Some Theoretical Explanations of the Shape of Age Earnings Profiles
1. The Human Capital Model 1 The General Framework
1.5 The Cohort Model
A further extension of the human capital model considers the role of cohort size in
determining eamings.The cohort model can be thought of as part of the human capital
approach because it focuses on the lack of substitutability between workers of different
ages and education levels. On-the-job training and experience are key factors in
explaining why earnings differ by age and are affected by cohort size. The cohort model
has implications for the expected shape of a cross section age earnings profile.
According to this theory, the presence of a large cohort of young workers would make
the cross section age earnings profile appear steeper by depressing the earnings of young
workers relative to older workers.
It has been argued that the size of a birth cohort will have a significant effect on its
relative earnings when the group enters the labour force and this may persist throughout
the working life of the cohort (see, for example Welch (1979)). Large birth cohorts are
associated with low relative earnings. A second potential cohort effect relates to changes
in the educational mix of those beginning work. Even without demographic changes, we
would expect a rise in the number of young people completing tertiary education to have
an effect on the earnings of young graduates relative to old graduates. Evidence from a
number of studies, mainly using US data, shows that in the 1970's the entry of a large
cohort to the labour force depressed the earnings of young males relative to prime age
males, though researchers dispute whether this was likely to continue into the later
working life of this group. 0 0 )
The "career phase" model used to explain the importance of cohort size,
emphasises the lack of substitutability between workers of different ages. According to
the model, a large cohort entering the labour market competes for a limited number of
jobs appropriate for those in the early part of their career and bids down its own wage
relative to those well established in the labour market. Alternatively, where relative
high level of unemployment among members of a large cohort. One (or both) of these
effects should be in evidence whenever a large increase in the size of a cohort has been
experienced.
The cohort effect on earnings has been analysed in a production function
framework by Welch (1979). Given a production function
Q= f (N I, N 2,...Ni, K) (9)
where N l, N2,...Ni are the number of workers in each education category, 1,
2 ,..i.
K is the physical capital input
Each schooling group is assumed to form a separable branch of the aggregate
production process and within each schooling group, there are workers of different ages
providing different labour services. Welch considered two types of labour, 'learners’ (a)
and 'qualified workers' (b).
Ni=g (Nia, Nib) (10)
From such a production function, we can generate inverse demand functions
relating the earnings of an age group to the quantity of its own labour input and the input
of other types of labour of the same educational background but different ages. The
theory as developed by Welch, with the assumption of the separability of labour of
different educational backgrounds, does not allow for any cross effects between
educational groups.
Inputs are defined to be q complements if an increase in the input of factor 1 raises
the marginal product and wage of factor 2 and q substitutes if an increase in the input of
factor 1 lowers the marginal product of factor 2. For a large increase in the size of a
particular age group to reduce only its wage and not that of all other workers within the
educational group, this group must not be a close substitute for workers of any other
age. In terms of Figure 2.3, a shift in the supply curve say of young workers, from SI
Figure 2.3: The Effect of Cohort Size on Earnings.
Number of Young Workers
of the total work force and they were close substitutes for older workers, then the
demand curve for young workers would be highly elastic and an increase in the
proportion of young workers in the workforce would have a small effect on their wage.
If workers were q complements, an increase in the number of say young workers,
would raise the wage of the group with whom they were complementary.
In the simple case where there are only two types of labour input, learners and
fully trained workers, the career phase model predicts that members of a large cohort will
always earn less than members of a normal cohort particularly in the learner phase. A big
cohort has a large proportionate impact on the stock of learners and therefore on then-
wage but a much smaller impact on the stock of qualified workers and consequently a
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large cohort in the learner phase will therefore exhibit a steep earnings profile. Another
cross section taken when this group is in the worker phase and followed by an average
size cohort, will be flatter but not very different from the cross section profile in the
absence of a large cohort.
An inference of the model is that the effects on wages of membership of a large
cohort is greater the smaller the elasticity of substitution between learners and workers.
We expect this elasticity to vary between groups with different levels of schooling. This
model predicts that the relative earnings of the educated young will suffer a greater
reduction than the uneducated. Welch argued that as those with more schooling are also
more likely to receive more on-the-job training, these groups take longer to move from
learner to worker status and experience larger reductions in their relative wage during the
learner phase. So, for example, while a twenty year old labourer can provide much the
same service as a forty year old labourer, this is not the case for professionals such as
doctors and lawyers. For these groups, there is a period during which they are in the
workforce but still learning on-the-job and the growth of experience is expected to make
them better at their profession.
This model has been criticised on a number of grounds. Berger (1985) argued that
"adverse cohort size effects on earnings do not diminish rapidly as Welch suggests and
may actually increase throughout the career of individuals in large cohorts" (p562).
Membership of a large cohort may retard the acquisition of on-the-job training and
impede progress up a career ladder for several reasons. Members of a large cohort may
face greater probability of unemployment, find themselves forced into jobs with little on-
the-job training or encounter greater competition for a small number of high level
positions. These groups moving from "learner" to "qualified worker" status should, like
a normal cohort, become close substitutes for other "qualified workers" but their
restricted opportunities in their early period in the labour market may prevent them from
levels. Reasons such as these would produce a flatter earnings profile for the group than
for a normal-sized co h o rt.
Figure 2.4 summarises the possible outcomes suggested by Welch and Berger.
Welch hypothesised that a large cohort entering the labour force would experience a
substantial reduction in their earnings in the learner phase but once they had achieved
worker status their earnings would remain only slightly below those of a normal-sized
cohort. In contrast Berger predicted a persisting adverse effect of large cohort size on its
members earnings. Welch and Berger's predictions are therefore similar for the early
part of working life and differ for older workers. A further issue which is not covered
by the simple career phase model is the effect of cross elasticities of substitution between
workers with different educational backgrounds.^ 1)
The cohort model thus implies that the differences in the aggregate male age
earnings profiles of the three countries, may be explained by the relative size of young
cohorts in each of the countries. A large young cohort would depress its earnings
relative to the earnings of prime age males and produce the appearance of a steeper cross
section age earnings profile.