The effect of R&D growth on employment and self-employment in local labour markets

The paper investigates the effects of firms’ investment in Research and Development (R&D) on employment dynamics in the British local labour markets (Travel to Work Areas). We distinguish between local areas characterised by the initial level of routinised employment of the workforce. We implement a instrumenting strategy to address endogeneity issues in the relation between innovation and employment. Our results suggest that increases in R&D investments mainly affect routinised areas, where the employment created is low skilled, concentrated in non-tradable sectors (like transport, construction) and services. A significant share of the jobs created is self-employment, concentrated in the 25-34 age cohort. We qualify the effect of R&D on self-employment by looking at local firms’ dynamics, which suggest that the increase in self-employment is reflected in a higher number of micro-firms. Rather, in non-routinized areas, R&D results in the expected increase in the demand of high-skilled workers and a reduced demand of low-skill employment

Isaacs' Equations for Value-Functions of Differential Games

The authors study value functions of a differential game with payoff which depends on the state at a given end time. They consider differential games with feedback strategies and with nonanticipating strategies. They prove that value-functions are solutions to some Hamilton-Jacobi-Isaacs equations in the viscosity and contingent sense. For these two notions of strategies, with some regularity assumptions, The authors prove that value-functions are the unique solution of Isaacs' equations