Post on 06-Aug-2015
description
Venty
Aslab Ekonometrika 1
Desember 2012
asumsi OLS yang ke4 adalah cov(x,u) = 0
Definisi pelanggaran: independent variable berhubungan dengan error.
Konsekuensi: tetap best dan linear, tetapi tidak lagi unbiased. Artinya, parameter yang dihasilkan tidak lagi sesuai dengan keadaan yang sebenarnya tapi masih tetap linear di parameter dan tetap minimum varians standar error, t, dan |p|>t masih tepat.
1. Ommited Variable
2. Error in variables
3. Persamaan Simultan
K = jumlah variabel predetermined didalam model termasuk intercept k = jumlah predetermined didalam persamaan. M = jumlah variabel endogen didalam model termasuk intercept m = jumlah variabel endogen didalam persamaan Suatu persamaan simultan dapat diidentifikasi apabila : overindentified atau just-identified (K-k ≥ m-1 ) 1. K-k < m-1 : under-identified tidak bisa
diidentifikasi (OLS) 2. K-k = m-1 : just- identified ILS/ TSLS 3. K-k > m-1 : over-identified TSLS
K = 2(Yt, Intercept)
ks = 1(b0) ms= 2 (Pt, Qt)
kd = 2 (yt, Intercept) md= 2 (Pt, Qt)
Qs K-ks = 2-1=1; ms-1= 2-1= 1 1=1 Just
Qd K-kd = 2-2 = 0 ; md-1=2-1=1 0<1 Under
tt
s
t PQ ,121 ttt
d
t YPQ ,2321
ttt
d
t YPQ ,2321
d
t
s
t QQQ
tt
s
t PQ ,121
Regresikan reduced form
reg lp ly
reg lq ly
Untuk mendapatkan β1 dan β2:
. reg lp ly
Source | SS df MS Number of obs = 40
-------------+------------------------------ F( 1, 38) = 179.30
Model | 16.2282752 1 16.2282752 Prob > F = 0.0000
Residual | 3.43932055 38 .090508436 R-squared = 0.8251
-------------+------------------------------ Adj R-squared = 0.8205
Total | 19.6675958 39 .504297328 Root MSE = .30085
------------------------------------------------------------------------------
lp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ly | 1.187918 .0887145 13.39 0.000 1.008325 1.367511
_cons | -1.061771 .4943153 -2.15 0.038 -2.06246 -.0610818
------------------------------------------------------------------------------
. reg lq ly
Source | SS df MS Number of obs = 40
-------------+------------------------------ F( 1, 38) = 28.73
Model | .669561451 1 .669561451 Prob > F = 0.0000
Residual | .885741053 38 .023308975 R-squared = 0.4305
-------------+------------------------------ Adj R-squared = 0.4155
Total | 1.5553025 39 .039879551 Root MSE = .15267
------------------------------------------------------------------------------
lq | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ly | .2412934 .0450207 5.36 0.000 .1501539 .332433
_cons | 8.140947 .250854 32.45 0.000 7.633119 8.648774
------------------------------------------------------------------------------
. disp .2412934/ 1.187918
.20312294
. disp 8.140947-(.20312294*-1.061771 )
8.356617
Rumus Umum:
ivregress 2sls depvar [varlist1]
(varlist2 = varlist_iv) [if] [in]
[weight] [, options]
. ivregress 2sls lq (lp=ly), small first
. ivregress 2sls lq (lp=ly), small first
First-stage regressions
-----------------------
Number of obs = 40
F( 1, 38) = 179.30
Prob > F = 0.0000
R-squared = 0.8251
Adj R-squared = 0.8205
Root MSE = 0.3008
------------------------------------------------------------------------------
lp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ly | 1.187918 .0887145 13.39 0.000 1.008325 1.367511
_cons | -1.061771 .4943153 -2.15 0.038 -2.06246 -.0610818
------------------------------------------------------------------------------
Instrumental variables (2SLS) regression
Source | SS df MS Number of obs = 40
-------------+------------------------------ F( 1, 38) = 17.09
Model | .066668846 1 .066668846 Prob > F = 0.0002
Residual | 1.48863366 38 .03917457 R-squared = 0.0429
-------------+------------------------------ Adj R-squared = 0.0177
Total | 1.5553025 39 .039879551 Root MSE = .19793
------------------------------------------------------------------------------
lq | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lp | .203123 .0491322 4.13 0.000 .1036601 .3025858
_cons | 8.356617 .2733294 30.57 0.000 7.80329 8.909943
------------------------------------------------------------------------------
Instrumented: lp
Instruments: ly
1. H0: variabel yang di-treat sebagai endogen adalah variabel yang eksogen
H1: variabel yang di-treat sebagai endogen adalah variabel yang endogen
2. Kriteria: tolak h0 jika p< alfa
. estat endog
Tes ini hanya bisa dilakukan jika persamaan kita itu overidentified tambah variabel eksogennya (ladv)
. estat endog
Tests of endogeneity
Ho: variables are exogenous
Durbin (score) chi2(1) = 24.4781 (p = 0.0000)
Wu-Hausman F(1,37) = 58.3489 (p = 0.0000)
Sargan test
1. H0: instrumen yang digunakan dapat diterima income & adv adalah instrumen yang tepat
H1: instrumen yang digunakan tidak dapat diterima
2. Kriteria : tolak h0 jika p < alfa
. estat overid
. estat overid
Tests of overidentifying restrictions:
Sargan (score) chi2(1) = .057264 (p = 0.8109)
Basmann chi2(1) = .053045 (p = 0.8178)
. reg y1 y2
. estimates store ols
. ivreg y1 (y2 = x1)
. estimates store iv menyimpan hasil regersi IV
. hausman iv ols
. reg lq lp
Source | SS df MS Number of obs = 40
-------------+------------------------------ F( 1, 38) = 6.85
Model | .237569823 1 .237569823 Prob > F = 0.0126
Residual | 1.31773268 38 .034677176 R-squared = 0.1527
-------------+------------------------------ Adj R-squared = 0.1305
Total | 1.5553025 39 .039879551 Root MSE = .18622
------------------------------------------------------------------------------
lq | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lp | .1099056 .04199 2.62 0.013 .0249013 .19491
_cons | 8.871788 .233921 37.93 0.000 8.39824 9.345336
------------------------------------------------------------------------------
. estimates store satu
. ivregress 2sls lq (lp=ly ladv)
Instrumental variables (2SLS) regression Number of obs = 40
Wald chi2(1) = 18.04
Prob > chi2 = 0.0000
R-squared = 0.0422
Root MSE = .19298
------------------------------------------------------------------------------
lq | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lp | .2034078 .0478901 4.25 0.000 .1095448 .2972708
_cons | 8.355043 .2664209 31.36 0.000 7.832867 8.877218
------------------------------------------------------------------------------
Instrumented: lp
Instruments: ly ladv
. estimates store dua
. hausman dua satu
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| dua satu Difference S.E.
-------------+----------------------------------------------------------------
lp | .2034078 .1099056 .0935022 .0230283
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 16.49
Prob>chi2 = 0.0000