recognizing spatial effects can impact hospital economies of scale estimates. In this paper we estimate a variety of cost function models, using annual data for each of Connecticut's 30 hospitals over a 10 year time period, and allow for spatial effects. We consider a variety of semi-parametric regression models as in McMillen and Redfearn (2010). One innovation is that we address both the space and time dimensions in the kernel weights of our panel data semi-parametric regression models. This approach also allows for a general functional form. We find that including a life expectancy measure for years above average lifespan has a negative and significant effect on hospital costs. Finally, we also address potential endogeneity of the life expectancy variable through an instrumental variables estimation approach for panel data semi-parametric models, as first suggested more generally by Baltagi and Li (2002). Monte Carlo simulations indicate our estimator performs well. When addressing the endogeneity with this instrumental variables semi-parametric regression model, the elasticities of scale estimates are smaller but still significant. We also find the hospital cost savings for each year of patients' years above average life expectancy is approximately $4,700 to $7,300 on average, depending on the choice of bandwidth. This life expectancy cost reduction ranges from as low as approximately $480 to as high as $35,000, varying by individual hospitals and by year.