Will a Declining Population Trend in Aomori-Prefecture
Worsen the Economic Welfare?
Hidetaka Kawano∗
School of Management and Economics
Aomori Public University

October 11, 2015

Abstract
The National Institute of Population and Social Security Research reported in March, 2014 that thedemographic trend in Aomori Prefecture will be a decline by about 30 percent of the current populationby the year 2040. In Aomori, the reaction of the general public to the report seems to be pessimistic
about the future state of the economy. My own intuitive reaction, however, seems to be encouraging. In
this paper, I have estimated the economy-wide eﬀects of a 30 percent decline in the current populationof Aomori Prefecture, in the framework of a 13-sector applied general equilibrium model. In addition
to the above simulation, I have also reduced the capital endowment by 30 percent, together with the
reduction in the labor endowment by 30 percent. With the use of year 2000 Aomori input-output data, themajor simulation results lead to the following conclusions: 1) Aomori Prefecture will have an increasingly
higher relative wage rate; 2) all 13 sectors, and the agricultural sector above all, will turn out to be
increasingly more capital-intensive, and the economy-wide prefectural capital-labor ratio will increase;3) labor productivity (relative marginal product of labor) will increase with high capital-labor ratios inall sectors; and 4) per capita income will increase, although the aggregate income will decline. Thesesimulation results also imply that the demographic outﬂow of population out of Aomori Prefecture will
result in an increase in the per capita income of the remaining population. “Voting with your feet” may
beneﬁt not only the people leaving the prefecture, but also the people remaining here.
JEL classification : C63; C68; D00; D58; F10; F11; F16; Q11; Q12; Q17; Q18
Keywords : General equilibrium; Factor intensities; Factor prices; Product prices; Welfare∗

Correspondence to: kawano@bb.nebuta.ac.jp1

1

Introduction

The National Institute of Population and Research reported in March, 2013 that the demographic
trend in Aomori Prefecture will be a decline by about 30 percent of the current population by the year
2040 (National Institute of Population and Research, 2013). The reaction of the general public in Aomori
to the report seems to be pessimistic about the future state of the economy. My own reaction, bycomparison, is more optimistic than pessimistic.
In this paper, I have estimated the economy-wide eﬀects of a 30 percent decline in the current population of Aomori Prefecture, in the framework of a 13-sector applied general equilibrium model. In addition
to the above simulation, I have also reduced the capital endowment by 30 percent, together with the reduction in the labor endowment by 30 percent. With the use of year 2000 Aomori input-output data, themajor simulation results lead to the following conclusions: 1) Aomori Prefecture will have an increasingly
higher relative wage rate by 50.1 % with no reduction of capital and 0.21 % with the reduction of capital,
which means that active productive labor will become extremely scarce and expensive if the eﬀect of thedeclining demographic trend is combined with the eﬀect of the aging population; 2) all sectors, and theagricultural sector above all, will turn out to be increasingly more capital-intensive with and without the
reduction of capital. 3) labor productivity (the relative marginal product of labor) will increase by 50.1
% with no reduction of capital and 0.21 % with the reduction of capital in all sectors, which means that
increasing the labor productivity with more employment of capital per unit of labor will make it possible
for the wage rate to go up; and 4) per capita income will increase by 0.85 % with no reduction of capitaland 5.5 % with the reduction of capital because of more capital inﬂow, although the aggregate income
will decline by 29.40 % with no reduction of capital and 26.15 % with the reduction of capital.
These simulation results also imply that the demographic outﬂow of population from Aomori Prefecture
will result in an increase in the per capita income of the remaining population. Voting with your feet
may beneﬁt not only the people leaving the prefecture, but also the people remaining here.
For the empirical characterization, calibration is achieved through the use of year 2000 date for Aomori’s 13-sector input-output (Kikaku Seisaku Tokei Bunsekika, 2005). The model closure assumes asmall open economy with free capital inﬂow and outﬂow, so that the balance of payments is balanced. In
this way, the original input-output data was used without any need for modiﬁcation.
A crucial step in the empirical characterization of an AGE is calibration, deﬁned as “the requirementthat the entire model speciﬁcation be capable of generating a base-year equilibrium observation as amodel solution” (Shoven and Whalley, 1992). An AGE model is a very powerful framework for analysis ofpolicy reforms that could be instituted for Pareto improvements in the current state of an economy. An
important development since Scarf (1967) has been the wider use of observed data, such as an input-output
table, in developing an AGE model.
The solution procedure for coding the model follows Shoven and Whalley (1992) by reducing thedimensionality of the solution space to the number of factors of production in this general equilibrium
structure. The solution algorithm used for calibration is a ﬁxed-point algorithm originally developed by
Kimbell and Harrison (1986) and modiﬁed by Kawano (2003). In his recent papers (Kawano, 2006, 2013),
seven alternative ﬁxed point algorithms were compared. Among the seven alternatives, the modiﬁed
Kimbell-Harrison approach was shown to be the best for AGE modeling.
These experiments were programmed in C-language, and conducted using the GCC version 4.0.1
compiler (Apple Computer, Inc.). The veriﬁed reliability of the simulation results in double precision(1.0e-15). The converged equilibrium values in this benchmark model were obtained through 66 iterations
over the entire model.
In the full paper, Section 2 reviews the empirical structure of an AGE model. In Section 3, thecalibration procedure is stated brieﬂy. Section 4 reviews the major simulation results of the 30 percent
decline of the current population in Aomori-Prefecture. In Section 5, policy implications are presented.
The conclusion follows in Section 6.

2

2
2.1

The Empirical Structure of the Model

The Main Features of the Model

The model was kept very simple. The supply side of a theoretical general equilibrium model is made more
empirically plausible by incorporating the Leontief type input-output accounting data. An important stepin building an empirical model is to incorporate ﬂow of intermediate goods into the model structure. The
ﬂow of intermediate goods among diﬀerent sectors is built into the model as part of production activity
in the economy
The model is simple and has only 13 sectors, 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 goods j ∈ 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 input-output
coeﬃcients aij are deﬁned as:qij,∀ i ∈ I, j ∈ J,
(1)
aij ≡
Qj
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.
Table 1. Input-Output Accounting Table Flows
Inputs to
Input toindustry 0
industry 1
Industry 0
q00 = a00 · Q0
q01 = a01 · Q1
Industry 1
q10 = a10 · Q0
q11 = a11 · Q1…
…
…
Industry 12 q120 = a120 · Q0 q121 = a121 · Q1

…
…
…
…

q012
q112

Domestic
consumption
X0
X1

q1212

X12

(Yen Trillion)
External
Total
sector output
ES0
Q0
ES1
Q1
ES12

Q1

Capital
K0
K1 …
K12
K̄
Labor
L0
L1 …
L12
L̄
Note: Capital is broadly defined as gross value added without labor income.

The input-output table in Table 1 can be looked at in either rows or columns. Here, the table isinterpreted in rows.
In row 0 in the table, the value of the domestic production in sector 0 is Q0 trillion yen. Sales valueof q00 trillion yen goes to its own sector 0, the other q01 trillion yen through q012 trillion yen go to sector
1 through sector 12 respectively. X0 trillion yen through X12 trillion yen for domestic consumptions for
sectors 0 through 12, and the remaining ES0 through ES12 trillion yen worth of net import/export fromexternal sectors.
In rows 1-12, the table is interpreted in the same way as row 0.
In row 13, the total endowment of capital is K̄ trillion yen, of which K0 trillion yen worth of capitalis used in sector 0, K1 trillion yen worth of capital is used in sector 1, and in the same way K2 − K12
trillion yen worth of capital are used in sectors 2 though 12, respectively.
In row 14, the total endowment of labor is L̄ trillion yen, of which L0 trillion yen worth of labor isused in sector 0, L1 trillion yen worth of capital is used in sector 1, and in the same way L2 − L12 trillion
yen worth of labor are used in sectors 2 though 12, respectively.

3

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:
Y = wL̄ + rK̄ + EF,

(2)

where
w := wage rate,
r := rental rate,L̄ := labor endowment,K̄ := capital endowment, andEF := external ﬁnance.
We assume a simple Cobb-Douglas utility function U (.) as a representation of consumer preference. The
function is:θi(3)
U (X0 , ..., X12 ) = Π12
i=0 Xi ,∵0 < θi < 1,12∑

θi = 1,∀ i ∈ I.

i=0

The ﬁnal demand for commodities Xi∈I is derived by the utility maximization for a representative consumer as:
θi Y
Xi =
, ∀ i ∈ I,
(4)
pi
where
θi∈I := share parameter in utility function,
pi := price of commodity.

2.3

The Production Side of the Model
The production function with intermediate inputs is modeled as:)(
q12j
q0j q1j,, ... ,, V Aj ,∀ j ∈ J,
Qj = mina0j a1j
a12j

(5)

where
Qj := commodity j ∈ J produced,
V Aj := value-added component of production
function j ∈ J.
The value-added component V Aj∈J of production function j ∈ J is modeled as Cobb-Douglas whichallows the substitution possibility between primary factors: capital Kj and labor Lj . The value-added
component V Aj is speciﬁed as:
V Aj ≡ Φi Ki αi Li 1−αi , ∵ 0 < αi < 1,

∀ i ∈ I,

(6)

where
αi∈I := factor share parameter in value-added component of production function(or value added output elasticity of capital),
Φi∈I := shift parameter in value-added
component of production function,
Ki∈I := capital employed in sector i ∈ I,
Li∈I := labor employed in sector i ∈ I.
The conditional factor demand functions can be derived by assuming no intermediate goods are neededin 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:()1−αi ( )1αiw 1−αiki =,∀ i ∈ I.
(7)
Φi 1 − αir42) The per unit labor demand function is:
1
li =
Φi

2.4

(

αi
1 − αi)−αi ( )w −αi,r∀ i ∈ I.

(8)

Zero Profit Conditions

Perfectly competitive behavior in producers will imply zero-proﬁt conditions. Zero-proﬁt conditions fortwo producers with intermediate goods are modeled as: For the producer in sector i ∈ I,∑pi =aij pj + rki + wli ,∀ i ∈ I,
(9)
j∈J

where
ki := capital employed for per unit production of commodity i ∈ I, andli := labor employed for per unit production of commodity i ∈ I.
Rewrite equations (9) in matrix as:
Solve for P as:

2.5(I − AT )P = W.

(10)P = (I − AT )−1 W.

(11)Market Clearing Conditions

The total output Qi∈I of commodity in sector i ∈ I is met by the total intermediate input demand∑j∈J qij , domestic consumption demand Xi∈I , and external consumption demand ESi∈I as:∑

qij + Xi + ESi ,∀ i ∈ I.

(12)

By equation (1), qij = aij Qj . Rewrite equation (12) as:∑Qi =aij Qj + Xi + ESi ,∀ i ∈ I.

(13)

Qi =

j∈J

j∈J

Further rewrite equation (13) in matrix as:

Solve for Q as:

3(I − A)Q = X + ES.

(14)

Q = (I − A)−1 (X + ES).

(15)

Calibration Procedure

Here, we calibrated the general equilibrium model to be consistent with an actual data set. In otherwords, chose the model parameters to replicate the real data at hand. The calibration procedure is asfollows:
Step 1: Read information from the year 2000 Aomori 13-sector input-output data ﬁle. The program
uses the input-output data to calibrate parameters. The calibrated parameters are: 1) consumption-share(preference elasticity) parameters θi∈I , 2) factor-share (output elasticity) parameters αi∈I , 3) inputoutput coeﬃcients ai∈I j∈J , and 4) shift parameters in production Φi∈I . These parameters are computedin double precision.
Step 2: Generate a micro-consistent data set summarized in the social accounting matrix for the year
2000 shown in the output ﬁle in the Appendix. Its zero-sum row shows that all goods and factor markets

5are cleared. Its zero-sum column shows that income equals expenditure in each sector. The generated
data set shows micro-consistent ﬁnancial ﬂows in all sectors of the economy. In other words, the data is
consistent with the underlying general equilibrium structure of the model.
Step 3: Conduct a replication check to see if the calibrated solutions in the model are error-free inbuilding and coding the model. The generated data is identical to the original input-output table datain the output ﬁle in the Appendix. When the replication check has passed, the data is considered as an
appropriate benchmark for comparative static experiments.

4

Simulation Results

I have estimated the economy-wide eﬀects of a 30 percent decline in the current population of Aomori
Prefecture, in the framework of a 13-sector applied general equilibrium model. In addition to the above
simulation, I have also reduced the capital endowment by 30 percent, together with the reduction in
the labor endowment by 30 percent. With the use of year 2000 Aomori input-output data, the major
simulation results lead to the following conclusions: 1) Aomori Prefecture will have an increasingly higher
relative wage rate by 50.1 % with no reduction of capital and 0.21 % with the reduction of capital,
which means that active productive labor will become extremely scarce and expensive if the eﬀect of thedeclining demographic trend is combined with the eﬀect of the aging population; 2) all sectors, and theagricultural sector above all, will turn out to be increasingly more capital-intensive with and without the
reduction of capital. 3) labor productivity (the relative marginal product of labor) will increase by 50.1
% with no reduction of capital and 0.21 % with the reduction of capital in all sectors, which means that
increasing the labor productivity with more employment of capital per unit of labor will make it possible
for the wage rate to go up; and 4) per capita income will increase by 0.85 % with no reduction of capitaland 5.5 % with the reduction of capital because of more capital inﬂow, although the aggregate income
will decline by 29.40 % with no reduction of capital and 26.15 % with the reduction of capital.

5

Policy Implications

In this rapid demographic outﬂow of the Aomori Prefecture population, the local government mustﬁrst consider the characteristic features that both private companies and Aomori Prefecture itself need to
thrive: a ﬂexible labor market. The central government of Japan must help devise a more ﬂexible labormarket 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 implied ﬂexible labor market is instituted more commonly to be found nationwide, it will
enable workers to move more easily from one prefecture to another. 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, and especially to Aomori Prefecture.
Domestic local economies need to adjust themselves to the changing environment. One loses one’s
job in one place one day, and the following day one ﬁnds another job in another place. In a world of
fast-changing economic conditions, one should be prepared to move from one place to another, which isexactly what “voting with your feet” means. The Aomori local government should not discourage people
from leaving the prefecture, by any means. At the same time, private ﬁrms will have more incentive tohire employees, because they can more easily ﬁre them, actively engaging in unraveling any knots betweenﬁrms and their employees.
The ideal environment of a thriving economy in which many private ﬁrm operates must be highly
competitive, where “Schumpeterian Creative Destruction” is at work in order to make the economic pie
larger before distributional policies are implemented. 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,

6this stagnation will continue to be reﬂected in the economy for a long time, just as Japan as a wholehas experienced the doldrums for more than two decades. What is crucial for a thriving economy is thehealthy functioning of both factor and product markets. Private ﬁrms and even the central government aswell as many local governments at all levels must stand on their own. Any form of government-subsidized
cartels, or monopolies need to be dismantled, which is also of paramount importance to the eliminationof rent-seeking and the reduction of the enormous public debts accumulated over the years.

6

Conclusion

In this paper, we have estimated the economy-wide eﬀects of a 30 percent decline in the current
population of Aomori Prefecture, in the framework of a multi-sector AGE model. The simulation results
show that the pessimistic reaction of the general public in Aomori to the government agency’s predictionof such a decline is unwarranted. The key policy question is how more competitive and more ﬂexible
product-factor markets, especially the labor market, can be facilitated to improve the future economic
prospects of Aomori.

References
Kawano, Hidetaka (2003) “A Simultaneous Multi-Factor Price Revision for Solving a Numerical General
Equilibrium Model,” Aomori Public College Journal of Management & Economics, Vol. 8, No. 2, pp.
2–27.
(2006) “Comparison of Four Alternative Fixed Point Algorithms for Applied General Equilibrium
Modeling,” Aomori Public College Journal of Management & Economics, Vol. 11, No. 2, pp. 15–21.
(2013) “Comparison of Seven Alternative Algorithms for Applied General Equilibrium Modeling,”
Aomori Public College Journal of Management & Economics, Vol. 18, No. 2, pp. 23–31.
Kikaku Seisaku Tokei Bunsekika (2005) “Year 2000 Aomori’s 13-input-output data.” Available at:
http://www6.pref.aomori.lg.jp/tokei/(accessed September 4, 2013).
Kimbell, Larry J. and Glenn. W. Harrison (1986) “On the solution of general equilibrium models,” Economic Modelling, Vol. 3, pp. 197–212, July.
National Institute of Population and Social Security Research (2013) “Nihon no Tiikibetu Syourai
Suikei Jinko (The future trend of Regional Population Estimates in Japan).” Available at:
http://http://www.ipss.go.jp/pp-shicyoson/j/shicyoson13/t-page.asp.
Scarf, Hubert E. (1967) On the Computation of Equilibrium Prices. In Ten Economic Essays in the
Tradition of Irving Fisher, New York: Wiley.
Shoven, John B. and John Whalley (1992) Applying General Equilibrium, New York: Cambridge University Press.

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