General Overview
The focus of this book is on (1) developing a plausible basis for reasoning in situations involving incomplete- partial information and (2) developing principles and procedures for learning or recovering information from a sample of economic data. What makes this information recovery process interesting is that
- usually the conceptual model is incomplete or incorrectly specified;
- the data underlying an econometric analysis are limited, partial or incomplete;
- the conceptual model contains parameters or components that are unknown and unobserved and, indeed, not subject to direct observation or measurement;
- the recovery of information on the unknown parameters or components requires the analyst to use indirect measurements based on observable data and then to solve the resulting inverse problem by mapping the indirect observations into information on the unknowns;
- the models may be ill-posed or, in the context of traditional procedures, may be underdetermined and the solution not amenable to being written in closed form;
- the procedures used for estimation may not be optimal and their properties may not even be precisely discernible;
- and
the inferences are subject to errors and distortions.
These problems, taken either individually or in some combination, represent the intellectual challenge of modern econometric analysis and research. Building on the productive efforts of our precursors in the areas of theoretical economics, inferential statistics and econometrics, our objective in this book is to provide an operational understanding of a rich set of estimation and inference tools that may be used in theoretical and applied econometrics. In search of this goal, we present and interrelate an array of modern estimation and inference solutions for basic econometric models and data-sampling processes ( DSPs ). Expanding on this base, the reader should then be able to use this basic foundation to sort out the statistical implications of alternative estimation and inference procedures as they apply to a range of econometric inverse problems normally found in practice.
This book contains material appropriate for a sequence of courses in graduate econometrics. We recognize the importance of a good statistical foundation when studying econometrics. Because a semester that covers the statistical foundations of probability theory and the principles of estimation and inference is not always possible, we have provided two chapters on the accompanying CD-rom that identify and interpret benchmark theorems and summarize the principal ideas involving the logic of probability and the principles of inference. The reader who does not understand all of the prerequisites should not be discouraged. Most of the book can be followed with a very basic knowledge of these areas. Moreover, we have tried to maintain a very deliberate pace in developing the proofs given throughout the book. In carrying through a range of fundamental economic DSPs, we first present details of the probability econometric model and then proceed to discuss estimation procedures, sampling properties, and a basis for inference.
The book is designed so the computer is a companion in each step of the teaching and learning process. By emphasizing the principles of estimation and inference for basic econometric models and then empirically demonstrating them on the computer, we hope to provide the reader with a deep understanding of the fundamental conceptual and empirical steps involved in econometric analyses. The hope is that students working their way through this book will acquire an operational understanding of a rich set of basic estimation and inference tools for use in applied econometric research. They should also develop a general framework for how information is integrated into a systematic approach for defining, structuring, estimating, and interpreting problems of estimation and inference.
Econometrics is a work in progress. Anyone who doubts this should review a sampling of econometric books starting in the mid-1930s and map the development of econometrics over time. Advances in econometric methodology have been substantial in both content and number, and they continue at a geometric rate. We have now reached a point in the development of econometrics at which no one book can possibly encompass even the majority of known procedures and results in the field. Given the rapid development of the field, econometric texts are to some extent outdated the moment they are published.
Our strategy in this book is to provide the reader with a firm conceptual and empirical understanding of those basic econometric models and procedures that provide the roots or foundations for the large majority of variations found in specialized books and journal articles. We hope to equip the reader with the ability to read and better comprehend alternative and more advanced econometric methodologies in the literature as well as to understand new developments in the field. Using modern techniques to address some basic problem areas in econometrics, we have tried to remove some of the confusion, tune out the noise, and set the mind in order for a time.
Organization of the Book
General
By design, the book starts with the specification and analysis of the simplest parametric and semiparametric probability models. Then, chapter by chapter, the specification and reasoning process is generalized. Our objective is to cover a sufficient scope of concepts and procedures to give the analyst an adequate conceptual foundation from which to choose, learn about, and implement methods of analysis that avoid assumptions he or she does not wish to make in the formulation, estimation, and inference of probability models consistent with economic sampling processes. Learning goals include a rigorous basic understanding of
- the rationale used to specify an econometric model consistent with the underlying data sampling process and available prior information;
- the corresponding rationale used to choose, design, and evaluate an appropriate estimation and inference procedure for a given information set;
- the programming of estimation and inference procedures on the computer based on commercial or custom-written (by the reader) software; and
- the interpretation of numerical results generated from each econometric procedure applied to a given information set and the types of legitimate inference statements one can and cannot make.
Specific
The book is organized into ten parts. In Part I, we discuss a general approach for searching out econometric knowledge and introduce an array of fundamental probability-econometric models that are used in practice to characterize economic DSPs. Part II is concerned with estimation and inference procedures for parametric and semiparametric variants of linear regression models. Here we consider estimation and inference in the case of both parametric and semiparametric models. Part III introduces the concept of extremum estimators and examines nonlinear-in-the-parameters regression models and nonnormal formulations. Part IV is concerned with stochastic right-hand-side variables, moment-based specifications of DSPs, empirical likelihood, and information theoretic procedures whose solutions cannot be written in closed form. In part V the possibly restrictive independent and identically distributed noise component structure of the probability model is relaxed, and estimation and inference procedures for handling this more general error covariance model are developed.
Part VI examines instrumental variables, the general method of moments for overdetermined problems, and the simultaneous equations probability model. Part VII takes up the important problem of discovering or choosing the underlying probability model. Information recovery in discrete choice, ill-posed, and nonparametric models is discussed in Part VIII. Part IX deals with basic concepts of Bayesian inference and their application to the regression model in the face of friendly and unfriendly posterior distributions.
Part X ends the book with an assessment of the econometric road that has been traveled and the econometric challenges ahead. A discussion of Monte Carlo methods for simulation and moment approximation purposes is presented in an appendix to the book.
Foundation chapters dealing with probability theory and principles of estimation and inference along with a chapter on information recovery in ill-posed inverse problems appear as fully text-searchable electronic documents on the CD at the back of the book. A computer interactive (ToolBook) Matrix Review manual is also included on the CD, as is a GAUSS light software package. These will help you compute outcomes and simulate the behavior of the econometric estimation and inference procedures, and the manual also includes tips on how to run and program with the GAUSS programming language. Finally, an electronic interactive (ToolBook) Examples manuals is included on the CD. It provides computer illustrations, written in the GAUSS language, of all of the principal econometric procedures developed in the text. A tutorial with solution guides to the questions and problems in each chapter can be downloaded by instructors from the internet.
We have made a valiant effort to get the chapter sequence right. In fact, we tinkered with it right up until publication. Although each student and instructor will follow the chapter sequence that best serves his or her teaching and learning goals, we ordered the chapters to ensure that the reader could enter each chapter with the tools necessary to understand it.
A Comment
Many view econometrics as a potpourri or bag of tricks, and the cookbook metaphor for econometrics textbooks has become commonplace. Unfortunately, this philosophy can produce analysts who know a list of econometric recipes but who have an insufficient understanding of which techniques to apply in a given situation or how to interpret the results of an application properly. As the inventory of econometric procedures has grown, the importance of understanding when it is appropriate to apply each econometric procedure, as well as knowing the appropriate interpretation of the results, has grown more than proportionately. The number of reference works that describe the growing inventory has expanded pari-passau. These reference works will be accessible to the well-trained analyst who has mastered the basic philosophy and principles on which econometrics is founded. However, analysts who have done little more than memorize the recipes in a conceptual econometric cookbook will find the growing literature on new econometric methods impenetrable. Our goal is for you to be able to determine or create the econometric procedures that are applicable to your problem and then be able to apply them empirically and interpret the results appropriately. This is what this book is about, and this is what we think modern graduate econometrics instruction should be about. Acknowledgements
This book represents the direct and indirect contributions of many individuals. A first step in the process involves finding an editor who understands the subject matter and shares your goals. In Scott Paris we found such a person, and he has been a full partner every step of the way from getting informed reviews of our prospectus through the book production phase. To write this book we have had to stand on the shoulders of many of our predecessors in theoretical and applied statistics and econometrics. We hope we have acknowledged these persons appropriately in the many references throughout the book. At a formative stage, the suggestions of William Barnett, Helmut Lutkepohl, and Scott Cardell were facilitative and enlightening regarding the scope of topics that should be covered, the depth of coverage, and the goals and overall focus of the book.
At a later stage, when the chapters were reaching a second rough form, Gene Savin, Tom Marsh, William Griffiths, Carter Hill, Arnold Zellner, Bruce McCullough, Tong Li, Rafic Fahs, and Marco van Akkeren Art Owen made major contributions in terms of scope and content. Special thanks to the "Econometric Applications" classes of 1997-1999 for enduring and providing real-time feedback relating to beta versions of the text and software as it was being developed.
We express our deep appreciation to the creators of GAUSS software--Aptech Systems, Inc., of Maple Valley, Washington, for granting us the right to use and distribute a version of their powerful programming package. In particular, expert consultations, support, and documentation with respect to software programming with GAUSS was generously provided by Ron Schoenberg, also of the University of Washington. Gordon Stone provided patient and knowledgeable technical assistance on implementing GAUSS and furnished helpful technical information at the computer-systems level. Gail Horecny and Dan Meine, our ever helpful liaisons to Aptech, paved the way for our intimate cooperation with Aptech-GAUSS and were always available to see to it that our questions would get answers.
We are also deeply grateful to the Asymetrix corporation of Bellevue, Washington, for generously allowing us to use their versatile and powerful multimedia authoring software package, ToolBook Instructor, to produce the electronic manuals that accompany the textbook. Special thanks to Scott Sherman for serving as liaison between Asymetrix and the authors and for providing us with expert help and software updates as needed.
Finally, we wish to acknowledge the support professionals that we worked with on an almost daily basis. Brenda Campbell was a word-processing and equation-rendering dynamo who also doubled as an expert multimedia consultant, layout advisor, and electronic document creator par excellence. Mary Graham, with intelligence and good humor, turned page after page of words and symbols written in red ink into beautiful copy. Working with Mary and Brenda, Dana Keil and Joel Adlen provided expert help in smoothing out computer-related word-processing problems, particularly the ticklish cross-platform challenges. It is hard to imagine that the project would have ever come to completion without the dedication and hard work of this fine team of professionals.
To these individuals, and all the others too numerous to mention, we wish to express our warm thanks and appreciation.
Ron Mittelhammer
George Judge
Douglas Miller
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