Discretization error cancellation in the plane-wave approximation of periodic Hamiltonians with Coulomb singularities

In solid-state physics, energies of molecular systems are usually computed with a plane-wave discretization of Kohn-Sham equations. A priori estimates of plane-wave convergence for periodic Kohn-Sham calculations with pseudopotentials have been proved , however in most computations in practice, plane-wave cut-offs are not tight enough to target the desired accuracy. It is often advocated that the real quantity of interest is not the value of the energy but of energy differences for different configurations. The computed energy difference is believed to be much more accurate because of `discretization error cancellation', since the sources of numerical errors are essentially the same for different configurations. For periodic linear Hamiltonians with Coulomb potentials, error cancellation can be explained by the universality of the Kato cusp condition. Using weighted Sobolev spaces, Taylor-type expansions of the eigenfunctions are available yielding a precise characterization of this singularity. This then gives an explicit formula of the first order term of the decay of the Fourier coefficients of the eigenfunctions. It enables one to prove that errors on eigenvalue differences are reduced but converge at the same rate as the error on the eigenvalue.Comment: 14 pages, 3 figures, improved result on main theorem, corrected typo

Loan portfolio loss distribution: Basel II unifactorial approach vs. Non parametric estimations

This paper analyzes the measurement of credit risk capital requirements under the new Basel Accord (Basel II): the Internal Rating Based approach (IRB). It focuses in the analytical formula for its calculation, since its derivation to the main assumptions behind it. We also estimate the credit loss distribution for the Uruguayan portfolio in the period 1999-2006, using a non parametric technique, the bootstrap. Its main advantage is that we don’t need to make any assumptions about the form of the distribution. Finally, we compare the requirements obtained using the IRB with the estimated ones, as an approximation of the application of the IRB in the Uruguayan financial system

The Assignment of Workers to Tasks, Wage Distribution and Technical Change: A Critical Review

This paper reviews the literature on two-sided atomeless assignment models of workers to tasks. Using simple parametric examples, the fundamental differences between the comparative advantage and the scale of operations models are illustrated. Holding the distributions of abilities and tasks and the production function of worker-task pairs constant, the two principles are shown to produce different wage distributions and wage inequality. These models are useful to evaluate the general equilibrium effect of technical change on the wage structure. In all models, skilled-biased technical change that impacts the production function of worker-task pairs lead to rising wage inequality.technical change, wage structure, assignment models

A Microfoundation for Production Functions: Assignment of Heterogenous Workers to Heterogenous Jobs

In very different fields of economics, economic inference and policy evaluation require economists to parametrize a production function that links measures of input factors to measures of output. While doing so, strong assumptions are implicitly made about microeconomic variables governing the shape of the aggregate production function. In this paper, I develop an assignment model that provides a microeconomic foundation for aggregate production functions. The shape of the production function depends crucially on the distribution of workers and jobs and the type of technological changes depends crucially on the evolution of these distributions. Sufficient and necessary conditions are provided for the production function to be of the Constant Ratio of Elasticities of Substitution form, a form nesting the broadly used Constant Elasticity of Substitution form. This model provides a way to evaluate how stringent assumptions about the type of production function or technological change are by comparing the implied distribution of jobs and its evolution over time to observations of the distribution of jobs and its evolution over time.microfoundations of production function, tasks assignment, technical change