Is Aomori’s Declining Demographic Trend Bad News?
Hidetaka Kawano∗
School of Management and Economics
Aomori Public College

Hiroshi Ohta†
School of International Politics, Economics and Communication
Aoyama Gakuin University
For Presentation at the 50th Annual Meeting of the Japan Section of
the Regional Science Association International,
University of Tokushima.

October 12, 2013
1

Introduction

income will decline.
These simulation results also imply thatthe demographic outﬂow of the population out
The government agency reported this Marchof Aomori prefecture will result in an increasethat the demographic trend in Aomori Prein the per capita income of the remaining popfecture will be a decline by about 30 percent
ulation. Voting with your feet may beneﬁtof the current population by the year 2040
not only the people leaving the prefecture, but(of Population and Research, 2013). The realso the people who have decided to remain
action of the general public in Aomori to thethere.
report is pessimistic about the future state of
For the empirical characterization, calibrathe economy. Our reaction, however, is moretion is achieved through the use of year 2000
optimistic than pessimistic by comparison.
In this paper, we have estimated the economy- Aomori’s 13-sector input-output data (Kikaku
Seisaku Tokei Bunsekika, 2005). The modelwide eﬀects of the 30 percent decline of theclosure assumes a small open economy withcurrent population in Aomori Prefecture, in
free capital inﬂow and outﬂow, so that the balthe framework of a multi-sector applied genance of payments is balanced. In this way, theeral equilibrium model (AGE).
original input-output data was used without
With the use of year 2000 Aomori inputmodiﬁcation.
output data, the major simulation results of
A crucial step in the empirical characterthe 30 percent decline of the current populaization of an AGE is calibration, deﬁned astion lead to the following conclusions: 1) the“the requirement that the entire model specAomori prefecture will have an increasingly
iﬁcation be capable of generating a base-year
higher relative wage rate; 2) all the sectors,
equilibrium observation as a model solution”
above all, the agricultural sector, will turn out(Shoven and Whalley, 1992). An AGE model
to be increasingly more capital-intensive, andis a very powerful framework for analysis of
the economy-wide capital-labor ratio will inpolicy reforms that could be instituted for Pareto
crease; 3) labor productivity (relative marginal
improvements in the current state of the econproduct of labor) will increase with the highomy. An important development since Scarf
capital-labor ratios in all sectors; 4) per capita(1967) has been the use of observed data, suchincome will increase, although the aggregateas an input-output table, in developing an AGE
model.
The solution procedure for coding the model
follows Shoven and Whalley (1992) by reducing the dimensionality of the solution space
to the number of factors of production in thisgeneral equilibrium structure. The solution algorithm used for calibration is a ﬁxed-point algorithm originally developed by Kimbell andHarrison (1986) and modiﬁed by Kawano (2003).
In his recent paper (Kawano, 2006, 2013), four
alternative ﬁxed point algorithms were compared. Among the four alternatives, the modiﬁed Kimbell-Harrison approach was shown tobe the best for an AGE modeling.
These experiments were programmed in Clanguage, and conducted on the GCC version
4.0.1 compiler (Apple Computer, Inc.). The
veriﬁed reliability of the simulation results indouble precision (1.0e-15). The converged equilibrium values in this benchmark model wereobtained through 66 iterations over the entire
model.
In the full paper, Section 2 reviews themain features of an AGE model. Section 3
reviews the major simulation results of the 30
percent decline of the current population in
Aomori-prefecture. In section 4, policy implications are presented. The conclusion follows
in section 5.

2

2.1

tors, shown by subscript i ∈ I = {0, ..., 12},and two ﬁnal consumption commodities Xi∈I .
The use of intermediate goods in production
activities shows that total output Qi∈I in sector i will go partly to meet domestic household consumption demand Xi∈I , external sector consumption ESi∈I , and also intermediate input demand qij for production of goodsj ∈ J = {0, ..., 12}. The production activities of ﬁrms include intermediate goods Qj∈J
supplied through output markets. The usual
primary factors of production are capital Ki∈I
and labor Li∈I . As in the Leontief system, intermediate inputs are required as a ﬁxed proportion of the total output Qi∈I . The inputoutput coeﬃcients aij are deﬁned as:aij ≡The model was kept very simple. The supply side of a theoretical general equilibrium
model is made more empirically plausible byincorporating the Leontief type input-output
accounting data. An important step in building an empirical model is to incorporate ﬂow ofintermediate goods into the model structure.
The ﬂow of intermediate goods among diﬀerent sectors is built into the model as part ofproduction activity in the economy
The model is simple and has only 13 sec-

∀ i ∈ I, j ∈ J,

(1)

where
aij := input-output coeﬃcient for commodity i used
as an intermediate good to produce one unitof commodity j
qij := amount of good i used as an intermediate
input for production of good j,
Qj := output in industry j.

2.2

The Demand Side of the Model

The level of disposable income for a representative consumer is determined by factor endowments, factor prices, and external ﬁnance.
The disposable income Y is:

The Underlying Theoretical
Structure of the AGE model
The Main Features of the Model

qij
,
Qj

Y = wL̄ + rK̄ + EF,

(2)

where
w := wage rate,
r := rental rate,L̄ := labor endowment,K̄ := capital endowment,
EF := external ﬁnance.
We assume a simple Cobb-Douglas utility function U (.) as a representation of consumer preference. The function is:
θi
U (X0 , ..., X12 ) = Π12
i=0 Xi ,∵0 < θi < 12,

1
∑
i=0

θi = 1,(3)∀ i ∈ I.

The ﬁnal demand for commodities Xi∈I is derived by the utility maximization for a representative consumer as:
Xi =

θi Y
,
pi

∀ i ∈ I,

(4)

where
θi∈I := share parameter in utility function,
pi := price of commodity.

2.3

The Production Side of the Model

2) The per unit labor demand function is:()−αi ( )
1
αi
w −αi
li =
,
∀ i ∈ I.
Φi 1 − αi
r
(8)

2.4

Zero Profit Conditions

Perfectly competitive behavior in producers will imply zero proﬁt conditions. Zero proﬁt
conditions for the two producers with intermediate goods are modeled as: For the producer
in sector i ∈ I,∑
aij pj + rki + wli ,∀ i ∈ I, (9)pi =The production function with intermediate inputs is modeled as:)(j∈J
q0j q1j∀ j ∈ J,
Qj = min,, V Aj ,a0j a1jwhere(5)ki := capital employed for per unit production
whereof commodity i ∈ I,
Qj := commodity j ∈ J produced,
li := labor employed for per unit production of
V Ai := value-added component of productioncommodity i ∈ I.
function j ∈ J.
Rewrite equations (9) in matrix as:
The value-added component V Aj∈J of production function j ∈ J is modeled as Cobb(I − AT )P = W.
(10)
Douglas which allows the substitution possiSolve for P as:
bility between primary factors: capital Kj andlabor Lj . The value-added component V Aj is
P = (I − AT )−1 W.
(11)speciﬁed as:
V Ai ≡ Φi Ki αi Li 1−αi , ∵ 0 < αi < 1,

∀ i ∈ I,(6)

2.5

Market Clearing Conditions

The total output Qi∈I of commodity in
where
sector i ∈ I is met by the total intermediate in∑αi∈I := factor share parameter in valueput demand j∈J qij , domestic consumption
added component of production function,
demand Xi∈I , and external consumption deΦi∈I := shift parameter in value-added
mand ESi∈I as:
component of production function,∑
Ki∈I := capital employed in sector i ∈ I,
Qi =qij + Xi + ESi , ∀ i ∈ I.
(12)
j∈J
Li∈I := labor employed in sector i ∈ I.
The conditional factor demand functions
can be derived by assuming no intermediate
goods are needed in the model, since a ﬁxed
proportion of the total output Qi does not affect the ﬁrst order conditions of the producers’
cost minimization.
1) The per unit capital demand function is:
ki =

1
Φi

(

)1−αi ( )αiw 1−αi,1 − αir∀ i ∈ I.
(7)

By equation (1), qij = aij Qj . Rewrite equation (12) as:∑Qi =aij Qj + Xi + ESi , ∀ i ∈ I. (13)j∈JFurther rewrite equation (13) in matrix as:(I − A)Q = X + ES.

(14)

Solve for Q as:
Q = (I − A)−1 (X + ES).

(15)

3

Simulation Results

With the use of year 2000 Aomori’s inputoutput data, the major simulation results of
the 30 percent decline of the current population lead to the following conclusions: 1)
the relative wage rate w/r increases by 50.1%;
2) all the sectors, above all, the agricultural
sector, will turn out to be increasingly more
capital-intensive, 13.2 than the bechmark, which
stands out. The capital-labor ratios in all sectors increase by 50.1%,and the economy-wide
capital-labor ratio will increase by 42.9 %; 3)
labor productivity (relative marginal productof labor) will increase by 50.1% with the highcapital-labor ratios in all sectors; 4) per capita
income will increase 0.85%, although the aggregate income will decline by 29.4%.

4

Policy Implications

In this rapid demographic outﬂow of the
Aomori prefecture population, the local government must ﬁrst consider the characteristic features that both private companies andAomori-prefecture herself need to survive: a
ﬂexible labor market. The central governmentof Japan must help devise “the most ﬂexible
labor market in the world” which would allow local governments all over Japan to act
on their own initiatives to adjust to the constantly changing economic environment. If that
happens, then the above simulation scenario
will come true. Once this ﬂexible labor market is instituted nationwide, then it will enable
workers to move easily from one prefecture toanother. With this government initiative, private ﬁrms can hire and ﬁre employees with relative ease, which is crucial for giving renewed
vitality to the whole economy of Japan, andespecially Aomori.
Domestic local economies need to adjust
them- selves to the changing environment. One
loses one’s job in one place in one day. One canget another job in another place the follow- ingday. In a world of fast changing environments,

one should be prepared to move from one place
to another, which is exactly what “Voting withyour feet” means. At the same time, private
ﬁrms have more incentive to hire employees,
because they can easily ﬁre employees if they
engage actively in unraveling any mismatch
between employees and ﬁrms.
The ideal environment of the economy inwhich the most private ﬁrm operates must be
highly competitive, where “Schumpeterian Creative Destruction” is at work. If more ﬂexible
local labor markets are instituted nationwide
by the central government, a local market like
Aomori will be bound to thrive.
If, on the contrary, the labor markets in
Aomori remain stagnant, and do not strive
for more ﬂexibility, this stagnation will continue to be reﬂected in the economy, much ofwhich Japan has experienced for more than
two decades. What is crucial for the thriving
economy is the functioning of both factor andproduct markets. Private ﬁrms and even thecentral government as well as many local governments at all levels must stand on their own.
Any form of government-subsidized organizations, cartels, and monopolies need to be eliminated, which is also of paramount importanceto the reduction of the enormous public debts
accumulated over the years. Limited resourcesin the economy must be used eﬀectively.

5

Conclusion

In this paper, we have estimated the economywide eﬀects of the 30 percent decline of thecurrent population in Aomori Prefecture, inthe framework of a multi-sector AGE model.
The simulation results show that the pessimistic
reaction of general public in Aomori to thegovernment agency report of a decline by about
30 percent of the current population are unwarranted. The key policy question should be
how more competitive and ﬂexible productfactor markets, especially the labor market,
can be facilitated to improve the future of theeconomy in Aomori.

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