A rational, economic model of paygo tax rates (2016), with Georges De Menil, Fabrice Murtin and Eytan Sheshinski.
We argue that paygo rates are determined by a representative agent and a benevolent government jointly maximizing the expected life-time utility of the agent. The distributions of labor and capital income are calculated from national data on real GDP, real wages and the real return to capital since 1950. With uniform risk aversion, predicted rates explain 83% of the variance of observed rates. The globalization of capital markets would lead to convergence of paygo rates. Our results are immune to crises like 2008.
Tidally generated internal-wave attractors between double ridges (2011), with Neil Balmforth, Paula Echeverri and Thomas Peacock.
A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment.