Age and Product Substitution and Cohort Preferences

Martins, Jo M.; Yusuf, Farhat; Swanson, David A.

doi:10.1007/978-94-007-1855-5_11

Jo M. Martins⁴,
Farhat Yusuf⁴ &
David A. Swanson⁵

Part of the book series: The Springer Series on Demographic Methods and Population Analysis ((PSDE,volume 30))

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Abstract

The eleventh chapter examines one of the demographic characteristics of consumer behaviour: product substitution, as people reach retirement age and their social and economic functions change. The chapter reviews behaviour traits that change with age, such as home and work orientation, changes in life styles due to alternative uses of time, physical functioning and capacity to cope with certain pursuits. To this end, it uses an analytical framework to identify given commodities associated with preferences as social and economic functioning changes in retirement, and substitution of some commodity types by others. In addition, this chapter looks at the association between given age cohorts that have experienced similar social and economic experiences and specific generic products that they continue to prefer during their life cycle. It discusses identification problems in cross-sectional and longitudinal surveys and the use of pseudo panels. It uses the concept of pseudo panels to examine age, period and cohort effects. It reviews the characterisation of generational cohorts. It looks at possible cohort effects in relation to a number of specific commodities over two decades using constrained regression models.

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Notes

1.
Many agencies, such as the UNDP (United Nations Development Program), divide the age distribution in three segments of dependent children under 15 years of age, the old 65 years of age and over, and those 15–64 years of age presumed to be in work force age and less dependent on others (UNDP, 2007). With some exceptions, most analyses of household consumer expenditures tend to use the age of 65 as the lower limit of the old population. See for example Paulin (2000).
2.
In addition, they have the advantage of offering readily accessible data of relevance to the analytical framework.

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Authors and Affiliations

Department of Marketing and Management, Macquarie University, Sydney, NSW, 2109, Australia
Jo M. Martins & Farhat Yusuf
Department of Sociology, University of California Riverside, Watkins Hall 1223, 92521, Riverside, California, USA
David A. Swanson

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Jo M. Martins
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Correspondence to Jo M. Martins .

Appendices

Appendix 1: Age Product Substitution Index Estimation – Example

An example is shown below of the estimation of the Age Product Substitution Index using data from a United States household expenditure survey (BOLS, 2009).

	Average household expenditures by age of household head
Type of expenditure	<35	35–44	45–54	55–64	>64	All ages
Home-orientation	7,045	10,121	9,647	8,973	7,409	8,565
Increasing disability	1,473	2,315	2,792	3,476	4,631	2,853
Alternative time use	66	107	137	151	143	118
Retirement preferences	8,584	12,543	12,576	12,600	12,183	11,536
Work related act. and dif. time use	6,578	8,711	8,911	8,148	4,849	7,395
Capacity for some pursuits	818	848	886	886	461	780
Ownership drive	8,505	12,620	10,249	8,713	4,532	8,931
Work-related	15,902	22,179	20,046	17,747	9,842	17,106
Total retirement and work	24,486	34,722	32,622	30,347	22,025	28,642

The following example uses the definitions and notation in Box 11.1

$$APSI = Age\;Product\;Substitution\;Index = APR^r/APR^w$$

APR ^r = Age Preference Ratio for retirement associated products

$$= \left[\left(g_n^r /g_a^r \right)/\big(g_n^{rw} /g_a^{rw} \big)\right]$$

APR ^w = Age Preference Ratio for work and pre-retirement related products

$$= \left[\left(g_n^w /g_a^w \right)/\big(g_n^{rw} /g_a^{rw} \big)\right]$$

(see Appendix 1 in Chapter 9 for an example of the estimation of Age Preference Ratios)

	Age Preference Ratios (APRs)
	<35	35–44	45–54	55–64	>64	All ages
Home-orientation	0.97	0.97	0.99	0.99	1.13	1.00
Increasing disability	0.61	0.66	0.86	1.15	2.12	1.00
Alternative time use	0.66	0.74	1.02	1.21	1.58	1.00
Retirement preferences	0.87	0.90	0.96	1.03	1.37	1.00
Work related act. and dif. time use	1.05	0.97	1.06	1.04	0.86	1.00
Capacity for some pursuits	1.23	0.89	1.00	1.08	0.77	1.00
Ownership drive	1.12	1.16	1.01	0.92	0.66	1.00
Work-related	1.09	1.07	1.03	0.98	0.75	1.00
Age product substitution index	0.80	0.84	0.93	1.05	1.84	1.00

The index show increasing substitution with age of work-related to retirement preferences, especially at the age of 65 and over (1.84).

Appendix 2: Age, Period, Cohort Analysis Constrained Multiple Regression – Example

The passage of time exposes people born in different periods to diverse events and changing environments. Cohort analysis is concerned with the identification of behaviour of people entering a system at the same time (Mason & Wolfinger, 2001), usually birth, that differs from that related to their changing age or the period when it takes place. Thus, cohort analysis involves three interrelated independent variables: age, period and cohort that affect behaviour expressed in terms of a dependent variable. The co-linearity of the three temporal variables leads to identification problems of the effects of each of the three variables on behaviour. Cohort analysis relies on consistent data collection either from panel surveys or pseudo-panels from cross-sectional surveys. Panel surveys are less common than cross-sectional surveys carried out at regular intervals and provide age, period and cohort data. The following example shows a pathway to a statistical method that has been used to identify cohort effects. It is outside the scope of this text to provide an explanation of the statistical issues involved. A review of these issues is contained in Mason and Wolfinger (2001). A paper by Reitz et al. (1983) also reviews the statistical issues and proposes an approach to assess cohort effects.

Average annual household expenditure on poultry age of the household head, United States, 1984, 1994 and 2004 at 1984 Prices ($US)

Note: Cohort 1 (C1) born in 1909 or earlier, Cohort 2 (C2) born between 1910 and 1919, Cohort 3 (C3) born between 1920 and 1929, Cohort 4 (C4) between 1930 and 1939, Cohort 5 (5) between 1940 and 1949, Cohort 6 (C6) between 1950 and 1959, Cohort 7 (C7) between 1960 and 1969, Cohort 8 (C8) between 1970 and 1979, and Cohort 9 (C9) born after 1979.
Source: BOLS (2010a, 2010b, 2010c, 2010d).

The above table gives an example on how pseudo-panels can be built from three cross-sectional surveys, such as the CEX (Consumer Expenditure Survey) carried out in the United States by the Bureau of Labor Statistics in the years 1984, 1994 and 2004. The data provides information on age, the period and by implication cohort on the diagonal. The identification problem lies in the linear dependency of the three variables.

A constrained multiple regression model has been used to overcome the co-linearity problem of the form

$$Y_{{\textrm{ap}}} = \mu + \beta _{\textrm{a}} + \gamma _{\textrm{p}} + \delta _{\textrm{c}} + \varsigma _{{\textrm{ap}}}$$

Y _ap = dependent variable for each age group and period
β _a = age effect
γ _p = period effect
δ _c = cohort effect
μ = grand mean of the dependent variable
ς _ap = random error

(Source: Reitz et al., 1983)

The above data can be used to build a data base as inputs in the constrained models for age, period and cohort for the analysis of variance (ANOVA) using a statistical package such as SPSS.

Data base (a1–a7, p1–p3 and c1–c9 refer respectively to dummy variables for age, period and cohort)
	Age	Period	Cohort
y	(x1)	(x2)	(x3)	a1	a2	a3	a4	a5	a6	a7	p1	p2	p3	c1	c2	c3	c4	c5	c6	c7	c8	c9
42	1	1	7	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0
81	2	1	6	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0
112	3	1	5	0	0	1	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0
105	4	1	4	0	0	0	1	0	0	0	1	0	0	0	0	0	1	0	0	0	0	0
94	5	1	3	0	0	0	0	1	0	0	1	0	0	0	0	1	0	0	0	0	0	0
69	6	1	2	0	0	0	0	0	1	0	1	0	0	0	1	0	0	0	0	0	0	0
55	7	1	1	0	0	0	0	0	0	1	1	0	0	1	0	0	0	0	0	0	0	0
53	1	2	8	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0
94	2	2	7	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0
133	3	2	6	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0
139	4	2	5	0	0	0	1	0	0	0	0	1	0	0	0	0	0	1	0	0	0	0
108	5	2	4	0	0	0	0	1	0	0	0	1	0	0	0	0	1	0	0	0	0	0
77	6	2	3	0	0	0	0	0	1	0	0	1	0	0	0	1	0	0	0	0	0	0
67	7	2	2	0	0	0	0	0	0	1	0	1	0	0	1	0	0	0	0	0	0	0
60	1	3	9	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1
91	2	3	8	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0
107	3	3	7	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0
116	4	3	6	0	0	0	1	0	0	0	0	0	1	0	0	0	0	0	1	0	0	0
92	5	3	5	0	0	0	0	1	0	0	0	0	1	0	0	0	0	1	0	0	0	0
73	6	3	4	0	0	0	0	0	1	0	0	0	1	0	0	0	1	0	0	0	0	0
55	7	3	3	0	0	0	0	0	0	1	0	0	1	0	0	1	0	0	0	0	0	0

From this data base three constrained models can be built. The constraints consist of the exclusion of at least one variable from each of the three matrices. A criterion for the selection in this case was the exclusion of older ages, older periods and older cohorts.

Age model (dropping the oldest age group, two oldest periods and two oldest cohorts)
y	a1	a2	a3	a4	a5	a6	p3	c3	c4	c5	c6	c7	c8	c9
42	1	0	0	0	0	0	0	0	0	0	0	1	0	0
81	0	1	0	0	0	0	0	0	0	0	1	0	0	0
112	0	0	1	0	0	0	0	0	0	1	0	0	0	0
105	0	0	0	1	0	0	0	0	1	0	0	0	0	0
94	0	0	0	0	1	0	0	1	0	0	0	0	0	0
69	0	0	0	0	0	1	0	0	0	0	0	0	0	0
55	0	0	0	0	0	0	0	0	0	0	0	0	0	0
53	1	0	0	0	0	0	0	0	0	0	0	0	1	0
94	0	1	0	0	0	0	0	0	0	0	0	1	0	0
133	0	0	1	0	0	0	0	0	0	0	1	0	0	0
139	0	0	0	1	0	0	0	0	0	1	0	0	0	0
108	0	0	0	0	1	0	0	0	1	0	0	0	0	0
77	0	0	0	0	0	1	0	1	0	0	0	0	0	0
67	0	0	0	0	0	0	0	0	0	0	0	0	0	0
60	1	0	0	0	0	0	1	0	0	0	0	0	0	1
91	0	1	0	0	0	0	1	0	0	0	0	0	1	0
107	0	0	1	0	0	0	1	0	0	0	0	1	0	0
116	0	0	0	1	0	0	1	0	0	0	1	0	0	0
92	0	0	0	0	1	0	1	0	0	1	0	0	0	0
73	0	0	0	0	0	1	1	0	1	0	0	0	0	0
55	0	0	0	0	0	0	1	1	0	0	0	0	0	0

Period model (dropping two oldest age group, one oldest period and two oldest cohorts)
y	a1	a2	a3	a4	a5	p2	p3	c3	c4	c5	c6	c7	c8	c9
42	1	0	0	0	0	0	0	0	0	0	0	1	0	0
81	0	1	0	0	0	0	0	0	0	0	1	0	0	0
112	0	0	1	0	0	0	0	0	0	1	0	0	0	0
105	0	0	0	1	0	0	0	0	1	0	0	0	0	0
94	0	0	0	0	1	0	0	1	0	0	0	0	0	0
69	0	0	0	0	0	0	0	0	0	0	0	0	0	0
55	0	0	0	0	0	0	0	0	0	0	0	0	0	0
53	1	0	0	0	0	1	0	0	0	0	0	0	1	0
94	0	1	0	0	0	1	0	0	0	0	0	1	0	0
133	0	0	1	0	0	1	0	0	0	0	1	0	0	0
139	0	0	0	1	0	1	0	0	0	1	0	0	0	0
108	0	0	0	0	1	1	0	0	1	0	0	0	0	0
77	0	0	0	0	0	1	0	1	0	0	0	0	0	0
67	0	0	0	0	0	1	0	0	0	0	0	0	0	0
60	1	0	0	0	0	0	1	0	0	0	0	0	0	1
91	0	1	0	0	0	0	1	0	0	0	0	0	1	0
107	0	0	1	0	0	0	1	0	0	0	0	1	0	0
116	0	0	0	1	0	0	1	0	0	0	1	0	0	0
92	0	0	0	0	1	0	1	0	0	1	0	0	0	0
73	0	0	0	0	0	0	1	0	1	0	0	0	0	0
55	0	0	0	0	0	0	1	1	0	0	0	0	0	0

Cohort model (dropping two oldest age group, two oldest periods and one oldest cohort)
y	a1	a2	a3	a4	a5	p3	c2	c3	c4	c5	c6	c7	c8	c9
42	1	0	0	0	0	0	0	0	0	0	0	1	0	0
81	0	1	0	0	0	0	0	0	0	0	1	0	0	0
112	0	0	1	0	0	0	0	0	0	1	0	0	0	0
105	0	0	0	1	0	0	0	0	1	0	0	0	0	0
94	0	0	0	0	1	0	0	1	0	0	0	0	0	0
69	0	0	0	0	0	0	1	0	0	0	0	0	0	0
55	0	0	0	0	0	0	0	0	0	0	0	0	0	0
53	1	0	0	0	0	0	0	0	0	0	0	0	1	0
94	0	1	0	0	0	0	0	0	0	0	0	1	0	0
133	0	0	1	0	0	0	0	0	0	0	1	0	0	0
139	0	0	0	1	0	0	0	0	0	1	0	0	0	0
108	0	0	0	0	1	0	0	0	1	0	0	0	0	0
77	0	0	0	0	0	0	0	1	0	0	0	0	0	0
67	0	0	0	0	0	0	1	0	0	0	0	0	0	0
60	1	0	0	0	0	1	0	0	0	0	0	0	0	1
91	0	1	0	0	0	1	0	0	0	0	0	0	1	0
107	0	0	1	0	0	1	0	0	0	0	0	1	0	0
116	0	0	0	1	0	1	0	0	0	0	1	0	0	0
92	0	0	0	0	1	1	0	0	0	1	0	0	0	0
73	0	0	0	0	0	1	0	0	1	0	0	0	0	0
55	0	0	0	0	0	1	0	1	0	0	0	0	0	0

The analysis of variance (ANOVA) for the three models can be carried out to assess the coefficients of determination (R²) for each model. Following Reitz et al. (1983), if the cohort effect is the one that fits best then the R² for the cohort model should be the highest of the three coefficients of determination.

ANOVA Results
Model	Adjusted R²	Standard error of estimate	Significance
Period	0.911	8.050	0.001
Age	0.908	8.184	0.002
Cohort	0.931	7.079	0.001

In this case, the cohort model is the best fit with a R ² of 0.931 that it is higher than those for the period and age models.

It is important to state that this method can give different results depending on the choices made in the selection of the constrained models.

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Martins, J.M., Yusuf, F., Swanson, D.A. (2011). Age and Product Substitution and Cohort Preferences. In: Consumer Demographics and Behaviour. The Springer Series on Demographic Methods and Population Analysis, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1855-5_11

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Published: 27 June 2011
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