Applied computational economics and finance.

• Main Author: J. Miranda, Paul L. Fackler.
• Format: Book
• Language: English
• Published: The MIT Press 2020
• Subjects: Business Mathematics, Macroeconomics, Business Finance
• Online Access: http://dspace.uniten.edu.my/jspui/handle/123456789/15362

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.