Uncertainty and Estimation in Economics (1969), by David Champernowne. **1.1. Review by: George F Brown.**

*Journal of the American Statistical Association***66**(334) (1971), 423-424.Champernowne's three volumes provide a new and interesting treatment of the meaning, interpretation, and effects of uncertainty within the social sciences. Volume I concerns the development of a general model of probability; Volume II, statistical techniques; and Volume III, the effects of uncertainty on economic decisions. The author's presentation is quite readable; he has done an exceptional job in blending philosophical discussions, technical material, and numerous examples. The books contain 258 questions at the ends of the chapters; these are both thought provoking and an excellent test of a student's comprehension of the textual matter. ... The comprehensiveness of the author's treatment of the problems of statistical estimation in the first two volumes is not matched by his discussion of the effects of uncertainty on economic behaviour in Volume III.

**1.2. Review by: J Fawthrop.**

*Journal of the Royal Statistical Society. Series D (The Statistician)***19**(3) (1970), 354-356.This work, which is divided into three volumes, covers a wide range of economic problems and gives in some detail the necessary statistical methodology. The underlying theme running through all three volumes is that "the more important economic problems arise from the ignorance and uncertainty influencing the economic decisions of individuals." The work is ambitious in that not only does it attempt to provide a full coverage of the theory and statistical techniques together with an indication of their application, but Mr Champernowne has also attempted to give a philosophical foundation to it: perhaps the weaknesses in the work arise from it being over-ambitious.

**1.3. Review by: Arthur S Goldberger.**

*The Journal of Business***44**(2) (1971), 220-221.Champernowne, reader in economics at the University of Cambridge, begins his work auspiciously enough with the assertion that:

"The more important economic problems involving probability arise not directly from the 'stochastic' or 'chance' element in economic change, but from the ignorance and uncertainty influencing the economic decisions of individuals. For this reason the 'objective' theories of probability, which are so useful and convenient in purely scientific applications, are quite ill suited to the solution of the important questions in economics. It is essential to use one of the 'personal' theories of probability, which deal with the effects of ignorance and uncertainty on the statements, choices or other behaviour of an individual."

The 800 pages which follow, however, do little to support this. The work indeed has a strong "personal" flavour, but in the idiosyncratic, rather than Savage, sense. ... The author proceeds through classical hypothesis testing, point estimation, and interval estimation. He develops none of these in any depth, but finds time for a ten-page digression on the generation of pseudo-random sequences, and for a short description of the "quaint old system of marking" used by "certain examiners at Cambridge, England."

**1.4. Review by: Michael Rothschild.**

*The Journal of Finance***25**(5) (1970), 1201-1202.[Review of Volume 3] I cannot recommend this obviously intelligent and original book to students seeking an introduction to the economics of uncertainty. It is too intelligent and too original to be a satisfactory text. In other words, it is difficult and idiosyncratic. Although part of a series aimed at "third-year undergraduates with an elementary knowledge of calculus and statistical methods," even the most advanced graduate students will find this volume very difficult - this, despite the fact that the book does not look very hard. In contrast to the usual practice, the author's lucid style masks genuinely difficult arguments. His reasoning is compressed and compact. Complex and occasionally questionable analyses lurk in sharp clean prose. ... I have made much of this book's unsuitability as a text because a text is what it is so obviously designed to be. Those already familiar with the field will find Champernowne's book generally fascinating because of the many novel simple models developed in the book. Chapter 21 is a tour de force in the art of economic modelling.

**1.5. Review by: Y R Sarma.**

*Sankhya: The Indian Journal of Statistics, Series B (1960-2002)***35**(1) (1973), 123.[Review of Volume 1] This is the first of the three volume series by the author The author stresses the fact that most important economic decisions are made on the basis of imperfect information and in the face of considerable uncertainty about the probable effects of alternative possible decisions. The objective of this work is to describe and acquaint the reader with the techniques available for interpreting imperfect or incomplete statistical information and obtaining statistical estimates or choosing decisions in the light of such evidence. ... This book is somewhat different from the usual books treating the same topics. The main point of departure is to deal with discrete probability models where events are represented by vectors. The usefulness and simplicity of the approach can only be judged by the users. Another point of departure is to explore the use of Bayesian Inference in economics. This certainly seems to be a very promising approach.

**1.6. Review by: Richard Stone.**

*The Economic Journal***82**(328) (1972) 1406-1410.In this fine work Professor Champernowne has provided an admirably comprehensive account of probability theory and its applications particularly suited to economists and other social scientists. As he makes clear at the outset, the need to use a theory of probability in economics arises primarily from the fact that most economic decisions are made against a background of uncertainty and imperfect knowledge; and only secondarily from the existence of random variation in the observations. Consequently the "objective" theories of probability, which are so appropriate for dealing with random variations due to causes beyond the control or direct observation of the experimenter, are ill-suited to dealing with the effects of ignorance and uncertainty on the statements, choices or other behaviour of individuals, for which "personal" (or "subjective") theories of probability are needed. For this reason Professor Champernowne concerns himself with both types of theory and, as a result, has written a book which is philosophical as well as being mathematical and technical, and which provides a probability model sufficiently versatile to suit a range of alternative interpretations. ... in my opinion, a comprehensive theory of probability such as Professor Champernowne describes is so important, particularly for economists. ... this [is a] monumental work. At £9 for 814 pages of highly interesting and thought-provoking matter, this book is not only the best buy in its field but likely to remain so for many years to come.

The Distribution of Income between Persons (1973), by David Champernowne. **2.1. Review by: Anthony Barnes Atkinson.**

*Journal of the Royal Statistical Society. Series A (General)***138**(1) (1975), 111-112.That a dissertation written in 1936 should still be of great interest when published in 1973 is a remarkable phenomenon. In part this can be explained by the fact that in the intervening period relatively few economists have addressed themselves to the subject with which it deals - the personal distribution of income - but, most importantly, it is a measure of the originality of Professor Champernowne's thinking. ... In his introduction (written in 1972) the author suggests that "the supply of otherwise idle young persons with mathematical training, paper qualifications in economics ... to enable them to play with and competently develop such theories [has] increased a hundred-fold since the dissertation was written .... It may be hoped that the revelation of so many imperfectly followed trails may tempt a certain number to carry through to a finish some of the tasks which are left uncompleted." If this should happen, then it will in itself justify publication of the dissertation, although it will remain a cause for regret that the process was not set in train 37 years earlier.

**2.2. Review by: Martin Bronfenbrenner.**

*The Economic Journal***84**(336) (1974), 990-991.Professor Champernowne's path-breaking monograph originated as a King's College, Cambridge, prize dissertation of 1935-36 vintage. It has lain for a generation in the Cambridge "oral tradition", overlapping the Sraffa Production of Commodities by Means of Commodities. Now it appears in print, with new materials set off clearly in footnotes, in chapter appendices (to Chapters 3 and 8), over-all Appendices 5 and 6 (Appendix 6 reproduces the author's "Model of Income Distribution" from the June 1953 issue of this Journal) and in Chapter 24 on "Income Distribution Revisited after 35 Years". ... It is no surprise to find the latter-day Champernowne taking his stand squarely in the egalitarian ranks of the "Cambridge critique" and disowning certain theoretical positions taken in 1935-36. Thus:

"It was taken for granted in chapter 6 that 'accumulation is a force tending to lower the rate of interest by lowering the value of those qualifications which can be constructed'. To claim this in Cambridge, England, today would be tantamount to suggesting that capital accumulation lowers the rate of profit, a lapse which would invite banishment to Cambridge, Massachusetts".

**2.3. Review by: Harold Lydall.**

*Journal of Economic Literature***12**(3) (1974), 901-902.This book was originally submitted in November 1936 as a dissertation for a prize fellowship at King's College, Cambridge. It arose from a suggestion to the author by J M Keynes "that he should search for an explanation of the remarkable degree of conformity with Pareto's law displayed by many statistics of income-distributions published by the taxation authorities of various countries." For more than a generation the dissertation has lain unpublished, although frequently consulted and referred to. Professor Champernowne has now added a chapter on "Income distribution revisited after 35 years" and a number of appendices, and the world is at last able to obtain the full benefit of this remarkable work by a young man of 24 years. ... Professor Champernowne's brilliant early work in this field is written with a clarity and style which suggest the influence of Keynes. The book evokes memories of a bygone age in which, it alleges, one-seventh of the income receivers in England shared one-half of total personal income; when directors were paid twenty times as much as errand boys; and when a man could make money by hiring out pianos. Such contrasts with the modern world make it difficult to believe that today's distribution of income in the United Kingdom has been determined mainly by a stochastic process.

**2.4. Review by: Anthony F Shorrocks.**

*Economica, New Series***41**(161) (1974), 468-469.Despite the importance of the topic, the study of the distribution of personal income and the factors which influence inequality has received little attention. Professor Champernowne's own "probabilistic" model of income distribution, first published in the Economic Journal, has been one of the most significant contributions to this research and is reprinted in this book. The main body of the book, however, consists of a fellowship dissertation dating back to 1936, to which several sections and appendices have been added. ... It is a tribute to Professor Champernowne that this book has aged so little in the long period since it was written. Some of the mathematical exposition would no doubt have benefited from subsequent advances in probability theory, but to compensate there are numerous worked examples to illustrate the main points. Even his suggested index of inequality anticipates the recent work of Atkinson. The only real complaint which can be made is that it should have been published many years ago.

Economic Inequality and Income Distribution (1998), by D G Champernowne and F A Cowell. **3.1. Review by: Markus Jantii.**

*Journal of Economic Literature***39**(3) (2001), 910-911.In the wake of the substantial increase in income inequality in the United States and the United Kingdom that started in the 1980s, interest in economic inequality surged, at least measured by the volume of research papers devoted to documenting and explaining the phenomenon. More than a decade later, however, few economics departments offer classes on economic inequality. Economic inequality and income distribution tend to be the topics of the odd chapter in either public or labour economics textbooks, and may or may not be taught for a lecture or two as part of classes in these branches of economics. ... The authors discuss the reasons why we should be interested in inequality, what aspects of it merit our interest, and what kinds of approaches to the study of inequality may provide useful insights into its determinants. ... The book is well written and even the slightly more technical parts are well explained (details being: given in appendices), which makes the book readable at both less and more advanced levels. Some economists may feel that the book is too talkative and lacks analytical rigour. This reviewer does not: what economists need is a balanced treatment of the why and how of inequality analysis. Champernowne and Cowell have provided just such a treatment, with a large number of pointers to additional texts that allow the interested reader to deepen his knowledge. But their main achievement is to combine in a readable fashion a wide range of ways to analyze and understand economic inequality. Both applied economists and students would do well to study this book.

**3.2. Review by: Patrick Moyes.**

*Social Choice and Welfare***17**(4) (2000), 749-758.Although it appears to be a rather neglected area in most general economics meetings, there seems to be a revival of interest in the topics of inequality nowadays which is illustrated by the number of books being published on the subject. D G Champernowne and F A Cowell have made significant contributions to the literature on inequality and a book written by two such specialists is particularly welcome. ... I would recommend this book to any scholar working in the fields of inequality and more generally distribution analysis. The reader interested in the more applied side will find a profusion of data with a careful discussion of the data; the more theoretically inclined reader will no doubt be stimulated by the formal models of income and wealth determination. Both of them will certainly find challenging ideas for further work.

**3.3. Review by: Thomas Piketty.**

*Economica, New Series***67**(267) (2000), 461-462.This is a great textbook on income distribution. It covers basically all the topics one can think of - inequality measurement, models of the distribution of earnings, models of the distribution of wealth, social welfare measurement, stochastic models of income distribution, policy, etc. It also includes lots of tables and graphs drawn from many different sources. ... In my view, the main criticism that could be addressed to this book is that the actual facts presented in it are too scarce, which makes its presentation of income inequality issues a little bit too abstract and non-historical.