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~ ;'!f~ ~$ J1l1* (6~ ~~ i( m)jJl]
-nt 1] z -6Jf 1t:*
A Test on Expost Forecasting Performanceof Rice Supply Model in Taiwan
..I.
At ' fJi jjllifjg:1) z ffij:lit
~ , ;;f~fij*~Iil:Zlf;:if{
lf~' J:&tl1li(j!§:1]z#Q5E]klt~
~"a.~.5E]k~~fi~~*'~~~fi**.~M~m~~M.m~,
~~m.~~.~~.~~.*moo~~~.5Ett(U~MW~y) o-.~M
rJii1lli~}J1*lt~ , 'liH-)'H:i1:~~}J1* (Econometric approach) fJijjllJ , tEfJillllJ
l~Ffl:t'l~~* 'llsIzm:~~~~.9='j::)'~t:i1:~~ (Econometric model) ~
m.I~*B~~~fio.~l:ffl~~~H:i1:~~~~Sm±~§~z-o~H
:i1:~1"!H1t~{&(~ffljjlli~~, ~~~l~H;5 : (1)~Jmt:<:~f)Jt2~~*~:hllj::)'*~1t, ffiiJUiU1!!~li-1W~~ft*fB~H~ , (2)~Jm~fi~lm~IlsI*:&fi*4rl3'zruJ(,f;~5~ik~~IUI(,f;1Jllj::).-f{1t '(3)~.!jl:1&f:&iltli (Ex-post forecast) :&~~{1strr
~1T:l1!!t:E~~filIH!HJi l1lli , (4)00~m~* J1JtE1nHit~~jJ1*2miilliftJt ftlr1Jif;1l!~rrr.o
* *JiffJEL5Ep.x*m:l'lI:j:l~*!¥.~JI~~lM~±fH'll~,\!;,,~X/QJi31'J' J'i)'jC:~i;:t ~
**~~~~:I'l*~*¥.~JI~¥*m~o
( 1 )
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.~~~~~~~~~-m,m~~~~~~~~~~n~~~,~~~~
~~&~*a~~~~<>~*~~~~~~~m~~~,~~~,~~~~.~
Jrrj,lj-mt~IHiH&ff-H!f:~il&~:l(Ufili't~r",mo ~f1fiiJ~ ~fi~*Ef;J{~U~{lE~{M~~iWS*
~~~~#~mm*~.ffl~z$~<>
~*~~§:lItfj§*~tmY~J~tt~~1ft5\;~fJ{llItlJtt; o ;rr~f*tE~f~i1iff5'G
~.~m~~m~~m*~m.~Z.ft(~~2'3) <>~~~~.(~~2
) :&lltllJt', (~~ 3) jilijtIZ~'f'C:lt:r(E.ftliJjtmi1trlZ~*{!~~:¥73fJ.5\;o {'ri';
~m~.~.=~~z.M~e&~.I~,~~~=~~••~.~Z.ftRlItrr:iE ' tJ~.~ffliJI[fjg1Jz~5Et(Yi'4'!A~W 0 *~~!I~t~m~rJT.ft~*.}-\;
Ott 1 J 9=t;fjrHlfj§*~tmH5}it1t.AZfflil!ij~1J;bn~J5HJT o Mc*~~~ § ~fg
}& : 1. ~~ffilll[flg1J~:Il~jj1t; o 2. ~'l'-~~.~*#Ui'i.;A;zfflIllUfjg1J c *~
~.t),Jjj:m (Expost) ffllll[:;IJ~ , ,HUtJ 1. Root Mean Square Percent
Error o 2. Theil's Inequality Coefficient o 3. Mean Square Error c ~
~.~~~.efi~••* ••~OO.jjfi5\;Zffllll[flg1J~U~~'%fiH.fjg
:t)~iMZlZSf~fiiItEc MtJ7Jf~~t*:lt~.Ail!ij}E~tE~.~mlllIJ*M~JJlz~.lIiJ
:ffmt~'t;it o
-Mrr.~~.~ffl.fjg1JZ~~liJU~jilijMMOO*~.<>~-~~~_~
f£fJtIllU (Ex-post forocast) Ef;JfFlj~JJl*~.I: ' ~=~JtIJ J;.X$-wJffllllU (Ex
ante forecast) l¥Jit3:1!U!t*lg;i: o mm$f&fJtllltlJiEflJ}¥l$:mi¥J?i-1=.fi!lt (Exogeneous variable) *ulWif&~f,{ (Lag-variable) *J&Jjl.1£:i¥JiJg~?i!f,{(Endogeneous variable) i¥Jf{{@ , ~f&oo:z~.~{[Unj;JJttl( , UIll~fflillrr~
~Z*/J'fIl!c~ii'l'-fJ'tz~~ c JltfitrJifJ't~~~.~MIJ1itZJt~ , :tEii'l'-fJ'tf5[m~Jt~
~9" <> ffil:$fttrffliJI[JlU:JE fUm fi'R f&1!IttJ~*%:l¥JJJ-xiB!:5Ea9?i-1:.fflt * PJ<**l¥Jpj
~~~i¥J~M'.f&._.fttrmR*.Mffllll[MIziteftJJl().fttrffl.z~.tl(
lIE ' -Jii11f~~~1I\i;.1~·HiRliJj;tJt~ , 5Z.ttfflllUI**fflRfjg~~~Umf~llIrrzmR
'.~fi*l=.~f,{~*~.m%:,Jltfi~m.~~Illl¥J~~<> ••ffllll[J1it.f&m.~liJffl*~••~zffl.~~,~~tt.~M~JJll¥J~.,*~~.it••mlIIftJlltJijjt§.lj o
~m~••M.~m.**¥~.~~~(.A~ziJgl=.~f,{)i¥J~*~., ff.~m~* ~~ /Jtf;f,0M7FI!ffif ' tJ?i-l=.J!f,{zffli!I[MIjlH~ .AzlZSf* IJfd 1'* ffil!t
C&1: 1) : ~~it,e, r_Mffl *J3i!i#if~{j1f~z~t.ll::7HJTJ 'D·~~..~Jt~~~.'~M~~~~~~'~E~~*~..~~~*~~~~.~~m~8Ao
( 2 )
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~~~~.~~um.o~u.¥~••~~~~~:~)5)T!I'I!iLz~~.AJ.;W, ¥,=a+,8xt+", t=1,2, .... ,T
"t-N (O,OZ)
AJ:? Y t ~m t :JtllzrAj1:i!f(X,~~t:Jtllz7I-1:~f(
a ». ,8 ~~f(
"t ~~~~]~i!l.llI{~ztlrrr7JtE*}~a:& ,8 i'~f ,:t'i..J;;il XH 1 z{lilU~, HU Yr+1
A
{1!J:!®10~j.-'? *~f~?J!llftfi~ YHI = E(YT+l) = a +,8 XT+1 ' JltlJ;jf~?J!llzij')t~~A A
tEa :&,8f..'§lit5EBJ[JZ~¥VT er+l = YT+l - YHI Jl;:Jtll~ft!!:&~~rdlrf:@nA •
E(eT+l)=O, a,=a z0 *3i'iit~1t a:& ,8f..'§*~, ~t)Ji1t~t1Jlt;1JlltJ.l1lll5E' mJ
a:&,8zm5E$~~~IT~~'~Jltm.~~~~§~a:&,8Zm5E~~'~.
~Zf~?J!ll~~~f..'§ 07 =oZ (1 +{ +~TX;= ~~:-) 0 f1JltJt'JfluRJ~--W~trnJl
i!l.ll{il!zi§titI@:Fa' (Confidence interval) ~ffltJ.W£5Ef~iltllftfizM'Ii10 -1lIl:*.,-m~••~.Afflm~*Z&a'RJ~m•• (p):&.~.(A)~Z
~~1JntJ.i'P1f0 m:jljfz~~j~\!N~ , 2Uj"~jttAZm?J!llfil§::J)>J~~fx:*~ili 0 j1(tJ.fJl?J!ll{W!:&.I~'d@r!3,zrMJ~lfiiIff,ftnr :
+ :\
I n+
p () p
N ][
- A
[Ji 1 milliJflliiWJ!.~fl~U#J~I@
( 3 )
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[c'lli11 <ftr'dEEl':t~*;r~jt~{t!Ii¥'.JC'A~ , ~~~*71,fJ[illU{@:l'J':JL>{z~ 0 ;ltJ:l'!''.!~{[~{t<
••~MftB.~M~~,~~~m.M~••M~~~~~~~~~o~~~~~mll·N.~~~B.Mft••~.re~~~ffi~'.~~~~~.~~~~{tMi:lr::IE~ , fJ[illl]f@:I'E1~{tf@:lli:lr::IE1J& ' RZ.~MB9~{I::MJE:fJJt%n#, f}'jiJ!lJ
M~.reM~~ft1J&o~*~~AMrr ,m.~~~~B.~ ••~~wre~('i] ffi&:; ill~~IlltB illl) {@:~.~ fItll'E17E: (.1) 1E ZI':;f§R ' Pfr tJYJ:.fiEf R'J ~{t{[l'U0lE
1J&a;f' BillU{ttl~.{t{ffiipXj)Ht1J& 0 tElltffi.~l~~1Blfii}~ijilljtrr~~iO'h':'~ (Turning
point error) 0 'i'Pfr1'f~iHHmtErr • N.~Hifm1ltfJ[illl):ff,tA1J!:~Ht}Jfi'iJIEli'i8''.J
.A°tE~l<fta~~UttW-.U~o~~IEM*~••~~~~,~mrr·N.m&9~lffi~ID,~~2m~o1lt••M~r%~m••J~~fi~A1lt
.~ffl'~~ffl.M~••Mm~ffi~&1'f~fto
.~~tE.rr.mlitE%~B••z~~Hif'~~B.~~(Wffi.M~~.moo) o*~~~tE1lt ••litE%~B••z~}JHif,~~m.~~(WB•• ~~••M) o'i'~MtE.N.mlitE%~B ••z~~~M~~m.~~(gp fj{ illq 00 r% ~.ltHffii) 0 * ~~~ Inllt~ IR'r3Z. tt'lt~ fJi ill1lffJRZ;{5jJai'jl1\U eft Jrc; fj{illlJfm(jI (QPfflllllJ(I!!([In~~fLlO 0
+
*w: :Vi· mii ~Sf X:(turning point error)
P :~.f· --I{I] res -....J;! v 1.ffIl "'1
(overestimation)Y·ff iUi]{W 1j~
(underestimation)
A 7C~ UUJIIJ ¥JUHi illl] -!Ii\! {t~(underes -tima-tion ) Hi tHiJ. -!Ii\! l'~:j .
(overestirnation)
+p
~\l Jrj· mr'i .~S! ;'(:(turning point error)
.\
ftfl 2
( 4 )
-129-
Jj!ltffijJlU{U[lU!{~{rlirs'iHV(lj\;z.Ntr~, (,[,FfH~·fJM.1~fP]Z'l}#f1Ji't 0 :tiit5t*3~.a~~&~m~~~kM~~:
H Root Mean Square Percent Error ~1JtfHl!:J35t~ (iff 2)
••aRM~E~~~~~~.ffl.M~.nM~.~~.E5tfto~~'ffi;5-\:~ :
RMSPE= ll--I-(_pi-.Ai )3T t = 1 At
o~RMSPE~oo
i=1,2, .... ,T
l:~r:p Pi af~i1!U{iR' TIff Ai ajl(~M ' TaMra' 0 J1tf\t1J~Hf,~) RMSPE
{iR~*'H~~fIliffli1!U~:hI¥J~{~'RMSPE M~{l£:1f~~ffllJlUfiJ;linl(~fi~~~
~~.'J\ , ZIJ\~~~~~fflillU~:h.i'iii 0
\:::) Theil's Inequality Coefficient (iff 3 )
••~~*.&~••ffl.~:h~1J~o~~*.U.~~~~ft.~*~rfl' (~~O~U~oo) JUt~~a:
u=
nl: (6.Pi-~Ai):i~l
n2:' (6.Ai)~
i = 1 . i=1,2, .... ,n
l:~r:p Pi A i ~~TJnJlIJM
Ai a i ~~.~@:Ai- 1a i-I ~~.~{iB:
naMrs'6Pi=Pi-Ai- 1
6Ai=Ai-Ai- 1
Jlt1JI;M'[JIlfiJ~illiJii~:h(J~tift1lJfxi'Jt~ U {i!!H9:Jd' , 'M U {Ifir.s%fh'HJiilliJ{@\¥)kJr•• ,J1t~ffl.~~~~ffl.oUfi~m~.~J1tffl.~~~~~~~ffl.,m
~)u fiR~'l"lR~mAH9 T~ illU ffg:h~~ 0 ;§:1lll.lit 11d!\li1'1; 1!r iff ft II'n~ illU~Et~~ Ih'~AA~~~~~~~~~~H9~~m~~l¥Jo~31lll1J1'1;~~U~~ULm~=
fi1J~~~~o
titt 2) : ji Pindyck, R. S. & D. 1. Rubinfeld, Econometrie Models & EconomicForooasts, 2nd ed.• 1981. P. 362.
c.itt 3) : 5? Leuthold. R. M., "on the Use of Theil's Inequality Coefficients",AlAE 57: P. 344-346.
( 5 )
--130-
(~ Mean-Square Error fflilJ.a~1'tZP:)jIr:FjS;lt;}~(ffij~:mMS E) ,~fjj1J
i'ldfJEll'1((:(flk8 nrt)'JI~flilla~~l¥Jmnt~~Mtffz , fr{:mfJUJlafJl§JJz1M.fi£~-~~~fiRMo~~.~~T(tt4J :
MSE= 1 i (Pi-ai)~ = 1 :i: (_Pi.- Ai )3n. 1 n. 1 AI- 1
1 = 1=
i =1,2 •....... , n
b\;~ Pi=(Pi-Ai-l)/Ai- 1
ai=(Ai-Ai-l)/Ai- 1
Pi ~ i ~~fflillU~Ai :If£ i ~Z.~~
Ai- l:lf£ i-I o¥z'Jlf~~
n:mwm.,EE ~~~I¥J*~~IPJ MS E PT~ntjifiH{j)r;lPJl¥Jm~ 0 M-mR::tm~~ , ~Bl<
:g.{])t;jtIPJ!!!!JPJi 0 @PR:: MS E=(p-a)2+(Sp-S.)2+2 (l-r) Sp S. M=til~!liiillJ!~ , ~f,fi9"i])tff~L~:r~ 0 gP:lf£ M S E = (P - a)2 + (Sp- r Sa)3+(l-r~)Si
i!EJ::iIDm~5t:m~~Jj;)'*f!'J.mm~~Jt{7lJ~ , ;It-~ UM+US+Uc= 1 0
j\'::::~ U~I+UR+UD= 1 '5t7JIJg-jtIJJ.l~Jt$Z~t~A~n-r:
U\{= (~S~2 (WuillJ!~Jt$)
(Sp-S.)2US=--MSE- (!J!~~Jt$)
Uc=2( 1M~~SESa (J!<IPJI!~~Jt$)
U R = (SPM~~)2 Ojijj~~Jt?¥)
U D = ( 1M~is; (fI~~T~Jt~)
llt:fij]"rt;~m:~:lf MSE ~)l-?pI¥JMf' ' itR::~*fflillUWu~IiAUM ~ UR
"&UD}jJG$i~UM ~ Us"& UczJt$, 1Jl.~~~Jt$Z~~*J¥lift1fJtilla~1Jl¥Jaa
ott1r'~5tM MSE 1Iif~~ UM+UR+UD= 1 1¥J~~Jt{7lJA' ;l'l;Mf'tl:Jt~J'!;
~~~o~:lf£lltmm~l¥Jnt~~PT~~.~~~ffl~~z~figffi~~~g-jtOOo
mU)l:;l'l;~mA:m
(itt 4) : Y1. Maddala, G. S. Econometric lst, ed. 1976. P. 344.
( 6 )
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Ai=a+j3PiA A
LA4t Ai ~"~fl!! ' Pi ~miJl%~ , a ~ j3~f*'~f@: , '&'a = 0 1l,8 = 1lf.fA
.~mmM.'~••M,~~~m.m••~ffl.o,&,a-O~,UM~••A
~~'.ffim.~~m.~fflm'.,8-1~,URM~~~'~ffimm~~m•• M~mHo~UM~UR.m~~ffl.~a~~.~~.$~m~,m~mm~~~~~M.~gM~,~m~.m.~~.~~g~~~.~(mUD-l
) 0 m-Ulllt UD ~!&~ 1~.ffi1'9h,\;fJ1iJlU~:1J~l~rl'iJl&~fJliJlij~A 0 • UM ~
UDZ~~~*~'.~~*~~~~-~~~tt'~M~~~~m~~u~~
j'n1-(fJJibllfPH!lI!J!iTiii!fJiilliJi~'J' 0 mU~f; UM ~ UR fi[;;p:ft~~'J'~ , 1Jtf1'~gtRJ
um~~~.~~A~~~~*W~m~~.&~m'~~~ffi~~.ili~~~
{l£ , 'I'~M.jIT~~~~ , ~1Iif~miJlij~:ft-1ll;;p~@trm~~.'$(fJffliJlij 0
~lItffl*li:i:~~f(*7J~ 1m:?1I~,%',~~FJfm~~ r~~lffi*f)~'W~fj{~ ~
n.~fiJ~~R* ••~~f(A,~~f(A"~.I~~6o~.A%m~1ll11~:&~-~ ~=:WH'F 0 4tf~w::M%5JljiltU)Ejt1illtIUfifR ~ ¥&jlljf1t~;;&::&.~m:it
~iBi.A 0 ~!f1~ 1 :&. 2 ~JJIJ~~-:M*~:&.~':::M*R~~:fi1i:fltIjlljfJ1{ (Aij)
~iBi.;;/k 3 lk. 4 ~¥{ftm••• (Yij) ~~f(5'\ ; ~ 5 »» 6 Jtumlffi*.ffi~~ij)~~f(Ao~" ••~~.A4t~~.~.~:&..&~~:
Qij : ~*1::mat ( i ml&' j :MfF) (~*, =f~JT) 0
Aij : *RfiHlamf1t ( i ml&' j :MfF) (~~) 0
ATij : *~l::MfilflilmfR ( i m[;£, j :Mf'F) (~~) 0
Yij:¥&jlljfR•• (i~I&' j:MfF) (~JT/~~) 0
PGFAij: *~6-llJj~~Hllff1FP:~fJ~(i mlM>:' j :Mf'F) (7L;/~JT) 0
PGFBij: 1ltr~12Jj~*~5}jR~Hrtm~:MJjJm.0
(ifiH![' j:MfF) Of;/~JT) 0
GPSF: ~t7§~m1J{~ (5t/~~) 0
~F:fit7§~~~~(5t/~~JT) 0
PVF: .~l:mli~~~m. (604'--100) 0
WAij: Ij{ ( i tI~, j WH'F) (5t/I) 0
CWTij : *~1:..Ij{.ffl ( i tI~, j :MfF) (5[;/~~) 0
URij : $rtHtfJiHt (.pf,!i~plf(~*,) (i fi~' j :MfF) (%) 0
ern: *~1::.¥{ftiDit1U1!f1l(;*( i til&' j WH'F ( (5G/~I~J 0
( 7 )
-132-
"
,
i-1.53xlO-1
(-10.67)
~:". 1/{ 'h! J!t,t ljl ! J:l1IJfF1 ':~ .r.-1-'11.
~~
~W; !!..*: Constant PGFAiJ
I,
1 All 1.13xl03 ' 1.59xl02 :(0.85) I (3.60)
II
II
2 AZ1 2.03xlOt 3.07xl02 \(115.64) (6.07)
2: I . - ;k &. -i- I",m*n,-" ".,:,1 "1'."."",;,<,.~~J~L~~ r~~:.I~PijJ1U:;tK: J~rU~&,1tl
WAu i CWTiJ t URjJ 1 PVF_.---- ~-_._--- ---~----~ ~-----~--
8.53X102 !(8.34) I
I,
3 A31 6.28x104 \ 4 . .52xlQ2 -3.12xlO(36.33) (0.99) (-1.32)
i, -3.5xlOI (-1.69)ii
4 i A4 1 I 9.56xl04 2.5 x103 -1.26xIQ2! i (34.4) (2.75) (-5.52)
I
5 ' A,I I, 6.05xl03 2.76xl03 !I (1.82) (3.96)
6 Au, 3.65xl04 ! 2.l3xl03 I -6.97xlO• (3.l) i (4.00) I (-5.5)
I I
7 An 5.16xl03 i 2.26xlQ2! (1.24) (2.54)!
tt : f,'i~[\P'J~"f=i* t 1[1{DW Pi: Durbin-Watson statistic
( 8 )
-133-
~ (1963-1979) ~;H't~~ t5~ljjJj*0 L S
1.56
DW
ItRNNu ! ATU
I
;'~f!";':~"1I I
.----~~--------_. -_.~~_.~....--~-I-! 6.49xlO- 1 930 0.99
(9.09)
PSF
4. 14x1Q2 38.5
I0.89 1. 78
(l.95)
9.41 1. 73x10· 34.82 0.94 1.32(l.81) 01. 78)
-3.26 ! 7.67x103 8.3 0.73 2.07(-1.46) (2.23)
-2.97 5.81xl0-1! 119.42 0.97 I 2.3( -1.27) (4.2) I !
I I
! I
-9.22xl0- 2.22x10-1 1. 56xl03 14.94 0.87 I 2.18(-1.19) (1.17) I (0.94)
II
I
III
-5.67xl0- 7. C6xl0-11 28.17 0.87 i 1.9.4
(-1.43) (3.14) .!
( 9 )
-134-
CTIl
1. 28xl03
(5.41)
~ I ~Inp{tw.~ !Dtr M P.lG ;;$:I I
-----------
I URIJ
II -1.95xlOI (-2.75)
*'il ~ I ~ffl it Jjt ;llJlfE1i. -jMffji. I.
~ : I~onstant -PGFAIl . PG;~IjI !
------------ -------
1 AI2 9.94xl03 I 4.77x10z(4.38) (2.87)
2 AZ2 1. 95x10· 3. 39x1Q2 -1.02xlO(88.2) (5.78) (-2.89)
3 A32 3.51xI0· 1. 67xl:l2 -2.03xlO(5.62) (0.87) (-6.05)
.. A.2 1.01xlO s 3.68x103 -1.05(60.92) (7.42) (-12.48)
5 AS2 1. 26xlOs .83lx103 , -1.74xI02
(20.04) (1. 08) (-2.52)
6 AS2 1.77xI0· 8.2xl0z(1.32) (2.05)
7 An 1.07xl()4 i 2.72xl02
(2.79) I (2.68)I ,,
tt : fi!i5iJlpg~+{!(; t 1m:DW {3f: Durbin-Watson statistic
( 10 )
-135-
II
R2 i DW
I[;fiflll£~tk 11!fi'1J14~l'{1 I
r, :-_.~~~ I F I~'---"---'" ._. _.,-_.~-~-~~
189.78 0.95 1.03
1
AT1J II
-------~---------_._---
I
"U"'-:¥fP.<UIiIIM-'tr,f,hiIH'ibm' ~Wl3.fiij ! ""''''d.ldWI....,,"'w '/oiill.1.l'l.1'tl",'i'UfT-i'/m,m. [ij fft ; I!llO""73C'~\
____I
GPSF ! RNNiJ
-2.27(-3.42)
15.66 0.78 1.18
-7. 74xlO- 1
(-2.78)
0.93i 1.31
I0.94 1.67
0.56[ 0.86
I9.42 0.68 2.14
2.81
37.57
70.27
I ii1.80xl0·
(1.9)
1.22xlO4(4.59)
3.103(1.48)
3.75xl0- 1
(11.17)
I: ~6.26 I I
(-0.54) I
7.18XI0-11(3.57)
-0.176(-0.15)
4.01xlO- 11
(1.88) II
30.08 0.81 2.25
( 11 )
-136-
:1,3 ~~~~M-.~M*.&~.~~@
*1 'ft{ i~ ~ ~i~~AA~~I~~M~~lm~M~~ % JIE It ~j
~ ;------1 i--· ---1--·---mk ~ i Constant j TEMu \ RNo RNNo NFRlJ
_.~----
1 Yu ·2.22xl03 1 -4.3IxIO 1.23)(10- 1 1.71xl0(1.53) (-0.99) (0.5) (1.08)
2 Y21 5.19x103 I 7.52)(10-1 -1. 7xl0-9.83xl0 '(5.04) (-2.69) (1.37) ; (-1. 46)
3 Y31 2.86xl03 -6.84xl0 1.13)(10(3.6) (-2.7) (1.26)
Y41 1. 96xl03 -3.06xI0 3.33xl0(2.99) (-1.53) j (4.8)
II
5 YS1 1.56xl03I
2.03 2.28xl0(2.12)
i(1.22) (2.04)
I
6 Y6L 6.06xl03 -7.71xI0 \ -8.33(5.49) . (-2.12) (-0.62)
7 Yn 3.63xl03 ' -5.83xlO 2.98xl0-1
(7.59) (-2.21) (1.36)
itt : ffl~I!!}'~l$:'y:{!f: t {[Ii.
DW mDurbin-Watson statistic
( 12 )
-137-
~ FdI! m~---I
T II
-5.19x10( -1.25)
3.40.48)
F
0.93 0.30
DW
2.44
1. 47x102 -4.73(4.79) -2.81)
4.44x10 -1.46xlO- j
(1.7) (-0.11) II,
3.57x10(7.88)
3.71x10 II
(0.26) ,
19.95
1'6.26
28.42
0.9
0.88
0.87
1845
1.37
1.22
5.7x10 6.74x10 21. 22(4.16) (0.46)
1.2xl02 --6.07 4.11(3.18) (-2.93)
0.87
0.58
2.91
1.11
1.02x10 2 I -3.32(4.82) I (-2.88)
( 13 )
18.58 0.86 I 1.56
-138-
I ,
M! mS: 'it{ 'iirit:J1l ~~M~m!~~M~.\~~M~. :lIJHIJ!« ~JJBJt*j
• ~ .._-- --I
I~ If{ Constant TEMu I RNiJ RNNiJ SUNu NFRIJII
I \I
~_.--
1
\
Y'2 4.3xlQ3 I 4.03 -1.4xl0-1.14xl02 I(4.36) (-2.52) I (2.66) (-1.14)
iI
I2 Y22 6.59xlQ3 -9.6xl0 i-9.92xI0-' 5.08 -4.33xl0
(2.06) (-0.75) (-1.49) (l.ll) (-1.12)!
,
I3 Y32 2.29xlQ3 -2.9xl0 , I 7.45xl0-'
I1. 42xl0
(3.36) (-0.92)I
(1.99) (1.52),I
Ii
"' Y.z 2. 18xl03 -1. 96xlO- 1 i 4.31 -7.04(3.48) (-0.52) (2.53) (-0.91)
5 I I I IYo2 6.01xl03 . -1.18xlOZ -3.67
(1.8) (-0.89) (-0.24)
6
1
Y62 I 1. 45xl03
i (2.79)
Y7% 11. 23xlQ3I (1.27)
1
- 6. 72x I0- 1 I(-2.93) I
2.17(2.14)
7.87(1.0)
2.86xlO(1.87)
tt:m~pg~ff\tlll
DW ffi Durbin-Watson statistic
( 14 )
-139-
).\: (1963--1979) ~tt~~ fiS"i«u1Ji:* 0 L S
~ rdl m 'l!IiiliJ&*'J< IIII_ 'U\ [_.a___1I!tl :F R2 DW
T T' DlJ I 13 15 i\ i
. - _.._-_._-------~-----_. - - ".-._ ..._-~._.- -.. _---,I
0.69
12.81xlO -2.35 -1.47xl0 3.78 1.89
(0.52) (-0.74) (-1.36)
I
8.58xlO -4.41 -4.03xlOZ , 2.890.
691
2.28(0 ..59) I(-0.49) : (-1.45)
I-3. 32xl02 --2.04x102 0.71-4.26xl0 I 2.78 I 3.18 1.72
(-0.79) (0.9) (-3.32) (-0.87)
3.52xl0 -1.65xl0' I 9.8 0;81 3:17(3.98) ( -1.6()
I2. 43xl0 -3.37xlOZ -2.26xIOZ 2.19 0.57 I 1.82
(1.02) (-2.81) (-0.79)
1.12xl0! -5.83 -2.15xllr 4.38 0.67 2.41(2.97) (-2.72) (-2.97)
I
-7.(}JxlO 5,46 2XIOZ! 4.55 0.67 2.36(-1.04) (1.37) (1.24) I
I
( 15 )
-140-
TENu
I I-1.62x 103
(-1.9dII
-1.15xJ03i 1.77xl0: (-1. 72}1 (1. 93)
- 2.62xl0' -7.llxl03,(--2.19) (-4,07),
I
II
-6xl03\(-2.64)
I\
I
I
9.74xlO3(1. 85)
-1.621(-5.58)1
!
7. 32x103 - 1.33x 102
(2.79) (-1.07);I Iii
7.85xI031(2.21} "
1.68x10S:
(-0,61);
I1.03x105
(2.62)
4"'- He: "",..,. J5 II J:M I' -J" ~ '~ot1"{"+:!,fB' ,1f',t',v..-1ifIiik '1-1, I=ltIt""',,,,: :I1Jjf'J:M~"'- ',,", l'il 1«'.:>1 fEi '¥:m~ , - - ~ fl~ I) UC~ 0':: w ,*UH"fl' 1~J:'<ffl""'lJIIl! ffi .li
@i:,constant. PGF~~ I[ WAll '~i~- PVFi I
~I Qnr;~i~i:r9.2t~:;
21 Q21[ 6.78X10C\ 2.8x103
I i (5.47)1 (4.76)
31 Q31 2. 09xlOs! 1. 56x103:, (4.2); (1.09)
I
i71 Qn
!
I5. 59xl03, 2.33x1OC'-9.18x102 2.29xlO,
(0.03) (3.18) (-3.21) (0.27)IIII
1.63xlO3 9.07x102 ! 8.95x10~,(0.058) (l.87): (1.65) j
1. 73XIO(0.89)
itt : l'tWP>IIk*fYi t 1illDW fYi Durbin-Watson statistic
( 16 )
-141-
1 3.23x103 7.61xl0-)(2.91) (6.19)
3.22(6.15)
I _:jID i".tiM A~I ~)j('l.Jti-t'i U'!j:UJ t]!%'
--~UNiJ I-~~;- TDW
0.82 1.57
i
0.91 2.15
I
0.97 1. 64
0.93 1.31
\0.93 1.93
F
7.73 0.82\1.91
--~----
I30.98 0.88, 2.36
I,
iI
28.391
II
22. 871
i!
2.65XW!88.53(1.38)
i I\ 7.631
i 11 I
, 26.91
5.94X104!(1.55)
2.3:5(0.83)
9.37xl03
(2.63)
II
5.65xl03i(3.91)1
\2.22xI03 j
(1.33):!I
i1.55xl03
1
(3.25)1
! 2.06xl03
(7.18)
!5.58xI02
1
(0.55)
1
I
I1. 52x103
1
(1.68)1
I,-1.45xl0'i(-1.19):
I
III
( 17 )
-142-
Constant PGFAlJ I__ _~___ I
, iQ12-2.72xlQ3, 2. 24xl03I (-0.07) (3.59)
2
i-1. 57x103, -6.14
(-1.12) (-1.26)i
i -2.23 -6.31x103;(-1.86) (-2.26)
8. 52x103'-1. 99xIQ3i I(3.04 i (-2.59)1 I
I I
1
1. 99xl03. -5.85(0.99)'( -2.04),
I ': i II : ;
,2.82XI031-5.02Xl02 -1.87x101
(0.29), (1.45) (-0.9)I
II
7.llXIQ3(5.85)
Ii
I1. 72xl03,
(3.67>!
1.44x10'(3.51)
i
14xl05
(1.26)I
2. 93xlOS(3.88)
4.13xIQ3,(0.09)
8.56xl04
(2.65)
6. 48x105
(1.18)i
i6 QS2
7 Q7Z I!
3
41 Qu
tt:m~J7g~{,y;t-ft(
DW ff: Durbin-WAtson statiasric
( 18 )
-143-
R2 DW
I116.97 0.92 2.48
9.79 0.82 2.11
3.85xlO(1. 7)
10.5 0.86 1.95
I
i\ I' I
6.26X101
'2.86x103i-4.43Xl~1 II' 8.98xl~(0.85) I (1.32)1 (-2.38)i (IAn
l.87x1O I .,33XI"!'. 81XIO'I- 5.14xl"i' (2.54) : (5.15)1' (4.43) (-4.92)!
i !
i I I1.-2.54XI03
1
, II (-0.78)I !
( 19 )
5.86 0.,,1 3.21
II1.2 0.49 1. 47
21.87 0.94 2.38
8.12 0.73
11.99
-144-
NFRij : J<.\nE1~=:~*~eBl~Jt$ ( i ti~, j WJi'F) (%) 0
TEMij: ~*WJ7jS~f(m (i ti~, j WJi'F) caC) 0
RNij : ~*WJlf'-~f:ffi:l: ( i ,,~, j .Mff) (m. m.) 0
RNNij : ~J*:WJ7jS~f:ffi:l: ( i 'ti~, j .Mff) (m. m.) 0
SUNij : Mlf,t.M~~ B,~lI#~ ( i tI~, j WJff) (lI#~) 0
Dij: ••~.ZdM~.(~~.z~~a1'~@~OCao)0 (itll@:' j .Mi'F) 0
I :*.&••a.Zd.~.(~~.~~~~M*.~~ao,~~68~a 1 ; §J¥Hil@:f\;~tt3C*1!li ' 52-¥~62-¥a 0 ,63-¥¥68-¥a1 ; ~~til@:~~••J5c.Z~.'52-¥~621pao ,631p~68-¥a
1)0
T : lIi'jrl'l'~~i¥.J~.f\:;~~P.Elimi¥.JJJ!ib (52-¥=1, 53-¥= 2 , ...... ) 0
~u~~~~~*~.~zmm.~~m~~~~mo~-au.~z~.
ITiifJ!t (Aij) ~tJ¥&ilfi (Yij) nrf~~~Jl (Qij) ,~=ajfi~lflrr~Z$i.1tf
.l:i*il(i:;i-\: (Qij) ;j<1i 0
~~••Ai¥.Jmm~~••~~mW.'.7m~i¥.J~~~~.~~•••fflZ11tilL ' ~7JIJff§.~*dil!!~:l:Z.~.~~rJllllrr~1]Z~fj{ 0
§.~*m~••~~~~8~M.~M.omu~~••zm••nr~m~~~~m,~-.u.~Z~.ITii.(Aij)~U.&P.E.(Yij)*mW~H
Aij x Yij=Qij 0 ~=aJR~lllg~Z~~.i*i~~ (Qij) *m 0 l!P~~
Qij=F(PGFAij, WAij, URij, PVF, PSF, TEMij, RNij,· RNNij,SUNij, NFRij, T, Dij).
tJ~HR~~Z~*51-7JIJ*~ Theil's Inequality Coefficient OJnUflt!) ,RMSPE .tJ& MSE fit! (l!P U~l' UR • UD ) ~1&=r,tJJtiji\(, 1lI.~.IJI)-~j$j.
~mmjUi¥.Jmlllrr.Jt~rrJlii 0
U.1Ujf-~~7!=f:r' RMSPE fIt!1Ujf-~~8 rp, jffi UM • UR • UD MHIU1U~
~ 9!=f:r 0 fBt:~ 1k7 rp~WJi'F 7JIJ~tI~7JIJJiJT1Ujf-L U.nrtJtflli (1) ~.lflrr~A
, ~*~til& (Q 71) • (Q 72) 7l-' A~~-.JtIlffZmlllrr§g~:Jqiflim-~-:Wj('Fo tJJR~lflII;.E~gt.~A~-WJffUflt!lf'-:lt;)a 0.554656 , ~=;ltfji'FU.f~.
0.383423 ; nr;m~=;ltfji'F UfI1!Jt~-.JtIli'FtrJZj,'0.171233 0 tJ••ITiifl~tJ¥&~
.1llrr~~gt1lt:tf~~-WJi'FUMlf'-.t!;}f.i0. 745539 , tf~=Wl('F U.If'-:lt1aO.504111
( 20 )
-145-
1'< 7 ~*,l!.ffi:Jil:fJHltuff!g.1J Theil's U2 Inequality Cofficient
;z'ltfR
i~ :It ~ ~I Ulfii.fix¥.jSz&:itillJJ~~Wl },ltl :& ti ~ },ltl i *!! ill~
, I..-. -_.._-~~---~~_._------~_._-----_.
Qu 0.543539 1.813446
Q31 0.539874 0.441273
Q31 0.729934 0.726125
Qu 0.414800 0.541116
Q51 0.526364 0.571678
Qu 0.494692 0.549053
Q71 0.633386 0.576123, __·_:--"-------::..-..:...:.:..:...-=~c____ ~__ _.::;.
Qu 0.304080 0.433997
Q22 0.322236 0.419580
Q32 0.326355 0.393484
Q.2 0.414073 0.477376
QS2 0.380299 0.494485
Q52 0.2~3399 0.440959
Q72 0.693318 0.868896
( 21 )
-146-
.1< 8 m*Mt~:l:f~ ill~RgJJ RMSPEZj:t~
M BU &. t:i [.\K BIJ I~! & .n illq J:E ~I fjjWlffij~ x .1JT.~2:illqJ:E5:t
- ----._---~-~._,---- --
iQIl 1 0.06111 0.19658
Q21 0.03780 0.03092
Q31 0.16458 0.16473
Q41 0.01956 0.02485
QSI 0.06117 0.07682
Q61 0.03085 0.03442
Qn 0.03411 0.03118
Q12 0.06144 0.09199
Q22 0.15600 0.20339
Q32 0.04117 0.05102
Q~2 0.04257 0.04953
Q52 0.05639 0.06919
Q62 0.01768 0.03257
Q12 0.07167 0.09754
( 22 )
-147-
, I I . I I I1°.00359662,°.026572181°.9698312°,°.06169496,°. 69159609
1°.246708941°.000867571°.078297281°.920835151°.0019749710.04547274
1°.95255229
'0.06063374r 001091881°.938274391°.0604131°1°.0010803910.93850650
10.0037751510.011369241°.984859250.002568391°.26947763 0.727953971 I I 10.001947680.174653760.82339856 O.011606810.00000054 ° .98839265I I I 1 I I1°.008733081°.00077493
1°
.9904919810
OO095910.01492784סס.
1°.98506257
0.002106321°.003399060.99449462
O.01017745 O.00211453 0 .98770802I I I 1 Ii I .. I ... ....., -I ·-Y;0.00239146
1°.051085371°.9465231
?0051531310· 02841656r 96643031
,0. 00769711p. 03113034'°.96117255,0.001014011°.01737338,0.98161261
10.0017464910.0861621510.91209136.0.00150220 0.06834869'0.93014911i I I I 1 \0.008575590.034062940.95736147
1°.00248329
O.023221970. 97429474I I! I I.0.01646137
1°.01544411
0. 96809452 0.00945762.0.004687120.98585526I I I I I,.0 .01901168 0.01250661 O.96848170 0.001151260.091167980.90768075: II I ! i0.011565250.19183779 0.796596960.051003680.13\911340.81705498
I I 1 I I
; ~~rmj§ , ~=:MfF3Z.Jt~-Wlf'Fmj; , ~j,'0.241428 o (2)t)J~-WlfF*;ff ,~1i:Mti~ (Q21) :&tn'¥rSjl[ (Q31) :&*lfm~ (Q 71) 7l-' ~~~t)'~~.~~••~~m.~h•• , (WU~.~) ()~••~•••~~u~~~~O. 554656 , rma:flt!ITfff1t*t)'.Uz:.:i!:.~$••~ u ~~~mo. 745539 , p;;~
ZU~JtP;;H~j,'0.190883 o (3)t).~=~tJH'f*Y' .ftIJJtJWg.llIU~$ilE.~r~illU
~h.~,jt u ~~;Jqm 0.383423 , Jta·11!iITfff1t3f~u.Uz:•• llIrr~••1I:~z
0.504111, ~j,'TO.120688 c (4)U~:M*;ff , ~~-WJf'FZ1i:Jini~ (Q u) ».fi¥rtij;![ (Q31) :&*~ti~ (Q 71) ?f-, jt~~j;J.~.illrr7E~.it~r~llIU~:JJfl~' jt~:Mzu~~~m 0.469039 JtailiITffflt~t)'.Uz:~.llIU~l\!~.~z
0.624828m/J\ , ~~'O .155789 o
jt?kEB~ 8 z*:MfF.5Jll*ti~.5J'l.~.z RMSPE ~ZJt.IiJj;J.;ffili~~
-:MfF1i:1iiS[;j[ (Q u) :&*IHIjl[ (Q 71) 7l-~~~t).p;;~gp~~lIIJl~I1.:S:
( 23 )
-143-
'ifjtfJliJIIJfjl§:f]t(Ilf, (f!pRMSPEfJlit'l/j,) ~~jffi~~AZ RMSPE JRimO.6115
f.:1f.Ji:(-)AZfJliO. 0824481~j-'0. 021331 o
1't1E~9 *~WJ('FjIJ:&~.fI~Z/JZ U),I" UR .. u, Z(wfilJtJ.tfl±l : (1)~~ii:J!U5EAZ~~:~jUt~ (@pUo) Jt~~~ 0.938036, ijjjJIVlJlJtafi (@pVR ) Jt~~
~0.513134. rmf!jU1i~Jt~ (fWUM) Jt2jS~.m0.0106503; JI:t=~Jt$.Z7tftElft
, tJ~£lJlJt~Jllt* • {r'i7 0.938036 o JI:t~AzmillUfig1J:g~, (@pmiJ!U~~
~Jf;Y~m'flSl~~~~JH'O o (2):f!UtiUii.~tJ.¥{iLgt::I:~fj}EAZ?tUV~Jt$. (@OVo) Jt2jS:Jt;]mO.884997. ~JIV~Jt$. (@PUR) Jt2jS:Jt;]~mO.0992797, ifiHooMtlJl
Jtafi (@P Viol) Jt2jS:Jt;]~~ 0.157293; =lJiJt$.7tftEIftRf~JI:t~P:;Y1'~-m1i!~
zfJllllUmA (@p Uo zfiitt~) 0 (3) 1EP:;~btP:;Hz Viol .. UR .. u, fiiz.lt~
, A~zUiilMtlJlJt~ (Viol) ~:Jt;]f.£ 0.106503 JtAHz 0.0157293 ~/J' , @OA~•••}E~••*.~~~MzmillU<>~~~~z~~lJi.lt.(U~).~.0.0513134 .ltAHZ 0.0992797 .mf1£' @PA~j~U~illU}E~gt:.t*~.:1f~~zffl;}IJ o f}J!IJA¢':)Z?!l£lJiJt~l@P (Uo) .:Jt;]~ 0.9380362 .ltAHZ 0.8849972~~
; (gPA~ZfJliJ!U~~~*El:Q~~~lJi~J!J'< <» flSlifjjWI.il!U}EmC~:I:*gp~.
j-'~iiJili.Jl3!<:~ZfJlil!fj , MrJl:til!U}EAzf)lillUfig1].~ 0
fJliJ!Uflli1Jt¥.JWF~:1HJii1lUIfFz~:Q , m7~~fjfJiillU~*~filj~, Jf~iJ!U}E~
~millUflli1Jz~:I:~~~~~~-lJiIfF<>~~~.~u~~m*.:l:m~Am
iJlUf4!51JiItM* • it~=.:s••m*.:l:millU~A; (gpij[.iJ!fj~ml.:I::&:fi:/ltfoo
flt*tJ.¥{iLP-[:l:i1lU}E~i!t:;:)*.mRfJ&Z_A; 0 IIf£tJ.ij[.El:i~.:l:iJlfjJEA~fJliJIU
~*.~oJtm~.*·RfUM~m~~~flSl:
(l)ititiJ!U~tf!• .tml.EAmilt!IzM:J!:JtmlJlU~~./j, 0
(2)ij[itiJlU:iE.~:l:ilt!Il.E;A;~milt!I1ilifiMitt./j, 0
(3)mitiJ!fjl.Eiti:l:iJ!Ul.EA;;itmlJlfjMfA~.~z~afi • ifjjJ3.fii il!UI1~JIi! miJtU~~;t
*§lHIfMgOZ.lt.~ii <>
(4)j~J~ilt!I)£I;!l~:l:lJlfj~A;itfJiilt!I~~~*13 ~~J!~ 0
~~U~Z7t~·~L~.~m*~.~.~AOO~,~m~~*m~~~
~J&~~~l.E~~.ilt!I~A;~m~~U.MUii.~~¥{iL••~~~~~~,~
~~~~~~m~:fi:/ltfUii.&¥{iL~t~m~r,~m~.~miJtU·I3~~ffl~
~mIJ5Em~flmrJ~A;0
( 24 )
-149-
1. ~*~' ••~~~*'••&Mm.'~=~-M,W¥3na2. ~X~, ••~*~~~~Zm~,~~~~mm~~~ffi'~~4na3. W~~, ••~*~~~~~ZIT~~~,rr~~.~~,.~~S~~'~ft*~*~.&~M*,ro.8na
=.. ~ jl: ftlH5l- :1. Chen, Wu-Hsiung, "An Economic Study on Government Rice
Stock Operation in Taiwan" Unpublished doctoral dissertation,
Dept. of Agricul tural Economics, University of IIlionois, Urbana
Illinois, USA, May 1980.
2. Chen, Wu-Hsiung, "ARIMA Model and Regression EError" 1!l~
&Dti*:¥fU ' *~*~.&litf~)iJT ' 69.12n a
3. Leuthold, R. M., "On the Use of Theil's Inequality Coefficents",
AJAE 57: P. 344-346.4. Pindyck, R. S. & D. L. Rubinfeld. "Econometric Model & Eco-
nomic Forecasts", 2nd ed., 1981.
5. Maddala, G. S., "Econometric" lst. ed. 1976.
6. Koutsoyiannis, A., "Theory of Econometrics".
7. Intriligator, Michael D., "Econometric Models, Techniques, &
Applications" 1978.
( 25 )
-150-
A Test on Expost Forecasting Performanceof Rice Supply Model in Taiwan
Wang Shean-Ching
Summary
Rice is the staple food product in Taiwan. Accurate estimation
and forecasting of rice production and supply become important
not only. for rice market but also for policy maker. Among
various forecasting methods, econometric model has been the
most powerful tool. This paper is aimed at evaluating and
analyzing the econometric supply model of rice in Taiwan. The
supply function of rice includes two categories of equations; one
is directly estimated by total production and the other is derived
from multiplication of acerage response and yield functions.
There are totally seven regions of rice production in Taiwan,
each category of functions are estimated for each region with
two seasons respectively.
Three indices are employed in this study to measure the
efficiency of the forecasting model. They are, (1) Root mean
square percent error. (2) Theil's inquality coefficient. (3) Mean
square error.
The results show that the forecasting power of both categories
of estimated forecasting equations are acceptable. However, in
terms of forecasting efficiency the directed total production func
tions are better than the other set of equations. The comparison
are based On the following items: (1) Results of predict error.
(2) Predict value of unbiased. (3) Degree of the relation between
predict value and predict error. (4) The source of predict error.
( 26 )
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