# Advanced Econometrics Takeshi Amemiya

This book is intended both as a reference book for professional econometricians and as a graduate textbook. If it is used as a textbook, the material contained in the book can be taught in a year-long course, as I have done at Stanford for many years. The prerequisites for such a course should be one year of calculus, one quarter or semester of matrix analysis, one year of intermediate statistical inference (see list of textbooks in note 1 of Chapter 3), and, preferably, knowledge of introductory or intermediate econometrics (say, at the level of Johnston, 1972). This last requirement is not necessary, but I have found in the past that a majority of economics students who take a graduate course in advanced econometrics do have knowledge of introductory or intermediate econometrics.

The main features of the book are the following: a thorough treatment of classical least squares theory (Chapter 1) and generalized least squares theory (Chapter 6); a rigorous discussion of large sample theory (Chapters 3 and 4); a detailed analysis of qualitative response models (Chapter 9), censored or truncated regression models (Chapter 10), and Markov chain and duration models (Chapter 11); and a discussion of nonlinear simultaneous equations models (Chapter 8).

The book presents only the fundamentals of time series analysis (Chapter 5 and a part of Chapter 6) because there are several excellent textbooks on the subject (see the references cited at the beginning of Chapter 5). In contrast, the models I discuss in the last three chapters have been used extensively in recent econometric applications but have not received in any textbook as complete a treatment as I give them here. Some instructors may wish to supplement my book with a textbook in time series analysis.

My discussion of linear simultaneous equations models (Chapter 7) is also brief. Those who wish to study the subject in greater detail should consult the references given in Chapter 7.1 chose to devote more space to the discussion of nonlinear simultaneous equations models, which are still at an early stage of development and consequently have received only scant coverage in most textbooks.

In many parts of the book, and in all of Chapters 3 and 4,1 have used the theorem-proof format and have attempted to develop all the mathematical results rigorously. However, it has not been my aim to present theorems in full mathematical generality. Because I intended this as a textbook rather than as a monograph, I chose assumptions that are relatively easy to understand and that lead to simple proofs, even in those instances where they could be relaxed. This will enable readers to understand the basic structure of each theorem and to generalize it for themselves depending on their needs and abilities. Many simple applications of theorems are given either in the form of examples in the text or in the form of exercises at the end of each chapter to bring out the essential points of each theorem.

Although this is a textbook in econometrics methodology, I have included discussions of numerous empirical papers to illustrate the practical use of theoretical results. This is especially conspicuous in the last three chapters of the book.

Too many people have contributed to the making of this book through the many revisions it has undergone to mention all their names. I am especially grateful to Trevor Breusch, Hidehiko Ichimura, Tom MaCurdy, Jim Powell, and Gene Savin for giving me valuable comments on the entire manuscript. I am also indebted to Carl Christ, Art Goldbeiger, Cheng Hsiao, Roger Koenker, Tony Lancaster, Chuck Manski, and Hal White for their valuable comments on parts of the manuscript. I am grateful to Colin Cameron, Tom Downes, Harry Paarsch, Aaron Han, and Choon Moon for proofreading and to the first three for correcting my English. In addition, Tom Downes and Choon Moon helped me with the preparation of the index. Dzung Pham has typed most of the manuscript through several revisions; her unfailing patience and good nature despite many hours of overtime work are much appreciated. David Criswell, Cathy Shimizu, and Bach-Hong Tran have also helped with the typing. The financial support of the National Science Foundation for the research that produced many of the results presented in the book is gratefully acknowledged. Finally, I am indebted to the editors of the Journal of Economic Literature for permission to include in Chapter 9 parts of my article entitled “Qualitative Response Models: A Survey” (Journal of Economic Literature 19:1483-1536,1981) and to North-Holland Publishing Company for permission to use in Chapter 10 the revised version of my article entitled “Tobit Models: A Survey” (Journal of Econometrics 24:3-61, 1984).

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