Macroeconomic Multifunction Equilibrium
Growth Model of Wuhan
Guo Qincai
Institute of Economic research of Wuhan
3 Sanyang Road 430014. Wuhan.China.
Abstract
Macroeconomic Multifunction Equilibrium Growth Model of Wuhan and its
application) is the first development application; it also the continuation of
theory research and method research. This application mode] consists of 8486
parameters and 2689 equations. The results-can be gained just one time by
microcomputer. The sample period of the model is from 1978 to 1989. The
prediction period of the model is from.1990 to 1995. They. are .both an entirety
(whole)-Its caculation results are output simultaneously.
This application research report is written in 200 thousands of Chinese words
and consists of four parts: 1. Macroeconomic multifunction equilibrium growth
model of Wuhan} 2. The Jab of macroeconomic system of Wuhanj 3. The prediction
policy-making report of “the Eighth Five-year planning” of Wuhans 4. 607 kinds
of indexes output from the model.
Because the paper length is limited by conferenceyonly first part is translated
into English. It mainly introduces the theory characteristics and structure of
this application model, and the examination of the model as well as the new
function of system software. The frame graphy flow graph and mathematic equation
of the model are also introduced in theory and method research. Thus many places
in this report are not detailedly discussed and are cited in the reference (1).
( 1 )The theory background and auxiliary explanation of model-building
Wuhan macroeconomic multifunction equilibrium growth model is the first
practical development application.
Multifunction equilibrium growth model is based on realistic causal relation.
Realisty means that “equilibrium is the existing basis of the whole realistic
substance. Quantitative change of homogenuous substance is practically existing
in equilibrium. The equilibrium which loses homegeneity is qualitative changey or
realistic equilibrium or homogenuous equilibrium’(1). This kind of equilibrium
thought is different from traditional equilibrium theory. It is the theory basis
of multifunction equilibrium growth model-building. Traditional equilibroum
theory in economics issures from physics. In practice, it is an absolute
equilibrium pointy which is absolutely not ‘existing or unrealistic in a
complicated systems Nor is showed in the model. The model is not only a new
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model but also a kind of new method, or formally, an organized combination of all
kinds of methods in econometrics, planning theoryy control theory, input/output
analysis and system dynamics.
Input/output analysis is the result of econometrics and general equilibrium
theory development. Input/output table shows the general law of a complicated
system of social economy- As element period table shows element law, the
importance of input/output. table in social economy system is the same as that of
element period table in chemistry. It is more and more realized by peoples.
So far, input/output table has been successfully and effectively used. In
general, it is classified as two types: (1) After the complete consumption
coefficient was discovered, the general quantity can. be. gained from the final
quantity in equilibrium condition.(2) Combining linear planning with input/output
table can provide a way to search for optimal method. But at present, the
effective application of above two types of methods is only limited within static
application. Like the dynamic input/output model, the Wuhan macroeconomic
multifunction equilibrium model is the dynamic application of input/output table.
But the structure function and effectivity of the model(which can be known from
following introduction) excess greatly the limit of the traditional dynamic
input/output model. As this application is initial dovelopmend application and
lack of experience, in addition, the data are not enough. IL is far immature in
deepth and widthy and only the framework of application mode! was completed.
(Il)Structure of tne model
This application model is classified according to material production
department. It adopts eastern statistical accounting system. Because of the
difficulty in collecting datay the departments classified in the model only
include industry» agriculture, constructions transportationy post and
telecommunications as well as commerce. Industry is classified as metallurgy,
electrical powery coaly oil» chemical,» machinery, construction material» forest»
food, texture, leather and sewing, stationery and other subjects, up to 17
departments.
As a whole, Wuhan regional macroeconomy is a macromodel. But “Macro” in the
model is reflected by diverse industry department or “micro”. One of
characteristics of the model is the integration of “micro” and “macro”.
The coordinaton of system element among industry departments results in the
complicated structure of the model, or reciprical action of system elements in
relative equilibrium is the foundation of existences stablity and development of
system. As to a regional economical system, the coordination of investment,
constructionyproductiony circulation, consumption, outputy input of each industry
department as well~ as the cooradination among industry departments is the
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foundation of sustained, stable development of regional economy. The
characteristics of the model structure will be briefly explained by following
graph.
Each vertical line Ai (i stands for industry departmenty the. following is the
same) is an industry department classified in input/output table. For example.
agriculturey metallurgy, machineryy chemical,» texture and so on. The number of
industry department classified in the model» or the number of line Ai depends on
requirement and possibility of model-building. In this application model, i=17-
As a production departmenty it always develops forward. Thus we use a single
arrow to stand for it.
As every material production department, line Ai bunch constitutes industry
structures and forms general supply. The structure and operation way of line Ai
are explained in the reference (1). The realistic production of any industry
department must possess laborer. Labor material and labor object at any time. The
integration of those three elements is the neccessary. condition of the normal
production of any society. We call it as production equilibrium. For exampley
only as for labor object, all middle products are neccesary condition of normal
production of any society. The normal production of society requires not only the
coordination of middle products or production equilibrium in any societyy but
also the final products of all societies. For example, we regard accumulation,
consumption and input-output coordination as social production equilibrium.
Therefore production equilibrium is the neccessary condition of normal society
production. Social production equilibrium is the full and neccessary condition
of normal production of any society.
We use hoare horizontal line Bi(t) to stand for social production equilibrium.
(t stands for time). Because social production equilibrium is a_ reciprocal
supplying and satisfying procedure among indusrty departments and in the whole
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societyy we use double-arrow to stand for it. The gap between horizontal line or
time t evaluation is generally confined to economical year» Thus the number of
line Bi(t) depends on not only the classification of industry department but also
the length of time. ty,» including sample period and prediction period, in this
application model, t=18 years. Sample period is 12 years, prediction period is 6
years.
In the model» line Bi(t) is the horizontal in input-output table, and consists
of middle products; big repairmenty productive and nonproductive fixed..asset
accumulations flow asset accumulations social and personal consumption and input-
output. Therefore line Bi(t) bunch constitutes demand structure and forms general
demand. The model program of line Bi(t) can be obtained from the reference (1).
After explaining line Bi(t), we emphase the followings: Social production
equilibrium including production equilibrium is relative even if in normal
condition. The relative equilibrium degree of a complicated social economy
dynamic system depends on every element of contemporary social production. These
elements include mainly development degree of science and technology, management
degree, as well as production, circulation and consumption degree. Of course, How
to check a normal social production procedure must be taken as a_ standard to
check above elements. Nonnormality or hetergeneity is nonequilibrium. Without
above principle, emphazing excessive stack and shortage is lack of systemetic
convincinge Here, we must repeatedly explain: traditional equilibrium view in
economics results from physics. In practice, it is an absolute equilibrium. This
kind of absolute eqailibrium point is not existent in a complicated system. It
is also nonrealistic and cannot be reflected in the model.
In normal society production, line Ai and line Bi(t) line bunch Ai and line
bunch Bi(t) are the supply and demand of every industry department. Now that the
equilibrium of general society supply and demand is relative, this kind of
relativity is limited or called relative equilibrium degree. For example.
shortage degree, slack degree and so on- Simultaneously these will be
neccessarily reflected in the indexes such as net output, net input and reserve
in final products. What variable adopted is fit depends on the detailed situation
of every industry department. After the variables are determined, they will
adjust the element of movement» change and development of every industry
department and even the whole system in relative equilibroum. They are indicated
in inclined thin line Ci in the graph. Line Ci results from the crosspoint
between line Ai and line Bi(t). It regulates the movement change and development
of every industry department and whole system in relative equilibrium. Thus like
line Aiy line Ci has single direction. It is shown by single arrow.
In the modely line Ci is regulation line. According to the relative equilibrium
degree of supply and demand of every industry department, it. regulates the
movement, change and development of every industry department in the emulation
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procedure. The difference of this kind of adjustment from object control of the
model is that it adopts close circulation feedback control, which is showed in
the reference (1) about the installment and control style of control variable.
The former is in the same emulation procedure. The latter is the emulation of a
tautological systems which makes respective object to lie in permited error scope,
or ‘it convergences to expection object value.
The installment of line Ci variable depends on requirement of the model and the
possibility of statistical materials supplied. For example, we use the
hypothetical final reserve quantity of every industry department as regulation
variables in system software experiment model (which is showed in the reference
(1)). In this application model, because the statistical materials collected are
limited. As requlation variables, the net output is net gap of the~ supply and
demand of every industry department.
Precisely speakings line Aiy line Bi(t) and Ci are the procedure in which line
Ai bunch, line Bi(t) and line Ci bunch move, change and develop coordinatedly
forward. They are also the procedure of sustained, stable and normal production
of any society+
CIl)Sample period, prediction period and parameter estimation of the
model.
One of the goals to establish model is to predict the future. Why the model ‘can
predict the future is that any thing movement has inertia. Inertia principle
(also called coherence) is one of theory basis which use model to predict the
future. This principle shows the importance of sample period to prediction period.
Nonlinar parameter estimation of prediction period of a complicated system is
far more complicated and difficult than the similar parameter simulation of
sample period. Through a large amount of examinatingy surveying, comparing and
analysing the parameter system of sample period, we discovered that the change
law and change cycle of some parameter are directly relative to the -change law
and cycle of other parmeters in the system. Fox example, the output rate of
productive fixed asset primitive value is directly relative to investments
stagnant and re-added fixed asset. The greater the re-added fixed asset change
ratey the smaller the output rate of fixed asset primitive value in constant time.
When it reduces to some degreey it begins to grow step by step againy and growth
tendency is rather quick. Afterward, it enters into relatively stable period.
That shows the reciprocal action of different parameters in the system
has regularity. This kind of interrelation commonly exists in the complicated
system of S0ciety and economy. Fox example, policy factor, technology and nature
factor belong to this type. They are the main reason of system nonlinar- Thus it
is not enough that the parameters of prediction period only imitate the similar
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parameter of sample period. The reciprocal action rules among’ different
parameters must be deeply researched and introduced into nonlinar parameter
estimation. In order to introduce them, we think it is neccessary to make
complete interrelated experiment and analysis about the whole structure of sample
structure.
Rightly based on above consideration, We highly pay attention to whole sample
period research of the model, especially, the structure research. Thereforey in
this application model, We use the systemetic histry stastical materials of Wuhan
macroeconomyy or 12 year sample which shows accurately system development and
change from 1978 to 1989 as foundation. In the sample period, all parameters of
the model come from statistic materials. In another wordy after sample period is
determined, a group of parameters in sample period are sole. Thus the output
results in model emulating or all variables value in sample period are identical
with practical statistic data.
The parameter estimation of six year (1990-1995) prediction period is based on
practical statistic parameters. In this application model, three kinds of
estimation methods are adopted in parameter estimating of prediction period.
The first is traditional quantitative estimation method. We use traditional
linar method such as regression and smooth to estimate many parameters in the
model prediction periods especially when their change tendency is rather obvious.
For example depreciation rate, reimbursement rate and price index.
The second is the estimation method combining qualitative with quantitative
method. We repeatedly made experiment and survey to some important and especially
sensitive parameters such as output rate of fixed asset primitive value, and
compared and analyzed the experiment results. Based on quantitative analysis, we
made qualitative analysis again.
This kind of qualitative analysis is to experiencedly handle the factors which
appear possibly in the prediction period or planning period supplied by planning
policy-making department through examinating and surveying sample period.
The third is model internal-production. For exampley the investment rate of
every department was gained by using this kind of method. They are internally
produced parameters after the model converges automatically to object.
Generally speakings this application is initial development use and _ lack of
experiences.The parameter estimation of prediction period is still very primitive.
The application of sample period is not enough. But we think it is an important
beginning. Because every statistic parameter in system can be surveyed in the
model sample period, the effect degree and change tendency of these parameters to
system can be tested, the object experiment of the model can make some parameters
to became internal-production- These will open up a path for searching for
nonlinar parameter estimation. Undoubtly, this is an important aspect of the
future research of the model.
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(W)The data arrangement of the model
Statistical data is the foundation of establishing macroeconomic model. However
scientific and perfect the model devise isy the model only stays on theoryy and
has no practical effect if data problem cannot be solved. Therefore we must spend
a large amount of time and energy on collecting and arranging statistic data.
1. The basic content of datas According to the needs and possibility of the
model, subject research team established four principles in arranging statistic
data. They are: (1) In the system, the statistic data is supplied by material
product equilibrium accounting system (MPS). (2) In department classifications
material production department is classified as 17 industry departments. or
industry includes 13 departments. Agriculture, construction, transportation as
well as post and telecommunication respectively have one department. (3) In time
seriesy sample period is from 1978 to 1989, having 12 year materials. (4)
In price. contempory practical price is mainly adopted. Some indexes such as
general production value, net production value and general national: production
value supply simultaneously the data calculated at unchanged price in 1980. The
statistic data supplied by above rules includes 15 aspects:
(1) General output value of every department.
(2) Net output value of every department.
(3) Fixed asset primitive value of every department.
(4) The total amount of fixed asset investment of every department.
(5) Re-added fixed asset of exery department.
(6) Reimbursed fixed asset of every department.
(7) The depreciation fund of fixed asset of every department.
(8) The net value of fixed asset of every department.
(9) Input-output value form graph.
(10) Input-output direct comsumption coefficient.
(11) Fixed asset investment structure coefficient.
(12) Flow asset investment proportion coefficient.
(13) Fixed asset reimbursement rate of every department.
(14) Fixed asset depreciation rate of department.
(15) Consumption fund.
2. The main resource of the material.
The whole series of materials is supplied by Wuhan Municipality Statistics
Bureauy Wuhan Municipality Statistic Bureau do its best to collect history
materials. The foundamental part comes from yearly report form of 1978-1989 and
history material compilation, auxiliary part comes from those data submited by
municipal management department and County Statistical Bureau. These materials
(not include those materials in 1989) now are collected in Books «Wuhan 40 years)
System Dynamics '91 Page 471
(Wuhan Univer-sity Press). Wuhan statistial materials (1949-1988)) (Bookl-4)
and Wuhan input-output graph in value form) . ‘These books are compilated by
Wuhan Municipal Statistical Bureau.
3. Main handling methods
(1) Adjusting statistical index standard. Before 1984, the general output value
of country and below country is calculated in agricalture output, value as by-
industry» Because of the change of country economy structures nation stipulated
that the genaral industry output value of country and below country would be
completely listed in industry statistic scope. Therefore, the materials in this
model have been seperated and adjusted.
(2) Integrating industry department classification. Industry general output
value from 1978 to 1984 is classified by trade from the beginning of 1985. Jt is
converted to department classification. According to correspondence principle, we
arranged out 15 industry departments and 40 industry trades contrast table) as
basis of adjusting trade as department. Then based on 15 departments we merge
sewing with leather, paper-making with culture and education, and make them to
become 13 industry departments determined by the model.
_ (3) Paying attention to statistical data joining. If statistical materials from
a.complete sety the logical relationship of data must coincide. For example.
fixed asset primitive value at the end of this year should equal to fixed asset
primitive value of the end of last year plus the increased fixed asset (newly
increased and input) and substract the decreased fixed asset (reimbursed and
output) in this year. In these aspects, there are some unjoining problems in the
stastistic materials of Wuhan. Thus we assembled related book «National industry
enterprise fund equilibroum table) from Wuhan Municipality Finance Bureau and
according to it, we also calculated yearly indexes such as fixed asset
reimbursement rate and depreciation rate of every department on the basis of not
changing fixed asset primitive value we adjusted the increased value or
decreased value of fixed asset, and improved logicality of data.
(4) Suitably estimating insufficient materials. The model needs to supply input
-output direct consumption coefficient in sample period and prediction period.
Although Wuhan began relatively early in input-output. there are only three year
materials. Thus we adopted interrelated year direct consumption coefficient to
estimate them or adopted practical material consumption proportion of every
department as control. The input structure in 1983 is quoted from 1984 to 1986,
that in 1987 from 1988 to 1989, that in 1983, 1985 and 1987 comprehensivly from
1990 to 1995. The needs of the model to statistical matevials are basically met.
But the lack of inherent complete ststistic system and good stastistic basis
causes poor stastistical date quality and influences the accuracy of prediction
results to some degree.
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( V)The model examination and explanation
“Practice is the sole standard of examinating truth”. Of courseypractice is the
most ideal way of examinationing the model. On the basis'of above consideration.
Comparing the prediction results of the model with practical value is the
examination method we edopted in the model.
The model uses the samples from 1978 to 1985, and takes the practical input
from 1986 to 1989 as input condition. “The Seventh five-year planning” period, or
from 1986 to 1990 was simulated in the model. Now we only regard social general
output value in unchanged price as analysis object.
1. From the point of four year accumalative total amount, the practical total
amount in early four years during “the Seventh five-year planning” period, is
102.88 billion, and the emulation value of the model is 102.86 billion, the error
rate is only 0.1%.
Among them, agriculture practical value is 5.44 billion and emulation value is
5.487 billion, error rate is 0.9%. Industry practical value is 81.18 billion yuan,
the error rate is 2.6%. Practical value of transportation and Post-tele-
communications is 3.536 billion yuan and emulation value is 3.652 billion yuany
the error rate is 3.3%. Commercial practical value is 7-745 billion yuan, and
emulation value is 7.89 billion yuan, the error rate is 1.9%.
2. From the point in yearly unit, the practical total of the whole city in 1986
is 22.7 billion yuany the emulation value is 22.76 billion, the error rate is
0.24%. In 1987 whole city practical total is 24.96 billion yuan and emulation
value is 24.51 billion yuan. The error rate is 1.84%, In 1988 the practical
total is 27.51 billion and emulation value is 26.88 billion. The error rate is
2.34%. In 1989, the practical total is 27-71 billion yuan and emulation value
is 28.71 billion yuan, the error rate is 3.61%.
3. From the point in yearly unit and department, there are 68(17#4) year times
in the early four years during “The Seventh five-year planning” only, the error
of 18 year-times among them is beyond 10%. The percentage is 26%. The error of 21
year-times is from 5 to 10 percent. The percentage is 31%. The error of 23 year-
times is from 1 to 5 percent. The percentage is 34%. The rest error is below 1
percent. The percentage is 9%.
Above three kinds of analysis show that the-error of accumulative total from
1986 to 1989 is very small, less than 1 percent. The more detailedly the trade
departments are classified. The more shortly time is divided, the greater the
error is.
The model starts from micro department and reflects macro-whole regional macro
economy. Even if micro-error is rather great’; the mocro-accurancy reflected is
also rather high. Therefore we can say that the model is successful to draw up
whole planningy especially middle, long-term planning, starting from trade
System Dynamics '91 Page 473
department. That “the micro” reflects. “the macro” shows the advantage and
practicality of the model.
(MW) The new function of system software. DYNAMO-S1.
Because of complicated structurey long sample period, large amount of date and
various functions and usages (used in prediction and experiment) of multifunction
equilibrium growth model. We also added database and model base function in new
system software- In order to meet more perfectly different requirement on basis
of previous emulation optimum and control function.
The main function of database is to fillful data input, output in the procedure
of emulating and various data handling through combining database and management
system with model system.
The main function of the model is to store various submodel and model bunches
having different function and action- In the model basey in the process of mode]
operatings according to the requirement, various submodels and model bunches
constitute automatically a model which executes certain function and fillfuls
certain tast.
Reference:
1.Guo Qincai- 1989, Realisfic Equiliblium Growth Theorys Model and Software)
Wuhan Press.
