InputHoldingOutput Model and its Applications in Grain Output Prediction and Water Conservancy Inves

1
Input-Holding-Output Model and its Applications
in Grain Output Prediction and Water Conservancy
Investment

• CHEN Xikang1, YANG Cuihong1 and GUO Ju-e2
• 1-Academy of Mathematics and Systems
  Science,
• Chinese Academy of Sciences, Beijing
• 2-Management School of Xian Jiaotong
  University, Xian

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Outline

• 1. Input-Output Model (I-O) and Its Development
  in China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

3
Input-Output Model and Its Development in China

• I-O model was founded by Wassily W. Leontief in
  1936, for which he won the Nobel Memorial Prize
  in Economic Science in 1973
• The major advantage of I-O Reflect the relations
  of production and consumption among all sectors,
  for example, several hundreds sectors, of an
  economy in a chessboard table
• Basic model of I-O
  then
• where

4
Table 1 Framework of a Traditional Input-Output
Table
5
Input-Output Model and Its Development in
China(cont. 1)

• Successfully projected the large volume demand
  for iron and steel in the US after World War II
• I-O was introduced to China in the 1960s
• During 1966-1976, I-O was criticized as
  capitalist economy in China, on the other hand,
  it was criticized as too socialism in the US
  since it has a strong planning.

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Input-Output Model and Its Development in
China(cont. 2)

• In 1972 Chen Xikang and his colleagues suggested
  the State Planning Commission to construct
  national input-output table to improve the
  planning work of China.
• They constructed the first physical I-O table of
  China for 1973 during 1974-1976, which was proved
  very helpful in testing physical balance of main
  products.

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Input-Output Model and Its Development in
China(cont. 3)

• National Input-Output(I-O) Tables
• China has compiled national input-output tables
  for 11 years including 1973, 1979, 1981, 1983,
  1987, 1990, 1992, 1995, 1997, 2000 and 2002
• Those for 1987, 1992, 1997 and 2002 are benchmark
  tables based on general and special surveys
  conducted by the National Bureau of Statistics of
  China (NBS)
• In 1987 the State Council decided that every 5
  years (1987, 1992, 1997, 2002) China would
  conduct special IO survey to construct national
  and regional IO tables. Since 1987 NBS constructs
  I-O table regularly.

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National Input-Output Tables in China

9
Input-Output Model and Its Development in
China(cont. 4)

• Regional and Interregional Input-Output Tables
• All provinces, autonomous regions, and
  municipalities except Tibet and Hainan
  constructed their regional input-output tables.
  The sector classification and the scale of
  regional tables are the same as national
  input-output tables.
• Input-Output Tables for Special Sectors
• Enterprise Input-Output Tables

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Outline

• 1. Input-Output Model and its development in
  China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

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2. Input-Holding-Output(I-H-O) Model

• Holding and Using of Assets
• Input-Holding-Output Model (I-H-O)
• Comparison between I-O and I-H-O
• New formulae under I-H-O

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Holding and Using of Assets

• In 1982, when we constructed I-O table for
  agriculture to study grain issues in China,
  finding that
• Although both cultivated land and capital play a
  critical role in agricultural production,
  traditional I-O model did not include land,
  labor, or any forms of capital assets used in
  agricultural production.
• Holding and using assets is a prerequisite of
  production
• No production process can proceed without
  required quantities of assets, incl. capital,
  skilled or unskilled labor, natural resources.

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Input-Holding-Output Model(I-H-O)

• Prof. Chen Xikang proposed an input-holding-output
  model or extended input-output model with assets
  in 1989

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Framework of Input-Holding-Output Table
15

• Comparison between I-O and I-H-O
• Traditional I-O model does not include an asset
  section nor does it reflect the
  inter-relationships between assets and outputs.
  I-H-O model reflect not only the relation between
  inputs and output, but also that between input
  and stock(holding of assets), output and stock.
• The current I-O model may lead to a misconception
  that by using the following equations, the vector
  of total output of all sectors can be determined
  given a final demand vector.
• 
  
• In fact, even if f has been determined, x cannot
  be obtained if certain quantities of holding of
  assets, such as fixed assets, natural resources
  and labor etc., are not prepared.

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Some New Formulae under I-H-O

• Total input coefficient (total consumption
  coefficient) with indirect input of fixed assets
• where
  represents a diagonal matrix of depreciation
  rates of fixed assets and is a matrix of
  direct holding coefficients of fixed asset.
• For comparison, in I-O model, total input
  coefficient matrix is obtained as follows
• in matrix form

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The Formation of Total Input, Steel Products as
an Example
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Some New Formulae under I-H-O (cont. 4)

• Total consumption coefficient of labor payment
• where represents row vector of
  labor input consumption
• Total Holding Coefficient of Asset
• Total holding coefficients of labor force

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Backward Linkage and Forward Linkage

• Forward linkage relation of a certain sector
  with its lower sectors (sectors using its
  products) Backward linkage relation of a
  certain sector with its upper sectors (sectors
  supplying input products to it)
• In I-O model, the coefficient of backward
  linkage(Ea) and of forward linkage(Eb)
• where

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Backward Linkage and Forward Linkage

• In I-H-O model, the coefficient of backward
  linkage
• where
• The coefficient of forward linkage
• where

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Forward Sectors and Backward Sectors of Steel
Sector
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Outline

• 1. Input-Output Model and its development in
  China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

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3. Applications of I-H-O Model in China

• National grain output prediction of China
  (1980-2005).
• Constructing water conservancy I-H-O tables of
  China and of its nine major river basins for
  1999, to study water conservancy investment etc.
  (Key Project of Ministry of Water of China).
• Constructing extended I-O tables of China for
  foreign trade and estimating of effects of
  Chinas exports on domestic value-added and
  employment.
• Township and Village Enterprises (TVE) extended
  I-O table of China and Shanxi
• Study the key sectors of Chinese economic
  development in urban and rural economies, and to
  calculate the amount of surplus labor
  (unemployment) in rural areas
• Constructing extended I-O table for Xinjiang,
  From a 1987 base, to predict economic development
  indicators in Xinjiang in 1990, 1995, and 2000
  and to study relations between Xinjiang and other
  regions of China.
• Study of energy utilization and environmental
  pollution.

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Outline

• 1. Input-Output Model and its development in
  China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

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4. Application of I-H-O Model in Grain Output
Predication

• China has a population of 1.3 billion. Feeding
  1.3 billion citizens is a critical issue. Grain
  production is one of the most concerned issues of
  the Chinese Government.
• At the end of 1970s, the former Rural Development
  Research Center under the State Council requested
  the Chinese Academy of Sciences forecast national
  grain output with two requirements.
• First, the prediction lead time should be half a
  year prior to harvest season so as to plan
  storage, imports, exports and grain consumption
  as early as possible.
• Second, the prediction should be accurate, i.e.
  with an error rate lower than 3.

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Three Alternative Approaches

• Meteorological approach
• Use statistical method to predict cereal yield.
  In forecasting equations of this approach main
  variables are temperature, sunshine,
  precipitation, and so on.
• Statistical dynamic simulation approach
• Study relationships between grain yield and
  effects of environmental factors such as
  temperature, sunshine and concentration of CO2 on
  crop photosynthesis, transpiration, respiration,
  solid material and seed formation.
• Remote sensing approach
• Since different crop has different optic
  spectrum characteristics, it is possible to
  forecast cereal output using the reflected and
  radiant electrical and magnetic waves of ground
  objectives gathered by satellite sensors.

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Three Alternative Approaches(cont.)

• The above approaches predict grain output mainly
  by meteorological factors.
• Up to the present it has been
  extremely difficult to predict the
  weathertemperature, sunshine, rainfall, and so
  on of two to three months ahead.
• These approaches normally have a 510 error
  rate compared with reported output and a
  two-month prediction lead time.

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Systematic Integrated Approach(SIA)

• In the late 1970s we suggested predicting grain
  output mainly by factor inputs and the holding of
  assets, and presented a systematic integrated
  approach(SIA)

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Three Theoretical Presumptions of SIA

• First, different factors that affect grain
  production must be comprehensively considered.
  Mainly four factors
• Social, economic factors, for example policy,
  management, price
• Production and technical factors, e.g, improved
  variety, fertilizer, farm manure, irrigation,
  farm machinery, agricultural chemicals, mulching
  plastic, farmers education level, and so on
• Natural factors, incl. meteorological and
  non-meteorological factors
• Random factors
• Second, social, economic and technological
  factors determine long-term trends of grain
  output.
• Third, social, economic and technological factors
  are also important issues causing grain output
  variation year by year

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Key Technique of SIA

• I-H-O model
• Nonlinear forecasting equation with consideration
  of diminishing return
• Minimum sum of absolute value technique

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I-H-O tables of Chinese Agriculture

• The Institute of Systems Science constructed
  input-holding-output table with assets in
  agriculture for 1982, 1984, 1987, 1992, and 1997,
  under the support of the former Rural Development
  Research Center of the State Council of China,
  the Chinese Academy of Sciences and National
  Natural Science Foundation of China
• In other years, in order to predict output of
  grain, cotton, and oil-bearing crops we did some
  updating calculations based on the above basic
  I-H-O tables.

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New Results from I-H-O tables on Agriculture

• Using data in the asset part of our I-H-O model,
  we calculate many important indicators, such as
• consumption of chemical fertilizer and
  electricity per mu (1 hectare is equal to 15 mu)
  of sown area,
• fixed assets per mu of sown area,
• ratio of irrigated area to cultivated area,
• labor per mu,
• total power of agricultural machinery per mu,
  tractors per mu,
• ratio of areas covered by natural disasters to
  total sown areas,
• ratio of total areas affected by natural
  disasters (include flood, drought, wind, hail and
  frost, etc.) to total areas covered by natural
  disaster.
• In particular, to calculate the total income per
  mu of sown area for grain and other important
  farm crops, net income per workday, and profit
  rate of capital.

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Nonlinear Forecasting Equation with the
Consideration of Diminishing Return

• Using econometric technique, we have so far
  established 20 forecasting equations on grain
  output and grain yield with a high degree of
  accuracy.

34
Minimum Sum of Absolute Value Technique

• In regression analysis, the parameter ? is
  normally estimated by the least square (LS)
  method
• 
  
• The drawback is LS treatment will move the fitted
  curve to some exceptional points, thus reducing
  forecasting accuracy. One of the modifications is
  to minimize the sum of absolute value of errors
  between estimated and actual yields
• This equation can be solved by the linear
  programming method. The model is as follows
• It can be simply proved that uivi 0, if
  optimal solution exists.

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Forecasting Results and Evaluation

• Every year at the beginning of May, we send
  a report predicting national grain output to
  government agencies and top leaders of China.
  From 1980 to 2005 the main results are as
  follows
• First, predicted bumper, average, and poor
  harvests are correct every year
• Second, the prediction lead-time is more than
  half a year.
• Since 70 of the grain is reaped in the fall and
  the harvest is over in November, a forecasting
  report at the end of April provides government
  agencies with enough time to arrange for storage,
  imports, exports and grain consumption.
• Finally, the average error rate over 26 years is
  only 1.9 compared with statistical reports from
  sample surveys in about 3.15 million sample
  points of 857 counties of China.

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Comparison between Prediction Output and
Statistical Output(1980-2005)
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Forecasting Results and Evaluation(cont. 1)

• This forecasting has supported some important
  policy decisions, for example
• Given the predicted bumper harvest of
  1996, 1997 and 1998, the Chinese Government and
  China Agriculture Bank have given financial aids
  to grain enterprises to enlarge their storage
  capacities.
• 8 relevant Ministries and Bureaus of Chinese
  government, such as State Grain Administration,
  Ministry of Agriculture, Research Department of
  State Council, National Development and Reform
  Commission, and others paid much attention and
  gave excellent evaluation of our prediction.
• Since 1995 the top leaders of China praised the
  research more than 20 times.

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Outline

• 1. Input-Output Model and its development in
  China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

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5. Application of I-H-O Model in Water
Conservancy Investment

• China is one of the countries in water scarcity.
• Per capita water resource of China is 2200 m3, in
  2002, only about 1/4 of the world average.
• Besides water shortage, China suffered both from
  draught and flood at the same time.
• Drought e.g. in 2000 China met the most serious
  drought in the last 50 years. The crop areas
  covered by drought were 40.54 million hectares.
  The grain output of China decreased by 43.21
  million tons, compared with 1999.
• Flood. e.g. in 1998 flood, it is reported that
  there was 22.3 million hectares of farm crops
  areas covered by flood. The direct economic loss
  of flood and water logging in 1998 is about 22
  billion USD.

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5. Application of I-H-O Model in Water
Conservancy Investment (cont. 1)

• To solve this problem, one of the top priorities
  in China is to increase water conservancy
  investment to a suitable level and in addition,
  to allocate water resource as even as possible
  among different regions is also very important.
• Under the support of Ministry of Water of China
  and by use of input-holding-output model, we
  addressed this issue focusing on optimal ratio
  between water conservancy investment and national
  economic development, and proportional water
  resource allocation.

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Optimal Proportion of WCICC to GDP for China

• WCICC(Water Conservancy Investment in Capital
  Construction) is more likely to be affected by
  policy issues and public investments, causing
  sharp fluctuations in the past 50 years, which
  has greatly impacted its sustainable development
• Debate on specific amount of investment in water
  conservancy
• Differences between water conservancy
  departments and other relevant agencies----Because
  of total budgetary constraints
• Too high---no, it would greatly affect
  development in other sectors.
• Too low---no, water conservancy facilities may
  not be maintained at a level that can effectively
  stop flooding.
• How should the level of investment in water
  conservancy be determined?
• Immediately after the severe flood throughout
  China in 1998, this became a very urgent task to
  be solved

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General approach how?

• Function system of water conservancy facilities
• Water conservancy facilities play a crucial role
  in backward effects on GDP, flood control, water
  supply, irrigation, hydroelectric power, and soil
  and water conservation.
• From the perspective of the economy and because
  of the particularity of the water conservancy
  sector, WCICC has an opportunity costthat is,
  due to the increase in WCICC, investment in other
  sectors may be reduced.
• On the other hand, the construction, especially
  large projects such as the Three Gorges Dam, also
  causes migration, inundated fields, and
  destruction of other fixed assets, which have a
  negative effect on the economy.

43
Water Conservancy I-H-O Table
44
General approach how?

• Sketch chart---Proportion of WCICC to GDP and
  total benefits of WCICC

45
Total Impacts of WCICC

• The total impacts of WCICC comprise a
  comprehensive index including
• Benefits--- Backward benefits and Forward
  benefits
• Opportunity cost
• Negative social impacts
• Backward benefit is the increase in GDP directly
  induced by WCICC. We used a partially closed
  input-output model to calculate this.
• In this part, we used the 1999 national
  extended input-output table on water conservancy
  with 51 sectors.
• In addition, based on the national
  input-output table of China in the past several
  years, we constructed water conservancy
  input-output tables for 1981, 1987, 1990, 1992,
  1995, and 1997

46
Total Impacts of WCICC --- Forward benefits

• Flood control benefits
• Because of operation of water conservancy
  facilities, the amount of loss in life, loss in
  national wealth, and loss of GDP may be avoided
  or reduced during overflows of river and other
  natural disasters.
• Water supply benefits
• A direct economic benefit that WCICC creates
  in the process of supplying water to industrial
  and mining enterprises, institutions, urban and
  rural residents, and livestock.
• Irrigation benefits
• Reflected by the effect of WCICC on
  agricultural production.
• Hydroelectric power benefits
• Directly embodied in an increase in installed
  capacity of power stations and thus an increase
  in electric-power output.
• Benefit in soil and water conservation
• Other direct benefits, including environmental
  protection, freshwater aquaculture, and inland
  navigation.

47
Total Impacts of WCICC --- Opportunity Cost and
Negative Effects

• Opportunity cost of WCICC is the decrease in GDP
  induced by the decline in investment in non-water
  conservancy sectors.
• A decline in backward effect due to the reduction
  in investment in other economic sectors, and the
  resulting reduction in demand for products to
  these other economic sectors, etc.
• A reduction in forward effect due to the
  reduction of investment in other economic
  sectors, the reduction in supply in other
  economic sectors, etc.
• Negative Effects
• The construction of water conservancy facilities,
  especially large projects, is often accompanied
  by migration, submersion of resources such as
  cultivated lands, other fixed assets, damage to
  the natural landscape and environment.

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Results of Optimal Proportion of WCICC to GDP

• We finally obtain the equation between total
  benefit of WCICC and proportion of WCICC to GDP
• Y79.83EXP(X)865.49Ln(X)-395.9X2-591
  .58X1754.79 (1)
• where Y represents total benefit of WCICC
  X is the actual proportion of WCICC to GDP
• When dY/dX0, Y get its local extreme value
  point.
• dY/dX79.837EXP(X)865.49/X-2395.
  9X-591.580 (2)
• Solving equation (2) with the iterative method,
  we get
• X0.818.
• Therefore, when proportion of
  WCICC to GDP is 0.818, the total benefit of
  WCICC will be optimal.

49
Total Net Benefits of WCICC

50
Discussion

• Regarding the optimal proportion of WCICC to GDP,
  the results we get in this paper are mainly based
  on data during 1980 and 2000, closely related to
  recent economic and social situation, thus it
  will be very helpful to policy-making in recent
  years, for example between 2000 and 2010. While
  with the development of the Chinese economy, the
  optimal proportion of WCICC will probably change
  too.

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Other Results of Water Conservancy I-H-O Table

• Changing the production structure of economy and
  reducing output of sectors with high direct and
  total water input coefficients
• Studying the effect of water conservancy
  investment on GDP and employment of China,
  including backward effect and forward effect
• Using the tables for nine big rivers, we study
  the characteristic features of nine big rivers
  and calculate optimal proportions of investment
  between nine big rivers

52
Foreign Trade I-H-O table of China and US

• We compiled non-competitive I-H-O tables of
  import type for 2002 both for China and the
  United States. In the table for China, we divided
  exports into two kinds, processing exports and
  non-processing exports.
• Investigate the effects of exports of China and
  the United States on their GDP and employment.
• The results show that in 2002
• US1,000 of Chinese exports to US would generate
  Chinese domestic value-added(DVA), of about
  US177 directly and indirect DVA of US191,
  US368 in total.
• US1,000 of U.S. exports to China would generate
  U.S. domestic value-added, or U.S. GDP, of
  approximately US418 directly and US447
  indirectly, resulting in a total domestic
  value-added of approximately US865.

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Outline

• 1. Input-Output Model and its development in
  China
• 2. Input-Holding-Output(I-H-O) Model
• 3. Applications of I-H-O Model in China
• 4. Application of I-H-O Model in Grain Output
  Predication
• 5. Application of I-H-O Model in Water
  Conservancy Investment
• 6. Summary and Discussion

54
6. Summary and Discussion

• Holding and using of assets is a prerequisite for
  any production process. The introduction of
  holding and using of assets into I-O table makes
  it possible to investigate the relationship
  between input and stock, output and stock
• With the data in the asset part of our
  agricultural I-H-O model, we can calculate many
  important indicators, which are very critical for
  improving the accuracy of grain output prediction

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6. Summary and Discussion(cont.)

• Besides grain output prediction for China as a
  whole, we are now extending our grain output
  prediction to regional level, for example, a
  larger area including several main grain
  producers, such as Henan, Shandong, Hebei, Anhui
  and Jiangsu provinces.
• Due to data availability, however, it is
  currently difficult to investigate the
  relationship between inputs and holding of all
  assets, for example, holding of land. At present,
  we mainly focus on the assets parts including
  labor, fixed assets, circulating assets.

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Thank you very muchfor comments and questions!