KINH T LNG BC CAO HC

ECONOMETRICS

KINH T LNG C BN

Chng 1, 2, 3

KINH T LNG NNG CAO

Chng 4, 5, 6, 7,8

TI LIU

1. Nguyn Quang Dong, (2008), Bi ging Kinh t lng, NXB Khoa hc k thut.

2. Nguyn Quang Dong, (2002), Kinh t lng - Chng trnh nng cao + Bi tp Kinh t lng vi s tr gip ca phn mm Eviews, NXB Khoa hc k thut.

3. Nguyn Khc Minh, (2002), Cc phng php Phn tch & D bo trong Kinh t, NXB KHKT.

4. Damodar N.Gujarati, Basic Econometrics, 4th Edition, Mc Graw - Hill, 2004

KHI NIM V KINH T LNG

Econometrics = Econo + Metrics o lng kinh t

i tng: cc mi quan h, cc qu trnh kinh t x hi

Cng c: cc l thuyt kinh t, cc m hnh Ton kinh t, phng php ton, xc sut thng k, vi s h tr ca my tnh.

Kt qu: bng s, ty thuc mc ch s dng.

PHNG PHP LUN

t gi thit v vn nghin cu

Xy dng m hnh

- M hnh l thuyt

- M hnh ton hc

Thu thp s liu v c lng tham s

Kim nh v mi quan h Phn tch, d bo, minh chng hoc phn

bin l thuyt

KINH T LNG C BN

Basic Econometrics

CHNG 1. M HNH KINH T LNG

CHNG 2. C LNG V PHN TCH

M HNH KINH T LNG

CHNG 3. NH GI V M HNH

CHNG I. M HNH KINH T LNG

Econometrics Model

1.1. Phn tch hi qui

1.2. M hnh hi qui tng th

1.3. M hnh hi qui mu

1.4. M hnh hi qui tng qut

1.5. M hnh hi qui trong kinh t

PHN TCH HI QUY Nghin cu mi lin h ph thuc gia 1 bin

(bin ph thuc) vo mt hoc mt s bin s khc (bin c lp/bin gii thch).

Bin ph thuc, thng k hiu Y , i din cho i tng kinh t m ta quan tm nghin cu s bin ng (dependent, explained, exogenous variable).

Bin c lp, thng k hiu 1 2X , , ,...X X i din cho i tng kinh t gii thch cho s bin ng ca bin ph thuc (independent,

explanatory, regressor)

M HNH HI QUY TNG TH

iX XY X

= : xc nh Y l bin ngu nhin,

) ( / i

Quan h hm s : x ! y

[-1 ; 1] H s tng quan : X ,Y

Tng th (Population): tt c cc phn t cha du hiu nghin cu

Phn tch da trn ton b tng th

thun tin: m hnh mt bin c lp, X

Y

X gii thch cho Y, Y ph thuc vo X

M HNH HI QUY TNG TH

iX X i(Y / X )

i

= c quy lut phn phi xc

sut ! E(Y / X )

i

: trung bnh (k vng) c iu

kin

X X= ! E(Y i/ X )

(i

: quan h hm s

)i( / )E Y X f X= ) ( hoc )( /E Y X f X=

Gi l hm hi qui tng th

PRF: Population Regression Function

M HNH HI QUY TNG TH

Dng ca PRF ty thuc m hnh kinh t, gm cc h s (coefficient) cha bit

Nu hm hi quy tng th c dng ng thng:

E Y X X1 2 .( / ) = + 1 0 =E Y X( / )= : h s chn (intercept term)

2=E Y X

X( / )

: h s gc (slope coefficient)

PRF cho bit quan h gia bin ph thuc v bin gii thch v mt trung bnh trong tng th.

M HNH HI QUY TNG TH Hm hi quy tng th c gi l tuyn tnh

nu n tuyn tnh theo tham s. Gi tr c th i )iY Y X( / , thng thng

i i ). t i i i )Y E Y( / X E Y X( /u Y= : l yu t ngu nhin (nhiu, sai s ngu nhin - Random errors)

Tnh cht ca yu t ngu nhin : E(ui) = 0 i i din cho tt c nhng yu t khng phi bin gii thch trong m hnh nhng cng tc ng ti bin ph thuc.

M HNH HI QUY MU

Khng bit ton b Tng th, nn dng ca PRF c th bit nhng gi tr j th khng

bit.

Mu : mt b phn mang thng tin ca tng th. W = {(Xi, Yi), i = 1 n} c gi l mt mu kch thc n, n quan st (observation).

Trong mu W, tn ti mt hm s m t xu th bin ng ca bin ph thuc theo bin gii thch v mt trung bnh, = ) gi l hm hi qui mu (SRF- Sample Regression Function).

Y f X(

Hm hi qui mu c dng ging PRF

Nu PRF c dng i iE Y X X1 2 .= +

( / )

th SRF c dng =iY 1 + iX2 . V c v s mu ngu nhin, nn c v s gi

tr ca

j

1 v 2 l bin ngu nhin.

Vi mu c th w kch thc n, j l s c th.

Thng thng iY Yi , t iY v gi l phn d (residual).

i ie Y=

ie

iu Bn cht ca phn d ging nh ca yu t

ngu nhin

TM TT

E Y X X1 2 .( / ) = +

i

i iY 1 2= + X u. +

i iY X1= + 2

ie+

i i Y X1 2= +

iY , 1 , 2 , l cc c lng im tng

ng ca ie

iE(Y / X ) i, , ,u1 2

1 k

M HNH HI QUY TNG QUT M hnh hi quy k bin, 1 bin ph thuc v

) bin gii thch, h s (k c h s chn). ( k

i i k kiE(Y ) X X1 2 2 3 31= + + ... X+ +

+ +k ki iX u

= + + +1 2 2 3 31i iY X X ...

+ + k ki... X

+ +k ki i X e

0k

= + +1 2 2 3 31i i Y X X

= + + +1 2 2 3 31i i Y X X ...

1 2 3E(Y / X X ... X ) = = = = = : h s chn

jj

E(Y )( j 2,kX

= =

): h s hi quy ring-h s

gc

M HNH TRONG KINH T Hm bc nht

C Y u = + +1 2

D DQ P u = + +1 2 S SuQ P = + +1 2

Hm bc cao

TC Q Q Q u = + + 2 31 2 3 + +4

MC Q Q u' = + +2 32 3 +2

4

AD u

Q AD = + +1 2 +2

3

M HNH TRONG KINH T Dng hm m: v d hm sn xut dng

Cobb-Douglas LQ K = 320 tuyn tnh ha v xy dng m hnh kinh t lng:

Ln( Q ) Ln( K ) Ln( L ) u = + +1 2 +3 Hm th hin tnh xu th T l bin xu th thi gian, T = 0,1,2,

Y X T u = + + +1 2 3 M hnh c bin tr : tt tY X X u + +1 2 3 1 + =

M hnh t hi quy : tt tY X Y u= + +1 2 3 1 +

CHNG II. C LNG V PHN TCH

M HNH KINH T LNG

2.1. c lng m hnh 2 bin

2.2. c lng m hnh tng qut

2.3. Cc gi thit ca phng php OLS

2.4. Cc tham s ca c lng OLS

2.5. c lng khong tin cy ca cc h

s

CHNG II. C LNG V PHN TCH

M HNH KINH T LNG

2.6. Kim nh gi thuyt v cc h s

2.7. c lng v t hp cc h s hi quy

2.8. Kim nh v t hp cc h s hi quy

2.9. S ph hp ca hm hi qui

2.10. Kim nh thu hp hi quy

2.11. D bo

C LNG M HNH HI QUY HAI BIN M hnh hi qui hai bin l m hnh gm mt

bin ph thuc (Y) v mt bin gii thch (X). M hnh c dng: i iE(Y / X ) X +1 2

u

=

i i iY X = + +1 2

Vi mu kch thc n : W = {(Xi, Yi), i = 1 n}, tm , 1 2, sao cho SRF: i i Y X = +1 2 phn nh xu th bin ng v mt trung bnh ca mu.

Tm , 1i i

(Y Y ) e2 sao cho in n

i i=

= = 2

1 1

2 min

Gii c nghim XY X YX ( X )

2 =2 2

Y X = 1 2

t i ii i

x X Xy Y Y

= =

n

i ii

n

ii

x y

x =

=

=

1

22

1

, 1 2 c lng bng phng php bnh

phng nh nht - LS, gi l cc c lng bnh phng nh nht (cc c lng LS) ca 1 v 2.

C LNG M HNH TNG QUT Vic c lng m hnh hi quy tng qut

cng thc hin nh i vi hi quy n, vi

tiu chun l tm j sao cho n n

i ii i

(Y iY ) e= =

= 2 2

' X ) X'Y1

1 1

t cc tiu. S dng ngn ng ma trn, xc nh c ma

trn cc h s c lng vi ( X =

k

k

n n

X X ...X X .. X= .X X .

21 31

22 32

2 3

11

1 kn

X. X

.. X

1

2

n

YY

Y= ..Y

1

2

k

.

=

1

2

CC GI THIT CA PHNG PHP LS Gi thit 1: Hm hi quy tuyn tnh theo h

s Gi thit 2: Bin c lp l phi ngu nhin Gi thit 3: Trung bnh ca sai s ngu nhin

bng 0: 0 ( i ) iE( u ) =

Gi thit 4: Phng sai sai s ngu nhin ng

nht iVar( u ) =2 ( i )

Gi thit 5: Cc sai s ngu nhin khng tng quan

i jCov( u ,u ) ( i j )= 0

Gi thit 6: SSNN v bin c lp khng tng quan i iCov( u , X ) ( i )0 =

Gi thit 7: S quan st nhiu hn s h s

Gi thit 8: Gi tr ca bin c lp c s khc

bit ln

Gi thit 9: Hm hi qui c xc nh ng

Gi thit 10: Cc bin c lp khng c quan

h cng tuyn

Gi thit 11: Yu t ngu nhin phn phi

chun

NH L

Nu tng th tha mn cc gi thit

trn th c lng OLS s l c lng

tuyn tnh, khng chch, tt nht (trong

s cc c lng khng chch) ca cc

tham s.

(BLUE: Best Linear Unbias Estimate)

CC THAM S CA C LNG LS Vi hi quy n

K vng: j jE( ) ( j , = = 1 2 )

Phng sai:

n

iin

ii

XVar( )

n x

=

=

=2

211

2

1

Var( nii

)x

=

=2

22

1

lch chun: j j Se( ) Var( ) = (j = 1,2)

2 cha bit, c c lng bi : ie

n =

22

2

gi l lch chun ca hi qui (Se. of Regression)

Vi hi quy tng qut

j jE( ) ( j ,k = = 1

k

k

k

Cov( , ) Cov( , )

Var( )

1

2

)

k k

Var( ) Cov( , ) . Cov( , ) Var( ) . Cov( )=. . . . Cov( , ) Cov( , ) .

1 1 2

1 2 2

1 2

Cov( ) ( X ' X )= 2 1

ien k

= 2

2

vi k l s tham s cn c lng

C LNG KHONG CC H S HI QUY

tin cy 1 cho trc, c lng khong tin cy i xng, ti a, ti thiu ca cc h s hi quy

( n k ) ( n kj j / j j j /

Se( )t Se( )t ) < < +2 2

( n kj

( )t

( n k ) )t >

j j Se < + )

j j j

ngha v cch s dng cc khong tin cy

Se(

- Quan h thun chiu - Quan h ngc chiu

KIM NH GI THIT V CC H S

Cp gi thit Tiu chun kim nh

Min bc b Gi thit H0

*j j

*j j

H :

H :

=

0

1

( n k

qs /T t)> 2

*j j

*j j

H :

H :

>

0

1

*

j jqs

j

T

Se( )

=( n k

qsT t)>

*j j

*j j

H :

H :

( n k )

qsT t

Trng hp c bit, j = 0, thng kim nh v bn cht ca mi lin h ph thuc.

Khi jqsj

T Se( )

= T Statistic =

Trng hp c bit, kim nh cp gi thit H :

H :

0

0 j

j

=

0

1

c th s dng quy tc p-value (Prob) nh sau : Nu p-value < bc b H0 Nu p-value > chp nhn H0

BO CO KT QU C LNG M HNH BNG PHN MM EVIEWS 4.1

Dependent Variable: Q Method: Least Squares Date: 12/18/09 Time: 22:55 Sample: 1 20 Included observations: 20

Variable Coefficient Std. Error t-Statistic Prob. P -113.4178 32.03207 -3.540759 0.0025

AD -83.87101 15.27991 -5.488973 0.0000C 1373.239 171.4084 8.011507 0.0000

R-squared 0.739941 Mean dependent var 460.2000Adjusted R-squared 0.709346 S.D. dependent var 155.3125S.E. of regression 83.73264 Akaike info criterion 11.83062Sum squared resid 119189.6 Schwarz criterion 11.97998Log likelihood -115.3062 F-statistic 24.18486Durbin-Watson stat 1.938188 Prob(F-statistic) 0.000011

C LNG PHNG SAI CA YU T NGU NHIN

c lng im n

ii

e

n k =

2

1=2 = (Se. of Regression)2

c lng khong

( n k )( n k )

( n k )( n k )

1

<

0

1

i jqs

i j

( a b ) cT

Se( a )

b +

=( n k )

qsT t+>

i j

i j

H : a b c

H : a b c

+ +

S PH HP CA HM HI QUY

H s xc nh R2 i i

i i

i i i

y Y Yy Y Y

e Y Y

=

=

= i iy y e= + ii i

n n n

i i iy y e

=

= == + 2 2

1 1

2

1

TSS = ESS + RSS TSS (Total Sum of Squares): o tng mc bin ng ca bin ph thuc ESS (Explained Sum of Squares): phn bin ng ca bin ph thuc c gii thch bi

m hnh - bi cc bin gii thch trong m hnh.

RSS (Residual Sum of Squares): phn bin ng ca bin ph thuc c gii thch bi cc yu t nm ngoi m hnh - Yu t ngu nhin.

t ESSRTSS

= =2 ( R )RSSTSS

1 20 1

gi l H s xc nhca m hnh R-Squared

ngha H s xc nh R2 l t l (hoc t l %) s bin ng ca bin ph thuc c gii thch bi s

bin ng ca cc bin c lp (theo m hnh, trong mu).

H s xc nh hiu chnh (Adjusted R-squared) RSS / ( n k )R (TSS / ( n )

nR )k

n

= =

2 2 11 1 1

1 Kim nh s ph hp ca hm hi quy

H : RH : R

20

21

=

00

k

j

H : ...H : ( j )

= = =

0 2

1

00 1

H0: Hm hi quy khng ph hp (tt c cc bin gii thch cng khng c nh hng ti bin ph thuc)

H1: Hm hi quy ph hp (c t nht 1 bin gii thch c nh hng ti bin ph thuc)

qsESS / ( k ) RFRSS / ( n k ) R

= =

n kk

2

2

11 1

= F-

Statistic

( k ,n kqsF F

> 1

,n kqsF F

< 1

): bc b H0 ( k ): chp nhn H0

C th s dng gi tr Prob (F-Statistic) thc hin kim nh

Nu p-value < bc b H0

Nu p-value > chp nhn H0

KIM NH THU HP HI QUY

Nghi ng m bin gii thch Xk-m+1,, Xk khng gii thch cho Y

k m k m

j

H : k...H : : ( j k m k )

+ += = =+

0

k

=

0 1 2

1 0 1

kE(Y ) X X ... X = + + +1 2 2 3 3 +

k m k m

(L) E(Y ) X X ... X += + + +1 2 2 3 3 (N)

N L LqsL L

NRSS RSS n k RF R n kRSS m

= =

R m

2 2

21

Nu )( m ,n kqsF F> : bc b H0

KIM NH THU HP HI QUY

Kim nh thu hp hi quy cho php xem xt

c nn b i ng thi 1 s bin ra khi m

hnh hay a thm vo m hnh ng thi 1 s

bin.

C th s dng kim nh v cc rng buc

tuyn tnh v cc h s hi quy.

Nu cc rng buc tuyn tnh lm thay i

bin ph thuc ca m hnh th phi tnh Fqs

theo RSS.

Khi m = k-1 kim nh s ph hp hm HQ

D BO

Vi m hnh hi quy 2 bin

c lng khong cho gi tr trung bnh ca bin ph thuc khi bin gii thch nhn gi tr xc nh X = X0

( n ) ( n )/ /

Y Se(Y )t E(Y / X ) Y Se(Y )t < < +2 20 0 2 0 0 0 2

vi 0 v 0 1 2 Y X = +2

Se 00 21

i

( X X ) (Y )n x

= +

D bo bng c lng im

D BO

Vi m hnh hi quy tng qut

c lng khong cho gi tr trung bnh ca

bin ph thuc khi cc bin gii thch nhn gi

tr xc nh 0 02 310 0

kX ( , X , X ,...., X )=

( n k ) ( n k )/ /

Y Se(Y )t E(Y / X ) Y Se(Y )t < < +00 0 2 0 0 2

0'Y X

vi 0 00 1 0 Se(Y ) X '(X'X) X == v

D bo bng c lng im

CHNG III. NH GI V M HNH

(Diagnostic Tests)

3.1. a cng tuyn (Multicollinearity)

3.2. Phng sai sai s thay i (Heteroscedasticity)

3.3. T tng quan (Autocorrelation)

3.4. nh dng m hnh (Model specification)

C S NH GI

nh l Gauss-Markov: Nu m hnh tha

mn cc gi thit ca phng php LS th cc

c lng thu c khi s dng phng php

LS l tuyn tnh, khng chch, tt nht

Cc gi thit khng c tha mn: cc c

lng khng tt, kt qu khng ng tin cy,

khng dng phn tch c, cn phi khc

phc

A CNG TUYN M hnh 1 2 2 3 3 k kE(Y ) X X ... X = + + + +

Gi thit ca LS: cc bin gii thch khng c

quan h cng tuyn (m hnh c k 3).

Nu gi thit b vi phm m hnh c hin

tng a cng tuyn (Multicollinerity).

C 2 loi a cng tuyn

- CT hon ho

- CT khng hon ho

PHN LOI A CNG TUYN

a cng tuyn hon ho

j 0 (j 1) sao cho

1 + 2 X2i + + k Xki = 0 i

a cng tuyn khng hon ho

j 0 (j 1) sao cho

1 + 2 X2i + + kXki + vi = 0

NGUYN NHN V HU QU CT hon ho thng do lp m hnh sai: t

khi xy ra khng gii c nghim.

CT khng hon ho thng xy ra: do bn cht KTXH ca quan h, do thu thp v x l s liu.

CT khng hon ho vn gii c nghim, tm c cc duy nht, nhng kt qu khng tt, sai s ca cc c lng ln:

- Cc c lng LS khng cn l c lng tt nht

- Khong tin cy ca cc h s rng hn - Kim nh T khng ng tin cy, c th cho nhn nh sai lm

CT nng cc kim nh T v F c th cho kt lun mu thun nhau, cc h s c lng c c th c du khng ph hp vi l thuyt kinh t.

CT khng hon ho l hin tng gp vi hu ht cc m hnh, nu gy hu qu nghim trng th cn phi khc phc.

PHT HIN KHUYT TT Mt s du hiu cho php nghi ng s c mt

ca CT trong m hnh.

Nghi ng bin gii thch jX ph thuc tuyn

tnh vo cc bin gii thch khc, hi qui m hnh hi qui ph (auxilliary regression)

jj j j jX X ... X X ... v + += + + + + + +1 2 2 1 1 1 1 (*)

2

2

00

* =

0

1 *

H : RH : R

2

2* *

* *1 1qs

R n kR k

F =

k )qsF F

>

k )qsF F

<

th bc b H0 * *( k ,n1

m hnh ban u c a cng tuyn

cha bc b H0 * *( k ,n1

c th ni MH ban u khng c a cng tuyn

C th c nhiu hi quy ph xem xt v CT ca 1 m hnh nhiu bin ban u.

C th dng kim nh T cho cc h s gc ca m hnh hi quy ph v kt lun tng t.

C mt s tiu chun khc cng c th c s dng kim nh v CT ca m hnh

KHC PHC KHUYT TT

B bt bin c lp gy a cng tuyn

Ly thm quan st hoc thu thp mu mi

Thay i dng m hnh

S dng thng tin tin nghim bin i m

hnh

PHNG SAI CA SAI S THAY I Phng sai cc yu t ngu nhin l ng

nht, iVar( u ) ( i )= 2

khng i gi thit

ca LS

Nu gi thit c tha mn Phng sai ca sai s ng u (khng i - homoscocedasticity).

Khi gi thit khng tha mn: ji m

i jVar( u ) Va r( u )

i i)

Phng sai ca sai s

thay i (heterscocedasticity). 2 K hiu Var( u =

NGUYN NHN V HU QU Bn cht KTXH ca mi quan h: s dao

ng ca bin ph thuc trong nhng iu kin khc nhau khng ging nhau.

Qu trnh thu thp s liu khng chnh xc, s liu khng phn nh ng bn cht hin tng; do vic x l, lm trn s liu.

Cc c lng l khng chch, nhng khng hiu qu, khng phi l tt nht.

Cc kim nh T, F c th sai, KTC rng.

PHT HIN KHUYT TT

i2

e2 cha bit, phn on v s bin ng

ca n dng i hoc i i din. S dng cc

m hnh hi quy ph, da trn gi thit v s bin ng ca

e

i2.

- Kim nh Glejser: i i ie X v = + +2 2

1 2

e X

i i iv = +2

1 2 + ie X i iv= + +2

1 2

- Kim nh Park: L i i in( e ) ln( X ) v= + +2

1 2

- K da trn bin ph thuc: i i ie Y v = + +

2 21 2

Dng kim nh T hoc F kim nh

PHT HIN KHUYT TT - KIM NH WHITE

Hi qui bnh phng phn d theo t hp bc cao dn ca cc bin gii thch.

MH ban u i iY X X u = + + +1 2 2 3 3

iX .X V

MH hi qui ph :

i i i i i ie .X .X .X .X . = + + + + +2 2 2

1 2 2 3 3 4 2 5 3 6 +2 3

*RR

=

20

21

00

qs *nR

Kim nh gi thit H :H :

*

- Kim nh 2 : =2 2

Nu )qs *( k >2 2 1 th bc b H0.

- Kim nh F: * *qs* *

R n kF

R k=

2

*( k ,n k

2

1 1

Nu * )qsF F 1> th bc b H0.

Nu bc b H0 th m hnh ban u c phng sai ca sai s thay i v ngc li.

M hnh ph thc hin kim nh c th c hoc khng c tch cho gia cc bin c lp ban u, c th c ly tha bc cao hn ca cc bin c lp v phi c h s chn.

KHC PHC KHUYT TT S dng phng php bnh phng nh nht

tng qut GLS. 2

i, chia hai v m hnh cho Nu bit i

i ii i

Y X i

i i

u

= +1 21

+

*i iX u

* *i iY X = +

01 2 +

) = 1

khng i *iVar( u Nu cha bit , da trn gi thit v s thay i ca m c cch khc phc tng ng.

KHUYT TT T TNG QUAN

Hin tng thng gp vi s liu theo thi gian nn s dng ch s thay cho ch s . t i

X u MH ban u

kt t t k t tY X X ... = + + + + +1 2 2 3 3

i j )

p )

Gi thit ca phng php LS: cc sai s ngu nhin khng tng quan vi nhau

i jCov( u ,u ) (= 0 hoc

t t p Nu gi thit b vi phm m hnh c khuyt

Cov( u ,u ) ( = 0 0

tt t tng quan bc p (Autocorrelation Order p)

T TNG QUAN BC 1

Xt trng hp p 1 )

t tng quan bc 1 =

t t tu u ( = + 1 1 1 tha mn cc gi thit ca phng php LS t

c gi l h s t tng quan bc 1

1 < 0 : m hnh c t tng quan m

Tng qut: t tng quan bc : p

pu u u ... ut t t t p t = + + +1 1 2 2 p+ vi 0

NGUYN NHN V HU QU

Do bn cht ca mi quan h

Tnh qun tnh trong cc chui s liu

Qu trnh x l, ni suy, ngoi suy s liu

M hnh thiu bin hoc dng hm sai

Cc c lng LS l c lng khng

chch nhng khng phi c lng hiu

qu/khng phi c lng tt nht.

PHT HIN KHUYT TT Kim nh Durbin-Watson

- Dng pht hin t tng quan bc 1

- Dng phn d l i din cho te tu

- M hnh phi c h s chn v khng

cha bin tr bc 1 ca bin ph thuc lm

bin c lp (khng phi m hnh t hi

quy)

Cc bc thc hin kim nh

- c lng MH ban u thu c phn d

te

- Tnh

n

t tt

n

tt

( e e )d (

e)

=

=

=

21

2

2

1

2 1 = DW-

Statistic

trong

n

tt t

n

tt

e e

e

==

=

12

2

1

l c lng cho

1 1 d nn

k' k

0 4

- Vi n l s quan st v = 1

d ud

tra bng tm

gi tr v (bng ph lc). L

Quy tc quyt nh

T tng quan

dng

> 0

Khng c kt lun

Khng c t tng

quan

= 0

Khng c kt lun

T tng quan m

< 0

0 dL dU 2 4 dU 4 dL 4

KIM NH BREUSCH-GODFREY(BG) Kim nh v t tng quan bc p bt k.

Cc bc thc hin kim nh

- Hi quy m hnh ban u:

t tutY X = + + te

t

thu c phn d l 1 2

- Hi quy cc m hnh ph:

vt te X = + + 1 2

p te X e e ... e v

(*)

t pt t t t = + + + + + + 1 2 1 1 2 2

(**)

- Kim nh gi thit:

p

i

H : ...

H : ( i , p )

= =

= =

0 1 2

1 0 1

= 0

**( n p ) R

- Kim nh 2 : qs ** **n R = = 2 2 2

( p

Nu )qs >2 2 th bc b H0.

- Kim nh F: **qs**

* ** **R R nF kR p

** **( p ,n k

=

2 2

21

Nu )qsF F> th bc b H0.

Nu bc b H0 th m hnh ban u c t tng quan bc tng ng, ngc li th m hnh khng c t tng quan n bc . p

KHC PHC T TNG QUAN

S dng phng php bnh phng nh nht

tng qut GLS da trn m hnh dng sai

phn.

Bin i m hnh ban u v m hnh mi c

cng cc h s tng ng nh m hnh c

nhng khng c khuyt tt t tng quan.

Chi tit tham kho gio trnh.

NH DNG M HNH Cc thuc tnh ca m hnh tt

- M hnh y

- M hnh ph hp v l thuyt v thng k

- Kh nng phn tch v d bo

Cc sai lm thng gp khi nh dng m

hnh

- M hnh tha bin c lp

- M hnh thiu bin c lp

- Dng hm sai

PHT HIN M HNH THIU BIN C LP Kim nh Ramsey Reset

- Hi quy m hnh ban u: i i iuY X = + +

Y (

1 2

thu c gi tr c lng ca bin ph thuc

l v h s xc nh l )21

mm iY u

+ +1

R . i

- Hi quy m hnh

i i Y X Y Y ... = + + + + + 2 3

1 2 1 2

thu c h s xc nh l ( )22 R

- Kim nh gi thit:

m...

i

H :

H : ( i ,m )

= = =

=

0 1 2

1 0 1=

0

Kim nh F: ( ) ( ) (qs( )

)R R n kFR m

=

2 22 1

221

( ),n k )

2

Nu ( mqsF F> 2 th bc b H0.

Nu bc b H0 th m hnh ban u thiu bin c lp cn thit.

TNG KT PHN I

Nu m hnh khng c khuyt tt, cc c

lng l tt nht, c lng khong, kim

nh gi thit l ng tin cy, kt qu l tt

cho phn tch.

Phn tch s tc ng ca cc bin c lp

n s bin ng ca bin ph thuc thng

qua cc h s hi quy v h s xc nh.

Nu bit , chia hai v m hnh cho