Cohort Analysis

BIBLIOGRAPHY

A cohort is an aggregate of individual elements, each of which experienced a significant event in its life history during the same chronological interval. Cohort analysis consists of the quantitative description of dated occurrences from the time a cohort is exposed to the risk of such occurrences. Since parameters of cohort aggregate behavior can be arranged in temporal sequence by reference to the date of the event defining and initiating cohort exposure, a time series of cohort parameters can be assembled for use as evidence in the study of temporal variations in the behavior on which attention is focused. This is the most important application of cohort analysis. If, in the life of an individual, event E₁ occurs at time T and event E₂, conditional upon Ex , occurs at time t = T + i, then cohort analysis is concerned with the characteristics of functions E₂(i, T) for variations of i (intracohort) and T (intercohort) for the set of individuals in the class (E₁ T).

The idea of cohorts has long been familiar in historical and journalistic work, but under the name of “generations.” This word has so many meanings that it is easily misconstrued. It may be an approximate length of time, an identification of an era, a biological term for the process of procreation, or a structural term derived from the parent—child relationship. It is recommended that the term “generation” be restricted to the last usage, where it signifies an important concept without competitive designation, and that the term “cohort” be used to identify or locate an aggregate in time [seeGenerations].

Cohort analysis has been developed and used most extensively in demography, particularly in the study of time series of fertility. Therefore, the focus of this article is on methods and results in that area and in analogous demographic inquiries [seeFertility].

Cohort and period time series of fertility. Because the probability of childbirth varies markedly with maternal age, it is almost mandatory in fertility analysis to examine the set of birth rates for each separate age. Given this orientation, time series analysis becomes the study of sections of the following fertility surface: if birth rates are given for each maternal age and for each year, then the horizontal axes are used to represent age and time and the birth rates are plotted vertically. Two time series of fertility indices are provided, the first characterizing vertical sections of the surface over all ages, one for each time period, and the second characterizing vertical sections of the surface over all ages, one for each particular difference between time and age. The former are period sections; the latter may be called cohort sections, because the members of a cohort age pari passn with time. In terms of the symbolic statement that was used in the first paragraph, each cohort section consists of some function of E₂, over i for a particular T and each period section consists of the same function of E₂, over i for a particular t = T + i, where E₁ is birth, E₂ is parenthood, and i is age (see Ryder 1964b).

Of the various ways of summarizing period or cohort fertility, two are particularly useful for relating the nature of the interdependence between cohort and period fertility. The first is the total fertility rate, obtained by summing the birth rates over all ages, and the second is the mean age of fertility, that is, the arithmetic mean of the age distribution of those birth rates. It can be shown that the time series of period and cohort total fertility rates diverge to the extent that there is temporal change in the cohort (or period) mean age of fertility, and that the time series of period and cohort mean ages of fertility diverge to the extent that there is temporal change in the cohort (or period) total fertility rate.

As a specific example, if the cohort mean age of fertility is declining, then the period total fertility rate is higher than the fertility rate for the cohort whose childbearing is centered in that period. This relationship may be visualized as follows: the fertility occurring in any year depends on the degree of overlap in the age spans of childbearing of the successive cohorts represented in that year. A progressively younger mean age of fertility implies an increase in the extent of this overlap, which is manifested in an apparent increase in the amount of fertility from period to period even in the absence of change in the cohort total fertility rate (Ryder 1960).

These formal propositions show why cohort and period time series of fertility parameters differ but provide no basis for choice between them in a given problem. The critical question is whether the more useful units of observation in time series analysis are period aggregates or cohort aggregates. To choose the former is the conventional practice; the latter is the essence of the proposal of cohort analysis. Let us examine the alternatives, first for short-run and then for long-run variations through time.

From 1935 to 1955 the period total fertility rate for the United States rose abruptly. Cohort analysis reveals that this was attributable to a small rise in the cohort total fertility rate combined with a drop in the cohort mean age of fertility. This decline had two aspects: postponement of births by the affected cohorts, because of the depression, and transition toward an earlier age of childbearing. The phenomenon of postponement refers to the transfer of a birth from an earlier to a later time in a cohort’s history. Its direct observation requires cohort fertility records, since it is meaningless to posit recovery by one cohort of births postponed by another. Analysis of the fertility response to an economic fluctuation appears superficially to justify period-by-period aggregation of data, because all cohorts exposed to the events in question tend to react in the same direction. The difficulties with this view lie in the organic coherence and continuity of human behavior through time. Reproductive experience is not merely the sum of particular responses to the particular con-texts of successive years; present behavior depends on past experience and on expectations of future experience. Cohorts at different stages of development show different degrees of reaction to the same external circumstances, and the response is not confined to the time the disturbance occurs. If it is granted that the fertility movements to be explained are transitory, then the problem of measurement is the discrimination between short-run and long-run change, i.e., between the behavior that is idiosyncratic to the period and the behavior that would have occurred in the absence of disturbance. Thus cohort analysis to establish the long-run path is analytically prior to period analysis of short-run deviations of cohorts from that longrun path.

Advantages of cohort analysis. Despite the cogency of the argument for the place of cohorts in short-run analysis, period aggregation has persisted because the synthetic formulation makes up in convenience what it lacks in accuracy, particularly if the focus of analytic interest is the contemporary situation. The cohorts whose behavior contributes most to current experience have completed an unknowable proportion of their eventual fertility. Changing distributions of cohort fertility through time cause difficulties in measuring not only the fertility in a period but also the fertility of an incomplete cohort. The optimal procedures for coping with these difficulties are still a matter of investigation. Cohort analysis has at least made explicit the inherent indeterminacy of current analysis and has not concealed it behind apparently comprehensive period aggregations of unknown accuracy. Patience is a luxury some kinds of analysis require.

Cohort analysis can make a contribution not only to the study of fluctuations in the period total fertility rate, occasioned by temporary disturbance of’ the time pattern of childbearing, but also to the study of long-run distortions caused by permanent modification of that time pattern. For instance, from the time series of period total fertility rates for Sweden in the nineteenth century, it appears that fertility remained on a plateau until the 1870s, when decline began; the time series of cohort total fertility rates shows a decline that began in the 1830s. The discrepancy between these series is attributable to a rise and then a fall in the cohort mean age of fertility (Ryder 1956a).

Obviously the analyst attempting to trace the causation for this crucial phase in Swedish fertility history must have a basis for choice between the two temporal identifications. The implicit preference is for cohort analysis, judged by the terms used in verbal analyses of the determinants of long-run fertility change. Clearly, measurement techniques should be devised to provide observations corresponding to the concepts used in theoretical formulations. Yet the lone justification of this preference for cohort analysis, other than the assertion that it is only common sense to study consecutive human behavior when the data are available, is the observation that the time series of cohort total fertility rates tends to be much smoother than that for period total fertility rates.

The cohort in social change. A social system is embodied in a population, and its duration exceeds the life of any member. Society, as a functioning collectivity, has inputs of birth and outputs of death but persists despite its ever-changing personnel. Each entering cohort poses a challenge to the society to reproduce itself. To preserve the system, socialization procedures are instituted to equip the entrants with the rational and normative apparatus needed for participation in group activities. The continual entry of new cohorts may be viewed as a stability problem, but it is also a continuing opportunity for modification of the social structure, since flexibility as well as stability is a requirement for survival in a changing environment (Ryder 1965). Socialization is the progressive confinement of behavior potentialities within a culturally acceptable range. Sanity and order are maintained by assimilating new experience so that it makes sense within the prevailing structure of ideas and norms. The faith in education rests on belief in premature plasticity and persistent influence. If man were molded into final form during his premature years, then the only opportunity for change would lie in the appearance of a new cohort each year.

An important role in social change is played by the changing content and agencies of socialization to which new cohorts are exposed. One institutional response of a society when it moves from comparative stability into persistent change is the transfer of authority for socialization from the family to the school. This tends to increase the temporal distance between child and parent and identifies the child’s future with that of his contemporaries. The importance of this transition from an age-heterogeneous to an age-homogeneous context is increased by the growth of peer groups, subsets of the child’s cohort. Cohorts are further differentiated by a lengthening of the period prior to commitment to adult roles and by the presence of alternative sources of normative direction, which by their very multiplicity encourage choice and innovation. The phase of cohort differentiation is gradually terminated by progressive commitments of the individual to his spouse and children and to the occupational hierarchy in which he earns his living. Resistance to change thus increases with the price of deviation implicit in acceptance of the rewards and responsibilities of successive roles within age-differentiated organizations. Some reservations to this discussion are necessary to obviate the implication that cohorts are the exclusive agents of social change. Socialization is a continuous process within any system. An individual moves through different systems during the course of his life, each with its own socialization procedure and opportunity for reorientation. The capacity of the individual for normative reformulations cannot be dogmatically ignored. Indeed the form of socialization may emphasize a flexible and contingent set of principles which tolerates or encourages subsequent modification.

Nevertheless, the prominence of young adults in the vanguard of social change is well recognized, particularly when the change is rapid and discontinuous—as in transitions from war to peace, from depression to prosperity, or from one culture to another. Youthful deviance may sometimes be anarchic and confined to small and unconnected groups, but it may also become an organized and self-conscious movement, dedicated to a radical pioneering ideology. Contemporary revolutionary movements throughout the world draw most of their support from young cohorts. The same phenomenon is recognized by the many historians of political, literary, and artistic movements who choose the cohort (which they call “generation”) rather than the period as their unit of temporal analysis. With less drama but more fundamental significance, the cohorts of young adults have been central to the processes of urbanization and industrialization. The transformation from rural agriculture to urban industry has been accomplished primarily by the movement of cohorts of young adults from one sphere to the other. The continuing evolution of technological structure relies less on the retraining of older cohorts than on the recruitment of new ones. The annual entry of each new cohort provides one solution to the problem of transforming the distribution of personnel among roles as required by social change. In the process the cohort acquires a distinct shape which differentiates it from its predecessors. In fine, cohorts are differentiated from one another by the process of social change, and they are utilized to bring about social change. This is the core of the argument that the measurement of social change, as manifested in statistics of individual behavior, is most fruitfully accomplished by a temporal organization in cohort units.

Demographic applications. The approach described for fertility analysis was first used with the surface of mortality as a function of age and time. As before, the analytic justification for cohort analysis is the dependence of the behavior of the cohort at any age and time on its experience in previous ages and times. The practical difficulties associated with record keeping for a long-lived species have limited the employment of cohort analysis in mortality. Where such difficulties have been overcome, cohort analysis revealed some patterns of change that had been concealed by the synthetic construction implicit in conventional life tables, and these regularities have been exploited for projection purposes, inter alia [seeLife tables].

For example, an important substantive contribution to the study of tuberculosis mortality was made possible by the cohort approach. An apparent rise in the modal age of tuberculosis mortality, which was difficult to explain, was revealed to be an artifact of cross-sectional analysis. When the surface of rates was re-examined as a succession of cohort mortality functions by age, it became apparent that the age pattern from cohort to cohort was relatively fixed and that the rise in the modal age for successive periods was a reflection of the steady decline in the level of tuberculosis mortality from cohort to cohort (Frost 1939).

Similar rewards have accrued from the extension of the cohort approach to the study of nuptiality. It has long been recognized that the number of marriages is prone to fluctuate from period to period with changing economic conditions, despite stability in the eventual likelihood of marriage. This is now interpretable in terms of cohorts as a contrast between a period and a cohort time series, generated by temporary modifications in the time pattern of cohort nuptiality (Ryder 1956b). Development of translation formulas for nuptiality and mortality functions has proved more difficult than for fertility because the required indices have a multiplicative rather than an additive construction. Beyond the realm of analysis, the concept of birth cohort has proved useful both as an accounting device to link together age-specific information of the same type in successive time periods and as a possible projection method [seeNuptiality].

The cohort approach has also been applied to the study of occupational careers by time of entry into the labor force, educational careers by time of entry into school, and morbidity histories by time of first exposure to the condition (Goldfarb 1960).

Thus the concept discussed, up to this point, in reference only to the group born in the same time period can be extended to the identification and surveillance of any group in terms of the time it enters any category of exposure to an event or behavior pattern of interest. For example, fertility analysis has progressed by measurement procedures having been brought into closer alignment with phases of the reproductive sequence. First births have been studied as occurrences to marriage cohorts at successive marital durations, second births as occurrences to first parity cohorts at successive birth intervals, and so forth. Each event is studied in terms of frequency and time distribution for aggregates that enter exposure to the event during the same time period.

The preponderance of references to birth cohorts, and to age as time interval, within cohort analysis is probably explained by the capacity of age to serve as a surrogate for other types of intervals, where there is only a small variance in age at entry into the particular population being investi-gated. But age is merely the most important of the general class of measurements of the length of time elapsing since the occurrence of cohort-defining events. This suggests a broad application of the cohort approach. Most social surveys, for instance, include the age of the respondent as a variable because all classes of behavior show variations with age. Interpretation of age-specific results requires consideration of the double meaning of age—as temporal location in terms of both personal career and history—because those whose ages differ at any time are members of different cohorts. This double meaning is particularly worth observing in the study of change, because its relevance varies directly with the extent of change (Ryder 1964a).

Relation to other approaches. This article has emphasized the importance of cohort analysis for the study of social change. The distinction between social process (the routinized patterning of behavior throughout the lives of individuals) and soczaZ transformation (the modification of processual parameters through time) can therefore be characterized as the differentiation of intracohort and inter cohort variations.

The two cognate measurement procedures of cohort analysis are the study of aggregate life cycles of individuals from entry to exit with respect to any population and the study of parameters of these interval functions, arranged successively in time—in other words, intracohort measurement by age (or other interval) and intercohort measurement by time. Cohort analysis can therefore be seen as a blend of intensive small-scale studies that use a life-history format, with large-scale, extensive surveys of the population at one point of time. The organization of personal data in temporal sequence is the raison d’être of the case-history approach; records for individuals are collected on a longitudinal time axis simply because people live this way, aging year by year. But cohort analysis is distinct from longitudinal analysis in one important regard. Longitudinal analysis concerns the behavior of individual elements observed over successive times. Cohort analysis, on the contrary, concerns the changing characteristics of an aggregate through time; it is macrolongitudinal. The cohort analyst, in short, investigates the properties of populations rather than the behavior of individuals; he is concerned with specifying the net changes occurring to an aggregate rather than with identifying the changes particular to individual elements of that aggregate.

So long as extensive studies are framed within a period format of aggregation and index calculation, there will continue to be an unfortunate hiatus between two potentially complementary approaches to social analysis. Cross-sectional inquiries destroy individual sequences and thus imply that the past is irrelevant; they encourage static formulations because of the temptation to use age-cwm-cohort as if it were age, thereby creating the illusion of unchanging structure. The cohort is a device for providing a macroanalytic link between movements of individuals from one to another status, category, or residence during their lives and movements of the population manifested in changes of distribution and composition from one time period to the next. In this way statistical measurements of the aggregate are equipped with the appropriate time dimension for linkage with the results of intensive and individual-oriented research. The cost of relative inconvenience implicit in cohort analysis is well justified by the research potentiality.

N. B. Ryder

[See alsoGenetics, article ondemography and population genetics.]

BIBLIOGRAPHY

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Eisenstadt, Shmuel N. 1956 From Generation to Generation: Age Groups and Social Structure. Glencoe, iii.: Free Press.

Frost, Wade H. (1939) 1940 The Age Selection of Mortality From Tuberculosis in Successive Decades. Milbank Memorial Fund Quarterly 18:61–66.

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Ryder, N. B. 1965 The Cohort as a Concept in the Study of Social Change. American Sociological Review 30:843–861.

Whelpton, Pascal K. 1954 Cohort Fertility: Native White Women in the United States. Princeton Univ. Press.