Applied computational economics and finance.
Economists, however, have not embraced numerical methods as eagerly as other scientists. Many economists have shunned numerical methods out of a belief that numerical solutions are less elegant or less general than closed form solutions. The former belief is a subjective, aesthetic judgment that...
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| Format: | Book |
| Language: | English |
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The MIT Press
2020
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| Online Access: | http://dspace.uniten.edu.my/jspui/handle/123456789/15362 |
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| Summary: | Economists, however, have not embraced numerical methods as eagerly as other
scientists. Many economists have shunned numerical methods out of a belief that
numerical solutions are less elegant or less general than closed form solutions. The
former belief is a subjective, aesthetic judgment that is outside of scienti c discourse
and beyond the scope of this book. The generality of the results obtained from
numerical economic models, however, is another matter. Of course, given an economic
model, it is always preferable to derive a closed form solution|provided such
a solution exists. However, when essential features of an economic system being studied
cannot be captured neatly in an algebraically soluble model, a choice must be
made. Either essential features of the system must be ignored in order to obtain an
algebraically tractable model, or numerical techniques must be applied. Too often
economists chose algebraic tractability over economic realism.
Numerical economic models are often unfairly criticized by economists on the
grounds that they rest on speci c assumptions regarding functional forms and parameter
values. Such criticism, however, is unwarranted when strong empirical support
exists for the speci c functional form and parameter values used to specify a model.
Moreover, even when there is some uncertainty about functional forms and parameters,
the model may be solved under a variety of assumptions in order to assess the
robustness of its implications. Although some doubt will persist as to the implications
of a model outside the range of functional forms and parameter values examined, this
uncertainty must be weighed against the lack of relevance of an alternative model
that is explicitly soluble, but which ignores essential features of the economic system
of interest. We believe that it is better to derive economic insights from a realistic
numerical model of an economic system than to derive irrelevant results, however
general, from an unrealistic, but explicitly soluble model.
Despite resistance by some, an increasing number of economists are becoming
aware of the potential bene ts of numerical economic model building and analysis.
This is evidenced by the recent introduction of journals and an economic society
devoted to the sub-discipline of computational economics. The growing popularity
of computational economics, however, has been impeded by the absence of adequate
textbooks and computer software. The methods of numerical analysis and much
of the available computer software have been largely developed for non-economic
disciplines, most notably the physical, mathematical, and computer sciences. The
scholarly literature can also pose substantial barriers for economists, both because of
its mathematical prerequisites and because its examples are unfamiliar to economists.
Many available software packages, moreover, are designed to solve problems that are
speci c to the physical sciences.
This book addresses the diÆculties typically encountered by economists attempting
to learn and apply numerical methods in several ways. First, this book emphasizes
practical numerical methods, not mathematical proofs, and focuses on techniques that will be directly useful to economic analysts, not those that would be useful exclusively
to physical scientists. Second, the examples used in the book are drawn from
a wide range of sub-specialties of economics and nance, both in macro- and microeconomics,
with particular emphasis on problems in nancial, agricultural, resource
and macro- economics. And third, we include with the textbook an extensive library
of computer utilities and demonstration programs to provide interested researchers
with a starting point for their own computer models.
We make no attempt to be encyclopedic in our coverage of numerical methods
or potential economic applications. We have instead chosen to develop only a relatively
small number of techniques that can be applied easily to a wide variety of economic
problems. In some instances, we have deviated from the standard treatments
of numerical methods in existing textbooks in order to present a simple consistent
framework that may be readily learned and applied by economists. In many cases we
have elected not to cover certain numerical techniques when we regard them to be of
limited bene t to economists, relative to their complexity. Throughout the book, we
try to explain our choices clearly and to give references to more advanced numerical
textbooks where appropriate.
The book is divided into two major sections. In the rst six chapters, we develop
basic numerical methods, including solving linear and nonlinear equation methods,
complementarity methods, nite-dimensional optimization, numerical integration and
di erentiation, and function approximation. In these chapters, we develop appreciation
for basic numerical techniques by illustrating their application to equilibrium
and optimization models familiar to most economists. The last ve chapters of the
book are devoted to methods for solving dynamic stochastic models in economic and
nance, including dynamic programming, rational expectations, and arbitrage pricing
models in discrete and continuous time.
The book is aimed at both graduate students, advanced undergraduate students,
and practicing economists. We have attempted to write a book that can be used
both as a classroom text and for self-study. We have also attempted to make the
various sections reasonably self-contained. For example, the sections on discrete time
continuous state models are largely independent from those on discrete time discrete
state models. Although this results in some duplication of material, we felt that this
would increase the usefulness of the text by allowing readers to skip sections.
Although we have attempted to keep the mathematical prerequisites for this book
to a minimum, some mathematical training and insight is necessary to work with computational
economic models and numerical techniques. We assume that the reader is
familiar with ideas and methods of linear algebra and calculus. Appendix A provides
an overview of the basic mathematics used throughout the text.
One barrier to the use of numerical methods by economists is lack of access to
functioning computer code. This presents an apparent dilemma to us as textbook authors, given the variety of computer languages available. On the one hand, it is
useful to have working examples of code in the book and to make the code available
to readers for immediate use. On the other hand, using a speci c language in the
text could obscure the essence of the numerical routines for those unfamiliar with the
chosen language. We believe, however, that the latter concern can be substantially
mitigated by conforming to the syntax of a vector processing language. Vector processing
languages are designed to facilitate numerical analysis and their syntax is often
simple enough that the language is transparent and easily learned and implemented.
Due to its facility of use and its wide availability on university campus computing
systems, we have chosen to illustrate algorithms in the book using Matlab and
have provided an toolbox of Matlab utilities and demonstration programs to assist
interested readers develop their own computational economic applications.
The CompEcon toolbox can be obtained via the internet at the URL:
http://?? All of the gures and tables in this book were generated by Matlab
demonstration les provided with the toolbox (see List of Tables and List of Figures
for le names). Once the toolbox is installed, these can be run by typing the appropriate
le name at the Matlab command line. For those not familiar with the
Matlab programming language, a primer in provided in Appendix B.
The text contains many code fragments, which, in some cases, have been simpli ed
for expositional clarity. This generally consists of eliminating the explicit setting of
optional parameters and not displaying code that actually generates tabular or graphical
output. The demonstration and function les provided in the toolbox contain
fully functioning versions. In many cases the toolbox versions of functions described
in the text have optional parameters that can be altered by the user user the toolbox
function optset. The toolbox is described in detail in ?? on page ??.
Our ultimate goal in writing this book is to motivate a broad range of economists
to use numerical methods in their work by demonstrating the essential principles
underlying computational economic models across sub-disciplines. It is our hope
that this book will make accessible a range of computational tools that will enable
economists to analyze economic and nancial models that heretofore they were unable
to solve within the con nes of traditional mathematical economic analysis. |
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