Graduate Students Seminar

Speaker 1: Gaurab Hore

Title

Why We Learn Nothing from Regressing Economic Growth on Policies: A paper by Dani Rodrik

Abstract

Governments use policy to achieve certain outcomes. Sometimes the desired ends are worthwhile, and sometimes they are damaging. Cross-country regressions have been the tool of choice in assessing the effectiveness of policies and the empirical relevance of these two diametrically opposite views of government behavior. When government policy responds systematically to economic or political objectives, the standard growth regression in which economic growth is regressed on policy tells us nothing about the effectiveness of policy and whether government motives are good or bad.

Speaker 2: Sumaya Alzuhairy

Title

Multilevel Methods for Optimal Control of Elliptic Equation with Stochastic Coefficients

Abstract

We investigate the design and analysis of multilevel preconditioners for optimal control problems constrained by elliptic equations with stochastic coefficients. Assuming a generalized polynomial chaos expansion for the stochastic components, our approach uses a stochastic Galerkin finite element discretization for the PDE, thus leading to a discrete optimization problem. The key aspect is solving the potentially very large linear systems arising when solving the system representing the first-order optimality conditions. We show that the multilevel preconditioning technique from the optimal control of deterministic elliptic PDEs has a natural extension to the stochastic case, and exhibits a similar optimal behavior with respect to the mesh size, namely the quality of the preconditioner increases with decreasing mesh-size at the optimal rate. Moreover, under certain assumptions, we show that the quality is robust also with respect the two additional parameters that influence the dimension of the problem radically: polynomial degree and stochastic dimension.