Document 6568595

一的一
An Economic Analysis of the Dynamics of Taiwan's
Rice Sector
Tso-kwei Peng*
(彭作委〉
Introduction
Rice is a commodity with unique economic and political
significance for Taiwan's 17 millino people. It is grown by
almost 75% of Provinces' 860 ,000 farm families and since World
War II , it has generated an important portion of Taiwan's
foreign exchange earnings.
The analysis of factors that affected domestic consumption
and price of rice is necessary for carrying out programs to
achieve equitable income to rice producers and for determining
出e long-run economic ou tlook for the rice sector.
The specific objectives of this study are (1) to iden tify and
measure quantitatively the basic demand structure of the
Taiwan rice sector; (2) to estimate the short-run and long-run
impact multiplier matrix. The analysis deals only with aggregate demands for rice. The behavior of rice supplies is not
analyzed and assumed given i.e. , no attempt is made to explain
changes in production in this pape r.
In attempting to quantify the important underlying demand
structure of the Taiwan rice sector , a very simple and highly
aggregate econometric model is formulated in the first part , of
the study. The reason is adequate empirical data with which to
estimate a more complex and disaggregated model are lacking
on hand.
*The au thor is a professor , Research Institute of Agricultural
Economics , National Chung Hsing University , Taichung,
Taiwan , R.O.C.
(
1 )
一 10。一
The Mod eI
The sources of supply and types of utilization of rice in
Taiwan are shown , in simplified diagrammed form , in figure 1.
The physical variables are identified by a letter symbol in each
box. The subscript “ t" of ktter symbols refers to the current
time period , while "t-]" refers to the preceding time period.
As indicated in figure 1 , the sources of total current sUpply
(Qt) consist of current domestic production (Ot ), total import
(IM t ) and total carry-in stock from the previous period (S t- 1).
Domestic productìon and carry-in stock are the major sources
of total supply , imports of rice accounts for only a negligible
portion of total.
The total available supply is distributed into different
utilizatìon outlets-current domestic consumption (qt) , export
(EX t ) and carryout stock (St). The total carryout stock conS!sts of commercial stock (SC t ) and Government stock (SG t ),
but commercial stock is ignored owing to lack data. There are
three m 茍 or types of domestic rice consumption: (1) rice
consumed as food (Y ABt); (2) rice used for processing wine
(YBA t ) and (3) rice used as seed (YAC t ). The total aggregate
rice supply is normally in excess of domestic requirements for
food or other domestic used. The excess either enters export
channels or is retained as a carryout stock. Of total consumption , rice consumed as food is the major component , only a
negligible amount was as seed uses.
An Econometric Mod eI
As indicatεd in the preceding sector , imports of rice and rice
used as seed account for only a smalI part of the tota l. The
analvsis of these two sectors , therefore , were excluded from the
mode l. Also , no attempt was made to incorporate any analytical explanations of commercial stock.
Farm Price 胡 d Government Purchase Price Relation
In view of the role of rice as the traditional staple food and
as a wa宮e good in Taiwan , the Government establishεd rice
( 2 )
一 101-
Fìg. 1 Taìwan Rice Supply and Utiliza tÌ on
Production
。
Z
SE、
Export
Carry-out
Domestlc
Consumption
EX t
St
qt
Governmentll Commerciall I Seed IIProcessingllF ood üses
Uses
1 1 Uses 11
Stock
11
Stock
SG t
SC t
YAC t
( 3 )
YBA t
YAB t
一 102 一
policies since World War II in order to stabilize the market price
of rice as basis for economywide price stabilization. Taiwan
domeStic rice market has not operated under a free competitive
market situation.
Vnder the Government policies for rice
procurement and distribution , average rice price received by
farmers are influenced largely by the Government purchase
price and stock release. Therefore , in the model the fo Il owing
farm price and the Government purchase price relation is
postulated:
PRF t = f 1 (APG t , 5 t , Ot) 一一一一一一一---------一一一一 (2.1 )
where
PRF t
= average
rice price received by farmer at time t
(NT$jKg)
APG t = average rice purchase price at time t (NT$jKg)
Ot = total prodl叫ion at time t (m. t.)
St = Government stock at the end of time t (m. t.)
Under normal condition , the average rice pr吋iCe reCei扎丸vεd by
farmers 恥
WI山
II change in the same direction 站
as 由
t he change in 出
t hε
Gove
凹r‘-nmεnt purchase pr吐ice and total producti叮
on
爪， negati扎丸vely
related to changes in Go
叭丸vernment stock , i.e.:
a-a
R-PA
E-A
F-G
>
AU
gP R.L
一一一~L
g
Ot
PA3-a
R-S
F-t
>0
+EEW-
<
AV
Food Consumption Relation
On the basis 0 1' classical demand theory , the quan tity ,
demanded of a particular commodity is a function of its price,
thεprices of other commodities , and income.
But classical
theory gives no suggestion as to whether the demand function is
linear or nonlinea r.
Engel's law suggests that the relation
between food and income tends to be curvelinea r. Examination
of Taiwan per capita consumption 0 1' rice is associated with a
( 4 )
一 103 一
rise in per capita income only at lower income le\ els. Beynnd
a-certain low income level , per capita rice consumption declines
as income increases. Therefore , the per capita income variable
was transformed using a cornmon logarithm as following:
Y ABt
=
f2(PRR t' PF t' logIB t , TEM t ) 一一一 --(2.2)
where
YAB t = per capita consumption for food at time t (kg)
PRR t = average retail price of rice (NT$/Kg)
PF t = average retail price of flour (I、、叮、
T吋 EMt = 品a丸v宅甘
E盯rage temperature at time t (oC)
10gI~t = logarithm form of per capita income at time t
(NT$/Kg)
ln the ao叭'e formula , we would normally expect that
changes in per capita consumption of rice , YAB t , wiII (1)
negative relation with changes in retail price of rice , PRR t'
and temperatur亡， TEMt. and (2) positively or negatively related
to changes in income depending upon the levels of income and
to changes in retail price of flour , i.e.:
~ YAB t <(\笠坐上<仇芒竺玉之A
~PRRt
v.
~TEMt
v
~ 10gIB
t
<V
~YABt
>
~ PF
<0
t
Processing Utilization Relation
Rice is an important material for processing to be rice wine
in Taiwan. Annual demand for rice as raw material for processing is around 45 , 000 ton in terms of brown rice. It s demand
related to the retail price of rice and the per capita income ,
I. e. :
YBA t = f 3 (PRR t , IBt) 一一-------_-一一一一一一一一一 (2.3)
-( 5 )
-104 一
where
YBA t
= domestfc use
of rice for processing wine at time t
(m. t.)
PRR t = retail price of rice (NT$fKg)
KBt = per capita income (NT$)
The other source of rice for processin 思 wine is imports if the
domestic price is too high. As a consequence , wc would normally expect the partial derivative of. YBA t wÍth respect to
PRR t to be negative and positively or negatively related to
changes in incom 亡， l. e.:
A
，
〉一<
a-aB-B
A 一 -d
<
ιVA-7
A-R
Y-p
B-R
a-a
nu
Government Inventory Rclation
The principal objectives of rice policies in Taiwan have been
(1) to prod盯 e as much rice as possible from limited agricultur訓
.resourse; (2) to control (procure) as much rice as possible for
the Government; (3) to export as much rice as possible to earn
foreign excha呵e and (4) to stabilize the market price of rice as
a basis for economywide price stablization. Moreover , because
rice can be stored for a relatively long period , it is possible that
certain amounts of rice accumulated in a gi\'en year will be
carried in to the succeeding year. Therefore , a lagged stock
variable is included in the following postulated Government
inventory relation:
SG t
= f4
(PRR t , Ot' EX t , SGt_ t)一一-------------一 (2 .4 )
where
SG t = Government rice inventory at the end of time t (m. t.)
PRR t = retail price of rice (NT$fKg)
Ot = total rice production at time t (m. t.)
EX t = total export of 丘 ce at time t (m. t.)
( 6 )
一 105 一
The method of operating the inventory for rice has been an
implicit offer by the Government to buy (included compuIsory
purchase) the amount of rice produced as much as possible at
the harvest period that would export and/or release to market
when the price increase during the marketing year. As the
result , we would expect the Government inventory is positively
related to retail price , production , and !agged inventory , but
negatively r eI ated to export volume , i.e.:
~SG+
一---"一 >0
~PRRt - -,
~SG+
一一_" >。
~ Ot ~ -,
~SG+
~SG寸
一一一ι->0 一一一~
~SGt_1 - -, ~EXt
<0
Export Relation
Large portions of Taiwan export of rice were channeled
through the Government agencies. The pu中 oses of export are
(1) to earn foreign exchange; (2) to adjust the excess supply of
rice. As a consequence , we would expect normally total export
to be positively related to 出 e total output (Ot) and total car句，
in stocks (SG t _1 ). On the other hand , if per capita domestic rice
consumption is increased andfor retail price is risen , then we
would èxpect smaller exports of rice. Hence the variables
enterring 出 e following postulated export relation are:
EX t = f5 (YAB t' Ot' SG t _1 • PRR t ) 一一----------一--一 (2.5 )
where
EX t = total export of rice at time t (m. t.)
YAB t , Ot' SG t _1, PRR t are the same symboI with previous
models
According to the above formulation , we would expect the
changes of export with respect to the change of explain variables as following:
( 7 )
一 106 一
~EX會
一一一ι<0
~
YAB t
~EX.
一一→一 >0
'~Ot
~
EX.
~
SG t _1
一一一_.
'
>0
~
EX.
一一一ι<0
'
~PRRt
Price Iden 位ty
The connecting link between farm price and retail price ~s
the marketing margin. For rice , the marketing margin is defined
as the difference between the retail price in polished rice and
the farm price of paddy rice. Therefore , the processing cost in
terms of farm labor wage rate as the margin , the relation is
following:
PRR t
= f6
(PRF t' WR t ) 一一一一一一一----------一一一 (2.6)
where
WR t
= farm
level wage rate (NT$/day)
Labor market appears to be the most competitive market in
Taiwan.
For this reason , wage rate differentiation among
different labor can be treated as relatively homogeneous in
quality. Moreover , rice is processed at rural area. As a result ,
the processing cost can be in terms of farm level wage rate.
The change of retail price normally expect positively related to
the changes of farm price and wage rate , i.e.:
a-a
R-nk
p-p
R-F
>
AV
~PRRt
~WRt
>
0
Statistical Estimation
ln the preceeding section , six relations were formulated for
the mode l. The postulated relations do not include all the
relevant variables in the system. On the contrary , only main
variables for which reliable empirical data were available were
considered in each relation. The influences of such omitted
variables are treatcd as disturbances and explici tI y recognized
by in troducing a random disturbance term , Uit' into each of
( 8 )
一 107 一
these six relation.
For simplif可ling the estimation procedures , all postulated
stochastic relation in the formulatεd system are assumed to be
linear in parameters.
In estimating the parameters of the formulated system , the
variables were divided into the following sets of endogenous
variables and predetermined variables:
Endogenous Variables
PRF t = average rice price received by farmers at time t
(NT$JKg)
YAB t = domestic per capita use of rice for food at time
t (Kg)
YBA t = domestic use of rice for processing at time t (m. t.)
SG t = Government rice inventory at the time t (m. t.)
EX t = total J;Î ce exports at time t (m.t.)
PRR t = average rice retail price at time t (NT$JKg)
Predetermined Variables
The set of predetermined variables consisted of the lagged
endogenous variables in the system and the following exogenous
variables:
APG t = average rice Government purchase price at time t
(NT$JKg)
。 t = total rice production a t time t (m. t. )
PF t = average flour retail price at time t (NT$JKg)
TE:\l t =瓜lerage temperature at time t (oC)
logIB t = logarithm form of per capita income (NT$ per
capita)
WR t = farm level wage rate (NT$Jday)
The complete structural system formulated in the preceding
section can be summarized and written in the following simple
( 9 )
一 1 的一
matrix form:
AYt + BYt-1 + CX t = U t 一一一一 ---一一一一一一一一一一一一 (3.1 )
where
hγ= 附to
叫r 向
YAB t
YBA t
SG t
EX t
PRR t
川 = vect叫 of 1幣 d endogenous 叫仙 s =
尸
I PR
盯
F←
YAB tι-1
YBA t _1
SG 令
t -1
EX~
t-11
!I
PRRt-l J
Xt= 附間 of exogenous vari枕 s=
í
A悶
。t
PF t
TEM t
IBt
logIB t
WR t
l
( 10 )
一 109 一
A = matrix of parameter associated with endogenous
variables
1
。
。
a14
。
。
。
1
。
。
。
a26
。
。
1
。
。
a36
。
。
。
1
a4S
a生 6
。
aS2
。
。
1
aS6
a61
。
。
。
。
1
B = matrix of the parameters associated with the the lagged
endogenous variables
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
。
b 44
。
。
。
。
。
。
。
。
。
。
。
。
。
。
( 11 )
一 11。一
C == matrix of the parameters associated with the exogenous
variables
cll
c12
。
。
。
。
。
c18
。
。
c23
c24
。
c26
。
c28
。
。
。
。
c35
。
。
c38
。
c42
。
。
。
。
。
c48
。
c52
。
。
。
。
。
c58
。
。
。
。
。
。
c67
c68
and
U1t
U2t
U4t
U5t
U6t
There are two distinctive features of formulated structural
sy 咐m (3.1): (1) the matrix of the p 訂ameters associated with
the endogenous variables in the system , A , is not a triangular
matrix; (2) the matrix of the paramaters associated with the
lagged endogenous variables 扭曲 e system , B, is not a null
matrix. By difinition , the formulated structural system (3.1)
is a simultaneous dynarnic system.
Estimation Methods
The choice of an estimation method to be used in estimating the parameter of a stochastic structural system depends
( 12 )
-111-
critically on the specification of the mode l. The 2SLS method
was used to estimate the system because of the simultaneous
determination of prices and consumption.
Estimated Structures
The empirical estimates of the formulated structural system
(3.1) were listed as following. The figures in parentheses beldw
the estimated parameters are the standard errors of the
estimates , d.w. is Durbin-Watson statistic , h is D!l rbin's hstatlstlc.
Farm Price and Purchase Price Relation
PRF t = 5.858 - 0.000026 St +
0.0000008ιOt+
(0.0000098)b (0.0000012)d
0.8243 APG t
(0.06167)a
d.w.
= 2.067
Food Consumption relation
Y ABt = 3070.01 -
0.4生 97
PRR t - 6 1. 5292 PF t
(0.60555)d
一
(55 .4 989)d
716.10410gIB t - 18.5131 TEM t
(676.1 仿 )d
(23.6174)d
d.w.
= 2.0869
Processing Utilization Relation
YBA t = -2078.27 - 320.306 PRR t + 4.9736 IBt
(75.3014)a
(0.832303)a
d.w.
= 2.015068
( 13)
一 112-
Government Inventory Relation
SG t =-348107.0- 0.080579 EX t + 158 1. 23 PRR t +
(98.6961)c
(0.371412)e
0.0135899 Ot+ 0.84405 SG t _1
(0.22327)a
(0.023277)d
h == 1.54
d.w. = 2.15799
Export Relation
EX t = 243357.0 - 298.799 YAB t - 1216 .4 3 PRRt +
(572.942)b
(167.925)C
0.01588 Ot + 0.303379 SG t _1
(0.0190089)d (0.125994)a
d.w. = 2.092978
Price Identity Relation
PRRt ==-0.0643387+ 1. 2146 PRF t + 0.224125 WR t
(O.062043)a (O.0244679)a
d.w. == 2.076291
where
t-value is significant from zero at 0.5% significance level
t-value is significant from zero at 1% of significance level
t-value is signigicant from zero at 5% of significance level
t-value is significant from zero at 1 0% of significance
level
e: t-value is significant from zero at 20%of significance
level
d.w.: no autocorrelation at 1% of significance level
h: no autocorrelation at 1% of significance level
a:
b:
c:
d:
( 14 )
-113-
In the above estimated structures , the signs of all estimated
coefficients are in accordance with the theoretical and logical
expectation specified in the formulation of the mode l.
Analysis and Implications
Elasticities
Estimated of elasticities of food consumption can be
evaluated by means of the coefficients of price , income and
retail price of flour , and the means of the data of the observations. The elasticities are listed as following table:
Table 1 Price Elasticity , Cross Elasticity and Income Elasticity
of Food Consumptoin
Price Elasticity空
Income Elasticityb
一 0.0214
-0.037
Note:
~YABt
PRRt
~PRRt
YAB t
Cross ElasticityC
一 0.07
a: En=
盯
b:E1 =
ABt 尸
~logIBt
~YABt
PF t
c: E RF = 一一一一-﹒三三三三
。 PF t
YAB t
The demand elasticity is ，一 0.0214 ， very inelastic owing to
rice is the main staple food for Taiwan's consumer. The income
elasticity for rice demand shows a negative sign which indicates
由at rice is an inferior good. Both resu Its provide a ve可 im­
portant policy implications for Government to protect rice
producers and to stabili扭曲e price variation.
( 15 )
一 114 一
Impact Multiplier
In making economic policy decisions , one usually asks
questions such as these: (1) if a policy instrument was changed
during a given time period , what would be the effects on the
related policy target of on other' important variables in the
system during the same time period? (2) what would be the
impacts of such a change during each of the successive 、time
periods? (3) what would be the total impacts over a long
period of time? To answer such questions , we need a knowledge
of the underlying economic structure. In the framework of the
formulated model , the above questions are equivalent to the
general problem of finding the solutions of the short-run and
long-run impact multiplier matrices of a dynamic system.
Short-Run Impact Multipliers
To derive the short-run impact multiplier matrix for the
dynamic system (3.1) , we consider the followi時 reduced form
of the underlying structure (3.1):
Yt=D 1Yt-l +D 2 x t +V t
一一 -------四----一--一一一一一 (4.1 )
where
一
tdh
BCt
-K
'in/ 回
DDV
+-L
By the definition , the short-run impact multiplier is defined
品 the impact of a unit change of exogeneous variable during a
given time period on the endogenous variable during the same
time period. That is:
~Yt
一一= D2 =
I d 2ij I
axthf
is the short-run impact multipliers.
( 16 )
一 115 一
One important policy instrument variable among the
exogenous variables of the system (3.1) is the Government
purchase price variable (APG t , the Government has adopted the
support price policy since 1973). The short引m impact multipliers of the support price are summarized in table 2.
Table 2 Short-Run Impact Multipliers: Impacts of the Government Purchase Price on the Endogenous Variables in
the System
Endogenous Variables
Identification
Average farm price
(NT$/Kg)
Per capita consumption
(Kg)
Processing demand
(m. t.)
Government inventory
(m.t.)
Export (m. t.)
PRF t
0.8645
YABt
-0 .4 7146
YBA t
-336.22232
SG t
1,546.06199
EX t
1,418 .1 3625
Retail price (NTJIKg)
PR~
Short-run Impact Multiplier
of Support Price (NTJ/Kg)
1.05002
These estimates of the short-run Government purchase price
impact multipliers imply that an increase of NT$ 1 per Kg in
Government purchase price , with all other predetermined
variables in the system held constant , willlead to (1) an increase
of NT$ 0.86 per Kg in average farm price; (2) a decline of
0 .4 7 Kg per capita in rice food demand; (3) a decline 336 m. 1.
in rice for processing; (4) an increase of 1 ,546 m. 1. in Government stock; (5) an increase of 1 ,418 m.t. in total export and (6)
an increase of NT$ 1. 05 per Kg in average rice retail price during the same period.
( 17 )
-116 一
An increase of Government purchase price (and also farm
price and retail price) leading to higher exports is explained by
由e operation of a再justment stocks. When Govemment stocks
mounted to r eI ativ eI y high , the policy usuaIIy was to reduce
th凹n through export program to earn foreign exchange. The
surprising result is that the percentage of retail price increase is
higher than that of Govemment purchase price increase. In
other words , the retailers transfer whole cost to consumer and
make an unreasonable profit.
Long-Run Impact Multipliers
Given the dynamic system (生 .1) and given the initial conditions of endogenous variables (yo) and the time-path of
exogenous variables (門， for t== 1 ,2 ......，的 can be determined as
fo Il owing:
yl == D1y o + D2 x l
q4
X
唔，A
YK=
EA
官
qJh
qι
yqh-- D , vdo + Dq4x + D D
i
DPo+D仇 +D內xk-l
+
------一一-47.ID2X1
一一一----( 4.2)
If an exogenous variable is raised by one unit and remains at
its new level in successive time periods , i.e.:
xl = x2 == ....… ...H.H.--H.H.-...=xk=x*..一一一一一一一 (4.3)
Given (4.3) , the relation (4.2) becomes:
k-l
YK=DTYJ(I+DI+Df++D1)DJ一--(4 .4)
Taking the partiai derivative of yk with respect to x*'iι ，
( 18 )
一 117-
;::)Yk
-7=(I+DI+Di+Di + .
+
;::)x
D~-l) D 2 -一一一一 (4.5)
_j_y.,. 3
_j_n. k-l
But 1 + D 1 + Dî2 +
Dí + ........... +
Dr .l can be expressed as
_j_
(1 - D 1r 1 (1 - Df) ，帥的tion (4 .4) can be w耐心:
IT
k D x
Yk == DîY o + (1 - D 1 r-1.l (1
- n.
Dî)
2
For a 叫le dynamic 叮stem， the matrix k will approach
a null matrix as k increases. Therefore , the endogenous variable
vector will a approach the long-run stationary equ i1ibrium state:
Dr
lim yk=(I-D1) I D2X*
,
k →∞
Therefore , the Iong-run impact multiplier matrix of a stable
dynamic system is:
(1 - D1r1D2
The estimated long-run multiplier , as table 3 , shows that a
sustained increases of NT$ 1 per Kg in Govemment purchase
price wilI generate in 出e long-run (1) an increase in 9 ,913 m.t.
Govemment stocks; (2) an increase in total exports of 1 ,589
m.t.
1n making policy decision , it is useful to know the relative
magnitudes between the long-run and short-run impact multiplier resulting from a change in policy instrument variable.
Table 4 shows that the long-run effect of a change in Govemment purchase p~ice on Govemment rice stock will be 6 .4 times
as large as 出e coηesponding short-run effects. But the Iong-run
impact multiplier of the total export is only 1.1 times as large as
the short-run effec t. 1n other words , the Government stocks
wilI accumulated to a very high amount which wiU depress
average farm price.
( 19 )
-118-
Table 3 The Long-Run Impact Maltiplier
Endogenous Variables
Identification
Long-run Impact Multiplier
of Government Purchase Price
(NT$/Kg)
Average farm price
(NT$ /Kg)
Per capita consumption
(Kg)
Processing demand
(m. t.)
Government inventory
PRF t
0.8645
YAB t
-0 .4 7146
YB~
-336.22232
SG t
9 ,913.76771
Export (m.t.)
EX t
1,589.49268
Retail price
(NT$肢的
PRRt
1.05002
Table 4 Relative Magnitudes between Long-Run and
Short-Run Impact Multiplier
Endogenous Variable
Identification
Relative Effect of Govemment
Pu rchase Price
Government inventory
SG t
6 .3 5
Export
EX t
1.1 2
( 20 )
-119-
Summary and Conclusions
The purpose of this study has been to analyze the basic
demand structure of the Taiwan rice sector and to estimate the
short-run and long-run impact multiplie r. The sign of variables
in whole system are compatible with theory and logic expectation. The formulation of demand for the Taiwan rice sector
could be improved by incorporated as a whole and by means of
different estimation technique.
The result of emperical work shows that rice is an inferior
good and demand elasticity is very inelastic which is consistent
with the prior research (Chen , 1980). These results provide a
very important policy implications for Government to protect
rice producers and to stabilize the price variaties. 1mpact of the
Government purchase price on retail price indicate that the
percentage of retail price increase is higher than that of Government purchase price increase. 1n the long-run the Government
stocks accumulate to a very high amount but export increase
only slightly. This will increase the fiscal burden of the Govern口lent.
Multiplier analysis as a menas to examining policy alternatives in commodity markets are limited to partial equilibrium
analysis. One can answer the question concerning the impact of
a change in an exogenous variable on the endogenous variables
while all other variables are held constant.
This type of
analysis can be performed to evaluate short-run and long-run
effects..
On the other hand , the limitations of multiplier
analysis is where the exogenous variables undergo constant
or varying rates of change or the underlying model is nonlinear.
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References
Chen ,
W. 旺，
An Economic Study on Govemment Rice Stock
Operation in Taiwan , unpublished Ph.D. dissertation , Universi ty of Illinois , 1980
Kmenta , J. , Elements of Econometrics , New York: John
Hopkins Book , 1971
Labys , W.C. , Dynamic Commodity Models: Specification ,
Estimation , and Simulation , N ew Y ork: Lexington
Books , 1973
, Quan討tative Models of Commodity Markets ,
Cambridge: Ballinger Publishing Co. , 1975
Mo , W.Y. , An Economic Analysis of the Dynamics of the U.S.
Wheat Sector , USDA , Technical Bulletin , No.
1395 , 1968
Reutherger , S. ,“ Analysis of a Dynamic Model , with Particular
Emphasis on L. R. Projection ," JFE , 1966 (48):
88-106
Theil , H. , Pinciples of Econome 甘ics ， New York: John Wiley
& Sons , 1971
Vandenborre , R.J. ,“ Dynamic Impact Multiplier: A Case Study
of White Dry Edible Bean ," AJAE , 1968 (50):
311-327
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