Models with fine figures

The translation of this work from the French is a welcome addition to general texts on econometrics. Its focus is on econometric applications in statistical theory and its organising principles are the concepts of statistical theory, with econometric procedures figuring as frequent theoretical examples. That econometrics is treated as an integrated part of statistics rather than just a related topic is rewarding because it discourages any inclination to try to understand econometric techniques in isolation from their place in wider statistical theory.

The book commences with an introduction to decision theory followed by statistical ideas such as sufficiency, ancillarity, identification and information. These are related to each other and to concepts central to economic applications, such as exogeneity.

The concerns of the two volumes of the book are divided roughly into estimation and testing issues. The authors provide a general treatment of estimators divided into several classes. The treatment of maximum likelihood techniques is perhaps the most familiar. In practical applications, however, the form of the likelihood is unknown and, inevitably, frequently specified erroneously. Misspecified maximum likelihood estimation nonetheless still falls into the broader class of estimators calculated through the maximisation of some criterion function and can still be consistent for parameters in parts of the model which are correctly specified. Misspecification of higher moments need not jeopardise consistency in estimation of a correctly specified mean, for instance. The discussion of these so-called pseudo maximum likelihood estimates is one interesting feature of the book's discussion of this broader class of estimates, as is the discussion of more recent and less familiar methods such as maximum score estimation. Another chapter deals with increasingly popular alternative methods based on minimising the distance of predicted from observed values of particular moments.

Econometricians tend to pay a lot of attention to large sample properties in selecting estimators, largely because these properties are the best understood and increasingly relevant as availability of large microeconomic datasets becomes more common. When many estimates share common degrees of precision in large samples, large sample theory becomes less helpful. Higher order expansions can be useful as a guide to how properties may differ in less-than-very-large samples and the authors provide a useful discussion on the use of such expansions in bias elimination and higher order efficiency comparisons.

As a consequence of our ignorance about the proper model, the issue of model choice is prominent in econometrics. Where the choice is between more and less restricted models the problem falls into a classical testing framework, and the book covers the familiar results in this area. Frequently, however, neither of the models under consideration can be represented as a restriction on the other. The framework appropriate to such a setting is less often treated but also covered admirably here. The difficulty of choosing by goodness of fit is that this can always be trivially improved by adding further tenuously related "explanatory" variables. Appropriate penalties on such prodigality are required and these are discussed together with other methods such as the various information criteria. The authors coverage of nonnested testing procedures, such as the Cox procedure, is welcome and benefits from the earlier treatment of what happens to estimates of parameters in misspecified models.

Several other features of the book deserve comment. It is strong, for example, in areas where the authors have made their own contributions to the econometric literature, such as prediction and definition of residuals in discrete and limited dependent variable models and the nonstandard behaviour of test statistics regarding inequality constraints.

Ian Preston is lecturer in economics, University College London.