BI GINGKINH T LNGECONOMETRICSL Anh cKhoa Ton kinh t H Kinh t Quc dn

CHNG I: M HNH HI QUY HAI BIN , MT VI T TNG C BN1.1. Phn tch hi quya. Bn cht ca phn tch hi quyb. Phn tch hi quy v cc quan h khc1.2. Bn cht ngun s liu cho phn tch hi quya. Cc loi s liub. Ngun gc cc s liuc. Bn cht chung ca s liu kinh t x hi1.3. M hnh hi quy tng th1.4. Sai s ngu nhin v bn cht ca n1.5. Hm hi quy mu

1.1. Phn tch hi quy (regression analysis)Bn cht ca phn tch hi quyThut ng hi quy c Francis Galton s dng vo nm 1886.L phn tch mi lin h ph thuc gia mt bin gi l bin ph thuc (dependent variable) vo mt hoc mt s bin khc gi l bin gii thch (explanatory variable)Bin ph thuc, k hiu l YBin gii thch, k hiu l X hoc X1 , X2, Hi quy l mt cng c c bn ca Kinh t lng

Th d: Lut Francis Galton - Karl PearsonVn : nghin cu mi lin h ph thuc gia chiu cao ca cc chu trai vo chiu cao ca cc ng b.Y = chiu cao ca cc chu trai (inches) X = chiu cao ca cc ng b (inches) th (tham kho gio trnh trang 10). th ny c v vi mt tng th gi nh.

Kt qu nghin cu ca F.Galton K.Pearson : - Vi chiu cao bit ca ngi b th chiu cao ca cc chu trai s l mt khong, dao ng quanh gi tr trung bnh;- Chiu cao ca ngi b tng th chiu cao ca cc chu trai cng tng (h s gc ln hn 0);- Vi nhm cc ng b c chiu cao nh (thp) th chiu cao trung bnh ca cc chu trai cao hn b. Ngc li, vi nhm cc ng b c chiu cao ln (cao) th chiu cao trung bnh ca cc chu trai thp hn b (h s gc nh hn 1).

Cc th d khcChi cho tiu dng c nhn thu nhp kh dngMc cu giT l thay i ca tin lng t l tht nghipT l tin mt nm gi trong tng thu nhp t l lm phtMc cu mc chi cho qung coSn lng ca mt loi nng sn lng phn bn, lng ma, nhit , v.v

Mc ch ca phn tch hi quic lng gi tr trung bnh ca bin ph thuc khi bit gi tr ca bin c lp, tc l phi c lng cc tham s ca m hnh. Kim nh cc gi thuyt v bn cht ca mi quan h gia bin ph thuc v bin c lp m l thuyt kinh t a ra. Trong trng hp ny phi tr li hai cu hi:- C tn ti quan h gia bin ph thuc v bin c lp hay khng?- Nu tn ti quan h th mc cht ch nh th no?D bo gi tr trung bnh ca bin ph thuc khi bit gi tr ca bin c lp.

b. Phn tch hi quy v cc quan h khcPhn tch hi quy nghin cu quan h thng k (statistical relationship)Ta phn bit vi cc quan h sau:Phn tch hi quy v quan h hm s (functional relationship)Phn tch hi quy v phn tch tng quan (correlation analysis)Phn tch hi quy v quan h nhn qu (causation relationship)

Phn tch hi quy v quan h hm s- Trong quan h hm s:+ ng vi mi gi tr ca bin c lp cho duy nht mt gi tr ca bin ph thuc.+ Cc bin khng phi l cc bin ngu nhin.

- Trong phn tch hi quy+ ng vi mi gi tr cho trc ca bin c lp c th c nhiu gi tr khc nhau ca bin ph thuc.+ Cc bin l cc bin ngu nhin.

Phn tch hi quy v phn tch tng quan- Phn tch tng quan+ o mc kt hp tuyn tnh gia hai bin bng h s tng quan.+ Cc bin c tnh cht i xng.

- Trong phn tch hi quy+ c lng v d bo mt bin trn c s gi tr cho ca cc bin khc. + Cc bin khng c tnh cht i xng.

Phn tch hi quy v quan h nhn qu- Quan h nhn qu l h hai chiu gia hai i tng trong vai tr ca cc i tng c xc nh r u l nguyn nhn v u l kt qu.

- Trong phn tch hi quy bin gii thch khng nht thit l nguyn nhn gy ln bin ph thuc, mi quan h gia cc bin c xc lp tu thuc vo mc ch nghin cu.

1.2. Bn cht ngun s liu cho phn tch hi quyCc loi s liuS liu theo thi gian (Time series data)V d: CPI, GDP,S liu cho (Undate Cross section data)V d: Doanh thu, li nhun (ca cc DN)S liu kt hp (Pooled data)S liu bng (Panel data)

b. Ngun gc cc s liu

S liu t cc ngun c pht hnh nh: Nin gim thng k, tp ch,

S liu t cc cuc iu tra thc t hoc i mua.

c. Bn cht chung ca s liu KT XH

Phn ln l cc s liu phi thc nghim, mang tnh ngu nhin, km tin cy.C sn thu thp, tnh ton ph hp vi mc ch nghin cu.Ghi nh: Kt qu ca nghin cu s khng ch ph thuc vo m hnh c la chn m cn ph thuc rt nhiu vo cht lng ca s liu.

1.3. M hnh hi qui tng thTng th (Population) l ton b tp hp cc phn t ng nht theo mt du hiu nghin cu nh tnh hoc nh lng no .Gi s c mt tng th nghin cu gm N phn t vi hai du hiu nghin cu X, Y to thnh mt bin ngu nhin hai chiu (X, Y). nghin cu BNN (X, Y) ta lp cc bng phn phi xc sut.Tham kho th d 1.3 trang 14, sch bi ging

Bng phn phi xc sut ng thi ca X v Y

X1X2XkY1P(Y1, X1)P(Y1, X2)P(Y1, Xk)Y2P(Y2, X1)P(Y2, X2).P(Y2, Xk)YhP(Yh, X1)P(Yh, X2)P(Yh, Xk)

Cc bng phn phi xc sut c iu kin ca Y theo Xi (i = 1, 2, , k)

K vng ton ca Y vi iu kin ca Xi:

E(Y/Xi) l mt hm s v gi l hm hi quy tng th ca Y i vi Xi (Population Regression Function PRF). N cho bit gi tr trung bnh ca Y thay i nh th no theo Xi.

(Y/Xi)Y1Y2YhP(Y/Xi)P(Y1, Xi)P(Y2, Xi)P(Yh, Xi)

Nu hm hi quy tng th c mt bin c lp th gi l hm hi quy n - Simple regression.E(Y/Xi) = f(Xi)Nu hm hi quy tng th c hn mt bin c lp th gi l hm hi quy bi - Multiple regression. E(Y/X1i, X2i,) = f(X1i, X2i, )

)

Gi s PRF c dng tuyn tnh:

hoc Hm ny gi l hm hi quy tuyn tnh nTrong : gi l h s chn (intercept coefficient)

gi l h s gc (slope coefficient)

Ti mt gi tr c bit ca Yi ta c:

gi l m hnh hi quy tng th (Population Regression Model PRM)Thut ng tuyn tnh c hiu theo hai ngha+ Tuyn tnh i vi cc tham s+ Tuyn tnh i vi cc bin s (X, Y)Khi ni n hm hi quy tuyn tnh tc l hm hi quy tuyn tnh i vi cc tham s, n c th l tuyn tnh hoc phi tuyn i vi cc bin s.E(Y/X) = 1 + 2X2E(Y/X) = 1 + 2lnXE(Y/X) = 1X2

1.4. Sai s ngu nhin v bn cht ca nt Ui = Yi E(Y/Xi) gi l sai s ngu nhin (random errors)Sai s ngu nhin i din cho tt c nhng yu t khng phi bin c lp nhng cng tc ng n bin ph thuc.+ Nhng yu t khng bit+ Nhng yu t khng c s liu+ Nhng yu t m tc ng ca n qu nh khng mang tnh h thngS tn ti ca SSNN l tt yu khch quan v n c vai tr c bit quan trng trong phn tch hi quy, n phi tho mn nhng iu kin nht nh th th vic phn tch trn m hnh hi quy mi c ngha.

1.5. Hm hi qui muTrong thc t chng ta khng c c tng th hoc c nhng khng th (khng cn thit) nghin cu ton b tng th v vy khng th tm c PRF mc d dng ca PRF c th bit.Mu ngu nhin l mt b phn mang thng tin ca tng th c ly ra t tng th theo nhng nguyn tc nht nh.Gi s t tng th lp mt mu ngu nhin (mu c th) kch thc n: W = {(Xi ,Yi) ; i =1n}

Trong mu tn ti mt hm s gi l hm hi quy mu (Sample Regression Function - SRF) c dng ging nh PRF m t xu th bin ng ca trung bnh bin ph thuc theo bin c lp.Thc cht n l mt c lng im ca PRFNu PRF c dng: E(Y/Xi) = 1 + 2Xi SRF c dng:

Trong : (Estimated regression coefficients) l cc c lng im ca . (Fitted value) l c im ca E(Y/Xi).

Mu ngu nhin l ngu nhin c lng ngu nhin (estimates) ca tham s 1,2

Vi mu c th, l con s c th c lng c th (estimators) ca tham s 1,2

Ti mt gi tr c bit ca Y ta c

gi l m hnh hi quy mu (Sample Regression Model SRM)t gi l phn d (Residual) Phn d ei l sai s ngu nhin ca mu, thc cht chng l cc c lng im ca cc sai s ngu nhin Ui trong tng th.Bn cht ca ei ging nh cc sai s ngu nhin Ui

Tng th (Population)Mu (Sample)

Sai s ngu nhin UiPhn d ei

Cc thut ng c bn*

Ting AnhTing VitRegression analysisPhn tch hi quyDependent variableBin ph thucExplanatory variable/ Independent variableBin gii thch/ bin c lpTime series dataS liu theo thi gianCross section dataS liu choPooled dataS liu kt hpPanel dataS liu bngPopulationTng thPRF Population Regression FunctionHm hi quy tng thPRM - Population Regression ModelM hnh hi quy tng th

Cc thut ng c bn*

Ting AnhTing VitSimple regressionHi quy nMultiple regressionHi quy biIntercept coefficientH s chn hoc h s t doSlope coefficientH s gcRandom errorSai s ngu nhinSRF Sample Regression FunctionHm hi quy muSRM - Sample Regression Model M hnh hi quy muEstimated regression coefficientsCc h s hi quy c lng cResidualPhn d

*Cn nhb. Phn tch hi quy v cc quan h khc (8)E(Y/Xi) l mt hm s v gi l hm hi quy tng th ca Y i vi Xi (17)

41 A

76 B

14 C