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Chng 3

Cc m hnh vi bin gii thch nh tnh1

Domadar N. Gujarati

(Econometrics by example, 2011).

Ngi dch v din gii: Phng Thanh Bnh, MB (26/10/2017)

Hu ht cc m hnh hi quy chng ta tho lun n gi lin quan n mt

bin ph thuc nh lng v cc bin gii thch nh lng. Chng ta s tip

tc gi nh rng bin ph thuc l nh lng, nhng by gi chng ta s xem

xt cc m hnh trong cc bin gii thch l nh lng cng nh nh tnh.

Trong chng 8, chng ta s xem xt cc bin ph thuc v bn cht cng l

bin nh tnh.

Trong phn tch hi quy chng ta thng gp cc bin v c bn l nh tnh,

chng hn nh gii tnh, sc tc, mu da, tn gio, dn tc, vng a l, ng

phi, hoc cc xu hng chnh tr. V d, trong hm tin lng chng ta tho

lun chng 1, chng ta c cc bin v gii tnh, mi quan h cng on, v

tnh trng thiu s gia nhiu bin gii thch bi v cc bin nh tnh ny ng

mt vai tr quan trng trong vic quyt nh tin lng.

Cc bin nh tnh ny v c bn l cc bin vi thang o nh danh, khng c

bt k nhng gi tr bng s c th. Nhng chng ta c th lng ha chng

bng cch to ra cc bin gi (dummy variables), c cc gi tr 0 v 1, 0 cho

bit khng c thuc tnh v 1 cho bit c thuc tnh. V vy bin gii tnh c th

lng ha nh sau: n = 1 v nam = 0, hoc ngc li. Nhn y, lu rng

1 bit thm chi tit, xem Gujarati/Porter, Chng 9.

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cc bin gi cng c gi l cc bin ch bo (indicator variables), cc bin

phn loi (categorical variable), v cc bin nh tnh (qualitative variables).

Trong chng ny, chng ta cho thy cc bin gi c th c x l nh th

no trong khung phn tch ca m hnh hi quy tuyn tnh c in. thun

tin v mt k hiu, chng ta s t cc bin gi bng ch D.

vic phn tch tr nn d dng, chng ta bt u vi mt v d c th.

3.1 Xem xt li hm tin lng

Trong chng 1, chng ta xem xt nhn t quyt nh tin lng theo gi

ca mt mu cho gm 1289 ngi da trn d liu thu thp t iu tra dn s

hin hnh (CPS) thng 3 nm 2095. Cc bin c s dng trong phn tch v

cc kt qu hi quy c cho trong Bng 1.2.

Bng 1.2: Hm tin lng.

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Chng ta hy vit hm tin lng theo mt dng khc nhn mnh vai tr ca

cc bin gi trong hi quy ny:

Trong , D2i = 1 nu l n, 0 l nam; D3i = 1 cho da mu, 0 da trng; v D4i =

1 nu l thnh vin ca cng on, 0 nu khng phi thnh vin cng on;

y Ds l cc bin gi.

thun tin, chng ta to li kt qu hi quy c cho trong Bng 1.2, s

dng cc k hiu trc cho trong phng trnh (3.1) (Bng 3.1).

Bng 3.1: M hnh nhn t quyt nh tin lng.

Th nht, nu mt h s ct c a vo m hnh v nu mt bin nh tnh

c m phn loi, th chng ta ch a (m 1) bin gi vo m hnh. V d, gii

tnh ch c hai phn loi; v th chng ta ch a mt bin gi cho gii tnh. iu

ny bi v nu n nhn gi tr 1, th t bn thn n nam c gi tr l 0. D nhin,

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nu mt thuc tnh ch c hai phn loi, th s khng l vn g khi phn loi

nhn gi tr 1 hoc 0. V th chng ta c th m ha nam l 1 v n l 0.

Nu, v d, chng ta xem xt mi quan h chnh tr nh s la chn gia ng

dn d, ng cng ha, v ng c lp, th chng ta c th c ti a hai bin

gi i din cho ba ng. Nu chng ta khng tun theo quy tc ny, chng

ta s ri vo by bin gi (dummy variable trap), ngha l, tnh hung a cng

tuyn hon ho. V th, nu chng ta c 3 bin gi cho 3 ng chnh tr v mt

h s ct, th tng ca 3 bin gi s l 1, s ng bng gi tr ca h s ct

chung (common intercept) l 1, dn n a cng tuyn hon ho2.

Th hai, nu mt bin nh tnh c m phn loi, bn c th a m bin gi v

m hnh, min l bn khng a h s ct (chung) vo m hnh. Cch ny

chng ta khng ri vo by bin gi.

Th ba, phn loi nhn gi tr 0 c gi l phn loi tham chiu (reference),

phn loi c s so snh (benchmark hoc comparison). Tt c cc so snh

c thc hin theo phn loi tham chiu, nh chng ta s thy trong v d.

Th t, nu c nhiu bin gi, th bn phi theo d phn loi tham chiu [Din

gii: D nhin l ca tng bin]; nu khng, bn s rt kh gii thch kt qu.

Th nm, chng ta s thng xuyn phi xem xt cc bin gi tng tc

(interactive dummies), chng ta s minh ha cc bin tng tc ny di y.

Th su, v cc bin gi nhn cc gi tr 1 v 0, nn chng ta khng th ly

logart. Ngha l, chng ta s khng a cc bin gi dng log3.

2 Lu rng a h s ct vo m hnh tng ng a mt bin gii thch vo m hnh v bin ny lun lun c gi tr l 1. 3 Tuy nhin, nu thay v 1 v 0, bn chn 10 v 1 nh cc gi tr ca bin gi, th bn c th ly log ca chng.

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Th by, nu mu tng i nh, ng a qu nhiu bin gi vo m hnh.

Nh rng, mi h s ca bin gi s hao tn mt bc t do.

Gii thch cc bin gi

Quay li hm tin lng trong Bng 3.1, chng ta hy gii thch h s bin gi

ca gii tnh (-3.0748). H s ny c ngha l tin lng theo gi trung bnh ca

mt cng nhn n thp hn khong $3.07 so vi tin lng trung bnh ca mt

cng nhn nam, y nam l phn loi tham chiu, d nhin khi cc bin khc

c gi nguyn khng i. Tng t, tin lng trung bnh ca cc cng nhn

c tham gia cng on cao hn khong $1.10 so vi tin lng trung bnh ca

cc cng nhn khng c tham gia cng on (y l phn loi tham chiu) [Din

gii: D nhin l khi cc bin khc c gi nguyn khng i]. Tng t, tin

lng trung bnh ca mt cng nhn da mu thp hn khong $1.57 so vi mt

cng nhn da trng (y l phn loi tham chiu) [Din gii: D nhin l khi cc

bin khc c gi nguyn khng i].

Nhn tin, lu rng tt c cc h s bin gi u c ngha thng k cao, v

cc gi tr xc sut p thc t hu nh bng 0. [Din gii: Nh vy, cc yu t

nh nh l nhng bin quan trng quyt nh tin lng, nn nu chng ta s

khng a vo m hnh s dn n cc c lng OLS b chch (biased), v

y l nhng hu qu rt nghim trng. hiu b chch ngha l sao, v ti

sao n quan trng, hy xem chng minh v gii thch n tp #3, Tm lc

kinh t lng cn bn]. Cc h s bin gi ny ng c gi l cc bin gi

chnh lch h s ct (differential intercept dummies), v chng cho bit khc

bit trong cc gi tr ca h s ct ca phn loi c gi tr bng 1 so vi phn

loi tham chiu.

Gi tr -7.18 ca h s ct chung c ngha l g? Chng ta k vng l tin

lng theo gi ca mt cng nhn nam, da trng, khng tham gia cng on

(tc l cc phn loi tham chiu). Ngha l, gi tr h s ct chung cp n

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tt c cc phn loi c gi tr bng 0. D nhin, y l cch gii thch my

mc (mechanical interpretation) v h s ct4. Nh chng ta lu nhiu

trng hp, mt gi tr h s ct m thng khng c cch gii thch ngha

kinh t r rng.

Gii thch cc bin gii thch nh lng th kh r rng. V d, h s ca bin

gio dc 1.37 ngha l khi gi nguyn cc yu t khc khng i, mt nm i

hc tng thm th tin lng trung bnh s tng khong $1.37. Tng t, mi

nm kinh nghim lm vic tng thm th tin lng trung bnh s tng khong

$0.17, khi gi nguyn cc yu t khc khng i.

3.2 Lm r li hm tin lng

Chng ta thy rng tin lng trung bnh ca mt cng nhn n thp hn

tin lng trung bnh ca mt cng nhn nam v chng ta cng thy rng tin

lng trung bnh ca mt cng nhn da mu thp hn tin lng ca mt cng

nhn da trng. C th rng tin lng trung bnh ca mt cng nhn n da mu

khc tin lng ca mt cng nhn n hoc mt cng nhn da mu? Nu iu

xy ra, th liu rng chng ta c th ni g v kh nng phn bit i x

chng li cc cng nhn n da mu?

bit iu ny, chng ta c lng li hm tin lng bng cch a thm

vo m hnh tch (product) ca cc bin gi gii tnh (n) v da mu. Bin tch

c gi l mt bin gi tng tc (interactive dummy), v n tng tc hai

bin nh tnh. a thm bin tng tc, c c kt qu nh trong Bng 3.2.

H s ca bin gi tng tc (D2 x D3) l khong 1.10, nhng n khng c

ngha thng k, v gi tr xc sut p khong 28%.

4 C bn, n cho bit ni m ng hi quy (hoc mt phng) nm dc trc Y, th hin bin ph thuc.

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Nhng chng ta gii thch gi tr ny nh th no? Khi cc yu t khc c

gi nguyn, th mt cng nhn n c tin lng trung bnh thp hn khong

$3.24, mt cng nhn da mu c tin lng trung bnh thp hn khong $2.16

v mt cng nhn n da mu c tin lng trung bnh thp hn khong $4.30

(= -3.24 2.16 + 1.10). Ni cch khc, so vi phn loi tham chiu, th mt cng

nhn n da mu c thu nhp tin lng trung bnh thp hn mt cng nhn n

hoc thp hn mt cng nhn da mu.

Bng 3.2: Hm tin lng vi cc bin gi tng tc.

[Din gii: Trn Eviews, c kt qu hi quy nh Bng 3.2, chng ta nhp

dng lnh sau y: LS WAGE C GENGER RACE UNION EDUC EXPERI

GENDER*RACE].

Chng ta cho ngi c t tm hiu xem liu mt cng nhn n tham gia

cng on hoc mt cng nhn da mu tham gia cng on c mc tin lng

trung bnh khc bit so vi thuc tnh tham chiu hay khng. Bn cng c th

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tng tc cc bin gi n v cng on, cc bin gi n v kinh nghim, cc

bin gi da mu v cng on, v cc bin gi da mu v kinh nghim.

3.3 Mt cch khc xem xt li hm tin lng

Chng ta ngm gi nh rng cc h s dc ca cc bin nh lng: gio

dc, v kinh nghim l ging nhau gia cng nhn nam v na, gia cng nhn

da mu v da trng. V d, gi nh ny hm rng mi nm i hc tng thm

hoc mi nm kinh nghim lm vic tng thm, th cng nhn nam v n kim

c cng mc lng theo gi tng thm. D nhin, y ch l mt gi nh.

Nhng vi cc bin gi, chng ta c th kim nh gi nh ny mt cch r

rng hn.

Chng ta hy th hin hm tin lng nh sau:

Trong phng trnh (3.2), B2, B3, v B4 l cc bin gi chnh lch h s ct, nh

trc y, v B7 n B11 l cc bin gi chnh lch h s dc (differential

slope dummies). Nu v d, b7, l h s c lng ca B7, c ngha thng k,

th n cho bit rng t l tng lng trung bnh trn mt nm gio dc tng thm

n so vi nhm tham chiu (tc l nam) [Din gii: Gujarati ghi nhm l nam da

trng], c h s dc l B5 (ng ra l b5). Cc h s chnh lch dc khc

cng c gii thch mt cch tng t.

Kt qu hi quy phng trnh (3.2) c cho trong Bng 3.3. So vi kt qu

trong Bng 3.1 v 3.2, kt qu trong Bng 3.3 c nhiu im th v. Cc h s

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chnh lch dc i vi n theo gio dc v kinh nghim mang