Kiểm Định Độ Trễ Của Mô Hình

Chng trnh Ging dy Kinh t Fulbright

Cc phng php nh lng

Bi c Kinh t lng c s - 4th ed.

Ch.17: Cc m hnh kinh t lng ng: M hnh t hi quy v m hnh phn phi tr

Damodar Gujarati 1 Bin dch: Kim Chi Hiu nh: inh Cng Khi

Chng 17

CCcc mm hhnnhh kkiinnhh tt llnngg nngg::

MM hhnnhh tt hhii qquuyy vv mm hhnnhh pphhnn pphhii ttrr

Trong phn tch hi quy lin quan n s liu chui thi gian, nu m hnh hi quy khng ch

bao gm cc gi tr hin ti m cn bao gm cc gi tr tr (gi tr qu kh) ca cc bin gii

thch (cc bin X), m hnh c gi l m hnh phn phi tr. Nu trong s cc bin gii

thch ca m hnh bao gm mt hay nhiu gi tr tr ca bin ph thuc, m hnh c gi l

m hnh t hi quy. Nh vy, ta c:

Yt = + 0Xt + 1Xt-1 + 2Xt-2 + ut

Phng trnh ny tiu biu cho mt m hnh phn phi tr, trong khi phng trnh sau:

Yt = + Xt + Xt-1 + ut

l v d v mt m hnh t hi quy. Cc m hnh ny cn c gi l cc m hnh ng v

chng m t din bin theo thi gian ca bin ph thuc trong mi quan h vi cc gi tr qu

kh ca chng.

M hnh t hi quy v m hnh phn phi tr c s dng ph bin trong phn tch kinh t

lng, v trong chng ny, chng ta s xem xt k cc m hnh ny vi d nh tm hiu nhng

vn sau:

1. Vai tr ca tr trong kinh t hc l g?

2. L do ca cc tr l g?

3. C s gii thch l thuyt no cho vic s dng ph bin cc m hnh tr trong kinh t

lng thc nghim hay khng?

4. Mi quan h l g, nu c, gia cc m hnh t hi quy v m hnh phn phi tr? Ta c

th suy ra m hnh ny t m hnh kia hay khng?

5. Mt s vn thng k lin quan n vic c lng cc m hnh ny l g?

6. Mi quan h sm- tr gia cc bin c ng tnh nhn qu hay khng? Nu c, ta

c th o lng n nh th no?

17.1 Vai tr ca thi gian, hay tr trong kinh t hc

Trong kinh t hc, s ph thuc ca mt bin s Y (bin ph thuc) vo mt hay nhiu bin s X

khc (bin gii thch) him khi c tnh cht ng thi. Rt thng xuyn, Y tng ng vi X sau

mt khong thi gian. Khong thi gian nh vy c gi l tr. minh ha bn cht ca

tr, ta hy xem mt vi v d.


Cc phng php nh lng




V d 17.1 Hm tiu dng

Gi s mt ngi c tng lng 2000 USD trong mc lng hng nm, v gi s y l mc

tng lu di theo ngha l mc tng lng ny c duy tr lu di. nh hng ca mc tng

thu nhp ny i vi chi tiu dng hng nm ca ngi ny l nh th no?

Theo sau s gia tng thu nhp nh vy, ngi ta thng khng lao vo chi tiu ton b thu nhp

ngay lp tc. V th, ngi hng thu nhp ca chng ta c th quyt nh tng chi tiu dng

thm 800 USD trong nm u tin sau khi thu nhp tng; tng tiu dng thm 600 USD trong

nm k tip, v thm 400 USD na trong nm tip theo; v tit kim ch cn li. n cui nm

th ba, chi tiu dng hng nm ca ngi y s tng thm 1800 USD. Nh vy, ta c th vit

hm tiu dng ca ngi ny l:

Yt = Hng s + 0,4Xt + 0,3Xt-1 + 0,2Xt-2 + ut (17.1.1)

Trong Y l chi tiu dng v X l thu nhp.

Phng trnh (17.1.1) cho thy rng nh hng ca vic tng thu nhp 2000 USD s dn tri, hay

s phn phi trong khong thi gian ba nm. Do , nhng m hnh nh m hnh (17.1.1) c

gi l m hnh phn phi tr, v nh hng ca mt nguyn nhn cho trc (thu nhp) s c

tri di trong mt s thi on. V mt hnh hc, m hnh phn phi tr (17.1.1) c trnh by

trong hnh 17.1, hay cng c th c biu th bng cch khc nh trong hnh 17.2.

Hnh 17.1 V d v tr phn phi

Thi gian

Ch

i ti

u d

n

g, U

SD


Cc phng php nh lng




Hnh 17.2 nh hng ca s thay i mt n v bin X vo thi on t i vi bin Y vo

thi on t v cc thi on tip theo

nh hng i vi Y

Thi gian

Tng qut hn, ta c th vit:

Yt = + 0Xt + 1Xt-1 + 2Xt-2 + + kXt-k + ut (17.1.2)

Phng trnh (17.1.2) l mt m hnh phn phi tr vi mt tr xc nh bao gm k thi on.

H s 0 c gi l s nhn ngn hn hay s nhn tc ng v n cho ta bit s thay

i tr trung bnh ca Y ng vi s thay i mt n v ca bin X trong cng thi on.1

Nu sau , s thay i bin X vn c duy tr cng mc , th (0 + 1) cho ta s thay

i tr trung bnh ca Y trong thi on k tip, (0 + 1 + 2) cho ta s thay i tr trung bnh

1 V mt ton hc, 0 l o hm ring phn ca Y theo Xt, 1 l o hm ring phn ca Y theo Xt-1, 2 l o hm

ring phn ca Y theo Xt-2, v.v K hiu l: Yt/ Xt-k = k.


Cc phng php nh lng




ca Y trong thi on k tip na, v v.v Cc tng ring phn ny c gi l cc s nhn tc

thi. Cui cng, sau k thi on, ta c:

= 0 + 1 + 2 + + k = (17.1.3)

c gi l s nhn di hn, hay s nhn tng phn phi tr, min l tng ny c tn ti

(s c tho lun trong phn khc).

Nu ta nh ngha:

(17.1.4)

th ta thu c i chun ha. Khi , cc tng ring phn ca i chun ha s cho ta t l ca

mt thi on c th trong tc ng tng, hay tc ng di hn.

Quay li vi phng trnh hi quy tiu dng (17.1.1), ta thy rng s nhn ngn hn, chng qua

chnh l xu hng tiu dng bin ngn hn (MPC), bng 0,4, trong khi s nhn di hn, chnh l

xu hng tiu dng bin di hn, l 0,4 + 0,3 + 0,2 = 0,9. Ngha l, sau khi thu nhp tng 1 USD,

ngi tiu dng s tng mc tiu dng thm khong 40 cents trong nm tng thu nhp, ri tng

thm 30 cents na trong nm tip theo, v tng 20 cents na trong nm tip theo na. Nh vy,

tc ng di hn ca mc tng thu nhp 1 USD l 90 cents. Nu ta chia tng h s i cho 0.9, ta

ln lt thu c 0,44, 0,33 v 0,23, cho thy rng 44 phn trm trong tng tc ng ca s thay

i mt n v ca bin X i vi Y s c cm nhn ngay tc thi, 77 phn trm s c cm

nhn sau mt nm, v 100 phn trm s c cm nhn vo cui nm th hai.

V d 17.2 S to lp tin ngn hng (tin gi ngn hn)

Gi s H thng d tr lin bang rt 1000 USD tin mi vo h thng ngn hng thng qua vic

mua chng khon chnh ph. Tng gi tr tin ngn hng hay tin gi ngn hn cui cng c

to ra s l bao nhiu?

Theo h thng d tr bt buc, nu ta gi nh rng lut qui nh cc ngn hng phi d tr 20

phn trm h tr tin gi m h to ra, th theo qu trnh cp s nhn m ai cng bit, tng gi

tr tin gi c to ra s bng 1000 USD[1/(1 0.8)] = 5000 USD. L d nhin, 5000 USD s

khng c to ra trong mt sm mt chiu. Qu trnh ny s phi mt thi gian, v c th c

biu th trong hnh 17.3.


Cc phng php nh lng




Hnh 17.3 S m rng ly k ca tin gi ngn hng (d tr ban u 1000 USD v t l d

tr bt buc l 20 phn trm)

V d 17.3 Mi lin kt gia tin v gi

Cn c theo nhng ngi theo thuyt trng tin, lm pht thc cht l mt hin tng tin t theo

ngha l s gia tng lin tc ca mc gi chung l do t l m rng cung tin vt qu xa lng

tin m cc n v kinh t tht s c nhu cu. L d nhin, mi lin kt gia lm pht v thay i

cung tin khng c tnh cht ng thi. Cc nghin cu cho thy rng tr gia hai bin s ny

nm u trong khong t 3 n 20 qu. Kt qu ca mt nghin cu nh th c trnh by

trong bng 17.1,2 trong ta thy nh hng ca s gia tng 1 phn trm cung tin M1B (= tin

+ tin gi vng lai ti cc t chc ti chnh) c cm nhn trong khong thi gian 20 qu. Tc

ng di hn ca s thay i 1 phn trm cung tin i vi lm pht l vo khong 1 (=mi); h

s tc ng ny c ngha thng k, trong khi tc ng ngn hn vo khong 0,04, th khng c

ngha thng k, cho d cc s nhn tc thi xem ra c ngha mt cch tng qut. Nhn th

cng lu rng v P v M u c biu th di hnh thc t l phn trm, nn mi (hay i theo

k hiu thng thng) cho ta co gin ca gi P theo M, ngha l phn ng theo t l phn trm

ca gi c khi cung tin tng ln 1 phn trm. Nh vy, m0 = 0,041 c ngha l ng vi s thay

i 1 phn trm ca cung tin, co gin ngn hn ca gi l vo khong 0,04 phn trm. co

2 Keith M. Carlson, The Lag from Money to Prices, Review, Ngn hng D tr lin bang St. Louis, thng 10-1980,

bng 1, trang 4.

1000 USD

ban u Cc giai on m rng Cui cng


Cc phng php nh lng




gin di hn l 1,03 phn trm, c ngha l trong di hn s thay i 1 phn trm ca cung tin s

phn nh s thay i gi gn nh cng t l. Ni vn tt, s gia tng 1 phn trm ca cung tin s

i km vi s gia tng t l lm pht 1 phn trm trong di hn.

Bng 17.1 c lng phng trnh tin-gi: m t phng trnh gc

Thi on mu: Qu I nm 1955 n qu IV nm 1969: m21 = 0

= - 0.146 + -i

(0.395)

H s t H s t H s t

m0 0.041 1.276 m8 0.048 3.249 m16 0.069 3.943

m1 0.034 1.538 m9 0.054 3.783 m17 0.062 3.712

m2 0.030 1.903 m10 0.059 4.305 m18 0.053 3.511

m3 0.029 2.171 m11 0.065 4.673 m19 0.039 3.338

m4 0.030 2.235 m12 0.069 4.795 m20 0.022 3.191

m5 0.033 2.294 m13 0.072 4.694 mi 1.031 7.870

m6 0.037 2.475 m14 0.073 4.468 tr trung bnh

10.959 5.634

m7 0.042 2.798 m15 0.072 4.202

2 0.525

se 1.066

D.W. 2.00

K hiu: = t l thay i h s gim pht GNP hng nm kp.

= t l thay i M1B hng nm kp.

Ngun: Keith Smith Carlson, The Lag from Money to Prices, Review, Ngn hng D tr lin bang St. Louis, thng

10-1980, bng 1, trang 4.

V d 17.4 tr gia chi tiu nghin cu pht trin v nng sut

Quyt nh u t vo chi tiu nghin cu v pht trin (R&D) v thnh qu sau cng v nng

sut gia tng lin quan n tr ng k, m tht ra l mt vi tr, nh tr t lc u

t ngun vn n thi im m vic pht minh tht s bt u din ra, tr t lc pht minh ra

mt tng hay mt cng c n khi trin khai tng hay cng c thnh mt giai on ng

dng thng mi, v tr hnh thnh trong qu trnh truyn b cng ngh: phi mt thi gian

trc khi tt c nhng my mc c c thay th bng nhng my mc mi tt hn.3

V d 17.5 ng cong ch J ca kinh t hc quc t

Cc sinh vin kinh t hc quc t rt quen thuc vi ci gi l ng cong ch J, biu th mi

quan h gia cn cn thng mi v s mt gi ng tin. Theo sau s mt gi ng tin ca mt

nc (v d nh do ph gi), thot u cn cn thng mi b xu i nhng sau c ci

3 Zvi Griliches, Distributed Lags: A Survey, Econometrica, tp 36, s 1, thng 1-1967, trang 16-49.


Cc phng php nh lng




thin, gi nh rng cc yu t khc khng thay i. ng cong ny c trnh by trong hnh

17.4.

Hnh 17.4 ng cong ch J

Ti khon vng lai

(n v sn lng ni a)

Ngun: Paul R. Krugman v Maurice Obstfeld, International Economics: Theory and Practice, xut bn ln th ba,

Harper Collins, New York, 1994, trang 465.

V d 17.6 M hnh gia tc ca u t

Di dng n gin nht, nguyn tc gia tc ca l thuyt u t pht biu rng u t t l

thun vi s thay i sn lng. Biu th bng k hiu:

It = (Xt Xt-1) > 0 (17.1.5)

Trong It l u t vo thi on t, Xt l sn lng vo thi on t, v Xt-1 l sn lng vo

thi on (t 1).

Cc v d trn y ch l mt mu ng dng tr trong kinh t hc. R rng, c gi c th a

ra mt vi v d t kinh nghim ring ca mnh.

S mt gi thc din ra v ng cong

ch J bt u

Kt thc ng cong

ch J

Thi gian


Cc phng php nh lng




17.2 Cc l do ca tr4

Cho d cc v d trong phn 17.1 cho thy bn cht ca cc hin tng tr, cc v d ny khng

gii thch y l do pht sinh tr. C ba l do chnh:

1. L do tm l. Nh h qu ca thi quen (sc ), ngi ta khng thay i thi quen tiu

dng ca h ngay lp tc theo sau s gia tng hay gim st thu nhp, c l v qu trnh

thay i lin quan n s mt i tha dng tc thi. V th, nhng ngi trong pht

chc tr thnh triu ph nh trng s khng chc s thay i li sng m h quen

trong mt thi gian di, v c th ngay tc thi h khng bit phn ng trc khon lc

bt ng nh th no. L d nhin, vi mt khong thi gian nht nh, h c th hc

cch sng vi vn may mi c ca mnh. Cng nh, ngi ta khng bit chc liu s

thay i no l lu di hay nht thi. V th, phn ng ca ti trc s gia tng thu

nhp s ph thuc vo vic gia tng thu nhp c lu bn hay khng. Nu ch l s

gia tng mt ln khng cn ti din, v trong nhng thi on tip theo, thu nhp ca ti

s quay v mc trc , chc ti s dnh ton b mc tng thu nhp, trong khi ai

vo hon cnh ti c th sng ht mnh vi khon tng .

2. L do cng ngh. Gi s gi ca vn so vi gi ca lao ng gim, lm cho vic thay th

lao ng bng vn tr nn kh thi v mt kinh t. L d nhin, vic b sung thm vn

phi mt thi gian (thi k thai nghn). Hn na, nu ngi ta d kin vic gim gi vn

ch c tnh nht thi, cc doanh nghip khng chc s lao vo thay th lao ng bng vn,

c bit l nu h k vng rng sau t gim gi nht thi, gi vn c th tng cao hn

mc trc y. i khi, s hiu bit khng hon ho cng l nguyn nhn ca tr.

Hin nay, th trng my tnh c nhn trn ngp loi my tnh vi cc tnh nng v gi

c khc nhau. Thm vo , t khi my tnh c gii thiu vo thp nin 70, gi hu ht

cc loi my tnh c nhn gim mnh. Nh mt h qu, khch hng tim nng ca my

tnh c nhn c th lng l khi mua my cho n khi h c thi gian xem xt cc tnh

nng v gi c ca tt c cc thng hiu cnh tranh nhau. Ngoi ra, h c th chn ch

mua my vi k vng v s gim gi hn na hay v cc pht minh i mi.

3. L do th ch. L do ny cng gp phn dn n tr. V d, cc ngha v hp ng c

th ngn cn cc doanh nghip khng th chuyn t mt ngun lao ng hay nguyn vt

liu ny sang mt ngun lao ng hay nguyn vt liu khc. Nh mt v d khc, nhng

ngi gi tin vo cc ti khon tit kim di hn vi thi hn c nh nh 1 nm, 3 nm,

hay 7 nm, thc cht l b kha cht vo cc thi hn ny cho d tnh hnh th trng

tin t c th thay i khin cho nhng ni khc c th c nhng mc li sut cao hn.

Tng t, n v tuyn dng thng cho ngi lao ng chn la trong s mt vi hp

ng bo him y t khc nhau, nhng mt khi vic chn la c thc hin, ngi lao

ng khng th i sang hp ng bo him khc trong t nht mt nm. Cho d iu ny

4 Phn ny ch yu da vo nghin cu ca Marc Nerlove, Distributed Lags and Demand Analysis for Agricultural

and Other Commodities, S tay Nng nghip s 141, B Nng nghip Hoa K, thng 6-1958.


Cc phng php nh lng




c th c thc hin thun tin v mt hnh chnh, ngi lao ng b kha cht trong

mt nm.

V nhng l do tho lun trn y, tr chim mt vai tr trng tm trong kinh t hc. iu ny

phn nh r rt trong phng php lun di hn-ngn hn ca kinh t hc. Chnh v l do ny m

chng ta ni rng co gin theo gi hay theo thu nhp ngn hn ni chung nh hn (v gi tr

tuyt i) so vi co gin theo gi hay theo thu nhp di hn; hay xu hng tiu dng bin

ngn hn ni chung nh hn xu hng tiu dng bin di hn.

17.3 c lng cc m hnh phn phi tr

Bit rng cc m hnh phn phi tr ng vai tr ht sc hu ch trong kinh t hc, ngi ta c

lng nhng m hnh ny nh th no? Ni c th ra, gi s ta c m hnh phn phi tr sau y

theo mt bin gii thch:5

Yt = + 0Xt + 1Xt-1 + 2Xt-2 + + ut (17.3.1)

trong ta cha xc nh c di thi gian tr, ngha l ta mun i v qu kh bao xa. M

hnh nh vy c gi l m hnh tr khng xc nh, trong khi mt m hnh thuc loi

(17.1.2) c gi l m hnh phn phi tr xc nh v di thi gian tr k c nu c th.

Ta s tip tc s dng phng trnh (17.3.1) v phng trnh ny d x l v mt ton hc, nh ta

s thy.6

Lm th no ta c lng v ca phng trnh (17.3.1)? Ta c th s dng hai cch tip cn:

(1) c lng phi th thc v (2) nhng iu kin hn ch tin nghim v thng qua gi nh

rng cc gi tr tun theo mt din bin h thng no . Ta s xem xt cch c lng phi th

thc trong phn ny v cch c lng kia trong phn 17.4.

c lng phi th thc i vi cc m hnh phn phi tr

V bin gii thch Xt c gi nh l khng ngu nhin (hay ch t cng khng tng quan vi

s hng nhiu ut), nn Xt-1, Xt-2 v.v cng khng ngu nhin. Do , trn nguyn tc, cch tip

cn bnh phng ti thiu thng thng (OLS) c th p dng cho phng trnh (17.3.1). Alt7 v

Tinbergen8 p dng cch tip cn ny. H ngh rng c lng phng trnh (17.3.1),

ngi ta c th tin hnh ln lt, ngha l trc tin hi quy Yt theo Xt, ri hi quy Yt theo Xt

v Xt-1, ri hi quy Yt theo Xt, Xt-1, v Xt-2, v.v Tin trnh ln lt ny s dng li khi cc h

s hi quy ca cc bin tr bt u tr nn khng c ngha thng k v (hoc) h s ca t nht

mt trong cc bin s i du t dng sang m hay ngc li. p dng qui tc ny, Alt chy

5 Nu c hn 1 bin gii thch trong m hnh, mi bin c th c mt nh hng tr i vi Y. n gin, ta gi

nh ch c mt bin gii thch.

6 Tuy nhin, trong thc hnh, ta d kin rng h s ca cc gi tr X cch xa ch c nh hng khng ng k i

vi Y.

7 F. F. Alt, Distributed Lags, Econometrica, tp 10, 1942, trang 113-128.

8 J. Tinbergen Long term Foreign Trade Elasticities, Metroeconomica, tp 1, 1949, trang 174-185.


Cc phng php nh lng




hi quy lng tiu th du nhin liu Y theo cc n hng mi X. Da vo s liu hng qu cho

giai on 1930-1939, cc kt qu l nh sau:

= 8,37 + 0,171Xt

= 8,27 + 0,111Xt + 0,064Xt-1

= 8,27 + 0,109Xt + 0,071Xt-1 0,055Xt-2

= 8,32 + 0,108Xt + 0,063Xt-1 + 0,022Xt-2 0,020Xt-3

Alt chn phng trnh hi quy th hai l phng trnh hi quy tt nht v trong hai phng

trnh sau cng, du ca Xt-2 khng n nh v trong phng trnh sau cng, du ca Xt-3 c gi tr

m, kh l gii v mt kinh t.

Cho d c v n gin, php c lng phi th thc c nhiu nhc im nh sau:

1. Khng c s hng dn tin nghim v di thi gian tr l bao nhiu9.

2. Khi ngi ta xc nh cc tr ni tip nhau, t do cn li s t hn, lm cho s d

on thng k phn no b lung lay. Cc nh kinh t hc thng khng may mn c c

mt chui s liu di c th tip tc c lng nhiu tr.

3. Quan trng hn, trong s liu chui thi gian kinh t, cc gi tr ( tr) tip theo c xu

hng tng quan cao; v th tnh a cng tuyn s xut hin. Nh lu trong chng

10, tnh a cng tuyn dn n c lng khng chnh xc; ngha l cc sai s chun c

xu hng ln hn trong mi quan h vi cc h s c lng. Nh mt h qu, da vo

vic tnh ton cc t s t theo l thng, ta d c xu hng tuyn b (mt cch sai lm)

rng cc h s tr khng c ngha thng k.

4. Vic tm kim di ca thi gian tr bng cch lin tc thm vo cc bin tr nh trn

thng b co buc l khai thc s liu. ng thi, nh ta lu trong phn 13.4, mc

ngha danh ngha v thc t ca vic kim nh cc gi nh thng k tr nn mt vn

quan trng trong vic tm kim theo trnh t ny [xem phng trnh (13.4.2) chng

13)].

Khi xem xt nhng vng mc trn y, qui trnh c lng phi th thc rt t c kin ngh.

R rng, nu ta mun tin ti vi bi ton c lng, ta phi a ra cc cn nhc trc tin hay

cc cn nhc l thuyt xc nhn cc khc nhau.

17.4 Cch tip cn Koyck i vi cc m hnh phn phi tr

Koyck xut mt phng php ti tnh c lng cc m hnh phn phi tr. Gi s ta

bt u bng m hnh phn phi tr khng xc nh (17.3.1). Gi nh rng tt c cc u c

cng du, Koyck gi s cc gim dn v mt hnh hc nh sau:10

9 Nu di thi gian tr k c qui nh khng chnh xc, ta s phi vng phi vn sai s do xc nh sai nh

tho lun trong chng 13. ng thi cng nn lu cnh bo v vic khai thc s liu.


Cc phng php nh lng




k = 0k k = 0, 1, (17.4.1)11

trong tha iu kin 0 < < 1, c gi l t l gim ca tr phn phi v trong 1

c gi l tc iu chnh.

iu th hin qua phng trnh (17.4.1) l mi h s tip theo u nh hn v mt s hc so

vi h s trc (ta suy ra pht biu ny v < 1), ng rng khi ta i ngc v qu kh

cng xa, nh hng ca tr i vi Yt tr nn gim ly k, mt gi nh kh hp l. Suy

cho cng, ta d kin rng thu nhp hin ti v qu kh gn y s nh hng n chi tiu dng

hin ti nhiu hn so vi thu nhp trong qu kh xa xm. V mt hnh hc, cch tip cn ca

Kyock c trnh by trong hnh 17.5.

Hnh 17.5 Cch tip cn Kyock (phn phi hnh hc gim dn)

tr (thi gian)

Nh hnh ny cho thy, ngoi 0 chung, gi tr ca h s tr k cn ph thuc vo gi tr ca .

H s cng gn 1, tc gim ca k cng chm; trong khi cng gn 0, tc gim ca k

cng nhanh. Trong trng hp gn 1, cc gi tr qu kh xa xi ca X s pht huy tc ng

10 L. M. Kyock, Distributed Lags and Investment Analysis, North Holland Publishing Company, Amsterdam, 1954.

11 i khi phng trnh ny cn c vit l: k = 0 (1 )

k k = 0, 1, v nhng l do nu trong ch thch 12.


Cc phng php nh lng




ng k i vi Yt, trong khi trong trng hp gn 0, nh hng ca chng i vi Yt s mt

dn mt cch nhanh chng. Din tin ny c th c thy r trong minh ha sau y:

0 1 2 3 4 5 10

0.75 0 0,750 0,560 0,420 0,320 0,240 0,060

0.25 0 0,250 0,060 0,020 0,0040 0,0010 0,00

Lu cc c im ny ca cch tip cn Koyck: (1) Thng qua gi nh rng cc gi tr ca

khng m, Koyck loi ra hin tng i du ca cc h s ; (2) thng qua gi nh rng < 1,

ng gn tm quan trng t hn cho cc h s trong qu kh xa xi so vi cc h s gn hin

ti hn; v (3) ng bo m rng tng ca cc h s , cho ta bit s nhn di hn, l c hn, y

l:

(17.4.2)12

Nh mt h qu ca phng trnh (17.4.1), m hnh tr khng xc nh (17.3.1) c th c

vit l:

Yt = + 0 Xt + 0 Xt-1 + 0 2Xt-2 + + ut (17.4.3)

Nh th hin, m hnh vn khng th d dng c lng v ta vn cn phi c lng mt s ln

thng s (chnh xc l v hn) v thng s c a vo di dng phi tuyn tnh bc cao.

Ni chnh xc ra, phng php phn tch hi quy tuyn tnh (trong cc thng s) khng th p

dng cho mt m hnh nh vy. Nhng by gi Koyck xut mt cch gii quyt ti tnh. ng

lm tr phng trnh (17.4.3) i mt thi on thu c phng trnh sau:

Yt-1 = + 0 Xt-1 + 0 Xt-2 + 0 2Xt-3 + + ut-1 (17.4.4)

Sau ng nhn phng trnh (17.4.4) cho c:

Yt-1 = + 0 Xt-1 + 0 2Xt-2 + 0

3Xt-3 + + ut-1 (17.4.5)

Ly phng trnh (17.4.3) tr i phng trnh (17.4.5), ng c:

Yt Yt-1 = (1 ) + 0 Xt + (ut ut-1) (17.4.6)

Hay sp xp li:

Yt = (1 ) + 0 Xt + Yt-1 + vt (17.4.7)

12 iu ny l v:

k = 0 (1 + + 2 + 3 + ) = 0

v biu thc trong du ngoc n bn v phi l mt chui hnh hc v hn m tng ca n l

min l 0 < <

1. Nhn tin cng lu rng nu k c nh ngha nh trong ch thch 11, th v th k = 0(1 ) / (1 ) = 0 s bo m rng cc trng s (1 )k c tng bng 1.


Cc phng php nh lng




Trong , vt = (ut ut-1), bnh qun di ng ca ut v ut-1.

Tin trnh va m t trn y c gi l php bin i Koyck. So snh (17.4.7) vi (17.3.1), ta

thy s n gin ha tuyt vi m Koyck thc hin. Trong khi trc y ta phi c lng

v mt s v hn cc h s , by gi ta ch phi c lng ba n s: , 0 v . By gi khng

c l do g d kin tnh a cng tuyn. Theo mt ngha nht nh, tnh a cng tuyn

c gii quyt bng cch thay th Xt-1, Xt-2, , bng mt bin n, y l Yt-1. Nhng ta nn lu

cc c im sau ca php bin i Koyck:

1. Ta bt u bng mt m hnh phn phi tr nhng li kt thc vi mt m hnh t hi

quy v Yt-1 xem ra l mt trong cc bin gii thch. Php bin i ny cho thy cch ta c

th qui i mt m hnh phn phi tr thnh mt m hnh t hi quy.

2. S xut hin ca Yt-1 xem ra c th to ra mt s vn thng k. Cng nh Yt, Yt-1 c

tnh ngu nhin, ngha l ta c mt bin gii thch ngu nhin trong m hnh. Nn nh

rng l thuyt bnh phng ti thiu kinh in da vo gi nh rng cc bin gii thch

hoc phi ngu nhin, hoc nu c ngu nhin th phi c phn phi c lp vi s hng

nhiu ngu nhin. V th, ta phi tm xem Yt-1 c tha gi nh ny hay khng. (Ta s

quay li vi vn ny trong phn 17.8).

3. Trong m hnh gc (17.3.1), s hng nhiu l ut, trong khi trong m hnh bin i, s

hng nhiu l vt = (ut ut-1). Cc thuc tnh thng k ca vt ph thuc vo vic ta gi

nh g v cc thuc tnh thng k ca ut, v nh s thy sau y, nu cc ut ban u

khng c tng quan chui, th cc vt s c tng quan chui. Do , c l ta phi ng

u vi vn tng quan chui, thm vo l bin gii thch ngu nhin Yt-1. Ta s

lm iu trong phn 17.8.

4. S hin din ca bin Y tr vi phm mt trong cc gi nh nn tng ca kim nh

Durbin Watson d. Do , ta phi trin khai mt cch kim nh khc cho s tng quan

chui trong s hin din ca bin Y tr. Mt cch l kim nh Durbin h, s tho lun

trong phn 17.10.

Nh ta thy phng trnh (17.1.4), tng ring phn ca i chun ha cho ta t l trong tng tc

ng, hay tc ng di hn c cm nhn trong mt thi on c th. D vy, trong thc hnh,

ngi ta thng s dng tr trung bnh hay tr trung v m t bn cht c cu tr ca

mt m hnh phn phi tr.

tr trung v

tr trung v l thi gian cn thit cho mt na u tin, hay 50 phn trm ca tng thay i Y

xy ra sau s thay i 1 n v ko di ca X. i vi m hnh Koyck, tr trung v l nh sau

(xem bi tp 17.6):

M hnh Koyck: tr trung v =

(17.4.8)

Nh vy, nu = 0.2, tr trung v l 0.4306, nhng nu = 0.8, tr trung v l 3.1067.

Din t bng li, trong trng hp = 0.2, 50 phn trm tng thay i ca Y din ra trong cha

n mt na thi on; trong khi trong trng hp = 0.8, phi mt hn 3 thi on mi t


Cc phng php nh lng




c 50 phn trm thay i ca Y. Nhng ta khng l g s tng phn ny, v nh ta bit, gi tr

cng cao th tc iu chnh cng chm, v gi tr cng thp, th tc iu chnh cng ln.

tr trung bnh

Min l tt c cc h s u dng, tr trung bnh hay tr bnh qun c nh ngha l:

tr trung bnh =

(17.4.9)

y ch n thun l bnh qun trng s ca tt c cc tr lin quan, vi cc h s tng

ng ng vai tr trng s. Ni vn tt, l bnh qun tr trng s ca thi gian. i vi

m hnh Koyck, tr trung bnh l (xem bi tp 17.7):

M hnh Koyck: tr trung bnh =

(17.4.10)

Nh vy, nu = , tr trung bnh l 1.

T tho lun trn, ta thy r rng l tr trung bnh v tr trung v ng vai tr nh mt s

o tm tt tc phn ng ca bin Y theo s thay i ca bin X. Trong v d cho trong bng

17.1, tr trung bnh l khong 11 qu, cho thy rng bnh qun phi mt kha kh thi gian

nh hng ca s thay i cung tin c cm nhn qua s thay i gi (bi tp 17.8).

V d 17.7 Tiu dng c nhn trn u ngi

V d ny xem xt chi tiu dng c nhn trn u ngi (per capita personal consumption

expenditure, PPCE) trong mi quan h vi thu nhp kh dng trn u ngi (per capita personal

disposable income, PPDI) Hoa K trong giai on 1970-1999, tt c s liu u tnh bng USD

nm 1996. minh ha m hnh Koyck, ta hy xem s liu cho trong bng 17.2. Hi quy PPCE

theo PPDI v PPCE tr, ta c kt qu sau:

= -1442,169 + 0,6033PPDIt + 0,4PPCEt-1

se = (402,5784) (0,1502) (0,1506)

t = (-3,0855) (4,0155) (2,6561)

R2 = 0,9926 d = 1,0056 Durbin h = 5,119

(17.4.11)

(se = sai s chun)

Lu : Cch tnh tr thng k Durbin h s c tho lun trong phn 17.10.

Nu ta gi nh rng m hnh ny c hnh thnh t mt php bin i Koyck, th = 0.4106.

tr trung v l:

= 0,7786

V tr trung bnh l:

= 0,6966

Din t bng li, xem ra PPPE iu chnh theo PPDI ch trong mt khong thi gian tng i

ngn.


Cc phng php nh lng




Bng 17.2 PPCE v PPDI, 1970-1999

Quan st PPCE PPDI Quan st PPCE PPDI

1970 11,300 12,823 1985 16,020 18,229

1971 11,581 13,218 1986 16,541 18,641

1972 12,149 13,692 1987 16,398 18,870

1973 12,626 14,496 1988 17,463 19,522

1974 12,407 14,268 1989 17,760 19,833

1975 12,551 14,393 1990 17,899 20,058

1976 13,155 14,873 1991 17,677 19,919

1977 13,583 15,256 1992 17,989 20,318

1978 14,035 15,845 1993 18,399 20,384

1979 14,230 16,120 1994 18,910 20,709

1980 14,021 16,063 1995 19,294 21,055

1981 14,069 16,265 1996 19,727 21,385

1982 14,105 16,328 1997 20,232 21,838

1983 14,741 16,673 1998 20,989 22,672

1984 15,401 17,799 1999 21,901 23,191

Ch thch: PPCE = chi tiu dng c nhn trn u ngi, tnh bng USD nm 1996.

PPDI = thu nhp c nhn kh dng trn u ngi, tnh bng USD nm 1996.

Ngun: Bo co kinh t ca tng thng, nm 2001, bng B-31, trang 311.

17.5 Hp l ha m hnh Koyck: M hnh k vng iu chnh (Adaptive Expectations, AE)

Cho d rt cht ch, m hnh Koyck (17.4.7) c tnh phi th thc v t c thng qua mt qu

trnh i s thun ty; n thiu nn tng l thuyt. Tuy nhin, khong trng ny c th c lp

y nu ta bt u t mt gc khc. Gi s ta a ra m hnh sau y:

Yt = 0 + 1 + ut (17.5.1)

trong Y = cu tin (s d tin thc)

X* = li sut cn bng, ti u, k vng di hn, hay danh ngha.

u = s hng sai s

Phng trnh (17.5.1) cho thy rng cu tin l mt hm s ph thuc vo li sut k vng (theo

ngh l li sut d on trc).

V bin k vng X* khng th quan st trc tip, ta hy a ra gi thit sau y v cch thc

hnh thnh cc k vng:

= (Xt ) (17.5.2)

13

13 i khi m hnh c biu th l

= (Xt-1 )


Cc phng php nh lng




Trong tha iu kin 0 < 1, c gi l h s k vng. Gi thit (17.5.2) c gi l gi

thit k vng iu chnh, k vng tin b, hay hc hi sai lm, do Cagan14 v Friedman15 ph

bin.

iu th hin qua gi thit (17.5.2) l cc tc nhn kinh t s iu chnh k vng ca h di

nh sng ca kinh nghim qu kh, v ni c th ra, h s hc hi t nhng sai lm ca mnh.16

Ni c th hn na, gi thit (17.5.2) pht biu rng cc k vng c iu chnh qua tng thi

on theo mt t l trong chnh lch gia gi tr hin ti ca bin v gi tr k vng trc

ca n. Nh vy, i vi m hnh ca chng ta, iu ny c ngha l cc k vng v li sut c

sa i trong tng thi on theo mt t l trong chnh lch gia li sut quan st c trong

thi on hin hnh v gi tr d on ca li sut trong thi on trc. C mt cch khc ta

pht biu iu ny l vit gi thit (17.5.2) di dng:

= Xt + (1 )

(17.5.3)

Gi thit ny cho thy rng gi tr k vng ca li sut vo thi on t l bnh qun trng s ca

gi tr thc t ca li sut trong thi on t v gi tr k vng trong thi on trc, vi trng s

ln lt l v 1 . Nu = 1, th = Xt, c ngha l k vng hin thc ha ngay tc thi

v hon ton, ngha l ngay trong cng thi on. Mt khc, nu = 0, th =

, c ngha l

k vng c tnh cht tnh, ngha l tnh hnh hin ti s c duy tr trong mi thi on tip

theo. Khi , gi tr tng lai k vng tr nn c nhn din bng cc gi tr hin hnh.17

Thay phng trnh (17.5.3) vo phng trnh (17.5.1), ta c:

Yt = 0 + 1 [Xt + (1 ) ] + ut

= 0 + 1 Xt + 1(1 ) + ut

(17.5.4)

By gi ta lm tr phng trnh (17.5.1) i mt thi on, nhn n cho 1 , ri ly (17.5.4) tr

cho tch s ny. Sau cc thao tc i s n gin, ta c:

Yt = 0 + 1 Xt + (1 )Yt-1 + ut (1 )ut-1

= 0 + 1 Xt + (1 )Yt-1 + vt (17.5.5)

Trong vt = ut (1 )ut-1.

Trc khi tip tc, ta hy lu s khc nhau gia (17.5.1) v (17.5.5). Trong phng trnh

(17.5.1), 1 o lng phn ng trung bnh ca Y trc s thay i mt n v ca X*, gi tr di

hn hay gi tr trng thi cn bng ca X. Mt khc, trong phng trnh (17.5.5), 1 o lng

14

P. Cagan, The Monetary Dynamics of Hyperinflations, trong sch ca M. Friedman (ch bin), Studies in the Quantity Theory of Money, University of Chicago Press, Chicago, 1956.

15 Milton Friedman, A Theory of the Consumption Function, Vn phng Nghin cu kinh t quc gia, Princeton

University Press, Princeton, N. J., 1957.

16 G. K. Shaw, Rational Expectations: An Elementary Exposition, St. Martins Press, New York, 1984, trang 25.

17 Nh trn, trang 19-20.


Cc phng php nh lng




phn ng trung bnh ca Y trc s thay i mt n v ca gi tr thc t hay gi tr quan st

c ca X. Cc phn ng ny khng nht thit l nh nhau, l d nhin tr khi = 1, ngha l

gi tr hin hnh v gi tr di hn ca X l nh nhau. Trong thc hnh, trc tin ta c lng

phng trnh (17.5.5). Mt khi thu c mt gi tr c lng ca t h s ca Y tr, ta c

th d dng tnh 1 bng cch chia h s ca Xt (= 1) cho .

S tng t gia m hnh k vng iu chnh (17.5.5) v m hnh Koyck (17.4.7) th hin r rt

cho d vic l gii cc h s trong hai m hnh khc nhau. Lu rng cng nh m hnh Koyck,

m hnh k vng iu chnh l m hnh t hi quy v s hng sai s ca n cng tng t nh s

hng sai s ca m hnh Koyck. Chng ta s quay li vi vic c lng m hnh k vng iu

chnh trong phn 17.8 v mt s v d trong phn 17.12. V chng ta phc tho s qua m

hnh k vng iu chnh, th th m hnh ny st thc t n mc no? Qu tht l m hnh ny

hp dn hn cch tip cn Koyck thun ty i s, nhng liu gi thit k vng iu chnh c

hp l hay khng? Thin v gi thit k vng iu chnh, ngi ta c th ni nh sau:

N mang li mt phng tin n gin lp m hnh cc k vng trong l thuyt kinh t ng thi vch

ra cung cch hnh vi ca nhng tc nhn kinh t m dng nh ht sc nhy cm. Nim tin rng con ngi

hc hi t kinh nghim hin nhin l mt im khi u c l hn so vi gi nh ngm n rng h hon

ton khng c hi c, c im ca lun k vng tnh. Hn na, khng nh rng nhng kinh nghim

qu kh xa xm pht huy nh hng t hn so vi kinh nghim gn y s ph hp vi cm nhn chung v

xem ra c xc nhn y bi nhng quan st n gin.18

Cho n khi xut hin gi thit k vng hp l (Rational Expectations, RE) thot u do J.

Muth a ra v v sau c Robert Lucas v Thomas Sargent ph bin rng ri, th gi thit k

vng iu chnh kh c a chung trong kinh t hc thc nghim. Nhng ngi xng gi

thit RE cho rng gi thit AE khng y v ch da vo cc gi tr qu kh ca mt bin khi

nh hnh cc k vng,19 trong khi gi thit RE cho rng cc tc nhn kinh t ring l s dng

thng tin sn c hin ti v ph hp trong vic nh hnh cc k vng v khng ch thun ty da

vo kinh nghim qu kh.20 Ni vn tt, gi thit RE cho rng cc k vng l hp l theo

ngha l chng bao gm mt cch hiu qu tt c nhng thng tin sn c vo thi im cc k

vng c hnh thnh21, ch khng ch nhng thng tin qu kh.

S ch trch gi thit AE t nhng ngi xng gi thit RE l hp l, cho d cng c nhiu

ph phn i vi chnh bn thn gi thit RE.22 y khng phi l ch ta sa ly vo nhng t

18 Nh trn, trang 27.

19 Cng nh m hnh Koyck, ngi ta c th chng minh rng, theo gi thit AE, cc k vng ca mt bin s l

mt bnh qun trng s theo hm s m ca cc gi tr qu kh ca bin .

20 G. K. Shaw, ti liu dn, trang 47. Tm c chi tit v gi thit RE trong nghin cu ca Steven M. Sheffrin,

Rational Expectations, Cambridge University Press, New York, 1983.

21 Stephen K. McNees, The Phillips Curve: Forward or Backward Looking? New England Economic Review,

thng 7-8/1979, trang 50.

22 Xem ph bnh ch trch gi thit RE gn y trong nghin cu ca Michael C. Lovell, Test of the Rational

Expectations Hypothesis, American Economic Review, thng 3-1966, trang 110-124.


Cc phng php nh lng




liu tranh lun gay gt v vn ny. C l ta c th ng vi Stephen McNees rng Trong

iu kin tt nht, gi nh k vng iu chnh cng ch c th c bin h nh mt gi thit

hot ng i din cho mt c ch hnh thnh k vng phc tp hn v xem ra ang thay i.23

V d 17.8 Xem li v d 17.7

Nu ta xem xt m hnh cho trong phng trnh (17.4.11), nh c xy dng bng c ch k

vng iu chnh (ngha l PPCE l mt hm s theo PPDI k vng), th h s k vng c th

thu c t phng trnh (17.5.5) nh sau: = 1 0.4106 = 0.5894. Khi , theo tho lun trn

y v m hnh AE, ta c th ni rng khong 59 phn trm ca chnh lch gia PPCE thc t v

k vng s c loi tr trong vng mt nm.

17.6 Cch khc hp l ha m hnh Koyck: M hnh iu chnh tr lng hay iu

chnh ring phn

M hnh k vng iu chnh l mt cch ta hp l ha m hnh Koyck. Marc Nerlove a ra

mt cch khc hp l ha m hnh Koyck trong ci gi l m hnh iu chnh tr lng hay

iu chnh ring phn (Partial Adjustment Model, PAM).24 minh ha m hnh ny, ta hy

xem m hnh gia tc linh hot trong l thuyt kinh t; m hnh ny gi nh rng c mt gi tr

tr lng vn trng thi cn bng, ti u, c mong mun, hay di hn, cn thit sn xut

ra mt sn lng cho trc ng vi tnh trng cng ngh v li sut cho trc v.v n gin,

ta gi nh rng mc vn mong mun ny l mt hm tuyn tnh theo sn lng X nh sau:

= 0 + 1 Xt + ut (17.6.1)

V mc vn mong mun ny khng th quan st c mt cch trc tip, nn Nerlove a ra gi

thit sau y, c gi l gi thit iu chnh ring phn, hay iu chnh tr lng:

Yt Yt-1 = ( Yt-1) (17.6.2)

25

trong tha iu kin 0 < 1, c gi l h s iu chnh, Yt Yt-1 = thay i thc t v

( Yt-1) = thay i mong i.

V Yt Yt-1, s thay i tr lng vn gia hai thi on, khng g khc hn l u t, cho nn

phng trnh (17.6.2) c th c vit l:

It = ( Yt-1) (17.6.3)

Trong It = u t vo thi on t.

23 Stepphen K. McNees, ti liu dn, trang 50.

24 Marc Nerlove, Distributed Lags and Demand Analysis for Agricultural and Other Commodities, ti liu dn.

25 Mt s tc gi khng cng s hng nhiu ngu nhin ut vo phng trnh (17.6.1) nhng li cng vo phng

trnh (17.6.2) ny, tin rng nu (17.6.1) tht s l mt mi quan h cn bng, th khng c ch cho s hng sai s, trong khi c ch iu chnh c th khng hon ho v c th i hi phi c s hng sai s. Nhn tin cng lu rng (17.6.2) i khi cn c vit l:

Yt Yt-1 = ( Yt-1)


Cc phng php nh lng




Phng trnh (17.6.2) cho thy rng s thay i tr lng vn thc t (u t) trong mt thi

on cho trc t l mt t phn trong s thay i tr lng vn m ngi ta mong mun trong

thi on . Nu = 1, c ngha l tr lng vn thc t bng vi tr lng mong mun; ngha

l tr lng thc t iu chnh theo tr lng mong mun mt cch ng thi (trong cng mt

thi on). Tuy nhin, nu = 0, ngha l khng c g thay i v tr lng thc t vo thi on

t cng ging nh tr lng quan st thy trong thi on trc . Thng thng, d kin nm

u khong gia hai cc oan ny, v s iu chnh theo tr lng vn mong mun c th

khng hon chnh do tnh cng nhc, tr , cc ngha v hp ng, v.v v th nn m hnh mi

c gi l m hnh iu chnh ring phn. Lu rng c ch iu chnh (17.6.2) c th c

vit di dng khc l:

Yt = + (1 ) Yt-1 (17.6.4)

Cho thy rng tr lng vn quan st thy vo thi on t l bnh qun trng s ca tr lng

vn mong mun vo thi on v tr lng vn tn ti trong thi on trc; vi v (1 )

l cc trng s. By gi thay (17.6.1) vo (17.6.4), ta c:

Yt = (0 + 1 Xt + ut) + (1 )Yt-1

= 0 + 1 Xt + (1 )Yt-1 + ut (17.6.5)

M hnh ny c gi l m hnh iu chnh ring phn (PAM).

V (17.6.1) tiu biu cho cu i vi tr lng vn trng thi cn bng, di hn, nn (17.6.5) c

th c gi l hm cu ngn hn i vi tr lng vn v trong ngn hn, tr lng vn hin

hu khng nht thit bng mc di hn. Mt khi ta c lng c hm ngn hn (17.6.5) v

c c gi tr c lng h s iu chnh (t h s ca Yt-1), ta c th d dng suy ra hm di

hn bng cch chia 0 v 1 cho v b i s hng Y tr, khi s cho ta (17.6.1).

Hnh 17.6 S iu chnh dn dn ca tr lng vn

Thi gian


Cc phng php nh lng




V mt hnh hc, m hnh iu chnh ring phn c th c trnh by nh trong hnh 17.6.26

Trong hnh ny, Y* l tr lng vn mong mun v Yt l tr lng vn thc t hin ti. V mc

ch minh ha, ta gi s rng = 0.5. iu ny ng rng doanh nghip c k hoch khp li

mt na khong cch gia tr lng vn thc t v tr lng vn mong mun mi thi on. V

th, trong thi on th nht, doanh nghip chuyn n Y2, vi u t bng (Y2 Y1); tip n,

u t ny bng mt na ca (Y* Y1). Trong tng thi on tip theo, doanh nghip khp li

mt na khong cch gia tr lng vn u k v tr lng vn mong mun Y*.

M hnh iu chnh ring phn tng t nh m hnh Koyck v m hnh k vng iu chnh

ch n l m hnh t hi quy. Nhng n c s hng nhiu n gin hn nhiu: s hng nhiu ban

u ut nhn cho hng s . Nhng lu rng cho d hnh thc tng t, m hnh k vng iu

chnh v m hnh iu chnh ring phn rt khc nhau v mt khi nim. M hnh k vng iu

chnh da vo tnh trng khng chc chn (v din bin gi c tng lai, li sut, v.v) trong khi

m hnh iu chnh ring phn l do tnh cng nhc v k thut hay th ch, tnh tr , chi ph

ca s thay i v.v Tuy nhin, c hai m hnh ny u vng chc v mt l thuyt hn so vi

m hnh Koyck.

V hnh thc ca m hnh k vng iu chnh v m hnh iu chnh ring phn l khng th

phn bit c, h s bng 0.5894 ca m hnh k vng iu chnh cng c th c l gii

nh h s ca m hnh iu chnh tr lng nu ta gi nh rng m hnh iu chnh tr lng

vn hnh trong trong hin ti (ngha l chnh PPCE k vng hay mong i c quan h tuyn tnh

vi PPDI hin ti).

im quan trng cn lu l v cc m hnh Koyck, k vng iu chnh v iu chnh ring

phn ngoi s khc bit v b ngoi ca s hng sai s - mang li cng mt m hnh c lng

sau cng, nn ta phi ht sc thn trng khi ni vi c gi rng nh nghin cu ang s dng

m hnh no v l do ti sao. V th, cc nh nghin cu phi nu r nn tng l thuyt ca m

hnh ca h.

17.7 Kt hp m hnh k vng iu chnh v m hnh iu chnh ring phn

Ta hy xem m hnh sau y:

= 0 + 1

+ ut (17.7.1)

Trong l tr lng vn mong mun v

l mc sn lng k vng.

V c v

u khng th quan st mt cch trc tip, ngi ta c th s dng c ch iu

chnh ring phn cho v m hnh k vng iu chnh cho

i n phng trnh c

lng sau y (xem bi tp 17.2):

Yt = 0 + 1 Xt + [(1 ) + (1 )]Yt-1

(1 )(1 )Yt-2 + [ut (1 )ut-1] (17.7.2)

26 Hnh ny phng theo hnh 7.4 trong sch ca Rudiger Dornbusch v Stanley Fischer, Macroeconomics, xut bn

ln th 3, McGraw Hill, New York, 1984, trang 216.


Cc phng php nh lng




= 0 + 1Xt + 2Yt-1 + 3Yt-2 + vt

Trong vt = [ut (1 )ut-1]. M hnh ny cng l m hnh t hi quy, im khc bit duy

nht so vi m hnh k vng iu chnh thun ty l Yt-2 xut hin cng vi Yt-1 nh mt bin

gii thch. Cng nh m hnh Koyck v m hnh AE, s hng sai s trong (17.7.2) tun theo mt

qu trnh bnh qun di ng. Mt c im khc ca m hnh ny l cho d m hnh tuyn tnh

theo cc h s , n khng tuyn tnh theo cc thng s gc.

Mt ng dng ni ting ca phng trnh (17.7.1) l gi thit thu nhp lu di ca Friedman,

pht biu rng tiu dng lu di hay tiu dng di hn l mt hm s theo thu nhp lu di

hay thu nhp di hn.27

Vic c lng phng trnh (17.7.2) cho thy nhng vn c lng ging nh trong m

hnh Koyck hay m hnh AE ch, tt c cc m hnh ny u t hi quy vi nhng c cu sai

s tng t nh nhau. Thm vo , phng trnh (17.7.2) lin quan n nhng vn c

lng phi tuyn tnh m chng ta s xem xt ngn gn trong bi tp 17.10, nhng khng c

o su trong quyn sch ny.

17.8 c lng cc m hnh t hi quy

Nh vy cho n gi t tho lun ca chng ta, ta c ba m hnh sau y:

Koyck:

Yt = (1 ) + 0 Xt + Yt-1 + (ut ut-1) (17.4.7)

K vng iu chnh:

Yt = 0 + 1 Xt + (1 )Yt-1 + [ut (1 )ut-1] (17.5.5)

iu chnh ring phn:

Yt = 0 + 1 Xt + (1 )Yt-1 + ut (17.6.5)

C ba m hnh u c dng chung l:

Yt = 0 + 1Xt + 2Yt-1 + vt (17.8.1)

Ngha l v bn cht c ba u l cc m hnh t hi quy. Do , by gi ta phi xem xt vn

c lng nhng m hnh nh th ny, v l thuyt bnh phng ti thiu kinh in khng chc

c th p dng trc tip cho cc m hnh ny. L do c hai phn: s hin din ca cc bin

gii thch ngu nhin v kh nng tng quan chui.

By gi, nh lu trn y, p dng l thuyt bnh phng ti thiu (OLS) kinh in, ta

phi chng minh rng bin gii thch ngu nhin Yt-1 c phn phi c lp vi s hng sai s vt.

xc nh liu c phi nh th hay khng, iu cn thit l phi bit cc thuc tnh ca vt. Nu

ta gi nh rng s hng nhiu gc ut tha tt c cc gi nh kinh in ca OLS, nh E(ut) = 0,

var (ut) = 2 (gi nh v phng sai ng nht) v cov (ut, ut+s) = 0 i vi (ut) =

2 (gi nh

khng c tnh cht t tng quan) th vt khng chc tha hng tt c cc thuc tnh ny. V d,

27 Milton Friedman, A Theory of Consumption Function, Princeton University Press, Princeton, N. J., 1957.


Cc phng php nh lng




ta hy xem s hng sai s trong m hnh Koyck, vt = (ut ut-1). ng vi cc gi nh v ut, ta c

th d dng chng minh rng vt c tng quan chui v:

E (vtvt-1) = 2 (17.8.2)

28

Phng trnh (17.8.3) khng bng zero (tr khi tnh c bng zero). V v Yt-1 xut hin trong

m hnh Koyck nh mt bin gii thch, nht nh n phi tng quan vi vt (thng qua s hin

din ca ut-1 trong n). Tht vy, ta c th chng minh rng:

Cov[Yt-1, (ut ut-1)] = 2 (17.8.3)

(17.8.3) cng ht nh (17.8.2). c gi c th xc minh rng iu ny cng ng vi m hnh k

vng iu chnh.

Nh vy trong m hnh Koyck cng nh trong m hnh k vng iu chnh, ta pht hin ra rng

bin gii thch ngu nhin Yt-1 tng quan vi s hng sai s vt; ngha ca pht hin ny l g?

Nh lu trn y, nu mt bin gii thch trong mt m hnh hi quy tng quan vi s

hng sai s ngu nhin, th c lng OLS khng ch b chch m cn khng nht qun;

ngha l, ngay c nu kch thc mu tng v hn, th c lng s khng xp x gn ng

vi gi tr thc ca tng th.29 Do , vic c lng m hnh Koyck v m hnh k vng

iu chnh bng qui trnh OLS thng thng c cho nhng kt qu sai lc nghim trng.

Tuy nhin, m hnh iu chnh ring phn th khc. Trong m hnh ny, vt = ut, trong 0 <

1. Do , nu ut tha cc gi nh ca m hnh hi quy tuyn tnh kinh in nu trn, th ut cng

tha cc gi nh . V th, c lng OLS ca m hnh iu chnh ring phn s cho ta cc

c lng c lng nht qun cho d cc gi tr c lng c xu hng b chch (trong nhng

mu nh hay c hn).30 Theo trc gic, l do ca tnh nht qun l nh sau: Cho d Yt-1 ph

thuc vo ut-1 v tt c cc s hng nhiu trc , n khng lin quan n s hng sai s hin ti

ut. Do , min l ut khng ph thuc chui, th Yt-1 cng s khng ph thuc, hay t nht cng

khng tng quan vi ut, nh vy m tha gi nh quan trng ca l thuyt OLS, y l khng

tng quan gia bin gii thch v s hng nhiu ngu nhin.

Cho d c lng OLS ca m hnh iu chnh ring phn hay iu chnh tr lng cho ta mt

c lng nht qun nh vo c cu n gin ca s hng sai s trong mt m hnh nh vy, ta

28

E (vtvt-1) = E (ut ut-1) (ut-1 ut-2)

= E(ut-1)2 v ng phng sai gia cc u l zero theo gi nh.

= 2

29 Vic chng minh vt ra ngoi phm vi quyn sch ny v c th c tm thy trong nghin cu ca Griliches,

ti liu dn, trang 36-38. Tuy nhin, hy xem chng 18 phc tho vic chng minh trong mt bi cnh khc. C th xem thm nghin cu ca Asatoshi Maeshiro, Teaching Regressions with a Lagged Dependent Variable and Autocorrelated Disturbances, The Journal of Economic Education, ma ng 1996, tp 27, s 1, trang 72-84.

30 Xem chng minh trong sch ca J. Johnston, Econometric Methods, xut bn ln th ba, McGraw Hill, New

York, 1984, trang 360-362. Xem thm nghin cu ca H. E. Doran v J. W. B. Guise, Single Equation Method in Econometrics: Applied Regression Analysis, Lot chuyn kho 3 ca i hc New England, Armidale, NSW, c, 1984, trang 236-244.


Cc phng php nh lng




khng nn cho rng n p dng kh hn m hnh Koyck hay m hnh k vng iu chnh.31 c

gi nn trnh lm nh th. Mt m hnh nn c chn trn c s nhng cn nhc l thuyt vng

chc, ch khng n thun ch v n dn n vic c lng thng k d dng. Mi m hnh u

nn c xem xt da vo u im ring, ch tha ng n nhiu ngu nhin xut hin

trong . Nu trong nhng m hnh nh Koyck hay k vng iu chnh, ta khng th p dng

OLS mt cch trc tip, th cn phi ngh ra cc phng php gii bi ton c lng. Ta

cng c mt vi phng php c lng khc cho d c th di dng v mt tnh ton. Trong

phn tip theo, chng ta s xem xt mt phng php nh vy.

17.9 Phng php bin cng c (Intrumental Variables, IV)

L do khin ta khng th p dng OLS cho m hnh Koyck hay m hnh k vng iu chnh l v

bin gii thch Yt-1 c xu hng tng quan vi s hng sai s vt. Nu bng cch no ta c th

loi tr mi tng quan ny, th ta c th p dng OLS thu c cc gi tr c lng nht

qun, nh lu trn y. (Lu : S c s thin lch mu nh.) Ta lm iu ny nh th no?

Liviatan xut gii php sau y:32

Gi s ta tm mt bin i din cho Yt-1 nhng khng tng quan vi vt trong vt l s hng sai

s xut hin trong m hnh Koyck hay m hnh k vng iu chnh. Bin i din gi l bin

cng c (IV), 33 Liviantan xut Xt-1 lm bin cng c cho Yt-1 v xut thm rng ngi ta

c th thu c cc thng s ca phng trnh hi quy (17.8.1) thng qua gii cc phng trnh

chun tc sau y:

Yt = n + Xt + Yt-1

Yt Xt = Xt + + Yt-1Xt (17.9.1)

Yt Xt-1 = Xt-1 + XtXt-1 + Yt-1Xt-1

Lu rng nu ta mun p dng OLS mt cch trc tip cho phng trnh (17.8.1), cc phng

trnh chun tc theo OLS thng thng s l (xem phn 7.4):

Yt = n + Xt + Yt-1

Yt Xt = Xt + + Yt-1Xt (17.9.2)

Yt Yt-1 = Yt-1 + XtYt-1 +

im khc bit gia hai h phng trnh c th hin r rng. Laviatan chng minh rng cc h

s c lng t h phng trnh (17.9.1) th nht qun, trong khi cc h s c lng t h

phng trnh (17.9.2) khng chc nht qun v Yt-1 v vt [= ut ut-1 hay ut (1 )ut-1] c th

tng quan vi nhau trong khi Xt v Xt-1 th khng tng quan vi vt. (Ti sao?)

31 ng thi, nh Johnston lu (ti liu dn, trang 350), din tin iu chnh c xut bi m hnh iu

chnh ring phn i khi c th khng hp l.

32 N. Liviatan, Consistent Estimation of Distributed Lags, International Economic Review, tp 4, thng 1-1963,

trang 44-52.

33 Cc bin cng c ny thng c s dng trong cc m hnh h phng trnh (xem chng 20).


Cc phng php nh lng




Cho d d dng p dng trong thc hnh mt khi tm c bin i din thch hp, k thut

Laviatan c th vng phi vn a cng tuyn v Xt v Xt-1 a vo h phng trnh (17.9.1)

c th tng quan cao vi nhau (nh lu trong chng 12, hu ht cc chui thi gian kinh t

thng c tng quan cao gia cc gi tr ni tip nhau). Khi , ngha l: cho d qui trnh

Laviatan mang li cc gi tr c lng nht qun, hm c lng rt c th khng hiu qu.34

Trc khi tip tc, cu hi hin nhin l: Lm th no ta tm c mt bin i din tt cho Yt-1

sao cho, mc d tng quan cao vi Yt-1, n khng tng quan vi vt? Trong t liu nghin cu

c mt vi xut m ta s xem xt thng qua mt bi tp (xem bi tp 17.5). Nhng phi ni

rng, vic tm cc bin i din tt chng phi lun lun d dng, trong trng hp no th

phng php bin cng c cng t c ng dng trong thc hnh v ngi ta c th phi tm n

cc k thut c lng gn ng ti a (maximum likelihood), vn vt ra ngoi phm vi quyn

sch ny.35

C chng mt php kim nh no m ta c th s dng xem th cc bin cng c c

chn c gi tr hay khng? V mc ch ny, Dennis Sargan trin khai mt php kim nh gi l

kim nh SARG. Kim nh ny c m t trong ph lc 17A, phn 17A.1.

17.10 D tm tnh t tng quan trong cc m hnh t hi quy: Kim nh Durbin h

Nh ta thy, tng quan chui kh d trong cc sai s vt lm cho bi ton c lng trong m

hnh t hi quy tr nn kh phc tp: Trong m hnh iu chnh tr lng, s hng sai s vt

khng c tng quan chui (bc mt) nu s hng sai s trong phng trnh gc khng tng

quan chui, trong khi trong m hnh Koyck v m hnh k vng iu chnh, vt c tng quan

ngay c nu ut khng c tng quan chui. Khi , vn l: lm th no ta bit c hay khng

c tng quan chui trong s hng sai s trong cc m hnh t hi quy?

Nh lu trong chng 12, tr thng k Durbin Watson d xem ra khng th s dng d tm

sai s chui (bc mt) trong cc m hnh t hi quy, v gi tr d tnh c trong nhng m hnh

ny ni chung c xu hng tin ti 2, l gi tr d k vng trong mt chui ngu nhin tht s.

Ni cch khc, nu ta c tnh tr thng k d mt cch my mc trong nhng m hnh nh vy, s

c mt s thin lch ni ti chng li vic pht hin ra mi tng quan chui (bc mt). Bt chp

iu ny, nhiu nh nghin cu vn tnh tr thng k d v mun c iu g tt hn. Tuy nhin,

gn y, chnh Durbin xut mt php kim nh mu ln v mi quan h chui bc mt

trong cc m hnh t hi quy.36 Kim nh ny c gi l kim nh tr thng k h.

34 xem tnh hiu qu ca c lng c th c ci thin nh th no, tham kho sch ca Lawrence R. Klien, A

Textbook of Econometrics, xut bn ln th 2, Prentice Hall, Englewood Cliffs, N. J., 1974, trang 99. Xem thm nghin cu ca William H. Greene, Econometric Analysis, Macmillan, xut bn ln th hai, New York, 1993, trang 535-538.

35 Xem tho lun c ng v phng php c lng gn ng ti a trong nghin cu ca J. Johnston, ti liu

dn, trang 366-371, cng nh ph lc 4A v 15A.

36 J. Durbin, Testing for Serial Correlation in Least Squares Regression When Some of the Regression Are Lagged

Dependent Variables, Econometrica, tp 38, 1970, trang 410-421.


Cc phng php nh lng




Ta tho lun v kim nh tr thng k Durbin h trong bi tp12.36. thun tin, ta trnh by

li tr thng k h (vi i cht thay i nh v k hiu):

h =

(17.10.1)

trong n l kch thc mu, var ( ) l phng sai ca h s ca Yt tr (= Yt-1) trong phng

trnh (17.8.1) v l mt gi tr c lng ca tng quan chui bc mt , nh tho lun

trong chng 12.

Nh lu trong bi tp 12.36, i vi mu ln, Durbin chng minh rng theo gi thit khng

= 0, tr thng k h ca phng trnh (17.10.1) c phn phi chun tiu chun. Ngha l:

hasy ~ N(0, 1) (17.10.2)

trong asy c ngha l tim cn.

Trong thc hnh, nh lu trong chng 12, ta c th c lng nh sau:

1

(17.10.3)

Tht th v khi nhn thy rng cho d ta khng th s dng tr thng k Durbin d kim nh

tnh t tng quan trong cc m hnh t hi quy, ta vn c th s dng n nh mt yu t u

vo tnh tr thng k h.

Ta hy minh ha vic s dng tr thng k h bng v d 17.7. Trong v d ny, n = 30, 1

(d/2) = 0.4972 (lu : d = 1.0056), v var( ) = var (PPCEt-1) = (0.1546)2 = 0.0239. a cc

gi tr ny vo phng trnh (17.10.1), ta c:

h = 0.4972

= 5.1191 (17.10.4)

V gi tr h ny c phn phi chun tiu chun theo gi thit khng, nn xc sut thu c c

gi tr h cao nh vy rt nh. Nn nh rng xc sut mt bin thin chun tiu chun cao hn

gi tr 3 l cc k nh. V th, trong v d ny, kt lun ca chng ta l c s t tng quan

(dng). L d nhin, lu rng h c phn phi chun tiu chun mt cch tim cn. Mu 30

quan st ca ta khng nht thit l mt mu ln.

Lu cc c im sau y ca tr thng k h:

1. Vic c bao nhiu bin X hay bao nhiu gi tr tr ca Y trong m hnh hi quy khng

quan trng. tnh tr thng k h, ta ch cn xem xt phng sai ca h s ca bin Yt-1

tr.

2. Php kim nh ny khng th p dng nu [n var ( )] ln hn 1. (Ti sao?) D vy,

trong thc hnh, iu ny thng khng xy ra.


Cc phng php nh lng




3. V y l mt php kim nh mu ln, vic p dng php kim nh cho nhng mu nh

s khng th l gii mt cch nghim ngt c, nh Inder37 v Kiviet38 chng minh.

Ngi ta cho rng kim nh Breusche Godfrey (BG) hay cn gi l kim nh s nhn

Lagrange nh tho lun trong chng 12 c sc mnh thng k khng ch trong mu ln

m c trong nhng mu c hn, hay mu nh, v do c a chung hn so vi kim

nh h.39

17.11 Mt s v d: Cu tin Canada, qu I nm 1979 n qu IV nm 1988

minh ha vic s dng nhng m hnh m ta tho lun cho n gi, ta hy xem mt trong

cc ng dng thc nghim u tin, y l cu tin (hay cu s d tin thc). Ni c th ra, ta hy

xem m hnh sau y:40

= 0

(17.11.1)

Trong = Cu tin mong mun hay cu tin di hn (cu s d tin thc)

Rt = Li sut di hn, t l phn trm

Yt = Tng thu nhp quc gia thc

c lng thng k, phng trnh (17.11.1) c th vit li cho tin di dng log nh sau:

= ln 0 + 1 ln Rt + 2 ln Yt + ut (17.11.2)

V bin cu tin mong mun khng th quan st mt cch trc tip, ta hy a ra gi thit iu

chnh tr lng, ngha l:

0 < 1 (17.11.3)

Phng trnh (17.11.3) pht biu rng mt t l phn trm c nh (ti sao?) ca chnh lch gia

cu s d tin thc thc t v cu s d tin thc mong mun s c loi b trong mt thi

on (mt nm). Di dng log, phng trnh (17.11.3) c th c vit l:

ln Mt ln Mt-1 = (ln ln Mt-1) (17.11.4)

Thay ln t phng trnh (17.11.2) vo phng trnh (17.11.4) v sp xp li, ta c:

ln Mt = ln 0 + 1 ln Rt + 2 ln Yt + (1 )ln Mt-1 + ut (17.11.5)41

37 B. Inder, An Approximation to the Null Distribution of the Durbin Watson Statistic in Models Containing

Lagged Dependent Variables, Econometric Theory, tp 2, s 3, 1986, trang 413-428.

38 J. F. Kivieet, On the Vigour of Some Misspecification Tests for Modelling Dynamic Relationships, Review of

Econometric Studies, tp 53, s 173, 1986, trang 241-262.

39 Gabor Korosi, Laszlo Matyas, v Istvan P. Szekely, Practical Econometrics, Ashgate Publishing Company,

Brookfield, Vermonth, 1992, trang 92.

40 Xem mt m hnh tng t trong nghin cu ca Gregory C. Chow, On the Long Run and Short Run Demand

for Money, Journal of Policital Economy, tp 74, s 2, 1966, trang 111-131. Lu mt u im ca hm s nhn l s m ca bin cho ta gi tr c lng trc tip ca co gin (xem chng 6).


Cc phng php nh lng




Phng trnh ny c th c gi l hm cu ngn hn ca tin. (Ti sao?)

minh ha cho cu s d tin thc ngn hn v di hn, ta hy xem s liu cho trong bng

17.3. S liu hng qu ny l ca Canada trong giai on t 1979 n 1988. Cc bin s c

nh ngha nh sau: M [c nh ngha l cung tin M1, triu dollar Canada (C$)], P [h s

gim pht gi ngm n, 1981 = 100], GDP theo gi c nh nm 1981 (triu C$) v R (li sut n

cng ty chun thi hn 90 ngy, t l phn trm).42 M1 c loi tr nh hng ca yu t gi P

thu c s liu v s d tin thc. Cu tin thc tin nghim d kin s c quan h ng

bin vi GDP (nh hng thu nhp dng) v c quan h nghch bin vi R (li sut cng cao,

chi ph c hi ca vic gi tin cng ln, v M1 c hng li rt thp, nu c).

Cc kt qu hi quy l nh sau:43

= 0,8561 0,0634 ln Rt 0,0237 ln GDPt + 0,9607 ln Mt-1

se = (0,5101) (0,0131) (0,0366) (0,0414)

t = (1,6782) (-4,8134) (-0,6466) (23,1972)

R2 = 0,9482 d = 2,4582 F = 213,7234 (17.11.6)

43

Hm cu ngn hn c lng cho thy rng co gin theo li sut ngn hn c du ng v kh

c ngha thng k, v tr thng k p gn nh bng khng. co gin theo theo thu nhp ngn

hn c gi tr m mt cch ngc nhin, cho d v mt thng k, n khng khc khng. H s iu

chnh l = (1 0.9607) = 0.0393, ng rng ch c khong 4 phn trm chnh lch gia s d

tin thc mong i v thc t mt i trong mt qu, s iu chnh kh chm.

Quay li vi hm cu di hn (17.11.2), tt c nhng g cn lm l chia hm cu ngn hn cho

(ti sao?) v b s hng ln Mt-1. Kt qu l:

= 21.7888 1.6132 ln Rt 0.6030 ln GDP (17.11.7)

44

41 Nhn tin, lu rng m hnh ny thc cht l phi tuyn tnh trong cc thng s. Do , cho d OLS c th cho ta

mt c lng khng chch, v d nh 1 hp li, n khng chc s cho ta mt c lng khng chch ca tng 1 v ring l, nht l khi mu nh.

42 S liu ny ly t sch ca B. Bhaskar Rao ch bin, Cointegration for the Applied Economist, St. Martins Press,

New York, 1994, trang 210-213. S liu gc l t qu I nm 1956 n qu IV nm 1988, nhng v mc ch minh ha, chng ta bt u phn tch t qu I nm 1979.

43 Lu c im ny ca sai s chun c lng. Sai s chun, v d nh ca h s ca ln Rt l sai s chun ca

, mt gi tr c lng ca 1. Khng c cch n gin no thu c cc sai s chun ca v mt cch ring bit t sai s chun ca , nht l nu mu tng i nh. Tuy nhin, i vi nhng mu ln, ngi ta c th thu c cc sai s chun ring bit ca mt cch gn ng, nhng cn phi thc hin vic tnh ton. Xem nghin cu ca Jan Kmenta, Element of Econometrics, Macmillan, New York, 1971, trang 444.

44 Lu rng chng ta khng trnh by sai s chun ca cc h s c lng do nhng nguyn nhn tho lun

trong ch thch s 43.


Cc phng php nh lng




Nh ta thy, co gin ca cu tin theo li sut di hn ln hn nhiu (v gi tr tuyt i) so

vi co gin tng ng ngn hn; v iu ny cng ng vi co gin cu tin theo thu nhp,

cho d trong v d ny, ngha thng k v kinh t ca n khng r rng.

Lu rng tr thng k Durbin Watson d l 2.4582, hay gn bng 2. iu ny xc nhn nhn xt

ca chng ta trn y rng trong cc m hnh t hi quy, d tnh c ni chung gn bng 2. Do

, ta khng nn tin vo gi tr d tnh c tm xem s liu ca chng ta c tng quan chui

hay khng. Trong trng hp ny, kch thc mu l 40 quan st, c th ln mt cch hp l

p dng kim nh h. Trong trng hp ny, c gi c th xc minh rng gi tr h tnh c l -

1.5008, khng c ngha thng k mc ngha 5 phn trm, c th cho thy rng khng c t

tng quan bc mt trong s hng sai s.


Cc phng php nh lng




Bng 17.3 Tin, li sut, ch s gi, v GDP, Canada

Quan st M1 R P GDP

Ch thch: M1 = cung tin, triu C$

P = h s gim pht gi ngm n (1981 = 100)

R = li sut n cng ty chun, thi hn 90 ngy, t l phn trm

GDP = triu C$, (gi 1981)

Ngun: Rao, ti liu dn, trang 210-213.


Cc phng php nh lng




17.12 Cc v d minh ha

Trong phn ny, chng ta trnh by mt vi v d v m hnh phn phi tr xem cc nh

nghin cu s dng nhng m hnh ny nh th no trong cc nghin cu thc nghim.

V d 17.9 Cc D tr lin bang v li sut thc

nh gi nh hng ca s tng trng cung tin M1 (tin + tin gi vng lai) i vi s o

li sut thc ca tri phiu hng Aaa, G. J. Santoni v Courtenay C. Stone45 c lng m

hnh phn phi tr sau y cho Hoa K, s dng s liu hng thng.

rt = Hng s + + ui (17.12.1)

trong rt = Ch s li sut tri phiu hng Aaa ca Moody tr i t l thay i bnh qun hng

nm ca ch s gi tiu dng iu chnh theo ma trong 36 thng trc, c dng lm s o li

sut thc, v Mt = tng trng M1 hng thng.

Cn c theo hc thuyt v s trung tnh (neutrality) ca tin t cho rng cc bin s kinh t

thc nh sn lng, vic lm, tng trng kinh t v li sut thc v lu di khng chu nh

hng ca cung tin v do , thc cht khng chu nh hng ca chnh sch tin t ng vi

lp lun ny, bt lun th no, Cc d tr lin bang s khng c nh hng lu di i vi li

sut thc.46

Nu hc thuyt ny c gi tr, th ngi ta s d kin rng cc h s tr phn phi ai cng nh

tng ca chng s khng khc khng v mt thng k. tm xem liu c ng nh th khng,

cc tc gi c lng phng trnh (17.12.1) trong hai khong thi gian khc nhau, t thng

2-1951 n thng 9-1979 v t thng 10-1979 n thng 11-1982; khong thi gian sau c xem

xt n s thay i chnh sch tin t ca Fed, m t thng 10-1979 chnh sch ny ch n

t l tng trng cung tin nhiu hn so vi li sut, vn l chnh sch trong giai on trc .

Cc kt qu hi quy c trnh by trong bng 17.4. Cc kt qu xem ra xc nhn hc thuyt v

tnh trung tnh ca tin t v trong giai on t thng 2-1951 n thng 9-1979, tng trng tin

hin ti cng nh tr (qu kh) u khng c nh hng c ngha thng k i vi li sut

thc. i vi giai on sau cng th, hc thuyt v tnh trung tnh xem ra cng ng v ai

khng khc khng v mt thng k; ch c h s a1 l c ngha thng k, nhng c du sai. (Ti

sao?)

45 The Fed and the Real Rate of Interest, Review, Ngn hng D tr lin bang St. Louis, thng 12-1982, trang 8-18.

46 The Fed and the Real Rate of Interest, Review, Ngn hng D tr lin bang St. Louis, thng 12-1982, trang 15.


Cc phng php nh lng




Bng 17.4 nh hng ca tng trng M1 hng thng i vi s o li sut thc ca tri

phiu hng Aaa, t thng 2-1951 n thng 11-1982

r = Hng s +

Thng 2-1951 n thng 9-1979 Thng 10-1979 n thng 11-1982

H s t* H s t

Hng s 1.4885** 2.068 1.0360 0.801

a0 -0.00088 0.388 0.00840 1.014

a1 0.00171 0.510 0.03960** 3.419

a2 0.00170 0.423 0.03112 2.003

a3 0.00233 0.542 0.02719 1.502

a4 -0.00249 0.563 0.00901 0.423

a5 -0.00160 0.348 0.01940 0.863

a6 0.00292 0.631 0.02411 1.056

a7 0.00253 0.556 0.01446 0.666

a8 0.00000 0.001 -0.00036 0.019

a9 0.00074 0.181 -0.00499 0.301

a10 0.00016 0.045 -0.01126 0.888

a11 0.00025 0.107 -0.00178 0.211

ai 0.00737 0.221 0.1549 0.926

2 0.9826 0.8662

D-W 2.07 2.04

RH01 1.27** 25.536 1.40** 9.838

RH02 -0.28** 5.410 -0.48** 3.373

NOB 344. 38.

SER (= RSS) 0.1548 0.3899

* t = Tr tuyt i ca t.

** Khc khng mt cch c ngha thng k mc ngha 0.05.

Ngun: G. J. Santoni v Courtenay C. Stone, The Fed and the Real Rate of Interest, Review, Ngn hng D tr lin

bang St. Louis, thng 12-1982, trang 16.

V d 17.10 Tng tiu dng ngn hn v di hn i vi Sri Lanka, 1967-1993

Gi s tiu dng C c quan h tuyn tnh vi thu nhp thng xuyn X*:

Ct = 1 + 2 + ut (17.12.2)

V khng th quan st trc tip , ta cn nu r c ch to ra thu nhp thng xuyn. Gi s ta

p dng gi thit k vng iu chnh nu trong phng trnh (17.5.2). S dng phng trnh

(17.5.2) v n gin ha, ta c phng trnh c lng sau y (xem 17.5.5):

Ct = 1 + 2 Xt + 3 Ct-1 + vt (17.12.3)

Trong : 1 = 1

2 = 2


Cc phng php nh lng




3 = (1 )

vt = [ut (1 )ut-1]

Nh ta bit, 2 cho ta bit phn ng trung bnh ca tiu dng trc s gia tng 1 USD ca thu

nhp thng xuyn, trong khi trong khi 2 cho ta phn ng trung bnh ca tiu dng trc s gia

tng 1 USD thu nhp hin ti.

T s liu hng nm ca Sri Lanka cho giai on 1967-1993 cho trong bng 17.5, ta thu c

cc kt qu hi quy sau y:47

C = 1038,403 + 0,4030 Xt + 0,509 Ct-1

se = (2501,455) (0,0919) (0,1213) (17.12.4)

t = (0,4151) (4,3979) (4,1293)

R2 = 0,9912 d = 1,4162 F = 1298,466

Trong C = chi tiu dng t nhn, v X = GDP, c hai u tnh theo gi c nh. Chng ta cng

a li sut thc vo m hnh, nhng n khng c ngha thng k.

Cc kt qu cho thy rng xu hng tiu dng bin ngn hn (MPC) l 0,4043, cho thy rng s

gia tng 1 rupee thu nhp thc hin ti hay thu nhp thc quan st c (th hin qua GDP thc)

s lm tng tiu dng trung bnh thm khong 0,4 rupee. Nhng nu s gia tng thu nhp c

duy tr bn vng, th cui cng xu hng tiu dng bin t thu nhp thng xuyn s l 2 =

2/ = 0,4043/0,4991 = 0,8100 hay khong 0,81 rupee. Ni cch khc, khi ngi tiu dng c

thi gian iu chnh theo s thay i 1 rupee thu nhp ca h, cui cng h s tng tiu dng

thm khong 0,81 rupee.

Bng 17.5 Chi tiu dng t nhn v GDP, Sri Lanka

Quan st PCON GDP Quan st PCON GDP

1967 61,284 78,221 1981 120,477 152,846

1968 68,814 83,326 1982 133,868 164,318

1969 76,766 90,490 1983 148,004 172,414

1970 73,576 92,692 1984 149,735 178,433

1971 73,256 94,814 1985 155,200 185,753

1972 67,502 92,590 1986 154,165 192,059

1973 68,832 101,419 1987 155,445 191,288

1974 80,240 105,267 1988 157,199 196,055

1975 84,477 112,149 1989 158,576 202,477

1976 86,038 116,078 1990 169,238 223,225

1977 96,275 122,040 1991 179,001 233,231

47 S liu thu c t a s liu trong nghin cu ca Chandan Mukherjee, Howard White, v Marc Wuyts,

Econometrics and Data Analysis for Developing Countries, Routledge, New York, 1998. S liu gc l t Bng s liu ca Ngn hng Th gii.


Cc phng php nh lng




1978 101,292 128,578 1992 183,687 242,762

1979 105,448 136,851 1993 198,273 259,555

1980 114,570 144,734

Ch thch: PCON = Chi tiu dng t nhn

GDP = Tng sn lng ni a

Ngun: Xem ch thch cui trang s 47.

By gi gi s rng hm tiu dng ca chng ta c dng:

= 1 + 2 Xt + ut (17.12.5)

Trong cng thc ny, tiu dng di hn, hay tiu dng thng xuyn Ct l mt hm tuyn tnh

theo thu nhp hin ti hay thu nhp quan st c. V khng th trc tip quan st c , ta

hy vn dng m hnh iu chnh ring phn (17.6.2). S dng m hnh ny, v sau cc thao tc

i s, ta c:

Ct = 1 + 2 Xt + (1 )Ct-1 + ut

= 1 + 2 Xt + 3Ct-1 + vt (17.12.6)

Nhn b ngoi, m hnh ny khng th phn bit c so vi m hnh k vng iu chnh

(17.12.3). Do , cc kt qu hi quy cho trong (17.12.4) c th p dng tng ng y. Tuy

nhin, c s khc bit ln trong vic l gii hai m hnh, y l cha cp n vn c lng

i km vi m hnh t hi quy v c th tng quan chui (17.12.3). M hnh (17.12.5) l hm

tiu dng di hn hay hm tiu dng trng thi cn bng, trong khi (17.12.6) l hm tiu dng

ngn hn. 2 o lng MPC di hn, trong khi 2 (= 2) cho ta MPC ngn hn; ta c th thu

c MPC di hn bng cch ly MPC ngn hn chia cho h s iu chnh .

Quay li vi phng trnh (17.12.4), by gi ta c th l gii 0,4043 l MPC ngn hn. V =

0,4991, nn MPC di hn l 0,81. Lu rng h s iu chnh khong 0,50 cho thy trong mt

thi on cho trc bt k, ngi tiu dng ch iu chnh tiu dng khong mt na mc chnh

lch hng ti tiu dng mong mun hay tiu dng di hn.

V d ny lm r mt im quan trng l, xt hnh thc b ngoi, cc m hnh k vng iu

chnh v iu chnh ring phn, hay m hnh Koyck u tng t nh nhau n mc ch thng

qua nhn vo phng trnh hi quy c lng, nh (17.12.4), ta khng th ni l theo qui cch

m hnh no. l l do khin vic quan trng l ta phi nu r cc gi nh nn tng ca m

hnh c chn cho phn tch thc nghim ri tin hnh mt cch ph hp. Nu thi quen hay s

tr l c im ca hnh vi tiu dng, th m hnh iu chnh ring phn l ph hp. Mt khc,

nu hnh vi tiu dng c tnh cht nhn v tng lai theo ngha l n da vo thu nhp tng

lai k vng, th m hnh k vng iu chnh l thch hp. Nu n l m hnh k vng iu chnh,

th ta phi ht sc ch n vn c lng thu c cc c lng nht qun. Trong

trng hp m hnh iu chnh ring phn, OLS s mang li cc c lng nht qun, min l

cc gi nh OLS thng thng c tho.


Cc phng php nh lng




17.13 Cch tip cn Almon i vi cc m hnh phn phi tr: Phn phi tr Almon hay

phn phi tr a thc (PDL)48

Cho d c s dng ph bin trong thc hnh, m hnh phn phi tr Koyck da vo gi nh

rng cc h s gim v mt hnh hc khi tr ko di (xem hnh 17.5). Gi nh ny c th

qu nghim ngt trong mt s tnh hung. V d, ta hy xem hnh 17.7.

Hnh 17.7 M hnh tr a thc Almon

tr tr

(c) (d)

Trong hnh 17.7a, ta gi nh rng cc thot u tng ln ri sau gim xung, trong khi

trong hnh 17.7c, ta gi nh cc tun theo mt din tin c tnh chu k. Hin nhin, cch tip

cn Koyck cho m hnh phn phi tr khng pht huy tc dng trong nhng trng hp ny. Tuy

nhin, sau khi xem xt hnh 17.7a v 17.7c, xem ra ta c th biu th nh mt hm s theo i,

di thi gian tr, v xc nh ng biu th ph hp phn nh mi quan h hm s gia v

i, nh th hin qua hnh 17.7b v 17.7d. y chnh xc l cch tip cn do Shirley Almon

48 Shirley Almon, The Distributed Lag between Capital Appropriations and Expenditures, Econometrica, tp 33,

thng 1-1965, trang 178-196.

tr tr


Cc phng php nh lng




xut. minh ha k thut ca b, ta hy chuyn sang m hnh phn phi tr c hn xem xt

trn y:

Yt = + 0 Xt + 1 Xt-1 + 2 Xt-2 + + k Xt-k + ut (17.1.2)

Phng trnh ny c th c vit mt cch c ng hn l:

Yt = + + ui (17.13.1)

Theo mt nh l trong c ton hc gi l nh l Weierstrass, Almon gi nh rng i c th

c tnh gn ng bng mt a thc c bc thch hp theo i, di thi gian tr.49 V d, nu p

dng din bin tr biu th trong hnh 17.7a, ta c th vit:

i = a0 + a1i + a2i2 (17.13.2)

y l mt a thc bc 2 theo i, (xem hnh 17.7b). Tuy nhin, nu tun theo din bin nh

trong hnh 17.7c, ta c th vit:

i = a0 + a1i + a2i2 + a3i

3 (17.13.3)

y l mt a thc bc 3 theo i, (xem hnh 17.7d). Tng qut hn, ta c th vit:

i = a0 + a1i + a2i2 + + ami

m (17.13.4)

y l mt a thc bc m theo i. Ta gi nh rng m (bc ca a thc) nh hn k ( di ti a

ca thi gian tr).

gii thch cch tip cn ca Almon vn hnh nh th no, ta hy gi nh rng cc tun theo

din tin trnh by trong hnh 17.7a, v do , php gn ng a thc bc 2 l ph hp. Thay

(17.13.2) vo (17.13.1),ta c:

Yt = +

+ ut

= + a0 + a1

+ a2

+ ut

(17.13.5)

nh ngha:

Z0t =

Z1t =

Z2t =

(17.13.6)

Ta c th vit (17.13.5) thnh:

Yt = + a0 Z0t + a1 Z1t + a2 Z2t + ut (17.13.7)

Trong cch tip cn Almon, Y c hi quy theo bin xy dng Z, ch khng phi bin gc X.

Lu rng, phng trnh (17.13.7) c th c lng bng qui trnh OLS thng thng. V th,

cc gi tr c lng ca v ai thu c s c tt c cc thuc tnh thng k ng mong i

min l s hng nhiu ngu nhin u tha cc gi nh ca m hnh hi quy tuyn tnh kinh in.

49 Ni tng qut, nh l ny pht biu rng, i vi mt khong ng c hn, bt k hm lin tc no cng c th

c tnh xp x gn ng mt cch ng dng bng mt a thc theo mt bc thch hp.


Cc phng php nh lng




Trn phng din ny, k thut Almon c mt u im r rt so vi phng php Koyck v nh

ta thy, phng php Koyck c mt vi vn c lng nghim trng hnh thnh do s hin

din ca bin gii thch ngu nhin Yt-1 v c th tng quan vi s hng nhiu.

Mt khi c lng c cc h s a t phng trnh (17.13.7), ta c th c lng c cc

h s gc t phng trnh (17.13.2) [hay tng qut hn l t phng trnh (17.13.4)] nh sau:

=

= + +

= + +

= + +

= + +

(17.13.8)

Trc khi p dng k thut Almon, ta phi gii cc bi ton thc hnh sau y:

1. di ti a ca thi gian tr k phi c nu r ngay t trc. y, ta c th nghe

theo li khuyn ca Davidson v MacKinnon:

Cch tip cn tt nht c l l trc tin nn gii p cu hi v di ca thi gian tr, thng qua

bt u vi mt gi tr rt ln ca q [ di thi gian tr] ri xem liu vic lm ph hp m hnh

c xu i ng k khi q gim xung m khng p t nhng gii hn bt k i vi hnh dng ca

phn phi tr.50

Li khuyn ny l theo tinh thn cch tip cn t trn xung ca Henry nh tho lun

trong chng 13. Nn nh rng nu c mt di thi gian tr thc s, vic chn s

tr t hn s dn n thin lch do b st bin ph hp m hu qu c th rt nghim

trng nh ta thy trong chng 13. Mt khc, chn nhiu tr hn mc cn thit s

dn n thin lch do bao gm bin khng ph hp, m hu qu nghim trng hn;

cc h s c th c c lng mt cch nht qun bng OLS, cho d phng sai c th

km hiu qu hn.

Ta c th s dng tiu ch thng tin Akaike hay Schwartz nh tho lun trong chng

13 chn di thi gian tr thch hp. Cc tiu ch ny cng c th c s dng

tho lun bc ca a thc ph hp b sung cho tho lun trong phn 2.

2. Sau khi xc nh k, ta cng phi xc nh bc ca a thc, m. Ni chung, bc ca a thc

t nht nn nhiu hn 1 so vi s im un trong ng cong lin h gia i v i. Nh

vy, trong hnh 17.7a, ch c 1 im un; v th mt a thc bc hai s l mt php tnh

gn ng tt. Trong hnh 17.7c c hai im un; v vy a thc bc ba s cho ta mt php

xp x tt. Tuy nhin, ta c th tin liu rng, ta khng chc bit s im un l bao

50 Russell Davidson v James G. MacKinnon, Estimation and Inference in Econometrics, Oxford University Press,

New York, 1993, trang 675-676.


Cc phng php nh lng




nhiu, v do , vic chn la m nhn chung mang tnh ch quan. Th nhng, l thuyt

c th cho ta mt hnh dng c th trong mt s trng hp. Trong thc hnh, ta hy vng

rng mt a thc bc thp (v d nh m = 2 hay 3) s cho kt qu tt. Sau khi chn gi tr

c th ca m, nu ta mun tm hiu xem liu mt a thc bc cao hn c cho thy mi

quan h ph hp tt hn hay khng, ta c th tin hnh nh sau.

Gi s ta phi quyt nh gia mt a thc bc hai v mt a thc bc ba. i vi a

thc bc hai, phng trnh c lng c dng phng trnh (17.13.7). i vi a thc

bc ba, phng trnh tng ng l:

Yt = + a0 Z0t + a1 Z1t + a2 Z2t + a3 Z3t + ut (17.13.9)

Trong Z3t = . Sau khi chy hi quy (17.13.9), nu ta thy a2 c ngha

thng k nhng a3 khng c ngha thng k, ta c th cho rng a thc bc hai cho ta

php gn ng kh tt.

Bng cch khc, nh xut ca Davidson v MacKinnon, Sau khi q [ di thi gian

tr] c xc nh, ta c th c gng xc nh d [bc ca a thc], cng bng cch bt

u vi mt gi tr ln ri gim dn.

Tuy nhin, ta phi thc vn a cng tuyn, c th pht sinh do cch thc xy dng

cc bin Z t cc bin X, nh trnh by trong (17.13.6) [xem thm (17.13.10)]. Nh

chng minh trong chng 10, trong nhng trng hp a cng tuyn nghim trng,

c th ha ra khng c ngha thng k, khng phi v thc t a3 bng zero, m ch n

thun v mu hin c khng cho php ta nh gi tc ng ring bit ca Z3 i vi Y. Do

, trong minh ha ca chng ta, trc khi chng ta chp nhn kt lun rng a thc bc

ba khng phi l mt chn la ng n, ta phi bo m rng vn a cng tuyn

khng nghim trng, m iu ny c th c thc hin bng cch p dng cc k thut

nh tho lun trong chng 10.

3. Mt khi ta nu r m v k, ta c th sn sng xy dng Z. V d, nu m = 2 v k = 5,

cc bin Z s l:

Z0t = = (Xt + Xt-1 + Xt-2 + Xt-3 + Xt-4 + Xt-5)

Z1t = = (Xt-1 + 2Xt-2 + 3Xt-3 + 4Xt-4 + 5Xt-5)

Z2t = = (Xt-1 + 4Xt-2 + 9Xt-3 + 16Xt-4 + 25Xt-5)

(17.13.10)

Lu rng cc bin Z l cc kt hp tuyn tnh ca cc bin X gc. ng thi cng lu l do

khin cc bin Z c th c tnh a cng tuyn.

Trc khi tin hnh vi mt v d bng s, ta hy lu cc u im ca phng php Almon.

Th nht, phng php ny mang li mt cch thc linh hot ta a vo nhiu c cu tr a

dng (xem bi tp 17.17). Mt khc, k thut Koyck kh cng nhc ch, n gi nh rng cc

h s gim dn v mt hnh hc. Th hai, khng nh k thut Koyck, trong phng php

Almon, ta khng phi lo lng v s hin din ca bin ph thuc tr nh mt bin gii thch

trong m hnh v nhng vn m n mang li trong vic c lng. Cui cng, nu ta c th


Cc phng php nh lng




s dng mt a thc c bc thp, s h s phi c lng (cc h s a) nh hn ng k so

vi s h s gc (cc h s ).

Nhng ta hy nhn mnh li cc vn vi k thut Almon. Th nht, bc ca a thc cng nh

gi tr ti a ca tr ni chung l mt quyt nh ch quan. Th hai, v nhng l do lu

trn y, cc bin Z c th c tnh a cng tuyn. Do , trong nhng m hnh nh (17.13.9), cc

h s a c lng c th c sai s chun ln (so vi gi tr ca cc h s ny), qua lm cho

mt hay nhiu h s ny tr nn khng c ngha thng k trn c s kim nh t thng thng.

Nhng iu ny khng nht thit c ngha l mt hay nhiu h s gc cng s khng c

ngha thng k. (Vic chng minh nhn nh ny kh phc tp nhng c trnh by trong bi

tp 17.18.) V th, vn a cng tuyn khng chc nghim trng nh ngi ta ngh. Bn cnh

, nh ta bit, trong nhng trng hp a cng tuyn, ngay c nu ta khng th c lng mt

h s ring l mt cch chnh xc, s kt hp tuyn tnh cc h s (hm c th c lng)

vn c th c c lng mt cch chnh xc hn.

V d 17.11 Minh ha m hnh phn phi tr Almon

minh ha k thut Almon, bng 17.6 trnh by sinh li v gi tr hng tn kho Y v doanh s

X ca Hoa K trong giai on 1954-1999.

V mc ch minh ha, ta gi nh rng gi tr hng tn kho ph thuc vo doanh s trong nm

hin hnh v trong ba nm trc nh sau:

Yt = + 0Xt + 1Xt-1 + 2Xt-2 + 3Xt-3 + ut (17.13.11)

Hn na, gi nh rng i c th tnh gn ng bng mt a thc bc hai nh th hin trong

(17.13.2). Khi , t (17.13.5) ta c th vit:

Yt = + a0 Z0t + a1 Z1t + a2 Z2t + ut (17.13.12)

Trong

Z0t = = (Xt + Xt-1 + Xt-2 + Xt-3 )

Z1t = = (Xt-1 + 2Xt-2 + 3Xt-3)

Z2t = = (Xt-1 + 4Xt-2 + 9Xt-3)

(17.13.13)

Nh vy, cc bin Z c xy dng nh biu th trong bng 17.6. S dng s liu i vi Y v

cc bin Z, ta thu c cc kt qu hi quy sau y:

= 25.845,06 + 1,1149Z0t 0,3713Z1t 0,0600Z2t

se = (6596,998) (0,5381) (1,3743) (0,4549)

t = (3,9177) (2,0718) (-0,2702) (-0,1319)

R2 = 0,9755 d = 0,1643 F = 517,7656

(17.13.14)

Lu : V ta ang s dng mt tr di ba nm, tng s quan st gim t 46 xung 43.


Cc phng php nh lng




Bng 17.6 Gi tr hng tn kho Y v doanh s X, cng nghip ch to Hoa K, v cc bin

Z xy dng c

Quan st Hng tn kho Doanh s Z0 Z1 Z2

Ch thch: Y v X tnh bng triu USD, iu chnh theo ma.

Ngun: Bo co kinh t ca tng thng, 2001, bng B-57, trang 340. Cc bin Z nh c biu th trong phng

trnh (17.13.13).


Cc phng php nh lng




Nhn xt ngn gn v cc kt qu trn y: Trong ba bin Z, ch c Z0 l c ngha thng k

ring l mc ngha 5 phn trm, nhng cc bin khc th khng c ngha thng k, nhng

tr thng k F li cao n mc ta c th bc b gi thit khng rng cc bin Z hp li khng c

nh hng i vi Y. Nh bn c th nghi ng, iu ny rt c th do tnh a cng tuyn. ng

thi, lu rng tr thng k d tnh c rt thp. iu ny khng nht thit c ngha l cc s d

c tnh t tng quan. Rt c th, tr thng k d thp cho thy rng m hnh m ta s dng xem

ra c xc nh sai. Ta s nhn xt v iu ny ngay sau y.

T cc h s a c lng c cho trong (17.13.3), ta c th d dng c lng cc h s , nh

th hin trong (17.13.8). Trong v d ny, cc kt qu l nh sau:

= = 1,1149

= + + = 0,6836

= + + = 0,1321

= + + = -0,5349

(17.13.15)

Nh vy, m hnh phn phi tr c lng c tng ng vi (17.13.11) l:

= 25.845,06 + 1,1150Xt-1 0,6836Xt-1 0,1321Xt-2 0,5394Xt-3

se = (6596,99) (0,5381) (0,4672) (0,4656) (0,5656)

t = (3,9177) (2,0718) (1,4630) (0,2837) (-0,9537)

R2 = 0,9755 d = 0,1643 F = 517,7656

(17.13.16)

V mt hnh hc, i c lng c th c trnh by nh trong hnh 17.8.

Hnh 17.8 C cu tr ca v d minh ha

Beta

tr


Cc phng php nh lng




V d minh ha ca chng ta c th c s dng trnh by thm mt vi c im ca qui

trnh tr Almon:

1. Ta c th thu c cc sai s chun ca cc h s a mt cch trc tip t hi quy OLS

(17.13.14) nhng ta khng th thu c cc sai s chun ca mt vi h s , i tng

quan tm chnh. Nhng ta c th thu c chng t cc sai s chun ca cc h s a c

lng thng qua s dng mt cng thc ni ting trong thng k, c cho trong bi tp

17.18. L d nhin, khng cn phi lm iu ny mt cch th cng, v hu ht cc gi

phn mm thng k c th lm cng vic ny mt cch bnh thng. Ta thu c cc

sai s chun trong (17.13.15) t phn mm Eviews 4.

2. Cc h s thu c trong (17.13.16) c gi l c lng khng hn ch theo ngha

l khng c s hn ch tin liu no t ra cho chng. Tuy nhin, trong mt vi tnh

hung, ngi ta c th mun t ra ci gi l hn ch hai u i vi cc h s thng

qua gi nh rng 0 v k (h s tr hin ti v h s tr th k) bng khng. Do nhng l

do tm l, th ch, hay k thut, gi tr ca bin gii thch trong thi on hin ti khng

chc c tc ng i vi gi tr hin hnh ca bin hi quy, qua bin minh cho gi tr

bng khng ca 0. Cng v l , vt qua mt khong thi g

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