Bahan Asistensi Lab Ekonometrika 1

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


-------------+------------------------------ 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


-------------+------------------------------ F( 1, 38) = 17.09

Model | .066668846 1 .066668846 Prob > F = 0.0002


-------------+------------------------------ Adj R-squared = 0.0177

Total | 1.5553025 39 .039879551 Root MSE = .19793

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

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


-------------+------------------------------ F( 1, 38) = 6.85

Model | .237569823 1 .237569823 Prob > F = 0.0126


-------------+------------------------------ Adj R-squared = 0.1305

Total | 1.5553025 39 .039879551 Root MSE = .18622

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

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

Bahan Asistensi Lab Ekonometrika 1

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