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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