Econometrics theory and methods

Author: Davidson (USA) / Mckinnon C. / Shen Genxiang
Publisher:
Publishing Date: 2006-04-01
Features: This book is an excellent textbook adopted in teaching at different levels in North America and Europe. Besides its detailed content and self-proclaimed nature indicating it as a textbook, the difficulty and depth of the problems it addresses are more akin to a monograph. This book enables readers with a general mathematical foundation to study modern econometrics at a deeper level. The book starts from a low level, introducing basic probability theory and mathematical statistics in the chapter, and also provides detailed explanations of some commonly used mathematical methods, such as Taylor series expansion of functions, matrices, the definition and properties of inverse matrices, etc. Of course, these introductions are limited to what is necessary and are often provided when needed. Compared to similar textbooks, this book offers more detailed treatments of related content and provides theoretical derivations for some commonly used methods. For example, White test, unit root test, and cointegration theory. The book often explains complex theories through simple examples. With a profound understanding of econometrics and years of teaching experience, the authors provide many classic examples that make abstract theorems and theories clear to readers. For instance, when explaining two different types of maximum likelihood estimators, they use the well-known uniform distribution to clearly illustrate the differences between the two estimators and their applications in different contexts. The numerous graphs and geometric explanations in the book also help beginners understand and grasp the theories.
This book enables readers with some background in econometrics to quickly stay at the forefront of econometric research. The content is innovative, with many methods appearing for the first time in such textbooks. For example, simulation moment methods (SMM), indirect inference methods (Indirect inference method), OPG regression, and double-length artificial regression. The references in the book primarily cite recent papers, with new references updated until 2004.
Compared to existing similar works, this book has distinct features in many aspects, including:
(1) A chapter (Chapter 2) dedicated to the geometric theory of linear regression, using projection as a tool to make the treatment of classical linear regression model theories concise and intuitive. The use of the FWL theorem greatly simplifies the handling of many problems and makes it easier to see the essence of these methods. For example, the treatment of seasonal adjustment, the explanation of the role of dummy variables, and the analysis of the impact of outliers on regression results.
(2) The application of bootstrapping. Modern econometrics is based on large-sample theory, but the lack of real-world samples often reduces the validity of large-sample theory conclusions. The application of bootstrapping can significantly improve the finite-sample properties of large-sample conclusions. At the same time, bootstrapping is also easy to implement. The application of bootstrapping runs throughout the book, becoming a distinctive feature compared to similar textbooks.
(3) The use of artificial regression. Like the FWL theorem, the clever application of artificial regression greatly simplifies the handling of many complex problems, with Newton–Gauss regression being a typical example.
(4) The treatment of confidence intervals differs from traditional methods. In Chapter 5, the methods for finding confidence intervals and regions are given by reverse inference from hypothesis testing, which might seem a bit awkward. The purpose of using reverse inference from hypothesis testing to find confidence intervals is to adopt bootstrapping in confidence intervals. Considering this, it is not difficult to understand why the authors chose this approach.
The data used in the exercises of this book can be freely downloaded from the authors' designated website, providing valuable resources for readers to simulate practical problems.
In the translation of this book, the names of well-known mathematicians, especially those used as names of important theorems and theories, are translated according to fixed conventions, such as Newton, Gauss, Pythagoras, etc. The names of other authors are retained in Western characters in the translation. The translation of terms refers to the English-Chinese Mathematical Vocabulary (Science Press, 1982) and the English-Chinese Mathematical Vocabulary (Tsinghua University Press, 2005). For terms that are easily ambiguous, translator's notes are provided.