G-SEC WORKING PAPER No.27
Labor Force Aging and
Growth of Per-Wor ker Income

Masaya SAKURAGAWA and Hideki TOYA
September, 2009

Abstr act
We provide a theoretical mechanism behind which the labor force aging adversely influences
economic growth by developing a human-capital based growth model in which humancapitals embodied in people of different age cohorts are imperfect substitutes as inputs in
production. The age distribution in the labor market can significantly influence wage profiles,
the young’s incentive of investing in human capital, and eventually economic growth. We
observe the cross-country empirical evidence showing that the advance of the labor force
aging leads to a slowdown of the subsequent economic growth of per worker GDP.

Keywords: Economic Growth, Human Capital, Labor Force AgingJEL Classiﬁcation: J24, O40, O57

Keio University. E-mail:masaya@econ.keio.ac.jp
Nagoya city University. E-mail:toya@econ.nagoya-cu.ac.jp

1. Introduction
As the episode of the ruin of the Roman Empire tells, a matured society with aging
population is declining. In a matured society, a smaller proportion of young people face lesspressure of competition, and have less incentive to invest in acquiring knowledge or humancapital, but rather exploit benefits of the existing knowledge. The proceeding quote from the
French demographer, Alfred Sauvy, reveals that "such a society (with aging population) would
hold a society of old people, living in old houses, ruminating about old ideas". Sauvy attributed
the slow technological progress in nineteenth century France to conservatism and aging.
Furthermore, he says, “Under the influence of population aging, the French government andParliament subsidized the Navy’s sailing ships while other countries were adopting
steam-powered craft.
Economic theories, however, have not yet provided any clear-cut answer to the impacts ofdemographic change on economic activities, but rather demographic factors are suppose to
influence the economy through various channels. One strand of literature argues a negative
impact of population growth on the economy. The standard growth theory argues the negativerole of population growth on the level of per-capita income since the seminal work of Solow(1956). Becker and Barro (1988) emphasize the negative role of fertility on economic growth.
On the other hand, another strand of literature argues the positive role of population growth on
the economy. Kuznets (1960) and Simon (1977, 1981) argue that a higher population means
more inventors. Kremer (1993) and Jones (1998) argue that an increased population raises
returns to new ideas and promote economic growth. Glaeser et al (1992), Ciccone and Hall
(1996), and Srinivasan and Robinson(1997) argue that more populated cities or an increase in
the size of employment can speed up the accumulation of human capital and knowledge.
Empirical evidence also provides conflicting evidence. Barro (1991), Mankiw, Romer, andWeil (1992), and Brander and Dorwick (1994) find that fertility or the population growth will
be negatively linked to per-capita income growth. On the other hand, Galor and Zang (1997)
and Williamson (1997) find that the growth rate of the labor force has a positive effect on
per-capita income growth. Kremer (1993) finds empirical evidence supporting the view that
total research output and hence per-capita income will increase with population.

2

There may be another channel that should not be overlooked through which a demographic
element influences economic growth. In practice, Germany, Italy, and Japan attained rapid andsustained growth with low unemployment rates after World War II. The successes of thesecountries are supposed to be relevant to the large replacement of elder by younger in theworkplace. In addition, growth miracle in the East Asian countries has been accompanied by anincreasing working-age population, which Bloom and Williamson (1997) call “demographic
gift”.
This mechanism is going to reverse itself in the 21st century. Advanced countries haveexperienced a fall in fertility and a rise in life expectancies over the last two decades, and aregoing to face the decreased working population and the labor force aging. Figure 1 shows theshare of workers aged 20-39 to all workers in all OECD countries. A number of countries
including Japan, Denmark, Finland, Iceland, and Sweden have experienced the decline in theshare of workers aged 20 to 39. Other countries except Ireland are supposed to face the similartendency by 2000 or 2010. This figure reveals that the aging in the labor force is a serious
problem in many advanced countries.
The main idea that we advocate in this paper is that the labor force aging of the consequent
increased elder relative to young workers provide a disincentive for young people to invest in
human capital, and eventually deters economic growth. We present a human-capital based
growth model in which human capitals embodied in people of different age cohorts areimperfect substitutes as inputs in production. This notion goes back to Welch (1979) who foundthe greater wage difference between new entrants and peak earners when the baby boom cohorts
entered the labor market in the United States. Murphy and Welch (1992) found that workers
with similar ages and education level tend to be substitutes, but those with different ages andeducation levels are complements in the United States. Also in Japan, Inoki and Ohtake (1997)
found that the baby boom cohorts earn the smaller lifetime earning relative to other cohorts.
An increase in the size of a generation or a cohort increases competition among people ofthis generation or cohort, driving down their wage rate relative to the one of the elder, andforcing them to make more effort to acquire skills for getting future higher salaries. In the aged
society with abundant elder and scarce young, young people take the “myopic” behavior in3

investment in human capital due to this adverse incentive effect.
We investigate the empirical analysis to find this hypothesis using the pooled data forOECD countries. The estimation result shows that an advance of the labor force aging leads to a
decline in the subsequent economic growth rate of per worker GDP. Forecasting per worker
GDP growth for 2000-2010 and 2010-2020, we observe that the growth rate for 2010-2020 will
be smaller than the one for 2000-2010 in all countries except for Ireland.

42. The Model
We present an overlapping-generations economy in which agents live for two periods andpeople of different generations are linked through altruism. The economy consists of agents wholive for two periods and sufficiently large numbers of firms that produce a single goodcompetitively. The production process requires physical capital and two types of workers,
skilled and unskilled workers. Two types of workers perform different tasks: skilled workers
engage in management and unskilled workers work as laborers. As argued just below, young
agents are identified with unskilled workers, and old agents identified with skilled workers or
managers.
Each of agents is born with endowment of one unit of the productive time in both the first
and the second period of life. Each of them consumes only in the second period of life. In thefirst period of life, each of them receives bequest from his parent and decides how much time toallocate between supplying in the labor market and investing in human capital. In the second
period of life, each of them supplies one unit of time in the labor market. Each of themconsumes only in the second period of life. At the beginning of the second period of life, eachparent gives birth to 1 + nt +1 children. We call the generation that appears at period t,N“generation t”. Letting N t denote the size of generation t and 1 + nt +1 = t +1

N t denote thepopulation growth rate, the total number of labor employed at period t , denoted Lt , is equal
to N t + N t −1 . The share of young workers to the total labor iselder workers is 1

(1 + nt )(2 + nt ) , the share of(2 + nt ) , and hence the evolution of the total labor is

Lt +1 (2 + nt +1 )(1 + nt )=.
Lt
2 + ntThe utility of an individual of generation t, Vt , depends positively not only on his own
second-period consumption ct+1 but also on the welfare of each of his children given by Vt+1 :
(2-1)

Vt =

1
{log ct +1 + (1 + nt +1 )Vt +1} ,1+ ρ

where ρ is a subjective discount rate, and nt +1 is assumed to be less than ρ . Although we

5

basically investigate the economy with a constant population growth rate, for later analyticalconvenience we denote time subscript for n .
An agent born at t is endowed with an amount of human capital hte . By investingut units of time in human capital, he can accumulate the amount of human capital up to hty inthe remaining first period of life and up to hto+1 in the second period of life according to theMicerian human capital investment functions, with

hty = θH (ut )ht , and hto+1 = H (ut )ht ,(2-2)

where ut ∈[0,1] is the fraction of productive time devoted to the accumulation of humancapital and H(.) is increasing, concave and continuously twice differentiable function; H(.)
satisfies lim H ' ( ut ) = +∞ , lim H ' (ut ) = 0 , and H( 0) = 1 , and 0 < θ ≤ 1 . Equation (2-2)
ut →0

ut →1

implies the feature of decreasing returns to human capital that captures the common recognition
that people accumulate human capital rapidly when they are young, but less rapidly when they
get elder.1 Psacharopoulos (1994) surveys evidence from many countries on returns toinvestment in education, finding that the rate of return is highest in primary education, next insecondary education, and lowest in higher education. The assumption of 0 < θ ≤ 1 may
capture the fact that, as the actual earning profiles reflect, even highly educated young workers
accumulate more human capital through the post-schooling investment including the acquisitionof skills and experiences in the workplace. Without of loss of generality we assume that θ = 1 .
In order to motivate the intergenerational transfer of human capital, assume that younger
agents inherit a fraction of the average level human capital of agents of the preceding generation,that is,hty+1 = (1 − δ )ht o+1 ,

(2-3)
o

where ht +1 is the average stock of human capital of older agents at period t+1. Note that the1

Empirical estimates of human capital production function indicate that the returns to

private inputs are diminishing (e.g., Heckman (1976) and Haley (1976) ).
6oinitial level of human capital is given by h0 . Children are brought up with better educational
environment in countries with higher average education level of adults. The parameter δ
captures the extent of inheritance of human capital which we set to be zero in order to simplify
the analysis. Investment in human capital may involve the formal education and thepost-schooling education that is made in the workplace to acquire skills and experiences needed
to perform jobs.
A single good can be produced, consumed, accumulated as physical capital. We assume that
all firms are identical and the production in period t requires three inputs: physical capital saved
by individuals of generation t-1, human capital of young workers of generation t, and humancapital of elder workers of generation t-1. Under the constant-returns-to-scale technology, theproduction function at the aggregate level is represented as the following technology:
(2-4)

[

Yt = AKtα (1 − ut ) N t hty] [N h ]βo 1−α − β；t −1 t0 < α < 1,0 < β < 1, A > 0 ，

where Yt is the output of the single good, Kt is the aggregate physical capital stock,(1− ut ) N t hty and N t −1hto are the aggregate efficient unit of time supplied by young and elder
workers, respectively, and A is an exogenous technological parameter. Physical capital fully
depreciates after one period. Competitive firms choose three different kinds of capital so as tomaximize the current profit, taking factor prices as given.
A crucial feature of (2-4) is that human capital of young and elder workers are ‘imperfect
substitutes’. Young workers have a comparative advantage in specializing tasks that theylearned in the school, while elder workers who acquired skills and experiences in the workplace
have a comparative advantage in managing the organization. Empirical evidence supports thenotion that human capital of young and of elder workers are imperfect substitutes. Welch (1979)
estimates that a 10 % increase in cohort size reduced wages of college graduates by 9 % and ofhigh-school students by 4 % on entry into the labor market. Freeman (1979) finds that such amodel could explain the differential change in the relative wages of younger and elder workers
over the period in which the Baby Boom cohort entered the labor market. Murphy and Welch(1992) find that workers with similar ages and education level tend to be substitutes, but thosewith different ages and education levels are complements. Korenman and Newmark (2000),

7

using time-series data on OECD countries, find that an increase in the youth share of theworking age population raises the youth unemployment rate relative to the prime age
unemployment.

3. The Equilibrium in the Balanced Growth PathIn this section we characterize an equilibrium of this economy. Under the assumption thatooindividuals are identical within generations, we will obtain ht = ht in equilibrium. From thisand (2-3), we obtain hte = hto . Letting k t ≡ K t Lt denote the physical capital divided by the
total number of workers, the firm’s profit maximization yields following optimality conditions,
α −1

(3-1)

k 
1 + rt = αA 0t  ht 

(3-2)

k 
w = β A 0t  (1 − ut ) β −1 H (ut ) β −1 (1 + nt ) β −1 (2 + nt )α ,
 ht 

(3-3)

k 
w = (1 − α − β ) A 0t  (1 − ut ) β H (ut ) β (1 + nt ) β (2 + nt )α ,
 ht 

(1 − ut ) β H (ut ) β (1 + nt ) β (2 + nt )α −1 ,

α

y
t

α

0
t

y

o

where rt is the real interest rate, and wt and wt are wage rates of labor supplied by young
and elder workers, respectively.
We now turn to the decision problem of individuals. Each young agent of generation t
receives bequest from his parent, and earns the labor income by supplying 1 − ut units of timein the labor market. The budget constraint of a young individual in period t is

wty (1 − ut )hty + bt = st ,(3-4)

where wt (1 − ut )ht denotes the labor income earned, bt is the bequest that he receives fromyyhis parent, and st is the saved income. When this agent is matured, he earns the labor income
and the interest income from his savings. These earnings are distributed between consumption
and physical bequest to his offspring. Thus, the budget constraint of an old individual in period8t+1 is(1 + rt +1 )st + wto+1hto+1 = ct +1 + (1 + nt +1 )bt +1 ,

(3-5)
o

o

where wt +1ht +1 denotes labor income earned when he is old.
The problem of an individual is to choose ct +1 , ut and bt +1 in order to maximize the utility(2-1), subject to (2-2), (2-8), (2-9), and taking the predetermined variables hte , bt , and factor
prices as given. Keep in mind that agents solve the problem not by taking the relation hte = hto
into account.
(3-6)

The optimality condition for consumption is given by

ct +1 =

(1 + rt +1 )ct.
1+ ρ

Finally, the agent choose the time for investment in human capital to equal the marginal cost
and the marginal benefit of investing one extra unit of time, satisfying
(3-7)

wto+1
w H (ut ) = w (1 − ut ) H ' (ut ) +H ' ( ut ) .
1 + rt +1ytyt

The LHS is the marginal cost of spending extra time on investment in human capital, and isexpressed as the forgone wage, while the RHS is the marginal benefit of that extra time. The
benefit is composed of two terms, that is, the benefit from increasing human capital in the first
period of life and the one in the second period of life.
The equilibrium in the good market implies(3-8)

K t +1 = Yt − Ct .

A competitive equilibrium must satisfy optimality conditions of firms, (3-1), (3-2), (3-3), thoseof households, (3-6), (3-7), the equations of the motion for human capital (2-2), (2-3), and thegood-market-clearing condition (3-8), with the consistency condition ht o = hto , at every period.
An equilibrium in the decentralized economy evolves according to the following
four-dimensional system with four variables {k t , ht , ct , ut } :α −1(3-13)

k 
kt +1(2 + nt )α(1 + nt ) β −1  t =Akt
2 + nt +1
 ht 

9(1 − ut ) β H (ut ) β −ct
2 + nt,(2 + nt +1 )(1 + nt ) kt

α −1

ct +1 αA  kt +1 =
ct 1 + ρ  ht +1 (3-14)(1 − ut +1 ) β H (ut ) β (1 + nt +1 ) β (2 + nt +1 )α −1 ,α(3-15)

β −1
kt +1 αβ A{H (ut ) − (1 − ut ) H ' (ut )}  kt 
(2 + nt )αβ −1
β −1 (1 + nt ),= h  (1 − ut ) H (ut )ht +1(1 − α − β ) H ' (ut )
2
+
n
t +1
 t

and

ht +1
= H (ut ) ,ht(3-16)

where we use new variable ht ≡ hte = hto . By defining new a variable X ≡ k h , we canreduce the system (3-13)-(3-16) to the two-equation system with two variables, X t and ut :(3-17)

X t +1 =αβ A{H (ut ) − (1 − ut ) H ' (ut )} α
(1 + nt ) β −1 (2 + nt )α,X t (1 − ut ) β −1 H (ut ) β −1
(1 − α − β ) H ' (ut )2 + nt +1

and(3-18)

1−

αβ H {(ut +1 ) − (1 − ut +1 ) H ' (ut +1 )}(1 − α − β )(1 − ut +1 ) H ' (ut +1 )=α (2 + nt +1 )(1 + nt )  (1 − α − β )(1 − ut ) H ' (ut )− 1 .
(1 + ρ )(2 + nt ) αβ {H (ut ) − (1 − ut ) H ' (ut )} 

We analyze the equilibrium around a balanced-growth path in which k t , ht , and ct growat the same rate. Substituting ut +1 = ut = u and nt +1 = nt = n into (3-18) and rearranging theterms, we finally obtain(3-19)(1 − α − β )(1 + n)
H (u )=+1.
(1 − u ) H ' (u )β (1 + ρ )The L.H.S. is increasing, and approaches zero as u → 0 and infinity as u → 1 . There exists a
unique value of u in the interval (0,1) satisfying (3-19). It is straightforward to derive thatk t , ht , and ct grow at the same rate. In the balanced-growth path, per-worker output,
per-worker consumption, physical capital, and human capital grow at rate H (u ) , which isincreasing in investment in human capital (e.g., Lucas (1988))).
Our main concern is to investigate a causal link between the labor market aging andper-worker income growth. We obtain the main finding from investigating (3-19). Assuming a
once-and-for-all decline in the population growth rate, the advance of the labor force aging,

10

captured by a decline in the population growth rate, leads to a reduction in investment in humancapital and as a result deters economic growth.
The economic reasoning behind this finding is stark. From (3-2) and (3-3), we obtain the“wage (rate) profile” as(3-21)wow

y=(1 − α − β )(1 + n)(1 − u ) H (u )β,which is increasing in the population growth rate, given u . A rise in the young workers share in
the working population leads to a rise in the relative wage rate of young to elder. Facing it,
young people find it beneficial to invest less in human capital and supply more labor, which
eventually discourages per-capita income growth.2 A decline in the young cohort weakens thepressure for competition for good jobs, which is reflected in the rise in the relative wage rate,
and motivates young people to make less effort to acquire skills for getting future higher salaries.
In the aged society with abundant elder and scarce young, young people take the “myopic”
behavior in investment in human capital due to the adverse incentive effect for earning future
higher salaries.
Rigorously, as suggested by (3-18), this finding comes from a combination of two different
effects. From (3-18) we implicitly derive(3-20)

ut = φ (ut +1; nt , nt +1 ) ,with ∂φ (.) ∂ut +1 > 0 , ∂φ (.) ∂nt > 0 , and ∂φ (.) ∂nt +1 > 0 at ut +1 = ut ≡ u andnt +1 = nt ≡ n . The current and the future population growth rates have positive but different
qualitative effects on the current investment in human capital. In the face of the decline in thecurrent population growth rate, young people find it beneficial to invest less in human capital
because the wage rate of young workers tends to be high, ( ∂φ (.) ∂nt > 0 ). Additionally, in the
expectation of the decline in the future population growth rate, they also find it beneficial toinvest less in human capital because the wage rate of them as elder workers tends to be low,2

The resulting decline in u in response to a decline in n would increase the supply ofyoung human capital, and tends to lead to a rise in wo w y . However, this indirect effect is too
small to offset the direct effect.
11

( ∂φ (.) ∂nt +1 > 0 ). These two effects are reinforcing.
This nature leads to different effects according to whether the demographic shock is either
temporary or persistent, or either anticipated or unanticipated. Consider, for example, the effectof a baby bust (or baby boom) which is captured by a one-time change in the population growthrate. In the face of the decline (or rise) in the current population growth rate, people find it
beneficial to invest less (or more) in human capital, but if they accurately expect this shock to be
temporary, they do not expect the wage rate of them as elder workers to be low (or high), andhence the adverse effect is limited. When the shock is persistent, the effect is greater to theextent that the shock is anticipated, while when the shock is temporary, the effect is conversely
greater to the extent that the shock is unanticipated.
Literally interpreting the model, the level of human capital of young workers should begreater than that of elder workers. The determinants of the relative magnitude are more complex.
For one thing, it depends on the value of δ , the extent of inheritance of human capital(equation(2-3)), and for another thing, on the effect of the adoption of new technology on thequality of the existing human capital. A drastic technological change might make the humancapital of elder workers rapidly obsolete (e.g. Hobjn and Jovanovich (2001)).
One may wonder whether the positive link between population and economic growththrough the labor market channel is dependent entirely on the fact that the cross-partial
derivative between young and old human capital is positive, as is keen in the Cobb-Douglas
production function. In order to see the robustness of the main finding, we examine a moregeneral production function. In doing so, we consider the following quasi-CES production
function;(3-22)1−α1−σ1−σ  1−σ
1−α − β o
 β(1 − ut )hty N t+
Yt = AK t 
ht N t −1  , σ ≥ 0 .
1−α
1 − α


α

[

]

[

]

where σ , the reciprocal of the elasticity of substitution between young and elder workers,
represents the degree of substitutability.3 A smaller σ implies stronger substitutability, which
may correspond to Angle-Saxon countries. Except for the case that σ approaches 0, young and3σin (4-1) is equal to 1-γ

in the production function given in footnote 10.
12elder human capital are imperfect substitutes, including two special cases: when σ → 1 , theCobb-Douglas case as in (2-4) and when σ → +∞ , a fixed-proportions technology between
two types of workers.
Note that the cross-partial derivative between young and old human capital may be positiveor negative, depending on the sign of (σ − α ) , such that
(3-23)1−σ
1−σ
Aβ (1 − α − β )∂ 2Yt= (σ − α )(1 − ut )hty N t
hto N t −1yo
∂ (1 − ut )ht N t ∂ ht N t −1
1−α

{

}{

[

}

] [

1−α

1−σ
1−σ 1−σ
1−α − β o
 βht N t −1 
(1 − ut )hty N t*+1−α1 − α


[

]

[

]

]

−1

4

With the production function given by (3-22), however, we derive the counterpart of (3-12) as(3-24)(1 − α − β )(1 + n)σH (u )=+1.
(1 − u )σ H ' (u )β (1 + ρ )We obtain two remarkable features. First, when σ approaches 0, u is independent of n .
The positive link between population and economic growth through the labor market channel
disappears when young and elder workers are perfect substitutes. Secondly, unless σ = 0
holds, u is always increasing in n , irrespective of the sign of the cross-partial derivative. The
labor market channel works so long as human capital of young and elder are not perfect
substitutes.
Equation (3-23) represents that a decrease in the young workers relative to elder workers(i.e., aging in the labor force) reduces the marginal productivity of elder workers when σ > α ,while it raises the marginal productivity of elder workers when σ < α .

However, we canshow that the relative wage rate w y w o is inversely related to the population growth rateirrespective of the sign of the cross-partial derivative. This implies that the sign of thecross-partial derivative sign may have an effect but is not a dominant factor to derive thepositive link.
Contrary to the prediction of the standard neoclassical growth theory, an increase inpopulation growth promotes economic growth. Srinivasan and Robinson (1997, p1268) argue

4

It is immediate that the sign of cross-partial derivative is always positive for the standard

CES case.
13

the positive correlation by assuming that the growth of per-capita human capital is an increasing
function of the growth of the aggregate employment. Our model can be interpreted to provide
one micro-foundation behind their setting. Jones (1998) constructs a R&D-based growth modelin which a more populous economy leads to a richer economy by focusing on the nonrivalrous
nature of ideas. The economic implication can be reconciled with that of the R&D-based growthmodel in its spirit. New ideas, inventions, and new methods for improving productivity could be
more produced in a society where young are so vigorous that they devote more resource ininvesting themselves.

4. Empirical Evidence
In the theoretical part we developed a theoretical mechanism behind which a decline in theshare of young workers in the working population deters the subsequent growth of per-worker
income. The purpose of this section is to investigate whether the cross-country data will support
our hypothesis. Before proceeding to the estimation, we state data used in the regressions.
For the measure capturing the young’s incentive effect of investing in themselves, we use
the population share of each age group in the total working population, which is available froman International Labor Office database (web site; http://laborsta.ilo.org/). Let ACTxxyy denotethe population share of workers aged xx to yy at the starting year. In dividing the working
population into the two age groups, let ACT2544 denote the share of young workers and let
ACT45OVER denote the share of elder workers in the working population. A decline in thevalue of ACT2544 than the previous decade will, for example, capture the advance of the labor
force aging. The coefficient of ACT2544 is expected to be positive, and that of ACT45OVER
be negative. Following the theoretical finding, if the labor markets are well organized in thelisted countries, the relative wage of young to elder workers might be a better measure. But we
do not use this approach for two reasons. First, data on wage distribution by ages is available
only for small countries. Second, various distortions and regulations inherent in the labormarkets may prevent the increased competition in the workplace from being reflected in wages.
Even if data on the relative wage is available, the possible simultaneity problem between

14

economic growth and the relative wage could make it necessary to explore appropriate
instruments. As the theoretical finding points out, the share of each age group in the total
working population could become a good candidate for instruments.
Additionally, as another aging variable, we use the population share of the total population
aged 14 and under at the starting year, denoted POP14. While ACTxxyy is meant to capture theeffect of the size of the current generation on investment in human capital, POP14 is meant tocapture the effect of the size of the next generation on investment of the current generation. The
coefficient of POP14 is expected to be positive.
We conduct cross-country growth regressions using OLS estimates with the pooled data forOECD countries. Our sample includes 22 countries and 4 periods, 1965-1974, 1975-1984,
1985-1994, and 1995-2003.
We begin by regressing per worker GDP growth (GROWTH) on the log of initial per
worker GDP level (GDP) and the initial stock of human capital variable (HUMAN). Notice that
the GDP variables are measured in terms of per worker term, but not of per capita term. This isintended to eliminate the possible effect of demographic transition coming from an increasing
ratio of the working to the non-working people. The stock of human capital is measured by theaverage years of school attainment at secondary and higher levels of a population group aged 15
and older. The school-attainment data are available from the web site of Center for International
Development at Harvard University (web site;
http://www.cid.harvard.edu/ciddata/ciddata.html.)
In column 1 of Table 1, we present the simple regression. The initial level of per worker
income is negative and significant, and the initial stock of human capital is positive but
insignificant. We control for decade dummies distinguishing between four periods, 1975-1984,
1985-1994, 1995-2003 all the regressions. Numbers in parentheses are based on the White’sheteroscedasticity-consistent covariance matrix in all the regressions.
In column 2 we add the aging variable ACT2544. ACT2544 is positive and significant. Thisfinding shows that the greater is the population share of workers aged 25 to 44, the higher is thesubsequent per-worker GDP growth, which is consistent with our theoretical finding. The
human capital variable is positive and significant at 10% level. We tried other school attainment

15

variables, including ratios of school attainment at secondary and higher levels and average yearsof school attainment at higher level. The finding is robust in using any of human capitalvariables listed here.
In column 3 we add another aging variable POP14. POP14 is positive and significant at
about 10% level. There emerges a positive effect of a size of the next generation on thesubsequent growth, as will be suggested by the theoretical finding. A decreased number ofchildren can lead to a decline in economic growth.

We regressed the human capital variable on the possible its determinants, including
ACT2544, POP14, and GDP, but none of them except for GDP was significant.

In column 4 we check the robustness by controlling for two demographic variables, thepopulation growth rate, denoted by POPG, and the growth rate of the working population,
denoted by WOKG. The result remains unchanged even controlling for these variables. The
coefficient of ACT2544 is 0.081, which implies that one percent change in the population shareof workers aged 24 to 44 leads to a change in the annual growth rate of about 0.08%.
In column 5 we replace ACT2544 by ACT45over. ACT45OVER is negative and significant.
The interpretation needs comments. As the theory suggests, an increased size of elder workers
can have a negative impact on investment in human capital by young people because it weakens
the young’s incentive for human capital through the route of a looser wage profile. An increased
size of elder workers who are less able to have access to new knowledge and technology has anegative effect on the subsequent growth. Anyway, this finding may support our theoretical
hypothesis that young human capital contributes more to growth than elder onr.
In column 6 through 12, we use the aging variable covering the 10 year interval, including
ACT2534, ACT3544, ACT4554, ACT5564, and ACT65OVER, respectively. ACT2534 ispositive and significant, neither ACT3544 nor ACT4554 is significant, and ACT55OVER is
negative and may be significant. An important finding is that people seem to accumulate morehuman capital in the former half period of age 25-44 than the latter one. Many papers in thelabor economics report that wages increase most rapidly in the first 10 years after school

16

education (e.g. Mincer, and others). This finding suggests that the effect of human capital on
growth arise not only through formal education, but also through trainings and educations in theworkplace.
The results show that as age gets older, the contribution to the subsequent growth is smaller,
and is even negative beyond 45. This finding also suggests that our age variables do not capture
the demand effect because, if the positive coefficient of ACT2544 captures the consumption
boom in the middle age, the coefficient of ACT3544 should be strongly positive.
Some readers might wonder if the positive and significant coefficients of ACT2544 or
ACT2534 may simply capture a high proportion of workers who are earning growing salaries.
Note that that effect, if it exists, is the effect of demographic transition that does not last long for
any one country. Kotlikoff and Gokhale (1992) find evidence showing that the laborproductivity grows until forties in the U.S. data.
In order to provide more persuasive interpretation on the above finding, we explore analternative measure that will influence the young’s incentive for increasing human capital andmay complement ACT2544 or ACT2534.
We use an “unemployment rate” as another variable to capture the young’s incentive effect,
although there never emerges unemployment in the theoretical model. In recent decades, inmany OECD countries young people face difficulty in finding jobs. The unemployment rate ofyoung workers is far higher than the country’s average in many OECD countries. Although thehigh unemployment rate may be a result of economic stagnation, it is conversely expected toplay a disciplinary role in inducing young people to invent in themselves for good jobs,
following the notion of the efficiency wage hypothesis (e.g. Shapiro and Stiglitz (1984) and
Akerlof and Yellen (1981)).
Before proceeding to the main regression, we check the correlation between the school
enrollment rate and the unemployment rate in order to examine whether the unemployment rate
can be used for the variable capturing the incentive effect. Table X shows the results. In column
1(equation 10), the coefficient of UR is positive and significant. This result suggests that a highunemployment rate tends to work to play a disciplinary for young people in spending more timeon education. In column 2(equation11), the coefficient of ACT2544 is also positive and17significant. These two finding jointly suggest that, ACT2544 and UR are both variables that
capture the young’s incentive for investing in human capital and may complement with eachother.
In Figure Y we report the result of the growth regression. In column 1(column17) the
coefficient of UR is positive and weekly significant. In column 2(equation19), ACT2544 andPOP14 enter as additional variables. The coefficient of UR is again positive and weekly
significant. ACT2544 and POP14 remain positive and significant, but the sensitivity of
ACT2544 declines by including UR. This result may reflect the complementary role of UR andACT2544 in the regression. In column 3 through 6, aging variable covering the 10 year interval
enters, jointly with UR. The result of each aging variable remains unchanged by including UR.
Note that when the coefficient of the aging variable is insignificant or negative, the statisticalsignificance of UR increases. For example, in column 5 (equation23), the coefficient of UR issignificant. The overall result is consistent with the hypothesis that ACT2544 and UR are bothvariables that capture the young’s incentive for investing in human capital.
Figure 2 illustrates the time series of the population share of workers age 25 to 34 in the
average of OECD countries, Japan, U.S.A, and the average of European countries. Except forJapan, the population share of workers age 25 to 34 increase over time. Surprisingly, even in
Europe, it increases up to 1990s although the aging population advances in many of European
countries. Migration might explain this seemingly contradictory observation.
The behavior of labor migration can become an instrument to identify a theoreticalmechanism through which the labor force aging influences economic growth. If the positivecoefficient of the share of young age group only captures a high proportion of workers whoselabor productivity grows faster, the inflow of migration could lead to a slowdown of economic
growth because it deteriorate the average level of human capital. On the other hand, if it
captures the “incentive effect”, the inflow of migration can be consistent with promoting
economic growth. The evidence in Europe may suggest the latter channel.
The empirical finding may have a few comments on the “Lost Decade” in Japan. At 1990,
ACT2534, ACT3544, ACT4554, ACT5564, and ACT65OVER are 19.2%, 25.0%, 21.9%,
14.7%, and 5.8%, while those of the average values in OECD countries are 27.1%, 25.2%,

18

18.4%, 9.7%, and 1.8%&, respectively. The age distribution in Japan is obviously skewed toelder ages. Compared to the average, the smaller share of workers aged 25 to 34 leads to a
decline in the annual per worker growth rate by (27.1%-19.1%)×0.111=0.89%, and moreover
the greater share of workers aged 55 to 64 may leads to a decline in the annual per worker
growth rate by (14.7%-9.7%)×0.069=0.35%. These figures reveal that the skewed age
distribution in the labor market can explain significant part of sources of the lost decade.
Finally, we report the prediction of per worker GDP growth in the feature although theestimation is made based on the regression in earlier version and so a little different fromfigures of the results here. Table 2 provides the result. It reports that Greece, Portugal, andSpain will experience relatively high growth in per worker GDP, while the growth rate in the
United States will decline over the next two decades in statistically significant levels. The
growth rate for 2010-2020 will be smaller than the one for 2000-2010 in all countries except for
Ireland.

5. Discussion
Departure from the “Age-Dependent” Society
Thus far we have argued on the premise that the society is highly “age-dependent”. In thissection we relax this restriction by allowing for elder workers to compete with young workers in
the labor market.
We have assumed that all the agents get promoted when they are old. However, this situation
is not true in the actual society, and pronounced in the aged society with a greater number of
elder workers relative to young workers. In the actual labor market some elder workers have tocompete with young workers. In order to capture this situation, assume that any of young
workers is employed as a skilled worker with the probability π when he or she is old. It turns
out that the remaining fraction 1- π of old agents fails in promotion and remain to be employed
as unskilled.
The promotion probability π is supposed to depend on several factors, including firm
growth, nature of internal organization, and demographic factors. In terms of the concern in thispaper, the relationship between the population growth and the promotion probability may be

19worthwhile investigating. For example, an agent of a baby boom generation may evaluate theirpromotion probability to be low because they find themselves to face severe competitiveenvironments for promotion. Although we admit the possible impact of the demographic factors
on the promotion rate, their links are supposed to be complicated. Thus we investigate the effectof the “exogenous” change in the promotion rate on the aggregate economy and pursue
implications of the effect of the aged society.
In order to focus on the effects of a change in the mobility of the labor market, we abstractfrom the effects of uncertainty about the future wage income. Consider the existence of life
insurance companies that behave competitively. With the assumption that administrate costs percontract are negligible, payments are made on an actuarially fair basis. Letting w t+1 denote thewage rate that agents receive in the second period of life, we obtain w t +1 = πwt +1 + (1 − π ) wt +1 .
oyInvestment in human capital is eventually determined to satisfy(4-1)(1 + ρ ) β H (u )= (1 − α − β )(1 + n)(1 − u ) + (1 − α )(1 − π ) .
H ' (u )Compared to (3-20), you will find that the marginal effect of a change in the population growthrate on investment in human capital is qualitatively the same irrespective of the promotion
probability.
We are now ready to investigating the effect of a change in the promotion probability on theinvestment in human capital. There are potentially offsetting effects of a rise in the promotion
probability. On one hand, a rise in the promotion probability tends to encourage young people toinvest in human capital. On the other hand, it tends to increase a population share of skilled
relative to unskilled workers, driving down the relative wage rate of elder workers, whichconversely tends to provide a disincentive for them to invest in human capital. A simple
calculation of (4-1) implies that the latter effect always dominates the former effect; the more
severe is the competition among workers of different generations in the sense that people finddifficulty in getting promotion, the faster the economy grows. When Confucianism is dominant,the elder are respected, and the occupational position is “age-dependent”, the economy tends tobe stagnant.
We are now in a position to discuss the indirect effect of an advance in the labor force aging

20

through the change in the promotion probability. An agent of a baby bust generation, in the
faced of the less competitive environment for promotion, may invest less in human capital. If he
expects that the baby bust will go on until the next generation, he may conversely expect thathis promotion probability is low because the organization to which he belongs is predicted toshrink. However, if the promotion probability has inertia as the efficiency wage hypothesis
suggests, he may evaluate his promotion probability not to decline so much. When the
promotion probability does not decline even in the aged society, investment in human capitaldeclines and the economic growth goes down.5

Migration and Economic Growth
Typical human-capital-based growth models could predict a negative impact of labor
migration on economic growth. Migrant workers tend to possess the lower level of humancapital than people of the host country, and so the inflow of migration could deteriorate theaverage level of human capital and deter economic growth of the host country (e.g., Lucas(1988))The developed model provides an alternative channel through which migration influences
economic growth. Assume that there is a once-and-for-all flow of migration of young workers
with the size of mN t to the host country at each period t. Migrants are endowed with σht unitsyof human capital and have access to the technology available in the host country. Empiricalobservation shows that in the U.S. the average skill of migrant workers is less than that ofdomestic workers. Typically, we have in mind the case for σ < 1 . They work as unskilledworkers in the first period of life and consume in the second period of life. The preference of the
migrant worker is given by Vt = ρ log ct +1 + ρ (1 + n m )Vt +1 , where n is the population growthmrate of the migrant worker. For analytical simplicity, migrant workers are assumed to go back totheir home country after two periods and die.
Here the sum of human capital supplied by domestic young workers and migrant workers is

5

Ariga et al(1992) and Brunello et al(1995) investigate the relationship among corporate

hierarchy, promotion, and firm growth from the prospect of incentive approach.
21(1 − ut ) N t hty + σmN t hty . Wage rates are given by
α

(4-2)

k 
β −1
β −1
w = βA ot  (1 + σm − ut ) (1 + n ) (2 + n)α ,
h
 t 

(4-3)

k 
β
β
w = (1 − α − β )A ot  (1 + σm − ut ) (1 + n ) (2 + n)α .
 ht 

y
t

α

o
t

Investment in human capital is eventually determined to satisfy

βH (u )= (1 + n)(1 − α − β )(1 + σm − u ) .
ρH ' (u )(4-4)

An increase in the migration, captured by an increase in m, raises investment in human capitalmade by people of the host country, which eventually promotes economic growth. As will
typically be the case, the migration increases the labor supply of unskilled workers relative toskilled workers, driving down the wage rate of young workers, which in turn provides an
incentive for the domestic young agents to invest more in human capital. The change in theshare of unskilled workers as the total working population in the host country, on the one hand,
gives the short-run negative externality to young workers of the host country through the change
in the relative wages, but on the other hand gives the long-run positive externality through theenhancement of growth.6
Labor migration tends to deteriorate the average level of human capital, but enhances
economic growth. This finding is contrasted with several human-capital-based growth theories
that take the average level of human capital as an engine of economic growth (e.g., Lucas(1988)).

6

We obtain the same qualitative result assuming that there is a one time labor migrationand migrant workers live in the host country. Then the growth rate of the migrants should be thesame as the one of the host country.
22

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23

Manuscript. Stanford University.
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Kremer, Michael., (1993), “Population Growth and Technological Change: One Million B.C. to1990,” Quarterly Journal of Economics , 681-716.
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Mankiw, N. Gregory, David Romer, and David N. Weil, (1992), “A Contribution to the
Empirics of Economic Growth,” Quarterly Journal of Economics, 107,407-37.
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24

Figure 1-a: Share of workers aged 20-39 to all workers(G7-countries)

0.6
0.55

1960
1970
1980
1990
2000
2010

0.5
0.45
0.4
0.35
CanadaFranceGermany

Italy

Japan

UK

Figure 1-b: Share of workers aged 20-39 to all workers

USA(OECD countries)

0.65
0.6
1960
1970
1980
1990
2000
2010

0.55
0.5
0.45
0.4
0.35
Australia Austria

Belgium Denmark

Finland25

GreeceIceland

IrelandFigure 1-c: Share of workers aged 20-39 to all workers(OECD countries)

0.6
0.55

1960
1970
1980
1990
2000
2010

0.5
0.45
0.4
0.35

Luxembourg Netherlands New
NorwayZealandFigure 2

Portugal

Spain

SwedenSwitzerland

Share of workers aged 25-34

30.0%

25.0%

1970
1980
1990

20.0%

15.0%

10.0%

5.0%

0.0%
AVERAGE

JAPAN

USA

26

EUROPE

Table 1: Growth and Labor Force Aging
Dependent variable: Per worker GDP growth
1

2

3

4

5

6

1.397

1.381

1.376

1.176

1.422

1.393

(29.08)(35.97)(35.58)(5.585)(32.79)(28.42)log of initial income per-0.036-0.038-0.039-0.037-0.037-0.037

worker (GDP)(-7.377)(-10.36) (-10.56) (-8.916)(-8.649)(-7.050)

secondary and higher

0.001

0.002

0.002

0.001

0.001

0.001

schooling years(HUMAN(0.981)(1.784)(1.640)(1.443)(0.879)(0.856)

share of workers aged

0.096

0.090

0.081

25-44(ACT2544)(3.221)(3.003)(2.731)constant

share of workers aged 45-0.082and over (ACT45OVER)(-3.463)

share of workers aged

0.019

15-24(ACT1524)(0.337)

share of population aged

0.029

0.029

0.038

0.034

0-14(POP14)(1.617)(1.624)(1.819)(1.094)

0.590

Population growth(POPG(0.217)working population-0.4030.002

growth (WOKG)(-1.715)(0.045)no. of observations

88

88

88

88

88

88

Adj. R2

0.637

0.681

0.684

0.692

0.688

0.640

Note: Each data is pooled decade for four periods: 1960-1970, 1970-1980, 1980-1990, and1990-2000. Numbers in parentheses are t-values based on the White’sheteroscedasticity-consistent covariance matrix. Results for decade dummies are deleted.

27

Table 1: Growth and Labor Force Aging (Continued)
Dependent variable: Per worker GDP growth
7

8

9

10

11

12

1.397

1.381

1.376

1.176

1.422

1.406

(35.47)(35.97)(35.58)(5.585)(31.25)(35.65)log of initial income per-0.040-0.038-0.039-0.037-0.040-0.039worker (GDP)(-90910)(-10.36) (-10.56)(-8.916)(-8.779)(-9.616)secondary and higher

0.001

0.001

0.000

0.001

0.001

0.001

schooling years(HUMAN(1.622)(1.178)(0.370)(0.978)(1.287)(1.489)share of workers aged

0.143

0.111

25-34(ACT2534)(4.443)(2.731)constant

share of workers aged

0.108

35-44(ACT3544)(1.225)

share of workers aged

-0.11145-54(ACT4554)(-1.754)

share of workers aged

-1.319-0.06955-64(ACT5564)(-3.396)(-1.485)

share of workers aged 65-1.233and over(ACT65OVER)(-1.652)

share of population aged

0.028

0.036

0.044

0.037

0.036

0.034

0-14(POP14)(1.502)(1.857)(1.979)(1.836)(1.778)(1.094)

no. of observations

88

88

88

88

88

88

Adj. R2

0.685

0.661

0.662

0.671

0.653

0.687

Note: Each data is pooled decade for four periods: 1960-1970, 1970-1980, 1980-1990, and1990-2000. Numbers in parentheses are t-values based on the White’sheteroscedasticity-consistent covariance matrix. Results for decade dummies are deleted.

28

Table 2: Estimation of Per Worker GDP Growth for 2000-2010 and 2010-2020
GDP per worker

1990-2000

2000-20102010-2020(Estimated)(Estimated)

2.36%

0.42%

0.08%

(0.735)(-0.344)(0.221)

1.32%

1.01%

-0.42%(-0.299)(0.304)(-0.686)

1.15%

1.21%

0.13%

(-0.464)(0.522)(0.308)

1.28%

0.19%

-0.30%(-0.335)(-0.607)(-0.471)

2.01%

0.20%

-0.56%(0.391)(-0.592)(-0.933)

1.59%

0.27%

0.06%

(-0.025)(-0.520)(0.184)

0.79%

1.14%

0.32%

(-0.831)(0.447)(0.648)

1.14%

1.03%

-0.32%(-0.474)(0.326)(-0.504)

1.40%

2.58%

1.15%

(-0.222)(2.039)(2.127)

1.45%

0.37%

0.00%

(-0.170)(-0.402)(0.070)

4.39%

0.37%

0.45%

(2.769)(-0.401)(0.881)

0.79%

1.07%

-0.25%(-0.829)(0.371)(-0.377)

growthAustralia

Austria

Belgium

CanadaDenmark

FinlandFranceGermany

GreeceIceland

IrelandItaly

29

Japan

0.61%

0.96%

0.50%

(-1.006)(0.246)(0.959)4.15%-1.57%-1.24%(2.524)(-2.556)(-2.148)

2.00%

0.88%

-0.29%(0.385)(0.156)(-0.458)

1.12%

1.27%

0.14%

(-0.500)(0.598)(0.317)

2.44%

0.10%

-0.55%(0.820)(-0.708)(-0.913)

1.94%

2.40%

1.09%

(0.321)(1.842)(2.033)

1.28%

2.21%

0.62%

(-0.341)(1.631)(1.173)

1.01%

0.51%

-0.06%(-0.607)(-0.254)(-0.044)-0.26%

0.17%-0.70%(-1.870)(-0.624)(-1.193)

1.63%

0.86%

-0.02%(0.014)(0.136)(0.039)1.63%-0.72%-0.73%(0.015)(-1.612)(-1.235)

Average

1.62%

0.73%

-0.04%

Standard Deviation

0.010

0.009

0.006

Luxembourg

Netherlands

New Zealand

NorwayPortugal

Spain

SwedenSwitzerland

United Kingdom

United States

Note: Numbers in parentheses are normalized values of which mean is zero and standard
deviation is one, which represents how significant these values are from each decade averagevalue.

3031