# Separating Age, Cohort and Period Effects in Consumer Behavior

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Joseph O. Rentz and Fred D. Reynolds (1981) ,"Separating Age, Cohort and Period Effects in Consumer Behavior", in NA - Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Ann Abor, MI : Association for Consumer Research, Pages: 596-601.

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http://acrwebsite.org/volumes/5866/volumes/v08/NA-08

[Joseph O. Rentz is Assistant Professor of Marketing, McIntire School of Commerce, University of Virginia.]

[Fred D. Reynolds is Professor of Marketing, University of Georgia.]

Traditional research designs for the study of consumer aging confound the effects of age, cohort and period. Cohort analysis is a group of methods designed to separate the three effects. Problems with conventional designs are discussed and cohort analysis methods critically reviewed.

INTRODUCTION

Our purpose in this paper is to point out to consumer behavior researchers some advances in research designs and methods for the study of aging. Generally called cohort analysis, these methods attempt to separate the effects of age, cohort and period. Use of the methods over the past decade has resulted in an increased understanding of the aging process. Researchers have found that some phenomena once thought to be related primarily to the aging process are instead related primarily to the cohort membership of the groups studied.

In this paper we critically review the cohort analysis methods. First the relationships between age, cohort and period are discussed and some shortcomings of traditional research designs for the study of aging are pointed out.

RELATIONSHIPS BETWEEN AGE, COHORT AND PERIOD

Figure 1 graphically illustrates the relationships between age, cohort, and period. The figure represents the concomitant processes of aging and succession of four selected cohorts and reveals cross-sectional differences among age classes at any given point in time (Riley, Johnson and Toner 1972). Each cohort is comprised of people born at approximately the same time. People within each cohort age over time.

AGING, COHORT SUCCESSION AND AGE DIFFERENCES: SOURCE: RILEY, JOHNSON AND FONER (1972)

Specifically, a __cohort__ is an aggregate of individuals within a given population who experienced the same event(s) within the same time interval (Ryder 1965). In Figure 1 the defining event is birth although numerous types of cohorts can be identified including marriage cohorts, divorce cohorts, retirement cohorts and education cohorts. The word is typically used without a modifier to refer to birth cohorts. __Cohort succession__ refers to the immutable process whereby cohorts of people are born, live out their life courses and die, being replaced by other cohorts (Riley 1973).

Cohorts can be expected to differ from one another on a variety of dimensions for a variety of reasons. Each cohort occupies a unique interval in time. Since society is constantly changing over time, each cohort experiences unique events or experiences events differently because each cohort is at a different stage in the life course when the events occur. Cohorts also differ in initial size and composition (Ryder 1965). The problems faced by members of the post-war baby boom cohorts -- crowded schools and limited job opportunities, for example -- are examples of the effects initial size can have on cohorts. Thus we might expect cohorts to differ from one another in many respects.

__Age differences__ in the population at s given time are revealed by a cross section of the population at that time -- see the vertical line at 1980 in Figure 1. These cross-sectional differences can be important in their own right since they have implications for current marketing practice, public policy, etc. However from a developmental perspective, the important issue is what accounts for the current differences.

Figure 1 shows that there are two interpretations for cross-sectional differences in the age classes (Riley 1973). The "aging interpretation" is that the 1980 age class differences are due to the development (aging) of consumers. This is the interpretation that is nearly always given by consumer researchers to age differences. The alternative interpretation, the "cohort interpretation," is that the 1980 age class differences are due to the different cohort memberships of the age classes. If the cohort interpretation is correct then the characteristic of interest will remain relatively stable over the life courses of people in the cohorts and the characteristics of the age classes in the future (say in the year 2010 in Figure 1) will change as new cohorts occupy each of the age classes. For example elderly consumers in the future will be different from today's elderly consumers. When aging is producing the age class differences, the characteristic of interest will change over the life courses of people in the cohorts and the characteristics of the age classes in the future will be similar to the characteristics of the current age classes. For example, the elderly of the future will be similar to the elderly of today.

The clearest example of a variable which is related to cohort membership rather than aging is education. At any point in time, elderly people report having completed fewer years of formal education, on average, than young people. Clearly the number of years of education completed does not decline as an individual ages. Rather, age class differences in education are a function of cohort membership and we can expect the average educational level of the elderly, for example, to increase as more educated cohorts age into the elderly age classes and replace less educated cohorts.

Cohort membership accounts for a significant portion of age class differences in political party affiliation (Cutler 1970; Glenn 1972; Glenn and Hefner 1972; Knoke and Hout 1974), cognitive performance (Baltes and Reinert 1969, Schaie and Strother 1968a; Schaie and Strother 1968b; Schaie and Parham 1977), and consumption of a product class (Rentz 1980) as well as other variables.

Clearly the effects of aging are confounded with the effects of cohort membership in the cross-sectional design. Unless one has evidence that cohort effects are minimal, errors of interpretation can occur by attributing age class differences to the aging process.

A second research design, the longitudinal design, has also been employed by consumer researchers to study aging. For example, in Figure 1, one might measure a sample of individuals in a particular cohort at two or more points in time. The same individuals might be followed over tine or an independent sample from the cohort might be taken at each time point. The longitudinal design also has weaknesses. In longitudinal comparisons the effects of aging are confounded with "period effects." Period effects are environmental influences which affect aging cohorts at one point in time (between two times of measurement). They include marketing efforts, public policy, and social change in general. Because it is impossible to employ control groups who do not age, one cannot separate period effects and age effects in longitudinal comparisons. Thus age effects and period effects are confounded in longitudinal comparisons.

A third research design, the time-lag design, is sometimes used to study differences among cohorts (or among generations). The same age class is compared at two or more points in time. For example, in Figure 1, youth in 1980 might be compared to youth in 1950. Differences are typically attributed to differences in cohorts (or generations.) However the comparisons are made over time so cohort effects are confounded with period effects in time-lag comparisons.

The confounding of age, cohort, and period effects in empirical measures led Belies (1968, p. 153) to conclude: ". . . the conventional methods are in no way adequate research designs for the assessment of age effects."

How, then can consumer researchers separate the effects of age, cohort and period? A group of methods which fall under the general heading "cohort analysis" has been developed in an attempt to separate the effects of the three variables. The method can be used in studies of aging, in inter-cohort-studies, and in the forecasting of consumer behaviors. Reynolds and Rentz (1980) illustrate the use of cohort analysis in forecasting changes in women's roles. In the next section we discuss the basics of cohort analysis and then we discuss several cohort analysis methodologies.

COHORT ANALYSIS: SEPARATING AGE, COHORT, AND PERIOD

Cohort analysis refers to any study in which one or more cohorts are measured on some variable at two or more points in time (Glenn 1977). Either panel data or cross-sectional data may be used. Cohort analysis normally begins with the construction of a "standard cohort table" (Glenn 1977). Tables 1, 2 and 3 are examples of cohort tables and illustrate the pattern of variation resulting from "pure" age, cohort and period effects. Normally a series of cross-sectional studies comprise the columns of the table.

The tables are constructed so that the interval between any two times of measurement (periods) is the same as the intervals used to delineate age classes. In such a table cohorts are represented in the diagonals of the table. Trends in an aging cohort can be traced by reading down the diagonals of the table as illustrated for one cohort by the underlined measures in Table 1. Nine cohorts are represented in each of the cohort cables presented here.

Unfortunately, the interpretation of a cohort table is not straightforward. We have seen that age and cohort effects are confounded in cross-sectional comparisons (comparisons within any column in Table 1), age and period effects are confounded in longitudinal comparisons (comparisons within any diagonal in Table 1), and period and cohort effects are confounded in time-lag comparisons (comparisons within any row of Table 1). Comparisons between man values for rows, columns, or diagonals does not eliminate the confounding. For example the difference between the means of the first two rows in Table 1 is the same as the mean of the four cross-sectional differences between the two rows. In each of the four differences, age and cohort effects are confounded so the mean of the four differences also contains confounded effects.

To further complicate matters, there is a formal linear dependency between each of the independent variables of interest (age, cohort, and period) and the other two. That is, when age, cohort and period are indexed by chronological age, year of birth, and year of measurement respectively, then age equals period minus cohort, cohort equals period minus age and period equals cohort plus age.

Mason, et al. (1973) present a lucid discussion of the implications of the linear dependency and show that parameter estimation becomes impossible in most statistical models. Thus traditional techniques such as analysis of variance or regression are not appropriate without modification. The nonindependence of the variables is a case of the "identification problem" discussed by Blalock (1966). Identification of the operative variables is possible only through a priori assumptions.

COHORT ANALYSIS METHODS

Several methods have been proposed for separating age, period and cohort effects including "visual inspection" methods, methods to correct for period effects (Agnello 1973; Crittenden 1962; Klecka 1971), Schaie's (1965) sequential strategies, Baltes (1968) bifactorial model, the constrained multiple classification method developed by Mason, et al. (1973), and an approach developed by Palmore (1978). We prefer the methods of Mason, et al. and Palmore although there is by no means a consensus in the literature concerning which method is most appropriate.

In this section we critically review four of the methods which we feel merit the consideration of consumer behavior researchers. For a complete review, see Rentz (1980). Palmore's method is presented first because his approach clarifies much of the conceptual and terminological confusion which exists in the literature.

Palmore's Method

Palmore (1978) points out that much confusion surrounding the age-cohort-period problem has arisen from a failure to distinguish between three necessary levels of analysis: computing observable differences, inferring effects, and determining the theoretical causes of the effects. Cohort analysis involves inferring effects from observable differences. The causes of the effects can only be decided on the basis of evidence outside the cohort table.

__Observable differences__ are those differences which are calculated from empirical data. Three types of differences are observable (Figure 2). __Cross-sectional differences__ (cell C - cell A) are differences between younger and older cohorts (and younger and older age groups) at one point in time,

OBSERVABLE DIFFERENCES - SOURCE: PALMORE, 1978

__Longitudinal differences__ (cell B - cell A) are differences between early and later measurements on the same cohort (at different ages). __Time-lag differences__ (cell B -cell A) are differences between two groups of the same age, one from the older cohort measured at the early time and one from the younger cohort measured at the later time. Computation of the observable differences is not a difficult process once relevant data are collected.

Palmore's second level of analysis is __inferred effects__. Age, cohort and period effects are __inferred__ from the three observable differences. Each observable difference is composed of the effects of two and only two variables:

Longitudinal Differences = Age + Period Effects

Cross-Sectional Differences = Age + Cohort Effects

Time-Lag Differences = Period - Cohort Effects

The effects of age, period, and cohort can only be inferred from the observable differences. Since any one difference is composed of two effects one cannot equate any one effect with any one difference without further analysis or assumptions. For example, if one has other evidence or makes the assumption that cohort effects are zero, then cross-sectional differences can be equated to age effects.

One triad of data of the form shown in Figure 2 is the minimum number of cells necessary to compute the three observable differences. Palmore works with one triad of data at a time, inferring effects from observable differences in each triad. Each of the differences is tested for statistical significance. Three patterns of significant differences are possible: no significant differences, two significant differences and three significant differences. Because the three differences are related (the longitudinal difference is the sum of the cross-sectional and time-lag differences) one cannot obtain one significant difference except when sample sizes are markedly different.

We will illustrate Palmore's inference process using a pattern of two significant differences. The following data illustrate the pattern:

Here the longitudinal difference is ten, the cross-sectional difference is ten and the time-lag difference is zero. There are three possible interpretations of this pattern.

The first interpretation is that the age effect is ten and cohort and period effects are zero:

Longitudinal Difference = 10 = Age (10) + Period (0)

Cross-Sectional Difference = 10 = Age (10) + Cohort (0)

Time-Lag Difference = 0 = Period (0) - Cohort (0)

The second interpretation is that period and cohort effects are exactly counterbalancing one another in the time-lag difference and age effects are zero:

Longitudinal Difference = 10 = Age (0) + Period (10)

Cross-Sectional Difference = 10 = Age (0) + Cohort (10)

Time-Lag Difference = 0 = Period (10) - Cohort (10)

The third interpretation is that a complex combination of all three effects is producing the differences. Palmore argues that in the absence of other evidence the principle of parsimony favors the first interpretation over the other two. We have found that by making a priori assumptions about the directionality of two or three effects one can often rule out one or two interpretations. For example if one assumes that period and cohort effects are in opposite directions then the second and third interpretations in the preceding example can be ruled out since period and cohort effects could not counterbalance one another in the time-lag difference.

Palmore offers similar interpretative guidelines for the patterns of no significant differences and three significant differences. Once the effects are inferred in each triad of the cohort table one can summarize effects over groups of triads.

Palmore notes that the major advantage of his method is that it is not necessary to assume some systematic pattern of effects. Some methods require the assumption that effects are additive or that the effects are unidirectional and positive. Palmore's method provides a way of determining whether systematic patterns exist and what they are. However the method also has weaknesses. Often directionality assumptions do not allow a choice of alternative interpretations and one is forced to rely on the principle of parsimony. Also the method is oriented toward finding one main effect and works best when no differences or two differences are significant. The typical situation may be that all three effects are operative and three differences are significant.

Schaie's Sequential Methods

Recognizing that only two of the three independent variables of interest (age, cohort, and period) can be varied independently, Schaie (1965) proposes three bifactorial designs in which different combinations of the three variables are represented two at a time. His cohort-sequential method is an age by cohort design, his time-sequential method is an age by period design and his cross-sequential method is a cohort by period design. The analysis of variance is used as the test of significance in each case.

Schaie recognizes the confounding of the variables in each of his three methods and does not advocate using any one of the methods alone to estimate age, period, and cohort effects. Rather he advocates using two or more of the methods in conjunction. He presents a set of decision rules for inferring effects using the time-sequential and cross-sequential methods in conjunction or the cohort-sequential and cross-sequential methods in conjunction.

Schaie's decision rules require the assumption that age, period, and cohort effects are unidirectional and positive, that is, "an incremental progression exists from a younger to an older age, from an earlier to a later measurement time, and from a younger to an older generation" (Schaie 1965, p. 103).

Essentially, the estimates provided by the analysis of variance are estimates of either mean longitudinal, mean cross-sectional or mean time-lag differences. Schaie's decision rules follow a logic similar to Palmore's. For example the estimate of the period effect from the cross-sequential method is actually an estimate of the mean longitudinal difference (which contains age and period effects). One of Schaie's decision rules states that if this estimate is zero then variation in the table is a result of cohort effects. Since both age and period effects are assumed to be positive, (or zero) if the mean longitudinal difference is zero then both age and period effects must be zero and all variation must be due to cohort effects. Similar logic can be employed to verify Schaie's remaining decision rules.

Variations of Schaie's methodology have been employed by others and especially by Riley, Johnson, and Foner (1972), Their "period analysis" in the same as Schaie's cross-sequential strategy, their "cohort analysis" is the same as Schaie's cohort-sequential strategy and their "cross-sequential analysis" is the same as Schaie's cross-sequential strategy. They do not employ Schaie's decision rules but rather emphasize the need to make assumptions and use outside evidence in order to untangle age, cohort, and period effects.

The usefulness of Schaie's methods is limited by the necessity to assume that all effects are unidirectional and positive. However, Schaie's general approach of specifying the type of slope assumed for each of the three effects and developing decision rules based on the type of slope assumed is certainly valid when theory or outside evidence supports the assumptions.

Constrained Multiple Classification Method

Mason, et al. (1973) develop an approach to estimating age, cohort and period effects using multiple classification analysis. Multiple classification analysis is essentially a multiple regression analysis using dummy variables (Andrews, Morgan, and Sonquist 1967).

Mason, et al. employ a model of the following form:

Y

_{ij}= m + b_{i}+ g_{j}+ d_{k}+ e_{ij}

where the effect of the i-th age group is given by b_{i}, the effect of the J-th period by g_{j}, the effect of the k-th cohort by d_{k}; where m is the grand mean of the dependent variable and where e_{ij} is the random error. They show that the parameters of a model of the above form are not estimable because only one cohort exists for any given age and period (i.e., any one variable is linearly dependent on the other two). Mason, et al. also show that by constraining the above model such that any two ages, periods, or cohorts have identical effect parameters, linear dependency is eliminated and the parameters of the model are estimable. Mason, et al. proceed to show that when only two ages or two cohorts or two periods are constrained to be equal, the fit of the model to the data does not vary but the estimates do vary with different equality constraints. Thus one cannot judge the suitability of the many possible constraints. To remedy such a situation, Mason, et al. advise that the analyst place constraints on more than one dimension. For example, we have used the method by fitting three models with different sets of constraints: one with two ages and two cohorts set equal, one with two cohorts and two periods set equal and one with two ages and two periods set equal. The model that best fits the data is chosen as providing the best estimates of the effects,

The method of Mason, et al. is appealing since the assumptions involved appear to he minimal compared to other methods. Most investigators would be untroubled by assuming two ages, periods, or cohorts are equal. In many cases strong a priori reasons might exist for making the assumptions. In any case the model and assumptions are clearly specified. Another advantage of the method is that other independent variables can be included in the analysis along with age, cohort and period. (See, for example, Knoke and Hout (1974) and Hout and Knoke (1975). However, Glenn (1976; 1977) argues against the constrained multiple classification method because the model assumes that age, period, and cohort effects are additive, i.e., do not interact. The additivity assumption implies that age affects are the same for all cohorts and periods, that cohort effects are the same for all ages and periods, and that period effects are the same for all ages and cohorts. Glenn presents examples of theoretical and empirical evidence which suggest that the additivity assumption is unrealistic. For example, theory and empirical evidence suggest that attitudes tend to become less responsive to change as the individual ages. Thus Glenn maintains that period effects should not, as the additive model assumes, be the same for all age groups. Glenn concludes that for many additional and behavioral dependent variables, the additivity assumption is unrealistic.

We feel that, given the alternative methods, the additivity assumption is not unrealistic. Rather than reject the method we attempt to incorporate likely interactions in our interpretation of the effects.

Visual Inspection Method

The "visual inspection method," advocated primarily by Glenn (1977) [The term "visual inspection method" is the authors' and is not employed by Glenn.] centers around the researcher being familiar with the patterns of variation produced by age effects only (Table 1), cohort effects only (Table 2), and period effects only (Table 3). The researcher should then be able to recognize the effects which produce the pattern found in his own data. However, Glenn stresses that there are two explanations for the pattern of variation in __any__ cohort table. For example, the pattern shown in Table 1 could have been produced by age effects alone. There is no variation across periods or across cohorts in the table. However, the pattern also could have been produced by a combination of period and cohort effects. An increase in the percentages with each successive period combined with an offsetting decrease in the percentages with each successive cohort would produce the pattern of variation in Table 1. To further complicate interpretation, the pattern of variation also might result from a complex combination of all three effects.

Glenn maintains that the correct interpretation cannot be made by examination of the cohort table alone. He advocates the use of theory and evidence from outside the cohort table to choose the correct interpretation. For example, if one can assume on the basis of theory or other evidence that period and cohort effects result from the same causal influences, then period and cohort effects would tend to reinforce one another in the cohort table and one could rule out the interpretation of period and cohort effects offsetting each other in Table 1.

Glenn offers other interpretive aids to the visual inspector of cohort tables and concludes that by relying on theory and evidence from outside the cohort table, "there usually is only one __plausible__ explanation for a pattern of variation predicted by pure age, cohort, or period effects" (Glenn 1977, p. 52).

The visual inspection method requires that outside evidence be employed when interpreting a cohort table. Usually assumptions about the direction or magnitude of the three effects must be made. The necessity to use outside evidence and/or assumptions is not unique to the visual inspection method. However the visual comparison between one cohort table and another is unique to this method and is not analytically appealing. When reasonable assumptions can be made, more rigorous methods of cohort analysis are available.

Summary

The validity of the various cohort analysis methodologies depends on the validity of the assumptions necessary for their use. While we prefer the Palmore method and the constrained multiple classification method, we urge consumer researchers to make their own judgments based on the nature of the problem at hand and the assumptions required for the use of the methods.

While cohort analysis has its limitations, it has much to offer to the student of consumer aging. Recognition of the confounding of age, cohort and period in empirical measures and attempts to separate the effects using cohort analysis should produce more accurate descriptions and theories of consumer aging.

A LONG-TERM SOLUTION TO THE AGE-COHORT-PERIOD CONFOUNDING PROBLEM

The confounding of age, cohort, and period effects in empirical data is the result of the way researchers measure the three variables. Age is measured as chronological age, i.e., the number of years since birth. Cohort is measured as year of birth and period is measured as the year of measurement. The three operational measurements are formally dependent.

Each of the three measures is only a surrogate for more fundamental and meaningful variables. For example, chronological age is a surrogate measure of more meaningful dimensions of aging: biological, psychological, and social age (Glenn 1977; Maddox and Wiley 1976).

Maddox and Wiley (1976) and Mason, et al. (1976) point out that if we could measure these more fundamental and meaningful variables then the confounding problem would not exist. For example, Maddox and Wiley point out that replacing "period," indexed by time of measurement, with appropriate measures of environmental variables would be sufficient to remove the confounding since "there is no reason to suppose that age, cohort, and 'environment' are linearly dependent" (Maddox and Wiley 1976, p. 21). Similarly, cohort, indexed by date of birth, could be replaced by direct measures of environments which impinge on successive cohorts, and age, indexed by number of years since birth, could be replaced by direct measures of biological, psychological, and social age.

Unfortunately measures of biological, psychological, and social age are not well developed. Also, our understanding of the environmental conditions contributing to cohort and period effects is limited for many types of dependent variables. Because of these limitations, the direct measurement of the three basic dimensions of aging and the direct measurement of environments is not practical in most instances (Rosnow 1978). However, as our understanding and measurement capabilities increase, it is certainly desirable to replace measures of age, cohort, and period with the more basic variables which they index. As Mason, et al. (1976, p. 905) point out, "The replacement of proxies by the variables they index is a universal goal of research." Thus a long-term solution to the age-cohort-period confounding problem is to replace the confounded variables by the unconfounded variables they index.

REFERENCES

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