Returns to scale and curvature in the presence of spillovers: evidence from European countries

Drawing on a recent development on the interpretation of spatial econometric models we extend two classic characteristics of production (returns to scale and diminishing marginal productivity of factor inputs) to the spatial case. In the context of a spatial translog production function we deÖne internal (i.e. direct), external (i.e. indirect) and total (direct plus indirect) returns to scale. The spatial production function gives rise to direct, indirect and total productions functions so we set out empirical checks to establish if these functions are concave. The ideas of spatial returns to scale and spatial concavity/convexity can easily be applied to other technologies (e.g. cost and distance functions) and other functional forms (e.g. Cobb-Douglas). We apply these ideas to aggregate production of European countries using balanced panel data for the period 1990 2011.