Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE.Robust control ; Monetary policy

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. In addition, we study the cost, in terms of performance in the steady state of a central bank that acts to robustify learnability on the transition path to REE. (Note: This paper contains full-color graphics) JEL Classification: C6, E5E-stability, learnability, Learning, monetary policy, robust control

Robustifying Learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought after goals of policy design. And while some contributions to the literature (for example Bullard and Mitra (2001) and Evans and Honkapohja (2002)) have made significant headway in establishing certain features of monetary policy rules that facilitate learning, a comprehensive treatment of policy design for learnability has yet to surface, especially for cases in which agents have potentially misspecified their learning models. This paper provides such a treatment. We argue that since even among professional economists a generally acceptable workhorse model of the economy has not been agreed upon, it is unreasonable to expect private agents to have collective rational expectations. We assume instead that agents have an approximate understanding of the workings of the economy and that their task of learning true reduced forms of the economy is subject to potentially destabilizing errors. We then ask: can a central bank set policy that accounts for learning errors but also succeeds in bounding them in a way that allows eventual learnability of the model, given policy. For different parameterizations of a given policy rule applied to a New Keynesian model, we use structured singular value analysis (from robust control) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. A parallel set of experiments seeks to determine the optimal stance (strong inflation as opposed to strong output stabilization) that allows for the greatest scope of errors in learning without leading to expectational instabilty in cases when the central bank designs both optimal and robust policy rules with commitment. We compare the features of all the rules contemplated in the paper with those that maximize economic performance in the true model, and we measure the performance cost of maximizing learnability under the various conditions mentioned here.monetary policy, learning, E-stability, model uncertainty, robustness

Elements of Design for Containers and Solutions in the LinBox Library

We describe in this paper new design techniques used in the \cpp exact linear algebra library \linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified structure for containers, based on our \emph{founding scope allocation} model. We explain design choices and their impact on coding: unification of our matrix classes, clearer model for matrices and submatrices, \etc Then we present a variation of the \emph{strategy} design pattern that is comprised of a controller--plugin system: the controller (solution) chooses among plug-ins (algorithms) that always call back the controllers for subtasks. We give examples using the solution \mul. Finally we present a benchmark architecture that serves two purposes: Providing the user with easier ways to produce graphs; Creating a framework for automatically tuning the library and supporting regression testing.Comment: 8 pages, 4th International Congress on Mathematical Software, Seoul : Korea, Republic Of (2014

Exact quantum query complexity of EXACTk,ln\rm{EXACT}_{k,l}^n

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal algorithm (for some cases), and a nontrivial general lower and upper bound on the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint

Use of Cemented Rock Fill for Enhanced Pillar Recovery in Area 1 of the Doe Run Company

Area 1 of Doe Run Company’s Buick North Mine was selected for placement of cemented rockfill (CRF) to “trap” or encapsulate select pillars. This method of “trapping” pillars takes advantage of the passive confinement effect of CRF to increase the post-peak load bearing ability of trapped pillars so that other ore bearing pillars can be extracted while still maintaining local and global mine stability. A total of 73 pillars in this area were extracted from October 1998 thru January 2002. Thirteen of 73 pillars were totally trapped by CRF (i.e., the pillars were totally encased in CRF). Eight of the thirteen pillars trapped with CRF were instrumented with extensometers to monitor deformations that occurred during the extraction process. Of the remaining pillars, 18 were not confined in CRF; and the remaining pillars were partially trapped to some degree (one or more free faces). Data collected from the instruments showed that the rate at which pillars deformed (or converged) slowed and that most of the instrumented pillars were virtually unaffected until the late stages of pillar extraction. Two of the instrumented pillars showed considerable initial vertical strain at the onset of pillar extraction. The rate at which these pillars converged slowed as additionally pillars were extracted. This was attributed to the passive confinement effect of CRF in which this material compacts (the density increases) as the pillar dilates, becomes stiffer, and thus provides an increase in confining pressures or stress that acts to restrict pillar dilation. This study has provided valuable insight into the behavior of trapped roof supporting pillars during the extraction process. Future research is being undertaken to clearly develop procedures to predict the behavior CRF trapped pillars during extraction of other economically valuable pillars

Exotic magnetism on the quasi-FCC lattices of the d3d^3 double perovskites La2_2NaB′'O6_6 (B′' == Ru, Os)

We find evidence for long-range and short-range ($\zeta$ $=$ 70 \AA~at 4 K) incommensurate magnetic order on the quasi-face-centered-cubic (FCC) lattices of the monoclinic double perovskites La$_2$NaRuO$_6$ and La$_2$NaOsO$_6$ respectively. Incommensurate magnetic order on the FCC lattice has not been predicted by mean field theory, but may arise via a delicate balance of inequivalent nearest neighbour and next nearest neighbour exchange interactions. In the Ru system with long-range order, inelastic neutron scattering also reveals a spin gap $\Delta$ $\sim$ 2.75 meV. Magnetic anisotropy is generally minimized in the more familiar octahedrally-coordinated $3d^3$ systems, so the large gap observed for La$_2$NaRuO$_6$ may result from the significantly enhanced value of spin-orbit coupling in this $4d^3$ material.Comment: 5 pages, 4 figure