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Statistical decomposition analysis with applications in the social and administrative sciences
Journal of Econometrics
3 (1975) 319-320 0 North-Holland
BOOK
Publishing Company
REVIEWS
Henri Theil, Statistical Decomposition Analysis with Applications in the Social and Administrative Sciences, Studies in Mathematical and Managerial Economics, vol. 14 (North-Holland, Amsterdam, 1972) xvi+ 337 pp., U.S. $22.50. This is an excellent book on statistical decomposition analysis which, undoubtedly, will encounter the favors of many practically oriented researchers in a variety of fields. It is not a book on statistical methods, but, rather, on applications. It shows in a convincing way how well-established statistical techniques can be used successfully to solve real problems in many seemingly unrelated areas such as economics, management science, regional science, sociology, political science, accounting, etc. This unified treatment, to use the author’s own words, will substantially ‘contribute to breaking down the barriers that presently separate the social and administrative sciences’. The major merits of this book can be summarized as follows: a clear, intuitively appealing and yet profound way to introduce the basic methodological requirements; a sequential, detective-like approach to the problems, each new finding leading to a new, more refined development; and a relevant choice of substantive research problems. The pleasure of the nonprofessional reader is certainly enhanced by the fact that very little a-priori mathematical knowledge is required. Exercises are given at the end of each chapter to enable the reader to test his own progress and skill. Statistical decomposition analysis is concerned with the problem of the division of a given total into a number of components. Three major techniques dealing with this problem are presented in the book. Information theory and the concept of entropy are used to answer the question of how large is the degree of ‘dividedness’ (Chapter I). Several extensions to multidimensional decompositions are discussed in the two following chapters. To the reader of Theil’s Economics and Information Theory (1967) the topic is all too familiar. Yet the richness of possible applications may come as a surprise to him. Logit analysis is used in Chapter 4 to study the determining factors of a given decomposition. The evolution of a decomposition through time is analyzed in Chapter 5 (by means of a Markou-chain-model). The problem discussed in this chapter is that of social mobility (from one generation to the next). Given the reader’s subjective preferences, it is not difficult to conceive of a reader who might have wished a somewhat different product-mix. Some readers might have liked to find a discussion of other types of analysis dealing with the problem of finding the determining factors; others might question the not too critical use of Markov-chain-models and especially the hypothesis of temporal stability of the coefficients. But rather than indulging in such easily made remarks, the present reviewer prefers to raise a minor point on one of the unchallenged superior aspect of Theil’s analysis, the simplicity of exposition. Because he finds it hard to admit that the alternative proof of maximum entropy given on pp. S-10 is simple at all. In fact, this reviewer believes that many proofs on entropy can be made extremely simple by referring to the inequality x- 1 3 log x, which applies for natural logarithms. (A similar expression is used by the author on p. 60.) Now, letting x = l/(p,n) and summing over all i( cpi = l), we can prove the entropy theorem. Similarly, by letting x = pi/q,, multiplying through by Q~and summing over all i we can immediately prove the non-negativity of information expectation. (The symbols used here are the same as those of the author.) In summary, this excellent book, in addition to providing pleasant reading for the professional econometrician (an attractive way to learn about research in other fields), should be recommended to students and researchers engaged in empirical work. Pietro Balestra Universities of Fribourg (Switzerland) and Dijon
3 (1975) 319-320 0 North-Holland
BOOK
Publishing Company
REVIEWS
Henri Theil, Statistical Decomposition Analysis with Applications in the Social and Administrative Sciences, Studies in Mathematical and Managerial Economics, vol. 14 (North-Holland, Amsterdam, 1972) xvi+ 337 pp., U.S. $22.50. This is an excellent book on statistical decomposition analysis which, undoubtedly, will encounter the favors of many practically oriented researchers in a variety of fields. It is not a book on statistical methods, but, rather, on applications. It shows in a convincing way how well-established statistical techniques can be used successfully to solve real problems in many seemingly unrelated areas such as economics, management science, regional science, sociology, political science, accounting, etc. This unified treatment, to use the author’s own words, will substantially ‘contribute to breaking down the barriers that presently separate the social and administrative sciences’. The major merits of this book can be summarized as follows: a clear, intuitively appealing and yet profound way to introduce the basic methodological requirements; a sequential, detective-like approach to the problems, each new finding leading to a new, more refined development; and a relevant choice of substantive research problems. The pleasure of the nonprofessional reader is certainly enhanced by the fact that very little a-priori mathematical knowledge is required. Exercises are given at the end of each chapter to enable the reader to test his own progress and skill. Statistical decomposition analysis is concerned with the problem of the division of a given total into a number of components. Three major techniques dealing with this problem are presented in the book. Information theory and the concept of entropy are used to answer the question of how large is the degree of ‘dividedness’ (Chapter I). Several extensions to multidimensional decompositions are discussed in the two following chapters. To the reader of Theil’s Economics and Information Theory (1967) the topic is all too familiar. Yet the richness of possible applications may come as a surprise to him. Logit analysis is used in Chapter 4 to study the determining factors of a given decomposition. The evolution of a decomposition through time is analyzed in Chapter 5 (by means of a Markou-chain-model). The problem discussed in this chapter is that of social mobility (from one generation to the next). Given the reader’s subjective preferences, it is not difficult to conceive of a reader who might have wished a somewhat different product-mix. Some readers might have liked to find a discussion of other types of analysis dealing with the problem of finding the determining factors; others might question the not too critical use of Markov-chain-models and especially the hypothesis of temporal stability of the coefficients. But rather than indulging in such easily made remarks, the present reviewer prefers to raise a minor point on one of the unchallenged superior aspect of Theil’s analysis, the simplicity of exposition. Because he finds it hard to admit that the alternative proof of maximum entropy given on pp. S-10 is simple at all. In fact, this reviewer believes that many proofs on entropy can be made extremely simple by referring to the inequality x- 1 3 log x, which applies for natural logarithms. (A similar expression is used by the author on p. 60.) Now, letting x = l/(p,n) and summing over all i( cpi = l), we can prove the entropy theorem. Similarly, by letting x = pi/q,, multiplying through by Q~and summing over all i we can immediately prove the non-negativity of information expectation. (The symbols used here are the same as those of the author.) In summary, this excellent book, in addition to providing pleasant reading for the professional econometrician (an attractive way to learn about research in other fields), should be recommended to students and researchers engaged in empirical work. Pietro Balestra Universities of Fribourg (Switzerland) and Dijon