Good applied econometrics relies upon understanding of both statistical and economic theory. A firm grasp of statistical principles is required to understand what it is that usual estimation methods estimate, as well as to evaluate the strength of statistical evidence in any sample for claims that one might want to make about these.

The econometrician typically wants to go beyond this to use the statistical evidence to make claims about the structure of the economy. Doing this requires the introduction of economic theory as a justification for plausibly relating the estimated population characteristics to structural economic quantities of interest. A good introductory textbook ought to find a way of conveying both sides to the econometrician's task but can too easily end up as a text in statistics for economists.

Here are two econometrics textbooks for beginners, both by authors - Damodar Gujarati and Arthur Goldberger - responsible for more advanced textbooks on the same topic. * Essentials of Econometrics * is a revised edition amended to incorporate sections on fresh topics such as bootstrap sampling or unit root tests. These sections are brief, however, and give the impression of being motivated mainly by an over-keen wish for comprehensiveness. Given the context in which bootstrap sampling is introduced, for example, it is difficult to see anyone in the intended audience grasping its point. The overall organisation of topics is traditional but it is good to see the inclusion of a discussion of model selection acknowledging the role of theory.

* Introductory Econometrics * is more distinctive. Goldberger chooses to present econometric analysis "in the context of conditional expectation functions and best linear predictors, rather than in the setting of disturbed deterministic functions." That is to say, from the outset, attention is focused on the mean of the explained variable conditional on a set of regressors, both as a natural means of data summary and a natural focus in prediction. In some ways this is an attractive way of introducing regression techniques since it draws attention to the fundamental statistical properties of this central estimator. However, by focusing for the main part of the book on conditional expectation functions as the objects of interest, the economic issues that raise the most pressing questions are in practice sidelined, since the estimator will then always be, statistically speaking, consistent. Issues of identification associated with omitted variables, simultaneity and so on simply disappear since none of them brings into question the convergence in probability of the regression estimator to the conditional mean.

Simultaneous determination of dependent variable and regressors is, of course, eventually addressed, but only four fifths of the way through the book is the reader informed of "economists' focus on parameters of the structural form, as distinguished from I parameters of the best linear predictor." This is too late for my taste. Given the centrality of simultaneity as a practical issue and the admitted consequence that "the parameters that economists want to learn about are not the coefficients of the population conditional expectation function", it is unsatisfying that these coefficients should have been allowed to become such a focus of attention for the bulk of the book.

The other two books are textbooks in mathematics for economists. * Mathematics in Economics * is for undergraduate economists, covering linear algebra, including linear programming, differential and integral calculus, static optimisation and differential and difference equations. The explanations of linear algebra seemed to me to be particularly clear. I would have preferred optimisation to be treated differently - introducing Taylor series approximations in a section of their own would have been clearer than doing so as a means to explaining second-order conditions for extrema. The use of complex numbers may make later sections challenging for students with weaker mathematics.

* Numerical Methods in Economics * is a work on a different plane. With the growth of cheap computational resources available to the practising academic, the feasibility of extensive simulation as a tool for both the theorist and the econometrician has become increasingly apparent. Kenneth Judd argues that there are good grounds for expecting that the continuation of these trends will lead to shifts in academic economic research away from theorem-proving towards computation and that these should be welcomed.

Until now, familiarisation with these techniques has usually required consultation of textbooks in the mathematics library. Judd has changed that with this hugely impressive book. The set of economists with nothing to learn from this book will be very small. Topics covered include the standard numerical topics of solving equations, optimisation, approximation, integration and simulation, but also numerical methods for functional problems, including dynamic programming, perturbation methods and dynamic equilibrium analysis. Written for economists, the book renders advanced numerical techniques and ill-understood associated topics exceptionally clear.

Ian Preston is senior lecturer in economics, University College London.

## Econometrics. First Edition

Author - Arthur S. Goldberger

ISBN - 0 674 46107 X

Publisher - Harvard University Press

Price - £21.50

Pages - 250

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