Semi-parametric regression models and economies of scale in the presence of an endogenous variable

Microeconomic applications of semi-parametric models with an endogenous variable have been largely ignored. Recognizing spatial heterogeneity captured by semi-parametric cost function models can impact economies of scale estimates. We estimate several cost function models, using panel data for Connecticut's 30 hospitals over a 10 year time period. We consider a variety of fixed effects and semi-parametric models. One innovation is that we address both the space and time dimensions in the kernel weights of our panel data semi-parametric regression models. We find that a life expectancy measure for years above average lifespan is positively and significantly related to hospital costs. We also address endogeneity of life expectancy. Our instrumental variable (IV) estimation approach uses locally weighted regressions in panel data models, as Baltagi and Li (2002) suggest for endogeneity in general semi-parametric panel data models. With our semi-parametric IV approach the elasticities of scale estimates are smaller than with fixed effects estimation, but still less than 1, implying a greater degree of economies of scale. Monte Carlo simulations indicate that our semi-parametric IV estimator performs well.