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 de.ne own (i.e. direct), spillover (i.e. indirect) and total (i.e. 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 technical relationships (e.g. cost and distance functions) and other functional forms (e.g. Cobb-Douglas). We apply these ideas to aggregate production of European countries and find that the 2004 EU enlargement led to a sharp fall in direct, indirect and total returns scale across the EU.
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