1

HI QUY GI TRONG KINH T LNG

(Spurious Regression)

inh Cng Khi

Thng 05/2014

GII THIU

Trong cc nghin cu nh lng khng him trng hp

chng ta gp kt qu hi quy cho thy c s tng quan

gia 2 chui thi gian khng c lin quan vi nhau.

V d, chng ta to ra 2 chui thi gian nh sau:

Vi u ~ N(0,1); v ~ N(0,1); Cov(u, v) = 0; Y0 = 0; v X0 = 0

ttt

ttt

vXX

uYY

1

1

2

GII THIU

Hi quy Y theo X cho thy c s tng quan gia 2 bin ny.

Theo Yule (1926) tng quan ny l tng quan gi bi v 2

chui thi gian ny khng dng (k c trong trng hp mu

ln).

Theo Granger v Newbold (1974), nu R2 > d chng ta nghi

ng hi quy l hi quy gi

KIM NH TNH DNG

Phng php th

Hm t tng quan mu (SAC) v correlogram

H s tng quan mu k:

k ~ N(0, 1/n)

)(

),(

0 t

kttkk

YVar

YYCov

3

KIM NH TNH DNG

Q-stat test

H0: 1 = 2 = . = k =0

Ha: C t nht mt k 0

Dng Ljung-Box:

m

k

knQ1

2

m

k

m

k

knnnQ

1

22

~

)2(

KIM NH TNH DNG

Dickey-Fuller test (H0: chui thi gian khng dng)

H0: = 1 hay = 0

Yt = Yt-1 +ut

Yt = Yt-1 +ut

Yt = 1 + Yt-1 +ut

Yt = 1 + 2t+ Yt-1 +ut

Yt = 1 + 2t+ Yt-1 +i Yt-i +t (u c tng quan chui)

4

BIN I CHUI KHNG DNG

THNH CHUI DNG

i vi chui random walk (Yt = Yt-1 + ut)

Ly sai phn bc 1 hoc bc 2

i vi chui c tnh xu hng

Yt = 1 + 2 t + ut,

Kh tnh xu hng bng cch hi quy hm s trn , sau tnh

*

21

ttt YtYu

HI QUY NG KT HP

(Cointegrating Regression)

trong PCE l chi tiu tiu dng c nhn; PDI l thu

nhp kh dng c nhn

PCE v PDI l cc chui khng dng c th c hi quy

gi (hi quy khng xc thc)

Hi quy mt chui khng dng trn mt chui c khng

dng khc c th l hi quy thc vi iu kin sau y:

ttt uPDIPCE 21

5

HI QUY NG KT HP (tt)

iu kin: Nu mt t hp tuyn tnh gia cc chui khng dng

ny l mt chui dng th hi quy ny l hi quy thc v c

gi l hi quy ng kt hp (cointegration regression).

Nu ut dng hi quy ng kt hp

Kt qu hi quy th hin mi quan h di hn, hoc im cn

bng (equilibrium) gia cc 2 bin.

2 c gi l h s gc ng kt hp (cointegrating coefficients)

ttt PDIPCEu 21

KIM NH NG KT HP

Kim nh Engle-Granger (EG)

H0: u^ c unit root (khng dng)

S dng k thut kim nh ca DF nhng cc tr ti hn ca EG

Gi tr kim nh DF l -3,78 so vi cc gi tr ti hn ca EG

tng ng 1%, 5%, v 10% l -2,5899; -1,9439; v 1,6177

ut c tnh dng, hay PCEt v PDIt l 2 chui ng kt hp

6

KIM NH NG KT HP (tt)

Kim nh hi quy ng kt hp Durbin_Watson (CRDW)

Ho: d = 0 ( = 1; u^ l chui khng dng)

So snh DW trong kt qu hi quy ban u (d=0,5316) vi cc

tr ti hn ca CRDW tng ng vi 1%, 5%, v 10% l

0,511; 0,386; v 0,322

Nu d ln hn tr ti hn bc b Ho

NG KT HP v

C CH HIU CHNH SAI S (ECM)

Trong ngn hn, s ng kt hp c th b mt cn bng.

ut th hin sai s cn bng (equilibrium error)

C ch hiu chnh sai s c s dng sa cha s mt cn

bng ny (Engle v Granger)

7

NG KT HP v

C CH HIU CHNH SAI S (ECM)

nh l Granger

PCEt = 0 + 1PDIt + 2ut-1 + t

PCEt v PDIt th hin bin ng ngn hn ca PCEt v

PDIt, trong khi ut-1 th hin s hiu chnh hng ti di hn.

Du ca 2 c k vng l m.

|2 | th hin tc khi phc trng thi cn bng.

1 o lng tc ng ngn hn ca PDI ln PCE

NG KT HP v

C CH HIU CHNH SAI S (ECM)

PEt = 11,6918 + 0,2906 PDIt 0,086 u^t-1

t (5,32) (4,17) (-1,60)

R2= 0,17 d = 1,923