An Introduction to Classical Econometric Theory

An Introduction to Classical Econometric Theory By Paul A. Ruud. New York: Oxford Press, 2000. Pp. xxiv, 951. $85.00. An Introduction to Classical Econometric Theory is one of several recent entries into the PhD-- level econometrics market.1 Ruud has distinguished his text from these competitors in a number of ways, the most notable of which are its organizing principles of mathematical projection and latent-variable models. The former is used to develop the geometry of ordinary least squares (OLS), which is extended to generate theoretical insights into the properties of a variety of other estimators. The latter is adopted as a unifying approach to model specification, emphasizing the dependence of observables on unobservables. A successful graduate econometrics text will be a well-written and reasonable comprehensive guide to the current standard tools and techniques of econometric practice. As such, it will serve as both a primary course supplement and useful future reference. Of course, any judgement about a book will reflect the predilections of the judge. Thus, I should admit up front a preference for algebra over geometry when deriving the main results of OLS. I recognize that delving into the geometry can generate a depth of understanding that sometimes is elusive in the algebra. However, I suppose that, for most students in their first graduate econometrics course, the costs of pursuing that level of understanding outweigh the benefits. Clearly the textbook market thinks so, as there is only one other prominent book, Davidson and MacKinnon (1993), that places as much emphasis on least-squares geometry. In addition, I prefer an introductory text to have a more extensive treatment of time-series issues than is offered by Ruud. For the most part, the time-series material is confined to the modeling of serially correlated errors. Absent is any systematic consideration of how estimation should proceed under dependent sampling and, in particular, how to deal with persistent series. An example of a book that strikes roughly the right balance is Wooldridge (2000), which, interestingly, is targeted at undergraduates. With these qualifications in mind, there are many features of Ruud's book I like very much. First and foremost, the style is efficient but clear, rarely leaving the reader confused about the basics and usually providing reliable advice on the application of these results in real-world empirical settings. Further, most topics are introduced through an empirical example that motivates well the theoretical developments to follow, and end-of-chapter "Mathematical Notes" sections are wisely inserted to present the most technical arguments and proofs. I also appreciate that Ruud never relies on the fiction of fixed regressors, instead focusing on the estimation of E (y^sub n^ | X) (n = 1, . . . , N) under different assumptions about the conditional mean and variance of the model. At a more detailed level, the book is comprised of 28 chapters, organized into four parts: 1, Ordinary Least Squares (Chapters 1-5); II, Linear Regression (Chapters 6-12); III, Generalizations of the Linear Model (Chapters 13-23); and IV, Latent Variable Models (Chapters 24-- 28). The main text is supplemented by appendices containing the usual prerequisite material from matrix algebra, probability theory, and mathematical statistics, as well as a website that provides links to text figures, data used in examples, and solutions to the (excellent) end-of-- chapter exercises.2 Part I sets forth the principle of mathematical projection and establishes the fundamental algebra and geometry of OLS. Ruud sums up these chapters like this: "Starting with the concepts of (1) a vector space, (2) linear dependence, (3) an inner product, length of a vector, and orthogonality, we have developed the idea of a projection as the solution to a minimum-distance problem" (p. 97). The statistical treatment of the model begins in Part II, focusing on the small-sample properties of OLS and exact inference based on the OLS estimator under the usual assumptions of the classical model. …