Mass problems and intuitionistic higher-order logic

In this paper we study a model of intuitionistic higher-order logic which we call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the category of sheaves of sets over the topological space consisting of the Turing degrees, where the Turing cones form a base for the topology. We note that our Muchnik topos interpretation of intuitionistic mathematics is an extension of the well known Kolmogorov/Muchnik interpretation of intuitionistic propositional calculus via Muchnik degrees, i.e., mass problems under weak reducibility. We introduce a new sheaf representation of the intuitionistic real numbers, \emph{the Muchnik reals}, which are different from the Cauchy reals and the Dedekind reals. Within the Muchnik topos we obtain a \emph{choice principle} $(\forall x\,\exists y\,A(x,y))\Rightarrow\exists w\,\forall x\,A(x,wx)$ and a \emph{bounding principle} $(\forall x\,\exists y\,A(x,y))\Rightarrow\exists z\,\forall x\,\exists y\,(y\le_{\mathrm{T}}(x,z)\land A(x,y))$ where $x,y,z$ range over Muchnik reals, $w$ ranges over functions from Muchnik reals to Muchnik reals, and $A(x,y)$ is a formula not containing $w$ or $z$. For the convenience of the reader, we explain all of the essential background material on intuitionism, sheaf theory, intuitionistic higher-order logic, Turing degrees, mass problems, Muchnik degrees, and Kolmogorov's calculus of problems. We also provide an English translation of Muchnik's 1963 paper on Muchnik degrees.Comment: 44 page

Foreign ownership and productivity: new evidence from the service sector and the R&D lab

This paper examines the relationship between foreign ownership and productivity, paying particular attention to two issues neglected in the existing literature Ö the role of multinationals in service sectors and the importance of R&D activity conducted by foreign multinationals. We review existing theoretical and empirical work, which largely focuses on manufacturing, before presenting new evidence using establishmentlevel data on production, service and R&D activity for the United Kingdom. We find that multinationals play an important role in service sectors and that entry of foreign multinationals by takeover is more prevalent than greenfield investment. We find that British multinationals have lower levels of labour productivity than foreign multinationals, but the difference is less stark in the service sector than in the production sector, and that British multinationals have lower levels of investment and intermediate use per employee. We also find that foreign-owned multinationals conduct a substantial amount of UK R&D. We discuss the implications of these and other findings for the policy debate on incentives to influence multinational firms' location choices.Foreign Investment, Productivity, Knowledge Spillovers

Foreign Ownership and Productivity: New Evidence from the Service Sector and the R&D Lab

This paper examines the relationship between foreign ownership and productivity, paying particular attention totwo issues neglected in the existing literature - the role of multinationals in service sectors and the importanceof R&D activity conducted by foreign multinationals. We review existing theoretical and empirical work, whichlargely focuses on manufacturing, before presenting new evidence using establishment-level data on production,service and R&D activity for the United Kingdom. We find that multinationals play an important role in servicesectors and that entry of foreign multinationals by takeover is more prevalent than greenfield investment. Wefind that British multinationals have lower levels of labour productivity than foreign multinationals, but thedifference is less stark in the service sector than in the production sector, and that British multinationals havelower levels of investment and intermediate use per employee. We also find that foreign-owned multinationalsconduct a substantial amount of UK R&D. We discuss the implications of these and other findings for the policydebate on incentives to influence multinational firms' location choices.Foreign Investment, Productivity, Knowledge Spillovers

Factor price equalisation in the UK

This paper develops a general test of factor price equalization that is robust to unobserved regional productivity differences, unobserved region-industry factor quality differences and variation in production technology across industries. We test relative factor price equalization across regions of the UK. Although the UK is small and densely-populated, we find evidence of statistically significant and economically important departures from relative factor price equalization. Our estimates suggest three distinct relative factor price areas with a clear spatial structure. We explore explanations for these findings, including multiple cones of diversification, region-industry technology differences, agglomeration and increasing returns to scale.

Relative wage variation and industry location

Relative wages vary considerably across regions of the United Kingdom, with skill-abundant regions exhibiting lower skill premia than skill-scarce regions. This paper shows that the location of economic activity is correlated with the variation in relative wages. U.K. regions with low skill premia produce different sets of manufacturing industries than regions with high skill premia. Relative wages are also linked to subsequent economic development: over time, increases in the employment share of skill-intensive industries are greater in regions with lower initial skill premia. Both results suggest firms adjust production across and within regions in response to relative wage differences.Deindustrialization, Relative Factor Prices, Diversification Cones