Probability, Econometrics and Truth: The Methodology of Econometrics
This modern classic book on asymptotic theory for econometricians by Hal White has now been revised and updated. The  rst edition, published in 1984, quickly become required reading for graduate students interested in studying econometric theory and emerged as a standard reference for econometric theorists. In many ways, the original version was ahead of itself and helped to spur tremendous growth in developing asymptotic theory for econometric models. Soon after the  rst edition appeared, the literature on covariance matrix estimation began to grow and develop. Also at that time, the functional central limit theorem (FCLT) was emerging as a standard and useful tool for analyzing nonstationary models (unit roots) in time series econometrics. Ironically, one could argue that the  rst edition was too in uential, and that the econometrics literature almost instantly made the book appear outdated with respect to the research frontier. The new edition brings this book in line with the current state of the art in asymptotic theory used in econometrics. Most of the material from the  rst version is still here, with mistakes corrected and expositions improved. Covariance matrix estimation, in its infancy in 1984, is brought up to date. A new chapter on the FCLT has been added. Because the FLCT has become one of the workhorse asymptotic tools in time series econometrics, I was pleased to see this addition. The book takes as its starting point linear regressions and instrumental variable estimation. This provides a simple context from which to understand how asymptotic theory is useful. In the subsequent chapters, asymptotic theory is developed in a natural progression starting with laws of large numbers, followed by asymptotic normality and central limit theorems (CLTs). Within each of these chapters, results are  rst developed for independent identically distributed random variables and then generalized systematically for dependent and/or heterogeneously distributed random variables. Martingale difference sequences receive the  nal coverage in these chapters. Because a CLT is not operational in practice without an estimate of the asymptotic variance, a chapter on the theory of covariance matrix estimation follows the material on CLTs. Again, a natural progression is maintained, starting with uncorrelated (but possibly heteroscedastic) random variables and building up to serially correlated random variables with mixing. This chapter does an excellent job of laying out the conditions under which a covariance matrix estimator will be consistent. However, readers looking for guidance on the choice of truncation lag, or bandwidth, will not  nd it here. Following covariance matrix estimation is the completely new chapter on the FCLT. I would have put the FCLT before covariance matrix estimation, because a FCLT can be viewed as a generalization of a CLT for dependent data. But this is splitting hairs. The FLCT is introduced to the reader in the context of random walks and cointegration. Although it is true that a FCLT naturally applies to random-walk data, and one could argue that analysis of unit root processes lead to the use of FLCTs in time-series econometrics, FCLTs are much more widely applicable; consider, for example, the empirical process literature. My very minor concern here is that the reader is perhaps left with the implicit impression that a FCLT is useful only when data has unit roots in it. FCLTs can come in handy whenever one is analyzing partial sums of stationary random variables. Unit root processes are just one example. The book’s technical level remains rigorous and detailed. This is its main strength and what makes it useful to consult when one wants to see the underpinnings of asymptotic theory. Because of the relatively high technical detail, a strong background in probability theory is recommended before diving into this book. Those afraid of regularity conditions need not apply! And for those desiring additional intellectual stimulation, the book is packed with challenging theoretical exercises. Solutions are given in an appendix. I highly recommend Asymptotic Theory for Econometricians to those that already own the  rst edition and to the younger generation of would-be econometric theorists. This revised edition is again a must-have reference.