Aplikasi Data Panel Di Stata

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APLIKASI DATA PANEL DI STATA

Oleh :

Akbar Suwardi Dipresentasikan dalam Pelatihan Stata di Dept. Ilmu Ekonomi – Universitas Indonesia (2012)

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Outline

I.

Pengenalan Data Panel 1. Kuadrat Terkecil (Pooled Least Square) 2. Efek Tetap (Fixed Effect) 3. Efek Acak (Random Effect)

II.

Pemilihan Metode Estimasi dalam Panel Data 1. Pemilihan Kuadrat Terkecil (Pooled Least Square) atau Efek Tetap (Fixed Effect) 2. Pemilihan Efek Tetap (Fixed Effect) atau Efek Acak (Random Effect) 3. Pemilihan Kuadrat Terkecil (Pooled Least Square) atau Efek Acak (Random Effect)

III.

Evaluasi Hasil Regresi Data Panel 1. Kriteria Teori 2. Kriteria Statistik a. Uji signifikansi serentak (F-Test). b. Uji Signifikansi parsial (t-test). c. Uji Goodness of Fit. 3. Kriteria Ekonometrika a. Bebas dari Multikolinearitas b. Bebas dari Heteroskedastisitas c. Bebas dari Autokorelasi

IV.

Robust Method dan General Least Square (GLS) I. Robust Method: PLS & FE II. General Least Square (GLS) Method: PLS & FE 2


I. Pengenalan Data Panel • Gunakan data

– Data dari Buku Gujarati (2003), chpater 16 mengenai

• Lakukan Set Panel Data Xtset individu time, year Panel variable: individu (strongly balanced) Time variable: time, 1935 to 1954 Delta: 1 year

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I. Pengenalan Data Panel • Mengenal data Panel . xtsum y x2 x3 Variable | Mean Std. Dev. Min Max | Observations -----------------+--------------------------------------------+---------------y overall | 290.9154 284.8528 12.93 1486.7 | N = 80 between | 265.7954 42.8915 608.02 | n = 4 within | 165.786 -59.40462 1169.595 | T = 20 | | x2 overall | 2229.428 1429.965 191.5 6241.7 | N = 80 between | 1527.907 671.36 4333.35 | n = 4 within | 521.3062 688.2774 4137.778 | T = 20 | | x3 overall | 358.51 398.2685 .8 2226.3 | N = 80 between | 233.5919 85.64 648.435 | n = 4 within | 342.3096 -287.125 1936.375 | T = 20

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I. Pengenalan Data Panel GE

GM

US

WEST

0

500

1000 1500

Y

0

500

1000 1500

xtline y

1935

1940

1945

1950

19551935

1940

1945

1950

1955

Time Graphs by Id

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I. Pengenalan Data Panel

0

500

Y

1000

1500

• xtline y, overlay

1935

1940

1945 Time GE US

1950

1955

GM WEST

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I.1. Kuadrat Terkecil (Pooled Least Square) . reg

y x2 x3

Source | SS df MS -------------+-----------------------------Model | 4849457.37 2 2424728.69 Residual | 1560689.67 77 20268.697 -------------+-----------------------------Total | 6410147.04 79 81141.1018

Number of obs F( 2, 77) Prob > F R-squared Adj R-squared Root MSE

= = = = = =

80 119.63 0.0000 0.7565 0.7502 142.37

-----------------------------------------------------------------------------y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1100955 .0137297 8.02 0.000 .0827563 .1374348 x3 | .3033932 .0492957 6.15 0.000 .2052328 .4015535 _cons | -63.30413 29.6142 -2.14 0.036 -122.2735 -4.334734 ------------------------------------------------------------------------------

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I. 2. Efek Tetap (Fixed Effect) . xtreg

y x2 x3, fe

Fixed-effects (within) regression Group variable: individu

Number of obs Number of groups

= =

80 4

R-sq:

Obs per group: min = avg = max =

20 20.0 20

within = 0.8068 between = 0.7304 overall = 0.7554

corr(u_i, Xb)

= -0.1001

F(2,74) Prob > F

= =

154.53 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0175089 6.17 0.000 .0730608 .1428354 x3 | .3461617 .0266645 12.98 0.000 .2930315 .3992918 _cons | -73.84946 37.52291 -1.97 0.053 -148.6155 .9165759 -------------+---------------------------------------------------------------sigma_u | 139.05116 sigma_e | 75.288894 rho | .77329633 (fraction of variance due to u_i) -----------------------------------------------------------------------------F test that all u_i=0: F(3, 74) = 67.11 Prob > F = 0.0000 8


I. 2. Efek Tetap (Fixed Effect) Menggunakan Pendekatan Least Square Dummy Variable (LSDV) . reg y x2 x3 i.id Source | SS df MS -------------+-----------------------------Model | 5990684.14 5 1198136.83 Residual | 419462.898 74 5668.41754 -------------+-----------------------------Total | 6410147.04 79 81141.1018

Number of obs F( 5, 74) Prob > F R-squared Adj R-squared Root MSE

= = = = = =

80 211.37 0.0000 0.9346 0.9301 75.289

-----------------------------------------------------------------------------y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0175089 6.17 0.000 .0730608 .1428354 x3 | .3461617 .0266645 12.98 0.000 .2930315 .3992918 | id | 2 | 161.5722 46.45639 3.48 0.001 69.00583 254.1386 3 | 339.6328 23.98633 14.16 0.000 291.839 387.4266 4 | 186.5665 31.50681 5.92 0.000 123.7879 249.3452 | _cons | -245.7924 35.81112 -6.86 0.000 -317.1476 -174.4371 ------------------------------------------------------------------------------

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I. 3. Efek Acak (Random Effect) . xtreg

y x2 x3

Random-effects GLS regression Group variable: individu


= =

80 4

R-sq:


20 20.0 20


Random effects u_i ~ Gaussian corr(u_i, X) = 0 (assumed)

Wald chi2(2) Prob > chi2

= =

317.79 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1076555 .0168169 6.40 0.000 .0746949 .140616 x3 | .3457104 .0265451 13.02 0.000 .2936829 .3977378 _cons | -73.03529 83.94957 -0.87 0.384 -237.5734 91.50284 -------------+---------------------------------------------------------------sigma_u | 152.15823 sigma_e | 75.288894 rho | .80332024 (fraction of variance due to u_i) -----------------------------------------------------------------------------10


Ringkasan: FE, RE, dan OLS Untuk membandingkan ketiganya, terlebih dulu menyimpan hasil regresi masing-masing metode dengan command : estimates store (nama) . . . .

estimates estimates estimates estimates

store store store table

fe re ols fe re ols, star stats(N r2 r2_a)

-------------------------------------------------------------Variable | fe re ols -------------+-----------------------------------------------x2 | .10794807*** .10765546*** .11009554*** x3 | .34616168*** .34571038*** .30339316*** _cons | -73.849456 -73.035291 -63.304134* -------------+-----------------------------------------------N | 80 80 80 r2 | .80681613 .75652826 r2_a | .79376317 .75020432 -------------------------------------------------------------legend: * p<0.05; ** p<0.01; *** p<0.001

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II. Pemilihan Metode Estimasi dalam Panel Data

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II. 1. Pooled Least Square VS Fixed Effect: Restricted F-test . xtreg

y x2 x3, fe

Fixed-effects (within) regression Group variable: individu


= =

80 4

R-sq:


20 20.0 20


corr(u_i, Xb)

= -0.1001

F(2,74) Prob > F

= =

154.53 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0175089 6.17 0.000 .0730608 .1428354 x3 | .3461617 .0266645 12.98 0.000 .2930315 .3992918 _cons | -73.84946 37.52291 -1.97 0.053 -148.6155 .9165759 -------------+---------------------------------------------------------------sigma_u | 139.05116 sigma_e | 75.288894 rho | .77329633 (fraction of variance due to u_i) -----------------------------------------------------------------------------F test that all u_i=0: F(3, 74) = 67.11 Prob > F = 0.0000

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II. 2. Fixed Effect VS Random Effect Kriteria

FE

RE

Functional form Intersep

Bervariasi antar dan/atau waktu

Error variance

Konstan

Bervarisasi antar individu atau waktu

Slopes

Konstan

Konstan

Estimation

LSDV, within effect method

GLS, FGLS

Hypothesis test Incremental F test

individu

Konstan

BG LM test 14


II. 2. Fixed Effect VS Random Effect: Hausman test . . . . .

quietly xtreg y estimates store quietly xtreg y estimates store hausman fe re

x2 x3, fe fe x2 x3, re re

---- Coefficients ---| (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fe re Difference S.E. -------------+---------------------------------------------------------------x2 | .1079481 .1076555 .0002926 .0048738 x3 | .3461617 .3457104 .0004513 .0025204 -----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg Test:

Ho:

difference in coefficients not systematic chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 0.07 Prob>chi2 = 0.9678 15


II. 3. Pooled Least Square VS Random Effect Lakukan pengujian LM test tepat setelah melakukan estimasi dengan REM . xtreg y x2 x3, re . xttest0 Breusch and Pagan Lagrangian multiplier test for random effects y[individu,t] = Xb + u[individu] + e[individu,t] Estimated results: | Var sd = sqrt(Var) ---------+----------------------------y | 81141.1 284.8528 e | 5668.418 75.28889 u | 23152.13 152.1582 Test:

Var(u) = 0 chi2(1) = Prob > chi2 =

379.08 0.0000

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III. Teori Evaluasi Hasil Regresi •

Mengapa penting??? – Agar koefisien yang didapatkan efisien serta unbiased.

• Oleh karena itu kriteria teori, kriteria statistik, dan kriteria ekonometrika harus dilakukan. •

Menurut Baltagi (1981), dasar pembentukkan model panel masih menggunakan Least Square. Oleh karena itu, dalam mengevaluasi hasil model persamaan simultan-panel dapat dilakukan melalui pendekatan Least Square.

•

Khusus Random Effects Model (REM) metode yang dipakai adalah GLS regression. Jadi tidak perlu lagi untuk melakukan pengujian Heteroskedastisitas dan Autokolerasi 17


III.1. Kriteria Ekonomi atau Teori Dapat dilihat dari beberapa indikator: –Slope –Arah –Signifikansi Apakah sudah sesuai dengan teori? Tidak? ada kemungkinan data, variabel, dan spesifikasi model yang digunakan dalam regresi salah.

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III.2. Kriteria Statistik A. Uji signifikansi serentak (F-Test) • Uji ini untuk melihat secara global, apakah semua variable independent secara bersamasama mempengaruhi variable dependent. • Hipotesis: H0 : β0 = β1 = β2 = β3 = β4 = ….. = βk = 0 H1 : β0 ≠ β1 ≠ β2 ≠ β3 ≠ β4 ≠ ….. = βk ≠ 0

• Hipotesis nol akan ditolak jika nilai Fstatistik > nilai F tabel atau bila (Prob > F) <α. Jika nilai dari (Prob > F) = 0 berarti (Prob > F) <α (0.05), 19


III.2. Kriteria Statistik B. Uji Signifikansi Parsial (t-test). • Uji ini untuk melihat secara parsial atau pervariabel, apakah masing-masing independent variable secara signifikan berpengaruh terhadap dependent variable. • Hipotesis: H0 : βk = 0 H1 : βk ≠ 0

• Hipotesis nol akan ditolak bila (P>|t|)<α atau nilai t-stat > nilai kritis t-tabel. 20


III.2. Kriteria Statistik C. Uji Goodness of Fit.

• Untuk mengukur seberapa besar variasi dari nilai variabel dependen dapat dijelaskan oleh variasi nilai dari variabel independen. • Caranya? Lihat R-squared dari hasil regresi estimasi.

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III.2. Kriteria Statistik . xtreg

y x2 x3, fe

Fixed-effects (within) regression Group variable: individu R-sq:


corr(u_i, Xb)

= -0.1001

Number of obs Number of groups Uji Goodness of Fit Uji Global ( F-test)

= =

80 4


20 20.0 20

F(2,74) Prob > F

= =

154.53 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0175089 6.17 0.000 .0730608 .1428354 x3 | .3461617 .0266645 12.98 0.000 .2930315 .3992918 _cons | -73.84946 37.52291 -1.97 0.053 -148.6155 .9165759 -------------+---------------------------------------------------------------Kriteria sigma_u | 139.05116 Uji Ekonomi Parsial sigma_e | 75.288894 (t-test) rho | .77329633 (fraction of variance due to u_i) -----------------------------------------------------------------------------F test that all u_i=0: F(3, 74) = 67.11 Prob > F = 0.0000 22


III.3. Kriteria Ekonometrika 1. Bebas dari Multikolinearitas corr y x2 x3 (obs=80)

| y x2 x3 -------------+--------------------------y | 1.0000 x2 | 0.7980 1.0000 x3 | 0.7438 0.5783 1.0000 Diindikasikan multikolinearitas tinggi jika nilainya lebih dari 0.75 23


III.3. Kriteria Ekonometrika 1. Bebas dari Multikolinearitas VIF dilakukan setelah melakukan regresi dengan PLS

. reg y x2 x3 . vif Variable | VIF 1/VIF -------------+---------------------x2 | 1.50 0.665623 x3 | 1.50 0.665623 -------------+---------------------Mean VIF | 1.50 Diindikasikan multikolinearitas tinggi jika nilai VIF lebih dari 10 24


III.3. Kriteria Ekonometrika 1. Bebas dari Multikolinearitas VIF dilakukan setelah melakukan regresi dengan FE atau RE

. xreg y x2 x3, fe . vif, uncentered Variable | VIF 1/VIF -------------+---------------------x2 | 2.74 0.365614 x3 | 2.74 0.365614 -------------+---------------------Mean VIF | 2.74 Diindikasikan multikolinearitas tinggi jika nilai VIF lebih dari 10 25


III.3. Kriteria Ekonometrika 2. Bebas dari Heteroskedastisitas • Uji heterokedastisitas hanya dilakukan ketika menggunakan estimasi FE dan PLS • Hipotesis: H0 : Homoskedastis H1 : Heteroskedastis

• Hipotesis nol akan ditolak bila (Prob>chi2)<α atau nilai chi2> nilai kritis t-tabel. 26


III.3. Kriteria Ekonometrika 2. Bebas dari Heteroskedastisitas: PLS . quietly reg y x2 x3 . hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of y chi2(1) Prob > chi2

= =

3.08 0.0794

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III.3. Kriteria Ekonometrika 2. Bebas dari Heteroskedastisitas: Fixed Effect . xtreg y x2 x3, fe . xttest3

Modified Wald test for groupwise heteroskedasticity in fixed effect regression model H0: sigma(i)^2 = sigma^2 for all i chi2 (4) = Prob>chi2 =

240.33 0.0000 28


III.3. Kriteria Ekonometrika 3. Bebas dari Autokorelasi • Uji serial correlation in the idiosyncratic errors of a linear panel-data model oleh Wooldridge (2002).

• Hipotesis: H0 : No autokorelasi H1 : Autokorelasi • Hipotesis nol akan ditolak bila (Prob>chi2)<α atau nilai chi2> nilai kritis t-tabel. 29


III.3. Kriteria Ekonometrika 3. Bebas dari Autokorelasi

. xtreg y x2 x3, fe . xtserial y x2 x3 Wooldridge test for autocorrelation in panel data H0: no first-order autocorrelation F( 1, 3) = 1300.479 Prob > F = 0.0000 30


IV.1. Robust Method: PLS . reg y x2 x3, ro

Linear regression

Number of obs = F( 2, 77) = Prob > F = R-squared = Root MSE =

80 167.22 0.0000 0.7565 142.37

-----------------------------------------------------------------------------| Robust y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1100955 .0105705 10.42 0.000 .0890469 .1311442 x3 | .3033932 .0606153 5.01 0.000 .1826927 .4240936 _cons | -63.30413 22.90485 -2.76 0.007 -108.9135 -17.69474 ------------------------------------------------------------------------------

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IV.1. Robust Method: Fixed Effect . xtreg y x2 x3, fe ro Fixed-effects (within) regression Group variable: id


= =

80 4

R-sq:


20 20.0 20


corr(u_i, Xb)

= -0.1001

F(2,3) Prob > F

= =

55.79 0.0042

(Std. Err. adjusted for 4 clusters in id) -----------------------------------------------------------------------------| Robust y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0166046 6.50 0.007 .0551049 .1607912 x3 | .3461617 .036063 9.60 0.002 .2313933 .4609301 _cons | -73.84946 48.86551 -1.51 0.228 -229.3613 81.66242 -------------+---------------------------------------------------------------sigma_u | 139.05116 sigma_e | 75.288894 rho | .77329633 (fraction of variance due to u_i) -----------------------------------------------------------------------------32


IV.2. General Least Square (GLS) Method: GLS . xtgls y x2 x3 Cross-sectional time-series FGLS regression Coefficients: Panels: Correlation:

generalized least squares homoskedastic no autocorrelation

Estimated covariances = Estimated autocorrelations = Estimated coefficients = Log likelihood

1 0 3

= -508.6596

Number of obs Number of groups Time periods Wald chi2(2) Prob > chi2

= = = = =

80 4 20 248.58 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1100955 .0134698 8.17 0.000 .0836953 .1364958 x3 | .3033932 .0483626 6.27 0.000 .2086042 .3981821 _cons | -63.30413 29.05362 -2.18 0.029 -120.2482 -6.360075 -----------------------------------------------------------------------------33


IV.2. General Least Square (GLS) Method: Fixed Effect . xtgls

y x2 x3 i.id

Cross-sectional time-series FGLS regression Coefficients: Panels: Correlation:

generalized least squares homoskedastic no autocorrelation

Estimated covariances = Estimated autocorrelations = Estimated coefficients = Log likelihood

1 0 6

= -456.1032

Number of obs Number of groups Time periods Wald chi2(5) Prob > chi2

= = = = =

80 4 20 1142.54 0.0000

-----------------------------------------------------------------------------y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------x2 | .1079481 .0168395 6.41 0.000 .0749432 .140953 x3 | .3461617 .0256451 13.50 0.000 .2958982 .3964251 | id | 2 | 161.5722 44.68033 3.62 0.000 74.00038 249.144 3 | 339.6328 23.06931 14.72 0.000 294.4178 384.8479 4 | 186.5665 30.30227 6.16 0.000 127.1752 245.9579 | _cons | -245.7924 34.44203 -7.14 0.000 -313.2975 -178.2872 -----------------------------------------------------------------------------34


Reference • Gujarati, Damodar. 2006. Basic Econometrics. McGrawHill. • Manual Stata. 2011 • Suwardi, Akbar. 2011. MODUL STATA: Tahapan dan Perintah (Syntax) Mengolah Data Panel. Computing Laboratory of Economics Department - University of Indonesia. Depok

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Terimakasih!

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Aplikasi Data Panel Di Stata

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