Handbook of Computational Economics Vol. 3

667 Pages·2014·12.999 MB·English

by  Karl Schmedders and Kenneth L. Judd (Eds.)

VOLUME THREE
H
andbook of
COMPUTATIONAL
ECONOMICS
VOLUME THREE
H
andbook of
COMPUTATIONAL
ECONOMICS
KARL SCHMEDDERS
KENNETH L. JUDD
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CONTRIBUTORS
Eric M. Aldrich
Department of Economics, University of California, Santa Cruz, CA, USA.
Yann Algan
Sciences Po, Paris, France.
Olivier Allais
INRA, UR1303 ALISS, Ivry-sur-Seine, France.
Hans M. Amman
Utrecht School of Economics, Utrecht University, Heidelberglaan, Utrecht,
The Netherlands.
Yongyang Cai
Hoover Institution & NBER, USA.
Yu Chen
Department of Mathematics, Idaho State University, Pocatello, ID, USA.
Carl Chiarella
Finance Discipline Group, UTS Business School, University of Technology, Sydney.
Thomas F. Cosimano
Department of Finance, Mendoza College of Business, University of Notre Dame,
Notre Dame, IN, USA.
Wouter J. Den Haan
Centre for Macroeconomics, London School of Economics, London, UK.
CEPR, London, UK.
Alex A. Himonas
Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA.
Timothy P. Hubbard
Department of Economics, Colby College, USA.
Kenneth L. Judd
Hoover Institution & NBER, USA.
Boda Kang
Department of Mathematics, University of York, Heslington, York, UK.
David A. Kendrick
Department of Economics, University of T exas, Austin, Texas, USA.
iixx
x Contributors
Felix Kubler
Department of Banking and Finance, University of Zurich, and Swiss Finance Institute,
Switzerland.
Lilia Maliar
T24, Hoover Institution, Stanford, CA, USA.
Serguei Maliar
T24, Hoover Institution, Stanford, CA, USA.
Gunter Meyer
Department of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA.
Shinichi Nishiyama
Macroeconomic Analysis Division, Congressional Budget Office, USA.
Harry J. Paarsch
Department of Economics, University of Melbourne, Australia.
Adrian Peralta-Alva
Research Division, Federal Reserve Bank of Saint Louis, St Louis, MO, USA.
Pontus Rendahl
Centre for Macroeconomics, University of Cambridge, Cambridge, UK.
CEPR, London, UK.
Philipp Renner
Hoover Institution, Stanford, CA, USA.
Manuel S. Santos
Department of Economics, University of Miami, Coral Gables, FL, USA.
Karl Schmedders
Department of Business Administration, University of Zurich, and Swiss Finance
Institute, Switzerland.
Kent Smetters
Wharton School of Business, University of Pennsylvania, USA.
Marco P. Tucci
Dipartimento di Economia Politica, Università di Siena, Siena, Italy.
Andrew Ziogas
Lloyds Bank – Commercial Banking, Sydney, Australia.
ACKNOWLEDGMENTS
We thank all authors of the papers in this handbook volume for their contribution to
computational economics. Moreover, we are grateful to the many referees that wrote
detailed reviews and whose dedicated work led to many improvements in the papers
in this handbook. We also owe thanks to Kenneth Arrow and Michael Intriligator for
inviting us to edit this handbook and their thoughtful guidance along the way. Finally,
we are very much indebted to Kristi Anderson and Scott Bentley for their excellent
editorial support over the years. Without their constant and patient encouragement we
could not have finished this handbook.
xxii
INTRODUCTION TO THE SERIES
The aim of the Handbooks in Economics series is to produce Handbooks for various
branches of economics, each of which is a definitive source, reference, and teaching
supplement for use by professional researchers and advanced graduate students. Each
Handbook provides self-contained surveys of the current state of a branch of economics
in the form of chapters prepared by leading specialists on various aspects of this branch
of economics. These surveys summarize not only received results but also newer devel-
opments, from recent journal articles and discussion papers. Some original material is
also included, but the main goal is to provide comprehensive and accessible surveys. The
Handbooks are intended to provide not only useful reference volumes for professional
collections but also possible supplementary readings for advanced courses for graduate
students in economics.
KENNETH J. ARROW and MICHAEL D. INTRILIGATOR
xxiiiiii
INTRODUCTION FOR VOLUME 3 OF THE HANDBOOK
OF COMPUTATIONAL ECONOMICS
Computational power continues to explode in terms of both hardware and algo-
rithms. The previous volumes presented the state of the art in the past. V olume 1 of
the Handbook of Computational Economics [Amman et al. (1996)] surveyed the grow-
ing literature on computational methods for solving standard economic models such
as Arrow-Debreu-McKenzie general equilibrium models and rational expectations
models, and dynamic optimization. Volume 2 (Tesfatsion and Judd, 2006) focused on
the foundations and applications of Agent-based Computational Economics (ACE), a
computationally intensive approach to economics that offers an alternative to standard
modeling approaches in economics.
The increase in computational power over the past 20 years is measured in terms
of orders of magnitude. The chapters in this volume give some examples of how these
advances can be used to expand the breadth and quality of economic analyses. More
specifically, they update the advances in algorithms that have improved econometric
tools, solution methods for dynamic optimization and equilibrium models, and appli-
cations to public finance, macroeconomics, auctions, and finance. While much of the
advance in methods is basically the incorporation of existing mathematical methods,
many of these chapters show that economists are closing the gap between economic
practice and the frontiers of computational mathematics. However, that frontier is pro-
gressing rapidly, implying that there is much more that can be done to expand the value
of computational modeling in economics.
Some chapters also point to the opportunities arising from revolutions in computer
architecture over the past 20 years. In the past, computational speed was increased by
designing faster chips. The emphasis has switched to using massive parallelism to create
more powerful computers. This is reflected in the development of high power and high
throughput computing, as well as designing graphics processor units (GPU) capable of
scientific computation.
The first chapter, “Learning About Learning in Dynamic Economic Models,” is by
Kendrick, Amman, and Tucci. They summarize the long literature on dynamic learn-
ing and optimal control. These problems present challenges of both a theoretical and
computational nature because decisions today affect not only the current payoff and
the future state but also what is known about the system being controlled. This is an
important part of any dynamic optimization problem, but is generally ignored due to
the substantial difficulties. Kendrick, Amman, and Tucci summarize past research and
present some suggestions for future work.
xxvv
xvi Introduction for Volume 3 of the Handbook of Computational Economics
In their chapter, “On the Numerical Solution of Equilibria in Auction Models with
Asymmetries within the Private-Values Paradigm,” Tim Hubbard and Harry Paarsch
demonstrate the tight connections between theory, computation, and estimation in the
auction literature. The empirical auction literature has been especially active in the past
20 years. Auction models present novel computational problems, and computational
difficulties have often limited the range of models that can be estimated. Hubbard and
Paarsch give an integrated presentation of auction theory and computational methods
for private value auctions, describing past progress as well as current research which will
substantially increase the range of models that can be efficiently and accurately solved.
Financial market research has been an intensive user of computational methods.
The next two chapters cover two such areas. Asset pricing problems are the focus of
“On Formulating and Solving Portfolio Decision and Asset Pricing Problems” by
Chen, Cosimano, and Himonas. They discuss both the standard methods, such as
log-linearization, as well as methods based on tools from functional analysis. The new
tools, many of which were developed by the authors, are excellent examples of how
quantitative asset market models can benefit from the use of modern computational and
mathematical tools. Option pricing models are partial differential equations (or more
general functional equations), and require the use of PDE methods. “Computational
Methods for Derivatives with Early Exercise Features” by Chiarella, Kang, Meyer, and
Ziogas surveys the literature related to complex derivatives that holders may exercise early.
Public economics is one area of economics that has used computational methods
for close to 40 years. Nishiyama and Smetters summarize the current state of the art for
solving substantive dynamic models in “Analyzing Fiscal Policies in a Heterogeneous-
Agent Overlapping-Generations Economy.”
Macroeconomics research is becoming more computational, particularly as it moves
away from the paradigm of solving the social planner’s problem in a simple representa-
tive agent model. The next two chapters outline the current state of the art for solv-
ing such models. Algan, Allais, den Haan, and Rendahl describe methods for solving
models where the primary source of heterogeneity is idiosyncratic risk in “Solving
and Simulating Models with Heterogeneous Agents and Aggregate Uncertainty.”
“Numerical Methods for Large Scale Dynamic Economic Models” by Lilia Maliar and
Serguei Maliar present methods for models where there are many asymmetric states,
such as models with heterogeneity in tastes and technology, or when there are multiple
shocks and constraints such as in a New Keynesian model with the zero lower bound
on interest rates.
The Handbook continues with three papers on general software and hardware
aspects of numerical analysis. Any numerical computation has error, and economists
need to have confidence that numerical results are sufficiently accurate to support eco-
nomic arguments. Peralta-Alva an Santos discuss this in “Analysis of Numerical Errors.”
Introduction for Volume 3 of the Handbook of Computational Economics xvii
The phrase “computational economics” refers to computers. This is obvious but
we often ignore the fact that our choice of algorithms depends on the nature of the
hardware that we use. Graphic processor units (GPUs) represent a new kind of hard-
ware offering new challenges and opportunities. Eric Aldrich gives some economics
examples of GPU computing in “GPU Computing in Economics.”
Cai and Judd describe new combinations of numerical ideas and the use of parallel
hardware architecture for dynamic programming in “Advances in Numerical Dynamic
Programming and New Applications.” These tools are expanding the range of multidi-
mensional dynamic programming problems that economists can solve.
The final chapter ends the Handbook appropriately by giving us a peep into the
future. Economic models often have multiple solutions, creating problems for both
theorists and applied economists. Many economics problems can be represented as solu-
tions to polynomial equations. Mathematicians have long known that there are methods
for finding all solutions of systems of polynomial equations, but they doubted that these
methods could be used for nontrivial problems such as problems in economics. Such was
the case at the time that the chapters of Volume I of the Handbook of Computational
Economics were written. There has been great progress in the field of computational
commutative algebra in the past 20 years. The final chapter, “Computing All Solutions
to Polynomial Equations in Economics” by Kubler, Renner, and Schmedders, intro-
duces us to those advances and gives us a few hints as to the potential value they hold
for economists.
The progress on both the hardware and algorithm dimensions has increased the
power of computational machinery at a rate far faster than implied by Moore’s Law
alone. While other fields of study have incorporated computational power into their
mainstream research, there has been much slower progress in economics. It is the
Editors’ aim and hope that these chapters will help economists see the vast potential for
economics offered by modern computational methods.
Karl Schmedders and Kenneth Judd