Econometrics uses a collection of ideas from mathematics, statistics and statistical methods, and, more recently, computer science to study economic data. It is sometimes described as the branch of economics that aims to give empirical content to economic relations. As its title shows, the book under review includes topics from mathematics for econometrics, mainly from linear algebra and probability theory.
The present book is the fourth edition. As the author mentions, it differs significantly from the third edition in that it has undergone considerable expansion and revision. The author explains that the major expansion involves a more complete coverage of basic aspects of mathematics that have continued to play an increasingly significant role in the literature of econometrics.
The book begins with a rather extended review of topics from linear algebra in the three initial chapters. Then the author studies Matrix Vectorization and Vector and Matrix Differentiation. In the sixth chapter, DE Lag Operators, GLSEM (general linear structural econometric model), and Time Series are studied. Note that DE Lag Operators are called backward shift operators in the statistical literature.
The author treats Probability Theory in Chapters 7 and 8, and somewhat in Chapter 9. Chapters 10 and 11 are about The General Linear Model (GLM) and Panel Data Models and Chapter 12 is about GLSEM and TS Models. In the latter, the author gives two important applications involving simultaneous equations, the AR, and ARMA models. The last chapter is about asymptotic expansions and deals with situations in which it is required to approximate the limiting distribution of an estimator.
The book contains no exercises. Thus, if instructors wish to use it as a textbook, they will need to provide their own. In addition to people working econometrics, this book can be used for students in an applied linear algebra course to find some applications.
Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His fields of interest are Elementary, Analytic and Probabilistic Number Theory.