Book reviews
Applied econometricians have been waiting a long time for a successor to G.S. Maddala’s text, Limited-Dependent and Qualitative Variables in Econometrics. The recent publication of the English translation of Christian Gourieroux’s text, Econometrics of Qualitative Dependent Variables (originally published in French in 1991) seemed to provide hope that we could finally have a mathematically rigorous, yet conceptually general, textbook from which to teach the subject to graduate students. The book’s recent release also led us to hope that important questions at the heart of econometric research on qualitative dependent variables (QDVs) might be made available to a wider public.
Alas, this is not a book from which one could easily teach graduate students the econometrics of QDVs due largely to the discouragingly large number of typographical errors (especially in the equations) and occasionally misleading translations. The fact that the content has not been updated since its original appearance in 1991 also means that some subjects that have spawned entire books are given a cursory treatment, many interesting subjects are not treated at all, and other subjects that have been more or less abandoned receive chapters and chapters of attention. The examples that are used to illustrate various techniques are occasionally drawn from the French-language literature (which may not be accessible for the typical English-speaking graduate student) and sometimes focus on subjects that are barely taught in many North American graduate programs (although they attracted a lot of attention in the French research community in the 1980s). This book could indeed be useful for experienced applied researchers looking to deepen their understanding of the subject matter and its structure could serve as a basis for organizing a graduate course, but it is probably too early to abandon Maddala with complements from the recent literature.
The structure of the book is appealing, beginning with a discussion of dichotomous variables (chapter 2), which serves to motivate the rest of the book and present the basic approach, as well as introducing estimation methods and numerical techniques. The author brings in the particularities of using grouped data at the very beginning, which has its advantages (the reader is not surprised when similar notation reappears later) and its disadvantages (it complicates the discussion unnecessarily and introduces even more opportunities for typos). He introduces, in this context, Berkson’s method and the Minimum Chi-Square method of finding parameter values, which constitute perhaps interesting alternatives for the grouped data case, but receive as much attention as the more standard maximum likelihood methods. There is also no mention of GMM estimators anywhere in the book, and one has to wait until chapter 10 to see the word “moment” used, although without explicitly mentioning method of moments or GMM estimation. On the other hand, the treatment of specification error is rather complete and elegantly presented. The author does make some potentially misleading comments on occasion, in particular when he states that simple closed-form expressions do not exist for ML estimators. Although this is generally true, a standard exam question in an upper-level econometrics course is to derive the analytic expression for the ML estimator in the logit case with a single indicator variable and a constant and to calculate it from a 2×2 contingency table.
Chapter 3 discusses modeling in a relatively straightforward manner, although the translator might have preferred “multinomial” or “multivariate” (according to the context) to “polychotomous,” which is a direct translation of the French term. The importance of sampling methods is discussed here, although a short section on the importance and implications of choice-based sampling (absent from the book) would have appropriate here. The discussion of estimation methods and tests in the following chapter is also well done, and with the value of Lagrange Multiplier tests being presented in a particularly intuitive manner.
The log-linear model receives a detailed treatment in chapter 5, and this is perhaps the most problematic for those who would like to use the book as a reference for teaching. Beyond the fact that all mention of covariates disappears for the first 
of the chapter, the discussion is particularly removed from applied concerns and a professor could have a hard time motivating this chapter, which is unfortunate. Even more unfortunate is the density of typos in this chapter, in some cases introducing notational contradictions only 9 lines apart on the same page. For example, how can
while
as page 111 claims? Although the chapter provides a useful discussion on marginalization and conditioning in multivariate problems, the difficulty of rendering the text mathematically correct will probably lead most of us to skip the chapter completely.
Qualitative panel data and Markov chains are introduced in chapter 6, in a discussion that is clear and concise, with a straightforward treatment of aggregation/measurement issues and covariates. Again, typos are an issue here and it’s a pity that the author did not take the opportunity to add material on the recent work on dynamic panel data. A similar issue arises in chapter 7, which deals with the tobit model. The treatment of the basic and generalized tobit model is complete and well done, but the author could have paid some attention to the consideration of unobserved heterogeneity in selection bias models and to the semi- and non-parametric techniques that have been springing up in the literature.
The author then devotes an entire (short) chapter to the analysis of models of market disequilibrium (chapter 8). My personal opinion is that the subject does not merit this much attention, since many North American graduate programs barely deal with this material and the reader may end up being distracted by the economic issues. The point of this chapter is to present switching regression-type models, and although disequilibrium models are an appropriate vehicle, the section could be renamed to more clearly reflect the key concept and improved with a variety of examples from other, more widely known, subjects.
Chapters 9 and 10, respectively “Truncated Latent Variables Defined by a System of Simultaneous Equations” and “Simultaneous Equation Systems with Truncated Latent Variables,” aside from having confusingly similar titles, are particularly useful. Chapter 9 is full of instructive examples, both in terms of theoretical modeling of a variety of such cases and of empirical applications, although the translator unfortunately refers to E-M (Expectation-Maximization) algorithms as M-E algorithms. Chapter 10 begins with the difficult question of consistency and provides a geometric interpretation which is somewhat confusing. It provides useful examples, however, to illustrate this problem and other issues in the chapter, perhaps relying too heavily on disequilibrium models again.
Chapters 11 and 12, dealing with count data and duration models, have spawned entire books and literatures, so the treatment here in a single chapter each will necessarily be cursory. Poisson and negative-binomial models get full attention in chapter 11, and the author uses the opportunity to introduce pseudo-maximum likelihood methods. He also briefly sketches a moment-based method for estimation without talking directly about standard method of moments or GMM techniques, which is a pity. It also would have been useful had the author placed the Poisson and negative binomial models in the context of the ordered probit or ordered logit models discussed earlier in the book.
The final chapter, dealing with duration models, takes on too much and gets confusing in the process. u and v are used interchangeably and the notation is more generally inconsistent at different points within the same chapter. Censored data are referred to as truncated, and the terms “stock sampling” and “flow sampling” never appear, although they are critical to understanding the literature on duration models. Although the discussion of parametric Gamma-distributed unobserved heterogeneity is well treated, the discussion of non-parametric discrete (often called “Heckman-Singer”) heterogeneity is short and confused. Since the subject is dealt with much better and more completely elsewhere, this chapter probably should have been enormously simplified (perhaps dealing exclusively with flow-sampled, simple, proportional hazard parametric duration models without unobserved heterogeneity) or just eliminated, since this chapter can occasionally be more confusing than helpful for understand duration models in its current form.
In sum, Christian Gourieroux’s Econometrics of Qualitative Dependent Variables is a useful resource for an experienced econometrician to have as a reference, although it would be difficult for a neophyte to base his or her entire knowledge of the subject on just this book. A second edition, if it is forthcoming, should devote substantial attention to cleaning up the typos and translation issues (the latter of which are in the end, relatively infrequent), updating the material to cover more recent research and choosing examples that would be more easily accessible to graduate students coming from a North American doctoral program.
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