A SIMULATION SUPPORT SYSTEM FOR PUBLIC EDUCATION
INVESTMENT STRATEGY ANALYSIS
Wang Dingwei*,
Department of Industrial Engineering
North Carolina State University
Raleigh, NC 27695-7906, U.S.A.
Pei Weiming
Department of Automatic Control
Northeast University of Technology
Shenyang, P.R. of China.
ABSTRACT
A simulation model of education and economy is used to
analyze the education investment strategy in a region
of China. The simulation results show the proportion
of educational fees and investments must be suited to
the economic developing level. Thus, it is necessary to
continuously increase the proportions with economic
growth. In order to be convenient for decision makers,
a functional simulation support system is proposed.
INTRODUCTION
In recent years, owing to the inflation which follows economic
development, a serious shortage of public education funds became
a very notable problem in China. Research on reasonable public
education investment strategy has become an absorbing area to
many economists, educators and officials. Unfortunately, it is
very difficult to quantify the interaction between education and
economic growth, so most research is either non-quantitative
analysis. or based solely on the comparison of the education in-
vestment ratio of China with that of other countries. The former
can't tell. the decision makers how much money is necessary, the
later is: not believable to the decision makers who always em-
phasize that there are differences in the economic systems of
China and other countries. Thus, to find a quantitative and
believable analysis for public education investment strategies is
one of the most pressing tasks for the development of education
and the economy of China.
*Wang is a visiting professor from the Northeast University of
Technology, Shenyang, P.R. of China.
1226
System Dynamics '90 1227
As we know, the development of education depends on the economic
development, and education is an important factor to economic
growth (Denison 1974). So we must consider the education,
economy, population and the whole society as a system. The un-
certainty of social-economic systems make the problem extremely
complicated.
There is much literature that focuses on the interaction of
education and economic growth (Schuitz 1961, Hybison 1964, Ritzen
1977). However, owing to the fact that educational and economic
systems of China are really different from the Western Countries,
these approaches can't be applied directly to China.
System Dynamics is a very efficient strategy simulation tool
(Forrester 1969). The Club of Rome's world model (Meadow et al
1972) and Forrester's national model (1976) give us some good
ideas for modeling the whole social-economic system.
In order to make the development plan of education in a region of
China, we built a System Dynamics model to find a reasonable
education investment strategy. A new method similar to Schultz's
human capital theory is adopted to quantify the contribution of
education to the economic growth. In order to give a convenient
man-machine interface for the decision-makers, some techniques of
decision support systems and human-computer interaction ap-
proaches are adopted (Wang et al 1986, Wang 1988). The simula-
tion results prove that this Simulation Support Systems are a
very useful tool for the education investment strategy analysis
of China.
CONFIGURATION OF SIMULATION SUPPORT SYSTEM
The Simulation Support System for the education investment
strategy analysis consists of 10 main modules, as shown in Fig.1.
The human-computer interface module is composed of several menus
which can prompt the user to select different modules to do the
work desired.
The development goal setting module is used to acquire the
development goal of education and economy. It is composed of a
group of questions which can elicit the decision makers to tell
the system what his thinking is about the future. This informa-
tion is necessary to the strategy evaluation.
The statistical data input module is a data input interface. It
prompts the user to key into computer the main statistical data
about education and the economy over a history period. These
data are stored in the data base, they are useful for model
checking and the estimation of model parameters.
1228 System Dynamics '90
The parameter estimation module is a common least-square algo-
rithm. It uses the statistical data in the data base to estimate
the parameters which are necessary to the key module of the
simulation.
Human-computer
interface
Develop- Stati- Strategy Modifying Model
ment stical evalua- parameter modifying
goal data tion by given and he
setting input strategy evaluation
Comparing Simulation Model
Data results model of validity
base with goal education checking
and Eco-
nomy
+» Parameter
estimation
Figure 1: Configuration of the Simulation Support System
The nuclear part of this system is the simulation model of educa-
tion and economy. It was written in the Dynamo language accord-
ing Forrester's System Dynamics. Other modules are all around
it. We will discuss it in detail in the next section.
The model validity checking module is used to check the validity
of the simulation model. It compares the results of the simula-
tion with the statistical data. If there are not any large dif-
ferences between the results and the statistical data in the main
indexes of education and economy, the model can pass the validity
checking.
The model modifying and evaluation module is used to output the
the results of model validity checking by a group of formatted
tables, so they are easy to understand by the user.
System Dynamics '90 _ 1229
The modifying parameter by given strategy module is used to
translate the education investment strategy given by the deci-
sion makers to the simulation parameters in the model. Then the
simulation begins to run and store the simulation results in the
data file.
The comparing results with goal module is a result review module.
It opens the result data file and compares the simulation results
with the development goals given by the decision makers.
The strategy evaluation module is used to output the comparison
results of a given strategy and the goals. The strategies which
can not reach the development goals for education and the economy
will be considered as unsuccessful strategies. The decision-
makers can select the best strategy from the successful
strategies which can reach the stated goals.
We have not finished developing all modules, because there are
many functions required by the decision-makers that are not easy
to be realized. The development and improvement of the simula-
tion support system is still in progress.
SIMULATION MODEL OF EDUCATION AND ECONOMY
The simulation model of education and economy is the key module
in this system and the central work of this research. The
reduced cause-and-effect diagram of this model is shown in Fig.2.
From Fig.2, we see there are four main cause-and-effect loops
which are all positive feedback loops.
The first one is: National income increase makes the investment
in educational capital increase and educational capital cost in-
crease. This means that a capacity increase in schools makes the
students increase. After a delay, the labor force will increase,
and the national income will increase again.
The second one is: National income increase makes public educa-
tion fees. increase, then the shortage gets decrease. The in-
creased education fees can guarantee education quality, so the
quality of graduates will increase. Then the quality of social
labor will improve which can also increase the national income.
The third one is: National income increase increases the invest-
ment in capital of production. Then the total capital cost in-
creases, and makes the national income increase also.
The forth one is: National income increase makes the investment
in science and technology increase. This increasing investment
can quicken the technology process, and the national income will
increase again.
1230 “. ‘System Dynamics '90
The former two investments can be considered as investment in
human capital (Schulze 1961). The later two investments are in-
vestments in capital. These cause-and-effect relations are easy
to understand philosophically. The difficulty is how to quantify
these relationships.
Investment Investment
Population in educational + in science
in the capital + and tech-
region / nology
‘ +
Public aN
Accumulation Investment
+ + in the
capital of
Total + production
consumption
+ * *
Educational Private Public
capital education education
off cost », expenses suns
Number <— Number National
income
students Se teachers i
\. .
‘Requirement +, Shortage Gross
of + social
education me "BN
fees fees
+
Number and: _ — Ne
quality of Number and capital
graduates te matity of dT
labors
a
lumber and Technology ae seth oa
quality of process “*—~— of thchno-
technicians logy and
and scientist science
Figure 2: Cause-and-Effect Diagram of Simulation Model
of Education and Economy
System Dynamics '90 , . 1231
The effects of labor, capital and technology progress on gross
social production can be described by the Cobb-Douglas production
function (Solow 1957). Although the C-D function is a classical
production function, it is widely used in China now after some
improvements were developed (Wang et al 1988a). This is because
the parameter estimation of a C-D function is easier than other
production functions. The reason that we use the gross social
product instead of gross national product is that there are not
enough statistical data of GNP in China. The main difference be-
tween GNP and GSP is that the later is not a net product value.
Let Y(t) be the GSP in eth year,
K(t) be the total capital cost, in tth year, and
L(t) be the total labors in t‘" year.
¥(t)=A(t) *K(t)4-L(t)¥ (1)
where, A(t) is the technology progress in eth year, u and v are
the parameters to be estimated, and u+v=1.
In order to quantify the quality of labor, we can use the labor
simplifying ratio which was proposed by educational-economists in
the Soviet Union.
Assuming the value of a laborer without any education is 1 unit,
then the value of a laborer with a k level education is more
than 1 unit. The ratio of value of a laborer with a k level
education to the value of a laborer without any gaucation is
defined as the labor simplifying ratio of the ras education,
remarked as hy.
The labor simplifying ratios used in the simulation model are
determined by the results of a study of productivity of workers
with different levels of education, and a study of average in-
comes of peasants with different levels of education. The former
was done by the authors in a machine-tool plant. The later was
reported by the People Daily in China. The labor simplifying
ratios are shown in Table 1.
Table 1: The Labor Simplifying Ratios
Education level Labor simplifying ratio
Illiterate person 1.00
Primary school 1.20
Junior middle school 1.40
Senior middle school . 1.60
Skilled worker school 1.65
Polytechnic school 1.70
Polytechnic college 1.90
University 2.00 ~
Graduate school 2.20
1232 , System Dynamics '90
Then the total labors in tth year can be calculated by the fol-
lowing formula,
L(t) = L(t-1) +h, (t) +R, (t) ths (t) -Ro(t)+-+++h,(t) -R, (t)
) ) +h, (t) +R, (t) +h 2 eee (2)
where, | Rx (t) is the number of graduates of xth level schools in
the t year, r is the retired rate of labors, and n is the num-
ber of levels of schools.
We assume that the labor simplifying ratios are variable with
time. They can vary from their standard values with the change
of shortage in education fees. The relation between the two
variables is: described by a table function based on the ex-
periences of educators and the managers of schools.
Labor
Rural
Education Middle
System r+ School of Labor
Agriculture
nd Labor
CO Children
Rural before Primary Junior Senior }———~ Labor
popu- school School Middle Middle
lation age School School
CT ~~ Labor
migra-
tion Polytech-
nic School Univer-
sity
Children Labor
Urban before Primary Junior Senior
popu- school School Middle Middle
lation age School School |}———~ Labor
re Labor
Middle
Urban School for Labor
Education Occupation
System
Labor
Figure 3: Student Flow Diagram of Chinese Edutation System
The technology progress in the tthyear can be determined by the
following recurrence formula:
System Dynamics ’90 = 1233
A(t) = a-a(t-1)P-[s(t) /L(t)1°,- (3)
where, S(t) is the level of manpower in the science and tech-
nology section. It can be calculated by a formula similar to
(2). The parameters a, b and c are to be estimated.
This formula was developed by Wang et al (1988b) in the research
on forecasting of science, technology and education in this
region. It fits the statistical data very well. Its economic
meaning is that technology progress depends on the technology
level in last year and the proportion of scientists and tech-
nicians in the common laborer pool.
This model is composed of more than 350 equations. This number
does not include the equation numbers of parameters and tables.
The schools are divided into rural schools and urban schools be-
cause the two kinds of educational fund systems run in different
ways. The student flow diagram of the Chinese education system
is shown in Fig.3.
Based on the population forecasting data, we can determine the
number of children who will enroll in primary schools in future
years. Then according to the student flow rules and the
capacities of all kinds of schools, we can calculate the numbers
of students in all kinds of schools. These data are basic data
to determine the requirement of education fees. As space is
limited, we do not discuss the calculation approach in detail.
SIMULATION RESULTS AND STRATEGY ANALYSIS
The key module, Simulation Model of Education and Economy, was
programmed in Professional Dynamo Plus (PD-Plus). It was run on
an IBM PC/AT. After repeated simulations, reasonable educational
investment. and fund strategies have been achieved.
The current proportion of educational fees in the national income
of this.region is about 1.90%. The changes in GSP in 2000 and
2020, with: this proportion are shown in Table 2.
From Table 2, we see that when the educational fee proportion in-
creases from 1.9% to 2.8% and 3.0%, the GSP in 2000 and 2020 will
reach a maximum of 285.95 and 850.96 billion yuans respectively.
However, if the proportion is increased to more than 3.0%, the
values: in 2000 and 2020 will go down.
The current proportion of investment in educational capital con-
struction over the total investment in capital construction is
about 6.5% in this region. If we adjust this proportion with the
educational fee proportion, the economic growth can get a larger
increase. The results are shown in Table 3.
1234 System Dynamics '90
Table 2: The Effect of Educational Fee Proportion to
Economic Growth
(unit: billion yuan)
Proportion (%) GSP in 2000 GSP in 2020
1.5 280.35 824.20
1.9 283.68 838.16
2.0 284.09 840.28
2.5 285.62 848.15
2.7 285.88 849.81
2.8 285.95 850.39
2.9 285.95 850.75,
3.0 285.91 850.96
3.1 285.82 850.96
3.2 285.71 850.73
3.5 285.23 848.88
4.0 283.99 840.83
Table 3: The Effect of Educational Investment Proportion and
Educational Fee Proportion to Economic Growth
(unit: billion yuan)
Edu. fee Edu. investment GSP in GSP in
proportion (%)| proportion (%) 2000 2020
1.9 6.5 283.68 838.16
3.0 7.5 285.78 859.56
3.0 8.5 285.38 865.71
3.0 9.5 284.87 870.09
3.0 10.5 284.43 872.98
3.0 11.5 284.17 874.69
3.0 12.5 284.08 875.57,
3.0 13.0 284.08 875.74
3.0 13.5 284.08 875.74
3.00 14.0 284.08 875.60
3.0 14.5 284.08 875.30...
3.1 13.0 284.01 875.80
3.1 13.5 284.01 875.80
From Table 3, we see that the GSP in 2000 decreases as the educa-
tional investment proportion increases. This is because the
educational investment is delay-effective to the economic growth.
The GSP in 2020 increases with this proportion increase, but when
_ it is over 13.0% the GSP in 2020 will go down. When the educa-
tional fee and investment proportions are 3.1% and 13.0% respec-
tively, the GSP in 2020 can reach its maximum of 875.80 billion
yuans.
System Dynamics ‘90 1285
In above results we consider the educational fee and investment
proportions to be constants. This is not true. Owing to that
the requirement of education will continuously increase with the
economic growth and the technology progress, the educational fee
and investment proportions must be a function of time. The
simulation results show that when the fee proportion is taken as
3.0%, there will be a surplus of educational fees before 1995 but
a shortage after 1995.
According to the rule which requires educational fees to increase
with economic growth, it is better that the educational fee
proportion take following values in future years, as shown in
Table 4.
Table 4: The Required Educational Fee Proportion
in the Future
Year 1989 1990 1991 1992 1993 1994 1995
Fee prp.(%)| 2.09 | 2.26-| 2.37 | 2.52 | 2.70 | 2.86 | 3.02
Year 1996 1997 1998 1999 2000 2020 2030
Fee prp.(%)} 3.12 | 3.16 | 3.23 | 3.43 | 3.67 | 4.17 | 4.35
If this time series of educational fee proportions will be taken
the GSP in 2000 and 2020 will increase to:
GSP in 2000 = 289.56 billion yuans, and
GSP in 2020 = 929.26 billion yuans.
They are 2.07% and 10.87% more than the GSP in 2000 and 2020 when
the current fee and investment proportions will still be taken.
So we see that to take proper educational fee and investment
proportions can distinctly promote economic growth.
CONCLUSIONS
From this research on educational investment strategy, we can get
following conclusions:
1) The current proportions of educational fees in national income
and educational investment in total capital construction in this
region are too low, with the result that the speed of economic
growth has been limited. So it is an urgent matter to greatly
increase the two proportions at once.
2) However, it does not follow that a higher educational fee
proportion results in faster economic growth. There is an op-
timal matching of the educational proportions to the economic
1236 System Dynamics 'S0
development level. If the unvarying proportions were adopted,
the optimal values of the two proportions suitable to the
economic development level of this region would be 3.1% and
13.0%, separately.
3) The requirement of educational fees and investment will con-
tinuously increase with the economic growth, so the better way is
to increase the proportions continuously. The time series of
educational fee proportions shown in Table 4 can be taken as a
better alternative.
4) In the simulation model of education and economy, education,
population, economy and human society are considered as a whole
system, so we can get a good understanding of the interactions
between education and economy.
5) The simulation support system proposed in this paper has a
reasonable configuration and some useful functions, it will be-
come an efficient computer-aided decision tool for the decision-
makers as they select the correct education development strategy.
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