This book is the second graduate-level econometrics textbook that we have written. Our first one, Estimation and Inference in Econometrics, appeared eleven years ago and has been quite successful. Why then did we choose to write this book instead of a second edition of the first one? Although it would have been quicker and easier to write a second edition, there were several compelling reasons that drove us to write an entirely new book.
It seems unavoidable that the second edition of a book is longer than its predecessor. Estimation and Inference in Econometrics is by no means short. Indeed, it contains too much material even for most two-course sequences. This book is significantly shorter. The entire book can be taught in a two-course sequence, as we explain below in detail, and a substantial fraction of it can be taught in a single course, possibly at a somewhat lower level.
The subject of econometrics has evolved as rapidly in the last ten years as it did in the ten years prior to that. This means not only that there are many new things that students of econometrics should learn, but also that there are new and perhaps better ways of understanding older material. Although many parts of Estimation and Inference in Econometrics have held up well, we would have had to reorganize and rewrite it radically if we were to produce a second edition that we could be truly happy with.
Another reason for preferring to write a new book is that the level of our earlier one, especially in several key chapters in the first half, is too high for the first graduate courses at many institutions. With hindsight, this was a mistake. One of our goals in writing this book has been to start at a more modest level and work up from there gradually as the book proceeds. Some of the earlier chapters do contain some fairly advanced material, but much of it is confined to exercises, and the rest is in sections and subsections that can be skipped without serious loss of continuity.
Features of This Book
Cheap personal computers were already a fact of life around 1990. Since then, computers have become vastly more powerful and even less expensive. It is no surprise that econometrics, always a computer-intensive discipline, should have been profoundly affected by the development of computers. Ten years ago, one could have predicted that they would make the practice of econometrics a lot easier, and of course that is what has happened. What was less predictable is that the ability to perform simulations easily and quickly would change many of the directions of econometric theory as well as econometric practice. The use of the computer in econometrics, especially for simulation, has blossomed so quickly that no textbook like this one can reasonably avoid a serious discussion of simulation.
Simulation-based methods greatly enhance the asymptotic theory that has been at the heart of econometrics for many decades. Problems that are intractable analytically are often simple to handle by simulation, and a wide variety of new techniques that exploit this fact has been proposed during the last ten years. Of these techniques, the one that seems most general in its application is the bootstrap, and we make a point of introducing this important topic early on. Other methods can do things that the bootstrap cannot, and we discuss some of these more briefly in later chapters. We are happy to confess that we have ourselves learned a great deal by exploring new simulation-based methods while preparing this book, and we are now enthusiastic in our use of these methods.
We have for many years been advocates of the use of artificial regressions for many purposes in econometrics. They are useful not only for simplifying many numerical procedures but also for providing better theoretical understanding. The best-known, and no doubt tlie most widely used, artificial regression is the Gauss-Newton regression. We use it as a model for a host of other artificial regressions, some of which were developed expressly for this book.
Estimating functions and estimating equations are topics that are not terribly familiar to most econometricians. We ourselves became aware of them only in the mid-1990s, when V. P. Godambe, of the University of Waterloo, prodded us to look more closely at a theme that he had himself pioneered back in the 1960s. In this book, these concepts are not introduced until Chapter 9, but they are present implicitly in the earlier chapters, usually in the guise of the method of moments. Once introduced, estimating equations make it much easier to explore the theory of the generalized method of moments than the methods conventionally used in econometrics. Some of the more advanced topics that we treat in the last third of the book are also greatly simplified by an approach based on estimating equations.
Every chapter has a substantial number of exercises. We put a great deal of effort into posing and solving these, and we made numerous changes to the text itself as a result of doing so. There are several types of exercises, intended for different purposes. Some of the exercises are empirical, designed to give students the opportunity to become familiar with a variety of practical econometric methods. Others involve simulation, including some that ask students to conduct small Monte Carlo experiments. Many are fairly straightforward theoretical exercises that good students should find illuminating and, we hope, not too difficult. Some exercises have several parts, and instructors may want to assign only some of them. For obvious reasons, we urge instructors to look at the solution to an exercise before assigning all or part of it.
We have tried hard to present material in a logical way, introducing new ideas as they are needed and building on the material developed earlier. This applies also to mathematical and statistical techniques that, in many cases, students may already be somewhat familiar with. Instead of treating these in appendices, we discuss them when they are first used, in the context of their applications to econometrics. We have found that this approach generally works very well in the classroom. The sections on mathematics or statistics are never too long, and we make every effort to motivate them by indicating their relevance to econometrics. This probably means that the book is not appropriate for students with a really weak mathematical or statistical background. It also means that readers will need to use the Subject Index rather than the Table of Contents when they want to look up basic mathematical and statistical concepts. Although this book is intended more as a text than as a reference, we have put a great deal of effort into making the Subject Index as complete and comprehensive as possible.
While it is generally not hard to develop a consistent and appropriate notation for an individual topic, it is exceedingly hard to maintain notation consistent across all the chapters of a book of this length. We do not claim to have done so, but we have made strenuous efforts in that direction. We have been influenced by the suggestions of Karim Abadir, of the University of York, and Jan Magnus, of Tilburg University, on many vexed points of notation. Although we have not followed their counsel in all cases, we wholeheartedly support their efforts to develop a useful and consistent notation for modern econometrics, and we hope that this book will complement their efforts.
How to Use This Book
This book can be used for either a one-term course or a two-term sequence of courses at either the Master's level (in a serious graduate program) or the Ph.D. level. It could also be used in upper-level undergraduate courses for specialists if the students have sufficient background, motivation, and ability.
A two-term course sequence at the (North American) Master's level should be able to cover every chapter in the book, although instructors will undoubtedly wish to omit a few topics that are particularly advanced or specialized. A one-term course should be able to cover approximately the first ten chapters, although a certain amount of material will have to be omitted, depending on the background of the students and the interests of the instructor. See the chapter-by-chapter discussion below.
A two-term course sequence at the Ph.D. level should be able to cover the entire book with no difficulty. Some relatively elementary material in the first few chapters should probably be dealt with rather quickly, and instructors may wish to go into more depth on some topics than we have done in the text. A number of the exercises provide opportunities to do so. A wide variety of one-term courses at the Ph.D. level could be based on various combinations of chapters and sections.
Our earlier book has been used in many European countries, and it is still in use in a number of universities on that continent. We hope that this book will be at least as attractive to European readers. One of the authors (Davidson) teaches in France, and he has successfully used preliminary versions of the book in courses ranging from the senior undergraduate to the doctoral level. It would, however, be rash to make any specific suggestions as to how best to use the book in the European context. The efforts of the European Union to harmonize university education across countries with widely different traditions have, temporarily one hopes, thrown many educational structures into disarray.
Some of the exercises are really quite challenging, as we discovered while preparing solutions to them. These exercises are starred, as are a number of other exercises for which we think that the solutions are particularly illuminating, even if they are not particularly difficult- In some cases, these starred exercises allow us to present important results without proving them in the text. In other cases, they are designed to allow instructors to cover advanced material that is not in the text itself. Because the solutions to the starred exercises should be of considerable value to students, they are available from the website for the book. All the data needed for the exercises are also available from the website, as are corrections made since the book was printed.
An instructor's manual provides solutions to all the exercises. It is available, on CD-ROM, to instructors only. The URL of our website and instructions for obtaining the CD-ROM may be found in the section entitled `Data, Solutions, and Corrections` which immediately follows the Preface.