An Economic Model of Fertility, Sex and Contraception by Helge BrunborgReview by: David LamJournal of the American Statistical Association, Vol. 81, No. 395 (Sep., 1986), pp. 869-870Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2289040 .

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Book Reviews 869

serial correlation including the Durbin-Watson test, Durbin's h, and other tests for higher-order autocorrelation, (c) tests for linear versus log-linear relations, including the Box-Cox transformation, (d) comparisons of dif- ferent models with different conditional means, including the J test of Davidson and MacKinnon (1981) and the JA test of Fisher and McAleer (1981); (e) inferring model stability through predictive accuracy in a post- estimation sample of data; and (f) exogeneity tests including Hausman's (1978) test. Turning to the second conditional moment, more familiar tests are captured under this umbrella of variable addition. These include various tests for heteroscedasticity ranging from the early Goldfeld-Quandt test to the more recent test proposed by White (1980). Pagan notes that augmenting higher-order moments have been neglected in the literature except for testing normality. He then extends this analysis to the simul- taneous equation case and considers joint tests and small sample consid- erations.

Mizon's paper introduces the encompassing principle as part of a pro- gressive modeling strategy. This principle is "concerned with the ability of a model to account for the behaviour of others, or less ambitiously, to explain the behaviour of relevant characteristics of other models" (p. 136). Because the data generating process (DGP) is likely to remain unknown, the researcher should try to find a feasible model, given the data limitations, that will mimic the encompassing property that the DGP possesses. Such a model should satisfy a wide range of model adequacy criteria. It is then "used to make predictions about the behaviour of, and properties of, statistics from rival models. The accuracy of these predic- tions, which is an indication of the model's ability to encompass its rivals, is then a measure of that model's explanatory power as against that of competing models. The failure of one model to encompass another is instrumental in constructing 'better' models" (p. 139).

Mizon also shows how the encompassing principle can provide a simple framework for comparing nested and nonnested models, and he develops a class of Wald encompassing tests that generates a variety of test statistics used in econometrics. He then compares them with likelihood ratio La- grange multiplier tests.

Trivedi surveys the developments of distributed lag analysis and the possible sources of uncertainty in specifying distributed lags. He points out that the notion of a "true" distributed lag is tenuous and argues against the use of strong prior information, in favor of data-based priors. In a spirit similar to that of Pagan and Mizon, Trivedi suggests "testi- mation," an empirical specification strategy that searches for the proper model based on a blend of estimation and significance tests. For distrib- uted lags, the researcher should proceed with the most general dynamic model and impose restrictions consistent with the sample information, subjecting the model to a series of tests. Trivedi then contrasts this ap- proach with other methods of estimating distributed lags including (a) "Bayesianism" with informative normal-gamma priors, (b) "Vestigial Bayesianism," which is Trivedi's name for Leamer's "sensitivity analysis," (c) "Rule of Thumb" Bayesianism, including Shiller's lag, (d) shrinkage techniques, and (e) stochastic constraint formulation. Throughout, Tri- vedi lists the pros and cons of each technique and concludes that "each of these approaches has its own motivation and should be evaluated in terms of the investigator's loss function, the acceptability of the implicit or explicit characterization of prior information and the completeness of the data summary provided by it, rather than in terms of widely used but essentially arbitrary criteria" (pp. 209-210).

This book is intended for econometricians, working economists, and graduate students. Prerequisite reading for this book is at least one course in econometrics. Contrary to what its title might suggest, this is not a textbook of econometrics. It is a good readings text, however, that can be recommended for a second graduate course in econometrics. Statis- ticians who are not interested in economic problems per se may still find some of the articles worth reading, especially if their interests overlap with dynamic nonlinear time-series models, incomplete simultaneous equations, diagnostic testing, model evaluation, and prior-information and distributed-lag analysis. All of the articles are well written. Some authors summarize past and current contributions, others propose new ways of econometric thinking. Most of the economic applications pertain to the United Kingdom, but the modeling strategy emphasized throughout the book is general and applies to other sets of data as well.

I enjoyed reading this collection of papers, although I felt that the criticism of econometric textbooks in the preface and introduction was unduly harsh. Nevertheless, the London School of Economics philosophy and practice of econometric modeling comes across loud and clear, and it is in this regard that the book succeeds.

BADI H. BALTAGI University of Houston

REFERENCES

Davidson, R., and MacKinnon, J. G. (1981), "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, 49, 781-793.

Fisher, G., and McAleer, M. (1981), "Alternative Procedures and Associated Tests of Significance for Non-nested Hypotheses," Journal of Econometrics, 16, 103- 119.

Hausman, J. A. (1978), "Specification Tests in Econometrics," Econometrica, 46, 1251-1272.

Ramsey, J. B. (1969), "Tests for Specification Errors in Classical Linear Least- Squares Regression Analysis," Journal of the Royal Statistical Society, Ser. B, 31, 350-371.

Sargan, J. D. (1964), "Wages and Prices in the United Kingdom: A Study in Econometric Methodology," in Econometric Analysis for National Economic Planning, eds. P. E. Hart, G. Mills, and J. K. Whitaker, London: Butterworths.

White, H. (1980), "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, 48, 817-838.

An Economic Model of Fertility, Sex and Contraception. Helge Brunborg. Oslo: Statistisk Sentralbyra, 1984. 335 pp. kr 24,00 (paperback).

This book, based on the author's doctoral dissertation, offers theoret- ical and empirical contributions to the literature on the economics of fertility. Brunborg's major innovation is his attention to couples' choices regarding sexual activity, a choice variable occasionally mentioned but seldom formally included in the extensive body of research inspired by the influential writings of Gary Becker (see Becker 1980).

Critics who feel that Becker's work on the economics of fertility, mar- riage, and divorce is microeconomics run amuck may find Brunborg's derivation of a demand equation for frequency of intercourse per month and his calculation of a "satiation level of sex" to be the reductio ad absurdum of this school of economic research. Economists who have worked in the area will be more at home with Brunborg's approach, however, and will be convinced by Brunborg's case for considering a couple's direct satisfaction from sexual activity in the analysis of such issues as the effects of contraceptive availability on couples' fertility be- havior.

Economists familiar with the "new home economics" literature will appreciate the basic thrust of Brunborg's work, but they may be disap- pointed in the details. The theoretical discussion, an extension of work by Michael and Willis (1976), is an interesting and well-informed analysis using a simple two-period model of decision making under uncertainty to study the effects of economic variables on contraceptive behavior. Brunborg struggles with the interpretation of a number of results, how- ever, and few real insights emerge.

The theoretical discussion serves to motivate Brunborg's empirical analysis, based on the 1977 Norwegian Fertility Survey. The author pro- vides an informed discussion of the procedures that would have been appropriate to handle the numerous econometric issues complicating his analysis. Unfortunately, readers accustomed to the relatively high level of sophistication in the best of the recent literature on the economics of fertility and child spacing will be disappointed to find that Brunborg does not pursue most of the econometric solutions he describes. Apparently because of software limitations at the Norwegian Statistical Bureau, Brun- borg is only able to perform routine ordinary least squares (OLS) and two-stage least squares regressions, never taking account of such problems as one dependent variable being an ordinal categorical response. Dealing with such problems has become all but routine in the literature of which Brunborg is a part, leaving the empirical portion of the book well short of the cutting edge of current research.

Brunborg is aware of his econometric shortcomings, however, and the empirical analysis benefits from his candid and careful discussion of the potential biases introduced by his inability to use more sophisticated econometric techniques. The reader can only look forward to future research in which the author is better armed to exploit his substantial econometric skills.

The empirical results that emerge from Brunborg's study are largely consistent with other recent research on fertility behavior in developed and developing countries. Brunborg finds, for example, that female wage rates have a significant negative effect on the desire for an additional child. On the more novel issue of demand for sex, Brunborg finds that frequency of intercourse is negatively affected by the age of each spouse but positively affected by marital duration after controlling for age. Un- fortunately, the effects of economic variables such as wage rates receive only limited attention.

The most intriguing, even if not most convincing, of Brunborg's results are the estimates of the satiation level of sex, computed from the param- eters of an explicit utility function. These values range from .8 to 8.9

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870 Journal of the American Statistical Association, September 1986

times per month, depending on a couple's attitude toward additional births. Results such as these make Brunborg's analysis seem silly at times, but it should be viewed as a minor and somewhat entertaining distraction from what is, on the whole, a competent and creative, although not path-breaking, piece of economic research.

DAVID LAM University of Michigan

REFERENCES

Becker, Gary (1980), A Treatise on the Family, Cambridge, MA: Harvard University Press.

Michael, Robert T., and Willis, Robert J. (1976), "Contraception and Fertility: Household Production Under Uncertainty," in Household Production and Con- sumption, ed. N. E. Terleckyj, New York: Columbia University Press, pp. 27- 93.

Cohort Analysis in Social Research: Beyond the Identification Problem.

William M. Mason and Stephen E. Fienberg (eds.). New York: Springer-Verlag, 1985. viii + 400 pp. $38.00.

During the past two decades, cohort analysis has become a major methodological strategy in the social sciences. The conceptual foundation for this development was laid by Ryder's (1965) classic article, and the development of rigorous methods of cohort analysis received major im- petus from an article by Mason, Mason, Winsborough, and Poole (1973).

The greatest progress in cohort analysis has come since the middle and late 1970s, a period characterized by undue optimism about the utility of statistics for separating age, period, and cohort (APC) effects and by many naive, mechanical, and largely atheoretical cohort studies. Later developments, reflected in the volume reviewed here, include a scaling back of expectations and recognition that (a) an empirical separation of the different kinds of effects is possible only to the extent that the effects are nonlinear, (b) nonadditive cohort models are often useful and can be estimated, and (c) cohort analysis can be useful without an attempt at a complete and clean separation of APC effects.

Since this book reflects these important recent developments, it is, by a substantial margin, the best and most sophisticated book on the topic, and no one who has not read it carefully can claim to be well informed about cohort analysis. On the other hand, the origins of this edited volume virtually assured unevenness in the usefulness and quality of the selec- tions.

The book grew out of an interdisciplinary conference on cohort analysis in the summer of 1979 sponsored by the Committee on Methodology of Longitudinal Research of the Social Science Research Council. Five pa- pers were presented at the conference, all of which were revised to reflect the conference discussions and are included in the volume. The comments of 2 of the 18 conference discussants were developed into formal papers and included in the book. Ryder's classic essay was the first selection (after the introduction), and two papers by authors who did not partic- ipate in the conference appeared, apparently because the editors thought that all of the crucial issues were not covered by the conference papers.

The two best selections, in my opinion, are the two coauthored by coeditor Bill Mason. In the first of these ("Specification and Implemen- tation of Age, Period, and Cohort Models"), Fienberg and Mason give the best general treatment to date of the APC accounting scheme, the identification problem, and strategies and specific techniques for cohort analysis. Among other contributions, the chapter demonstrates some ways of allowing for nonadditive effects and shows that the identification prob- lem in cohort analysis is not due to crudeness of measurement. The authors close the chapter with an attempt to refute the major objections to APC specifications. I find most of their arguments convincing, but it is unlikely that they have put an end to the debate about the utility of statistical cohort analysis.

In the second of my favorite selections ("Age-Period-Cohort Analysis and the Study of Deaths From Pulmonary Tuberculosis"), Mason and Smith demonstrate the extraordinary patience, care, and diligence often required to do a meaningful cohort analysis. Space constraints preclude my giving even a brief description of the specifications, tests, respecifi- cations, and strategies for bringing "side information" into the study described in this 75-page paper. Suffice it to say that this selection should be required reading for any young researcher armed with a series of cross- sectional data sets, access to a computer, and a notion that it would be neat to do a cohort analysis.

The selection I like least is "Simultaneous Analysis of Longitudinal Data From Several Cohorts," by Joreskog and Sorbom. The authors briefly discuss the identification problem in cohort analysis in the first paragraph and then ignore it in the rest of the paper, which is a dem-

onstration of the use of the LISREL VI computer program to estimate a structural model with a single latent variable, the data being test scores from three cohorts of adolescents gathered at three points in time. The authors conclude that the variance of the latent variable (latent ability) increased over time, but they do not deal with the ambiguous meaning of the apparent change, that is, with the issue of whether it reflected age effects, period effects, or both. The piece may be useful for some pur- poses, but any contribution in it to the methods of cohort analysis escapes me.

Perhaps the most interesting part of the book is an exchange between David Freedman, who gives a general critique of the use of regression models in the social sciences (not just in cohort analyses), and Stephen Fienberg, who gives a rebuttal. Freedman accuses social scientists of mindlessly using canned models rather than developing highly original ones such as those created by pioneers in the physical sciences, whereas Fienberg argues that the physical sciences developed through model test- ing similar to that currently in vogue in the social sciences. Each gives a strong argument for his point of view (I find Freedman's a bit more persuasive), and the result is one of the most interesting debates I have read in recent years.

The remaining selections deal with several important issues in cohort analysis and illustrate promising, if not clearly fruitful, ways of dealing with those issues. For instance, analyses with attitudinal dependent vari- ables by Markus ("Dynamic Modeling of Cohort Change: The Case of Political Partisanship") and Duncan ("Generations, Cohorts, and Con- formity") illustrate that for some purposes a precise separation of APC effects is not necessary. Heckman and Robb ("Using Longitudinal Data to Estimate Age, Period, and Cohort Effects in Earnings Equations") show that panel data can help to overcome the limitations of the usual kind of cohort data. Hobcraft, Menken, and Preston ("Age, Period, and Cohort Effects in Demography: A Review") show how cohort analysis can be fairly straightforward and have clearly interpretable results when the dependent variable is biologically determined, as in the case of mor- tality, but that it becomes immensely complicated when the dependent variable is goal-directed behavior, as in the case of fertility in modern societies.

Although the volume reports cutting-edge ideas and developments, most of the materials in it should, with some effort, be understandable to anyone who has successfully completed one good graduate-level sta- tistics course. Therefore, it is likely to be widely used in graduate methods courses.

NORVAL D. GLENN University of Texas at Austin

REFERENCES

Mason, K. O., Mason, W. M., Winsborough, H. H., and Poole, W. K. (1973), "Some Methodological Issues in Cohort Analysis of Archival Data," American Sociological Review, 38, 242-258.

Ryder, N. B. (1965), "The Cohort as a Concept in the Study of Social Change," American Sociological Review, 30, 843-861.

Analyzing Change: Measurement and Explanation Using Longitudinal Data.

Ian Plewis. New York: John Wiley, 1985. xii + 182 pp. $29.95.

With interest in the analysis of longitudinal data growing steadily, an introduction to statistical techniques especially suited to longitudinal data is most welcome. Analyzing Change provides such an introduction for social scientiests, administrators, and psychologists interested in analyzing nonexperimental data. To reach this somewhat varied audience, Ian Plewis has written his book so that it will be accessible to readers who have no background in statistics beyond a solid command of multiple regression.

Plewis wisely omits methods for analyzing time series, as expositions of these methods are already available. Instead he focuses on panel data (data collected at several times for multiple units of analysis), both in- terval-level and nominal, and Markov models for transitions between states and duration of stay in a state. A chapter is devoted to the very important subject of measurement error. Event history analysis is men- tioned briefly, and pooling methods are overlooked altogether.

In general, the exposition is lucid, with numerous well-chosen examples from the social and behavioral sciences. Plewis has obviously thought long and hard about many of the issues that arise in modeling, estimating, and interpreting longitudinal data; his views on these are judicious and helpful, not only to the novice but also to the experienced researcher. Anyone who analyzes change statistically will want to have a copy of this book close at hand for reference purposes.

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