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

Abstract

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 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.

Spatial scale and product mix economies in U.S. banking with simultaneous spillover regimes

“…For European countries, Glass et al (2016) compute spatial ray-scale economies (RSE), which we discuss in due course, and Glass et al (2013) propose a partial spatial decomposition of total factor productivity (TFP) growth. Their decomposition is partial as its omits the changes in technical and allocative e¢ciency spillovers.…”

Industry‐Specific Productivity and Spillovers Through Input–Output Linkages: Evidence from Asia‐Pacific Value Chain

“…The imported intermediates and intra-industry flows are removed from the gross output for the calculation of Domar weights. We also provide the aggregation result with Domar weights that consider each country as an open economy and incorporate the influence of productivity change of imported intermediate inputs and simple gross output weighted average productivity change on country level in Appendix E. 17 The unrealistic assumption of a common ratio of the direct and indirect elasticities for all production factors in the SAR model, as discussed by Elhorst (2014) and Glass et al (2016a), may lead to misspecification in empirical studies of economic growth. log likelihood values.…”

“…The indirect elasticity refers to the percentage change in industry $$$ i $$$'s output due to a percentage increase in the sum of the input across all the other $$$ N-1 $$$ industries. Finally, the calculation of total elasticity is based on all $$$ N $$$ industries in the sample simultaneously changing their input, not just industry $$$ i $$$ or the other $$$ N-1 $$$ units (Glass et al ., 2016a). In the same way, we can describe the Hicks‐neutral technical change over time and the magnitude of spillovers between the industries through spatial correlation.…”

“…Using a spatial production stochastic frontier, the direct, indirect and total marginal effects of the input factors and time trends are calculated to describe the role of spillovers from input factors as well as how technical changes are distributed within the GVCs network. We also follow Glass et al (2016a) to calculate industry-specific productivity growth spillovers 1 As pointed out by Griliches (1979), there are two distinct notions of "spillovers," i.e. rent spillovers and pure knowledge spillovers.…”

“…We also follow Glass et al . (2016a) to calculate industry‐specific productivity growth spillovers by distinguishing between knowledge receiving and offering, which represent the two distinct directions of knowledge diffusion. Furthermore, we develop a method of using the quasi‐local Leontief inverse matrices to distinguish between domestic spillovers that transmitted within a country and the international spillovers that are transferred across the borders.…”