on the study of china's grain output prediction

On the study of China's grain output prediction1

Xikang Chena�, Xiaoming Panb and Cuihong Yanga�aInstitute of Systems Science, Academy of Mathematics and Systems Science, Academia Sinica, Zhongguancun, Beijing

100080, People's Republic of ChinabAsia/Paci®c Research Center, Stanford University, Stanford, CA 94305±6055, USA�Corresponding authors.

Received December 1998; received in revised form July 2000; accepted September 2000

Abstract

Feeding 1.2 billion Chinese is a critical issue both for China and for the world. This paper presents a systematic

integrated method (SIM), with the key elements of input-occupancy-output analysis, nonlinear variable coef®-

cient forecasting equations, and minumum sum of absolute value technique to predict China's grain output. Since

1980 this approach has been successfully implemented in China, and is appreciated by China's top leaders and

responsible governmental agencies.

Keywords: Systematic integrated method, input-occupancy-output analysis, nonlinear forecasting equation, minimum sum of

absolute value.

Introduction

Grain occupies a crucially important status in the economy of China, because it has been, and should

continue to be, supplied domestically for more than 1.2 billion Chinese, not imported to the level

predicted by Lester Brown in his alarming book Who Will Feed China (Brown, 1995). Grain production

also provides employment for 700m Chinese. In 1997, agricultural employment accounted for 48% of

total employment in China. Furthermore, the state of harvest will directly in¯uence people's

livelihoods, and the economic development of China this year, and in the future.

Towards the end of the 1970s the former Rural Development Research Center under the State

Council assigned forecasting of national grain output to the Chinese Academy of Sciences (Academia

Sinica) with two demands: the lead time of prediction should be half a year prior to harvest season so

as to arrange grain consumption, storage, import, and export as early as possible; high accuracy of

prediction, or the error rate should be lower than 3%.

Three leading approaches to predicting grain output used worldwide are as follows.

1The project is supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.

Intl. Trans. in Op. Res. 8 (2001) 429±437

# 2001 International Federation of Operational Research Societies.

Published by Blackwell Publishers Ltd.

Meteoric approach

The theoretical assumption of the meteoric approach is that grain output ¯uctuation is mainly caused

by meteoric factors, whereas the effect of economic and technological factors belongs to a gradual and

smooth long-run process that can be depicted as a trend output with time t. The forecasting equation is

as follows:

Y � Yt � Yw � u (1)

where Y denotes grain yield, Y t trend yield, Yw meteoric yield and u random items.

Thompson (1969) presented a forecasting model for winter wheat yield in Kansas, USA, in which Y t

is a linear function of time t, and Yw includes meteoric factors of precipitation and temperature in

April, May, June, and July. The standard error rate of this equation is 2.88 bushel/acre, about 10% of

yield. Williams et al. (1975) adopted the meteoric approach to predicting Canadian prairie-crop district

cereal yields at the end of June, prior to two months of harvest, with an error rate of 8.8%, 4.7% and

5.4% for wheat, oats, and barley, respectively. In other countries, the meteoric approach predicts output

with an error in the range of 5±10%.

Statistical dynamic simulation approach

This method studies relationships between grain yield and the effect of environmental factors such as

temperature, sunshine, and concentration of CO2 on the crop's photosynthesis, transpiration, respira-

tion, solid material, and seed formation. For instance, Murata and Ueno of Japan studied the relations

between rice yield and average temperature and sunshine hours in the pivotal season of rice-seed

formation (August and September). Wang (1995) and Wang et al. (1997) studied the effects of CO2

concentration on grain yield and found that doubled CO2 concentration can increase the yield of

China's winter wheat by 28.3%, corn by 22.9%, soybean by 67.1%, and cotton by 27.0%. Nowadays

this approach is combined with the meteoric approach. However, since it is hardly possible to get

comprehensive data from large areas in time, this approach is still in the experimental stage.

Remote sensing approach

Because different crops have different spectrum characters, it is possible to forecast grain output based

upon the re¯ectivity and radiation ratios of electromagnetic waves of objects on the ground gathered by

satellite sensors.

From 1974±1977 the US Department of Agriculture (USDA) launched the Large Area Crop

Inventory Experience (LACIE) using remote-sensing techniques to estimate the output of main crops

for many countries and regions, with an accuracy rate of 90% for wheat, and 78±90% for cotton and

corn. Since then, the remote sensing approach has been combined with the Geography Information

System (GIS) to increase the accuracy of prediction (Eerens et al., 1991). Hayes and Decker (1996)

have used the Vegetation Condition Index derived from NOAA/AVHRR (National Oceanographic and

Atmospheric Administration/Advanced Very High Resolution Radiometer) satellite data since 1982 to

estimate maize production in the corn belt of the United States. The results during 1985±1992 had a

two month lead-time and 4.9% average error rate in eight years; in four years the error rate was lower

430 X. Chen, X. Pan and C. Yang / Intl. Trans. in Op. Res. 8 (2001) 429±437

than 5%, in three years it was 5±10%, and in one year it was more than 10% (Hayes and Decker,

1996).

Besides the United States, other countries are also pursuing this line of research. Since 1989, the

Institute of Applied Remote Sensing of the Joint Research Centre of the European Union has been

engaged in a pilot project for the application of remote sensing to agricultural statistics. The accuracy

rate of estimated wheat and cotton areas in northern Greece, compared to of®cial reports, was 90%

(Quarmby, 1993). In Australia, researchers have predicted regional sorghum production using spatial

data and crop simulation modeling (Rosenthal et al., 1998). In Canada, researchers began to construct

the monitoring system of global crops in 1987, using AVHRR data to estimate the wheat yield of

Canada and the former Soviet Union (Pokrant, 1990). In England, the University of Reading used linear

mixture modeling and AVHRR data for crop-area estimation (Quarmby and Townshend, 1992). In

India, Sridhar et al. (1994) forecasted the wheat area between 1989±1992 based upon the data from the

Indian Resource Satellites, IRS-1A and 1B. The accuracy rate was 90% (Sridhar et al., 1994). Italian

researchers estimated the yield of wheat and corn by using the data of Multi-Spectral Scanners (MSS),

Thematic Mapper (TM), and AVHRR (Ascani, 1987). In Niger, Italian scientists predicted the yield of

millet and sorghum at the end of July using NOAA/NDVI data and environmental monitoring data. The

mean error of prediction was 0.08 ton per hectare, about 9% of the actual yield (Maselli et al., 1993).

In Thailand, Tennakoon and Murty (1992) of the Asian Institute of Technology estimated the planting

area and per unit-area yield of rice in Saraburi Province in 1989 by using satellite data, and studied the

relation between yield and the value of light-wave radiation (Tennakoon and Murty, 1992). In China,

researchers utilized the data of NOAA/AVHRR and Landsat to estimate the rice area of China. The

accuracy of the estimated rice area of Hubei Province was 89.5% in 1994 and 91.6% in 1995 (Fang,

1998).

Overall, the three approaches discussed above normally have 5±10% error rates compared to

reported output and two-month lead time, since it is dif®cult to use remote sensing or other techniques

to predict yield unless the crop has grown to a certain extent. Needless to say, the contemporary

capacity of world meteorology is unable to reliably forecast weather more than a month in advance. All

these factors limit the lead time and accuracy rate of prediction (Landau, 1998).

Methodology and model

The systematic integrated method (SIM)

The method we have used has a number of theoretical presumptions. First, social, economic, and

technological factors determine long-run trends of grain output. For example, China's grain output was

163.92m tons in 1952, but 494.17m tons in 1997, which means that grain output had more than doubled

in 45 years. This big change is mainly caused by social, economic, and technological factors, whereas

the climate change in that period is not so signi®cant.

Second, social, economic, and technological factors are also important, causing grain output

variation year by year. The meteoric approach assumes that the function of social, economic, and

technological factors belongs to a stationary process, and grain output variation year by year is

determined by meteoric factors. In China, however, changes in policy, price, fertilizer, irrigation, and

machinery power greatly contribute to the variation of grain output year by year, as well as change due

X. Chen, X. Pan and C. Yang / Intl. Trans. in Op. Res. 8 (2001) 429±437 431

to ¯uctuations in weather. Since 1952, for instance, there have been two big ¯uctuations of grain output

in China. The ®rst was the extensive loss during 1959±1961, when grain output declined from 200m

tons in 1958 to 143.5m tons in 1960, a decrease of 56.5m tons. The second was the great rise during

1981±1984, when grain output increased from 325m tons in 1981 to 407.3m tons in 1984, an increase

of 82.3m tons. These were mainly caused by social, economic, and technological, rather than meteoric,

factors.

In order to increase forecasting accuracy, it is important to incorporate social, economic, and

technological factors with natural factors. The forecasting equation we use is as follows:

Y � f (X 1, X 2) (2)

where X 1 denotes social, economic, and technological factors such as policy (dummy variable), price,

fertilizer, irrigated area, draught animals, machinery power, improved seeds, etc; X 2 denotes natural

factors such as area covered by natural disasters, intensity of disasters, precipitation and temperature.

This equation can be regressed through historical records. As for empirical study, some meteoric and

environmental factors that are rather hard to predict should not be incorporated into the equations.

Now we develop techniques to increase forecasting accuracy, i.e. input-occupancy-output analysis,

nonlinear forecasting equations with diminishing returns, and the minimum sum of absolute value

technique.

Input-occupancy-output analysis

Input-output analysis, introduced by the Nobel laureate W. Leontief, is a useful tool to investigate the

linkages between inputs and outputs. However, it does not explore the linkages between occupancies

and outputs, such as the effects of occupied natural resources (cropland, etc.), ®xed assets, and different

levels of skilled labor on outputs. We introduced input-occupancy-output analysis as an extension of

input-output analysis for predicting agricultural production (Chen, 1990; 1992).

With input-occupancy-output analysis, it is possible to study economic relations in agricultural

production, analyze the effects of inputs such as chemical fertilizer, improved seed, power and

agricultural service, and of occupancies such as cropland, water and labor force on crop output. More

particularly, based on the agricultural input-occupancy-output table, the following two indices can be

calculated. First, net incomes of different kinds of crops per mu (1 hectare � 15mu), net income per

labor day, and pro®t rate of capital. It has been shown that variations in China's grain output have a

close relationship with the variation in the net income from grain. Not only does the net income from

grain directly in¯uence the quantities of inputs and occupancies in grain production, statistical tests

also show that the net income of the previous year has a signi®cant linear correlation with the grain

output of the current year. Second, through the input-occupancy-output table, the total input coef®cient

can be precisely calculated (Chen, 1990). In normal input-output analysis the equation for the total

input coef®cient is as follows:

B � (I ÿ A)ÿ1 ÿ I (3)

where A and B are the direct input coef®cient matrix and total input coef®cient matrix, respectively,

and I is the identity matrix. In input-occupancy-output analysis, however, the equation for the total

input coef®cient is as follows:


B � (I ÿ Aÿ áD)ÿ1 ÿ I (4)

where á is the diagonal matrix of ®xed asset depreciation rate, and D is the direct occupancy

coeffecient matrix of ®xed assets. For example, in 1987 the direct input of electricity in wheat per ton

was 45.4 kilowatts; by using equation (3), the input of electricity was 157 kilowatts per ton, whereas by

using equation (4), it was 198 kilowatts per ton.

Nonlinear forecasting equation including diminishing return

We have so far formulated 16 forecasting equations with high accuracy and including different

variables. Since the effects of fertilizers follow the law of diminishing return, they are shown as

nonlinear viable coef®cients in the equations. Equation (5) is an example.

Y � 18:6566D(5:75)

ÿ 13:5552X 1

(ÿ2:01)� 1:2437X 2

(3:72)� 16:8942X 3

(6:52)

� 1:4380(8:53)

(6:15eÿ0:04762017X4 � 1:9)X 4

� 1:9093(2:67)

(1:53eÿ0:03335118X5 ÿ 0:11)X 5 � CA

R2 � 0:9951 F � 1571 N � 45 (1952±1996)

(5)

where Y : estimated grain yield per mu annually;

D: annual policy dummy variable (D � ÿ1 in the case of negative agricultural policy such as

the extensive loss of grain output during 1959±1961; D � 1 in the case of positive

agricultural policy such as the great increase in grain output during 1981±1984);

X1: annual intensity of disasters (including ¯ood, drought, wind, hail, and frost);

X 2: annual irrigated area;

X 3: annual agricultural machinery power;

X 4: annual chemical fertilizer input per mu;

X 5: annual farm fertilizer input;

CA: adjusted item;

R: multiple correlation coef®cient;

F: value of F-test;

N : number of data points. Data in parentheses are values of t-test.

In order to get the nonlinear equations, we selected about 95 functions with different mathematical

forms and different parameters, and used the historical data of 1952±1996 for the regression estimates.

The equation above is the one having the highest F value (F � 1571, R2 � 0:9951) and reasonable

t-test values of fertilizer terms with exponential forms.

The nonlinear items of chemical and traditional fertilizer are calculated from the historical data of

fertilizer inputs and yield increments, statistically tested by the data of yield increments related to

increased chemical fertilizer inputs in some regions of China. The yield increase effect of chemical

fertilizer is as follows (see Table 1).


In equation (5) the t-test value of chemical fertilizer is high (8.53). Without considering the

diminishing return, the t-test value would be only 0.6527, i.e., there is no signi®cant linear correlation

between grain yield and chemical fertilizer input.

Minimum sum of absolute value technique

In regression analysis, the parameter â is normally estimated by the least square (LS) method

min Z �P(Yi ÿ Yi)2 (6)

Its drawback is that the square treatment will move the ®tted curve to some exceptional points, thus

reducing forecasting accuracy. One modi®cation is to minimize the sum of absolute values of errors

between estimated and actual yields:

minZ9 �PjYi ÿ Yij (7)

This equation can be solved by linear programming. The model is as follows (It can be simply proved

that uivi � 0 if an optimal solution exists.)

minP

(ui � vi)

â0 � â1 X 1i � . . . � âk X ki ÿ Yi � ui ÿ vi i � 1, 2, . . ., n

ui $ 0, vi $ 0

8><>: (8)

Following is the modi®ed result of equation (5) using the minimum sum of absolute value approach:

Y � 20:0568Dÿ 21:3992X 1 � 1:1137X 2 � 17:6891X 3

� 1:4867 (6:15eÿ0:04762017X4 � 1:9)X 4 (9)

� 2:1946 (1:53eÿ0:03335118X5 ÿ 0:11)X 5 � CA

This equation reduces the average error of grain yield per mu from 3.788kg to 3.652kg, and the average

error rate (average error over average yield) from 2.28% to 2.20%. It should be noted here that in

certain equations, the error rate could be reduced by as much as 24%.

In order to increase forecasting accuracy, our research team also conducts ®eld studies in 11 main

Table 1

Yield increase effect of chemical fertilizers in China

Chemical fertilizer

input (kg=mu)

Marginal effect (kg) (increased

grain yield of chemical fertilizer per kg)

Average effect (kg) (increased grain

yield of chemical fertilizer per kg)

0 8.05 8.05

5 5.59 6.75

10 3.90 5.72

17 2.42 4.64

25 1.54 3.77

50 1.11 2.47


grain-production provinces of China, e.g. during March and April every year, consulting experts and

gathering their views (Delphi method) and other related information, doing technical and economic

analyses, and then modifying the results derived from forecasting equations. We also include new

factors such as household tenure systems and new improved grain varieties, and then we modify the

adjusted item CA based on data from experimental regions.

Application and evaluation

The grain output research team of the Chinese Academy of Sciences usually ®nishes the national grain

output forecasting report by the end of April, and submits it to China's top leaders and governmental

agencies responsible at the beginning of May. The forecasting results for the last 20 years are given in

Table 2.

This table shows a number of things. First, predictions of bumper, average and poor harvests are

correct. On July 30, 1990, the former Rural Research Center of the State Council sent an of®cial

document to the Chinese Academy of Sciences, saying: `Especially in those years with great ¯uctuation

of national grain output, this study supplied rather accurate prediction; for example in 1983 and 1984

Table 2

Forecasting results of China's grain output

Year Predicted output (m tons) Statistical output (m tons) Error rate (%) Date of prediction

1980 319.65 320.56 ÿ0.3 September 1980

1981 332.30 325.02 2.2 End of April 1981

1982 346.95 354.50 ÿ2.1 August 1982

1983 380.45 387.28 ÿ1.8 End of March 1983

1984 397.25 407.31 ÿ2.5 End of April 1984

1985 380.00 379.11 0.2 End of April 1985

1986 390.00 391.51 ÿ0.4 End of April 1986

1987 403.25 402.98 0.1 End of April 1987

1988 399.00 394.08 1.2 End of April 1988

1989 413.40 407.55 1.4 End of April 1989

1990 421.25 446.24 ÿ5.6 October 1989

1991 439.00 435.29 0.9 End of April 1991

1992 437.30 442.66 ÿ1.2 End of April 1992

1993 444.00 456.49 ÿ2.7 May 9, 1993

1994 443.50 445.10 ÿ0.4 April 30, 1994

1995 461.00 466.62 ÿ1.2 April 27, 1995

1996 484.00 504.54 ÿ4.1 April 28, 1996

1997 498.50 494.17 0.9 May 8, 1997

1998 498.00 512.30 ÿ2.8 April 28, 1998

1999 507.50 506.00 ÿ0.1 April 25, 1999

Sources: statistical output: State Statistical Bureau, China Statistical Yearbook, 1981±1999, China Statistical Publishing

House, 1981±1999; predicted output: Grain output research team of the Chinese Academy of Sciences, National grain output

forecasting report, 1980±1999.


forecasted the bumper harvest of that year prior to half year, and in April of 1985 also predicted the

poor harvest of that year . . . It acted as alarming to actively address to agricultural issues.'

Second, the lead time of prediction is more than half a year. Although 70% of China's grain output is

harvested in the fall and harvest ends in November, the forecasting report is ready by the end of April,

almost six months earlier than harvest. This helps the responsible governmental agencies with enough

time to plan for grain consumption, storage, imports, and exports.

Third, forecasting is very accurate. During 20 years, the error rates of eight years are lower than 1%,

that of ®ve years are 1±2%, that of ®ve years are 2±3%, and that of two years are between 3±6% (the

error rate in 1990 was greater than 5%, but it was predicted more than one year in advance). Overall,

the average error rate over 20 years is only 1.6% compared to the statistical reports.

This accurate forecasting has supported some important policy measures. For example, in response

to the predicted bumper harvests of 1996, 1997, and 1998, the Chinese government and the Agriculture

Bank of China gave ®nancial aid to grain enterprises to increase their storage capacities. In 1998 the

Agriculture Bank of China gave loans worth 1.284 billion RMB Yuans to expand simply-built grain

warehouses, which can store 7.7m tons of grain (Xu, 1998).

Former Premier Li Peng has praised this study several times (1996; 1997). `Estimation of outputs

in¯uences policy making. If grain output were estimated improperly, for example, lower than harvest,

the government would have to purchase unnecessary grain; whereas if estimates were higher than

actual harvest, but really short of grain, it would be dif®cult for the government to purchase grain

ef®ciently and economically . . . It should be noted that the grain output forecasting reports issued by

the Chinese Academy of Sciences in recent years are rather accurate' (Li, 1997).

This study has been awarded ®rst prize by Science and Technology Advancement of the Chinese

Academy of Science (1992) and third prize of Science and Technology Advancement of China (1996).

Since 1996 it has been successfully extended to cotton and oil-bearing crops.

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