Gerhard Tintner’s Review of Economic Models—An Exposition (1958)

Gerhard Tintner’s journal book review assesses E. F. Beach’s Economic Models—An Exposition as an introduction to mathematical economics and econometrics for economically knowledgeable readers whose mathematical preparation is limited. Its governing question is pedagogical: how successfully does Beach make modern analytical methods accessible to established non-mathematical theorists and promising students? Tintner’s answer is broadly favorable, but qualified by the brevity of the mathematical explanations and the omission of important techniques. The review proceeds through the book’s two parts before assessing its teaching resources, appropriate readership, and coverage.

Tintner presents Part I as a progression from elementary mathematical language to increasingly complex economic models. Variables and equations are introduced through Henry Schultz’s demand analysis; linear relations lead to Marshallian partial equilibrium, the distinction between endogenous and exogenous variables, and reduced forms. A simple Keynesian model and Colin Clark’s model of the United States economy connect this conceptual apparatus to macroeconomic applications. Derivatives and nonlinear models then support discussion of equilibrium stability and the systems of Hicks and Modigliani. The organizing principle is instruction through economic examples, rather than mathematical exposition detached from substantive problems.

The treatment of dynamics extends this progression into models involving time. Tintner notes the use of Schultz’s trend analysis and models by Domar, Samuelson, and Littler to introduce differential equations. Difference equations are explained through Harrod’s model, the cobweb theorem, and Samuelson’s interaction of the multiplier and acceleration principle. He closes this survey with a distinction that clarifies the transition to the second part:

All the models in Part 1 are deterministic.

Thus, the movement from mathematical economics to econometrics is not simply an increase in technical complexity. It introduces probability, sampling, and statistical inference into the study of economic relationships. Part II begins with probability distributions, estimation, small samples, and tests, then turns to regression and correlation, emphasizing multiple regression. Frisch’s confluence analysis and tests for autocorrelation broaden the treatment beyond elementary estimation.

Tintner gives particular attention to identification, presented through Haavelmo and Koopmans and illustrated by consumption-function estimation and a model containing demand and supply functions. The review also records Beach’s contrast between criticism of Klein’s elaborate model of American economic fluctuations and the greater success of commodity-demand models constructed by Stone and Wold using classical least squares. This comparison makes empirical performance, rather than complexity alone, a relevant measure of model building. Connections to prediction and policy appear, although Tintner describes these as indications rather than an extensive treatment.

The book’s exercises and concise bibliographical notes strengthen its instructional value. Tintner regards its many examples as a substantial advantage, while recognizing a limitation in the explanation of the methods themselves:

The mathematical and statistical ideas are perhaps presented too briefly, but the student or reader should gain a fair idea of their importance from the examples.

This qualification defines the review’s favorable verdict. Beach offers useful access to the significance and applications of mathematical economics and econometrics, even where the underlying techniques receive compressed treatment. Tintner accordingly recommends the book for readers with mature economic knowledge and somewhat advanced students, including those in advanced undergraduate or beginning graduate courses.

His principal criticism concerns the boundaries of that introduction:

It is, however, a pity that the mathematical subjects of determinants and matrices and the economic applications in input-output models and linear programming have not been included.

Tintner argues that these omitted subjects are no more intrinsically difficult than the material already included. Their absence therefore limits the reader’s exposure to developments he considers especially modern and useful, rather than reflecting an unavoidable pedagogical constraint. His suggestion that a second edition could remedy the omission preserves the constructive character of the assessment. The review’s central judgment is that Beach largely achieves his educational purpose, but could offer a more representative introduction by combining its successful example-driven exposition with a broader selection of mathematical tools and economic applications.