We will consider the weakly singular Fredholm integral operator $T:L^{1}([0,\tau^\star])\rightarrow L^{1}([0,\tau^\star]),\quad (T\varphi)(\tau)=\frac{\bar\omega}{2} \int_{0}^{\tau^\star}E_{1}(|\tau -\tau^'|)\varphi(\tau')\,d\tau',$ where $E_{1}$ denotes the first exponential integral function, $E_{1}(\tau)=\int_{1}^{\infty}\frac{\exp(-\tau\mu)}{\mu}\mu,\quad\tau>0,$ and $\bar\omega$ is a constant. The spectral elements of a matrix operator representing the discretization of the integral operator $T$ by a projection method on a subspace of dimension $n$ will be computed. These spectral elements will be refined iteratively, by a defect correction type formula to yield an approximation to the spectral elements of $T$.

This paper assesses how the influx of skilled and unskilled refugees affects the technological-knowledge-bias and, consequently, the skill premium in host communities, looking in particular at the case of Poland following the war in Ukraine. We use a dynamic endogenous R&D general equilibrium model, in which labour endowments are related to the direction (or bias) of technological knowledge, which in turn drives the dynamics of key economic variables. With price channel dominance, the shock of the war causes an increase in the technological-knowledge-bias and thus the skills premium, given the increased supply of unskilled labour. Fiscal policy, driven by country governments and materialized through direct and indirect subsidies to R&D activity, has stronger effects on the growth rate when applied to unskilled workers. Monetary policy, driven by the central bank through a decline in the nominal interest rate, influences R&D activity through liquidity constraints and is limited by the zero nominal interest rate. To promote competitiveness and growth, a fiscal policy that subsidizes unskilled workers must be promoted.