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The food sector is considered a mature and a research and development (R&D) extensive industry. Nevertheless, also food companies face numerous challenges and cannot abstain from innovation activity if they want to keep their competitive stance. We examine the impact of innovation on labor productivity in European food companies in comparison to results for firms operating in high-tech sectors. The central motivation of our study is that the observed low R&D intensity in the food sector should be mirrored in different productivity effects of innovation when compared to the high-tech sector. We use microdata from the European Union s Community Innovation Survey (CIS) and apply an endogeneity-robust multi-stage model that has been applied by various recent studies. Our results point out major differences between the examined subsectors. While we find strong positive effects of innovation on labor productivity for food firms, we find insignificant effects in the high-tech sector. This suggests that the returns to innovation might be best evaluated separately by sector rather than for the manufacturing sector as a whole. Acknowledgement

We show that the nerve complex of n arcs in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension. Moreover this homotopy type can be computed in time O(n log n). For the particular case of the nerve complex of evenly-spaced arcs of the same length, we determine the dihedral group action on homology, and we relate the complex to a cyclic polytope with n vertices. We give three applications of our knowledge of the homotopy types of nerve complexes of circular arcs. First, we use the connection to cyclic polytopes to give a novel topological proof of a known upper bound on the distance between successive roots of a homogeneous trigonometric polynomial. Second, we show that the Lovasz bound on the chromatic number of a circular complete graph is either sharp or off by one. Third, we show that the Vietoris--Rips simplicial complex of n points in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension, and furthermore this homotopy type can be computed in time O(n log n).