Ekonometrika 2 Program S1 Ilmu Ekonomi FEUI Maret 2012 Lab ke -3 Analisis Time Series 1
Gunakan data PHILLIPS.dta dengan deskripsi variable di PHILLIPS.txt. PHILLIPS.txt. . use
http://fmwww.bc.edu/ec-p/data/wooldridge/PHILLIPS.dta
“
”
. *Lakukan set time data terlebih dahulu sebelum melakukan estimasi times series . tsset year time variable: year, 1948 to 1996 delta: 1 unit
SOAL A
Estimasi persamaan persamaan statis kurva Phllips (1) dengan metode OLS:
inf t t=b 0+b1unemt +ut . reg
(1)
inf unem
Source | SS df MS -------------+------------------------------------------+-----------------------------Model | 25.6369575 1 25.6369575 Residual | 460.61979 47 9.80042107 -------------+------------------------------------------+----------------------------Total | 486.256748 48 10.1303489
Number of obs F( 1, 47) Prob > F R-squared Adj R-squared Root MSE
= = = = = =
49 2.62 0.1125 0.0527 0.0326 3.1306
---------------------------------------------------------------------------------------------------------------------------------------------------------inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-------------------------------------------------------+----------------------------------------------------------------------------------unem | .4676257 .2891262 1.62 0.112 -.1140213 1.049273 _cons | 1.42361 1.719015 0.83 0.412 -2.034602 4.881822 --------------------------------------------------------------------------------------------------------------------------------------------------------
Jelaskan parameter-parameter (signifikansi, (signifikansi, arah dan besaran) Prob > F
| R-squared
|
yang
diestimasi
dari
persamaan
(1)
P>|t|
Estimasi persamaan dinamik kurva Phillips (kurva Philips dengan asumsi angkapengangguran angkapengangguran alamiah alamiah konstan) (2) dengan metode OLS cinf=d 0+d 1unem+e
(2)
. reg cinf unem
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Source | SS df MS -------------+------------------------------------------+----------------------------Model | 33.3829988 1 33.3829988 Residual | 276.30513 46 6.00663326 -------------+------------------------------------------+----------------------------Total | 309.688129 47 6.58910913
Number of obs F( 1, 46) Prob > F R-squared Adj R-squared Root MSE
= 48 = 5.56 = 0.0227 = 0.1078 = 0.0884 = 2.4508
---------------------------------------------------------------------------------------------------------------------------------------------------------cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-----------------------------------------------------+------------------------------------------------------------------------------------unem | -.5425869 .2301559 -2.36 0.023 -1.005867 -.079307 _cons | 3.030581 1.37681 2.20 0.033 .259206 5.801955 --------------------------------------------------------------------------------------------------------------------------------------------------------
Jelaskan parameter-parameter (signifikansi, (signifikansi, arah dan besaran) Prob > F
| R-squared
|
yang
diestimasi
(2)
Bandingkan hasil regresi kedua persamaan di atas, model yang mana yang anda anggap sesuai untuk menjelaskan trade off antara inflasi dan pengangguran dalam jangka pendek? Jelaskan
b(%7.4f) stfmt(%7.4g) stfmt(%7.4g) star(0.1
Estimasi persamaan dinamik kurva Phillips (kurva Philips dengan asumsi angka pengangguran merupakan fungsi dari angka pengangguran pada periode sebelumnya) (3) dengan metode OLS cinf=q0+q1cunem+e
. reg
persamaan
P>|t|
. quietly reg inf unem . estimates store inf . quietly reg cinf unem . estimates store cinf . estimates table inf cinf, stat(N stat(N r2 r2_a aic bic) 0.05 0.01) ---------------------------------------Variable | inf cinf -------------+-------------------------unem | 0.4676 -0.5426** _cons | 1.4236 3.0306** -------------+-------------------------N | 49 48 r2 | .05272 .1078 r2_a | .03257 .0884 aic | 252.9 224.2 bic | 256.6 228 ---------------------------------------legend: * p<.1; ** p<.05; *** p<.01
dari
(3)
cinf cunem
Source | SS df MS -------------+------------------------------------------+-----------------------------Model | 41.8221976 1 41.8221976 Residual | 267.865931 46 5.82317242
Number of obs = F( 1, 46) = Prob > F = R-squared =
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48 7.18 0.0102 0.1350
2
-------------+------------------------------------------+-----------------------------Total | 309.688129 47 6.58910913
Adj R-squared = Root MSE =
0.1162 2.4131
---------------------------------------------------------------------------------------------------------------------------------------------------------cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------cunem | -.8421707 .3142509 -2.68 0.010 -1.474725 -.2096165 _cons | -.0781776 .3484621 -0.22 0.823 -.7795954 .6232401 -----------------------------------------------------------------------------
Jelaskan parameter-parameter (signifikansi, (signifikansi, arah dan besaran) Prob > F
| R-squared
|
yang
diestimasi
dari
(2)
P>|t|
Bandingkan hasil regresi persamaan (2) dan (3) di atas, model yang mana yang anda anggap sesuai dengan data? Jelaskan . quietly reg cinf cunem . estimates store cinf2 . estimates table cinf cinf2 , stat(N r2 r2_a aic bic) star(0.1 0.05 0.01) ---------------------------------------Variable | cinf cinf2 -------------+-------------------------unem | -0.5426** cunem | -0.8422** _cons | 3.0306** -0.0782 -------------+-------------------------N | 48 48 r2 | .1078 .135 r2_a | .0884 .1162 aic | 224.2 222.7 bic | 228 226.5 ---------------------------------------legend: * p<.1; ** p<.05; *** p<.01
persamaan
b(%7.4f) stfmt(%7.4g)
Bandingkan hasil regresi persamaan persamaan (1), (2), dan (3) di atas, model yang mana yang anda anggap sesuai dengan data? Jelaskan . estimates table inf cinf cinf2 , stat(N stat(N r2 r2_a aic bic) star(0.1 0.05 0.01)
b(%7.4f) stfmt(%7.4g)
----------------------------------------------------Variable | inf cinf cinf2 -------------+--------------------------------------unem | 0.4676 -0.5426** cunem | -0.8422** _cons | 1.4236 3.0306** -0.0782 -------------+--------------------------------------N | 49 48 48 r2 | .05272 .1078 .135 r2_a | .03257 .0884 .1162 aic | 252.9 224.2 222.7 bic | 256.6 228 226.5 ----------------------------------------------------legend: * p<.1; ** p<.05; *** p<.01
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SOAL B
Estimasi angka penggangguran alamiah berdasarkan hasil regresi persamaan (2) dan (3) pada soal A. . . . . .
* * * * *
Diketahui inft - infte = b1 (unemt - um) + et dimana infte = inft-1 jadi, inft - inft-1 = b1.um + b1.unwmt + et Dinft = b0 + b1.unwmt + et dimana: b0 = b1.um
. reg cinf
unem
Source | SS df MS -------------+------------------------------------------+-----------------------------Model | 33.3829988 1 33.3829988 Residual | 276.30513 46 6.00663326 -------------+------------------------------------------+----------------------------Total | 309.688129 47 6.58910913
Number of obs F( 1, 46) Prob > F R-squared Adj R-squared Root MSE
= = = = = =
48 5.56 0.0227 0.1078 0.0884 2.4508
---------------------------------------------------------------------------------------------------------------------------------------------------------cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-----------------------------------------------------+------------------------------------------------------------------------------------unem | -.5425869 .2301559 -2.36 0.023 -1.005867 -.079307 _cons | 3.030581 1.37681 2.20 0.033 .259206 5.801955 --------------------------------------------------------------------------------------------------------------------------------------------------------. * Jadi um (unemplaymet rate estimastion) . display 3.030581 / -.5425869 -5.5854297
Estimasi first order autocorrelation dari unem dengan menggunakan angka korelasi sample dari (unem ,unem t t-1) , Berdasarkan angka korelasi sampel; apakah unit root tsb mendekati satu?Apa artinya jika unit root mendekati satu? . . . . .
* * * * *
diketahui dalam pengujian Dickey-Fuller unit-root test test yt = p yt-1 + e yt - yt-1 = p yt-1 - yt-1 + e dyt = (p-1) yt-1 + e dimana q = (p-1)
. . . .
* * * *
diketahui dyt = b0 jika b0 signifikan jika q = 0 artinya jika b1 signifikan
+ q yt-1 + b1 year + e artinya random walk dengan drift tidak random walk atau no statisioner artinya random walk dengan trend waktu
. * DF memiliki hipotesis, H0: p=1 ==> q=0 ==> no statisioner || H1: p!=1 ==> q!=0 ==> stasioner . * jadi dalam pengujian Dickey-Fuller unit-root test untuk varibel unemt kita dapat melakukan regres dengan persamaan seperti berikut: . * diketahui dyt = q yt-1 +
e
. reg cunem unem_1, noc
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Source | SS df MS -------------+------------------------------------------+----------------------------Model | .288097988 1 .288097988 Residual | 58.7318998 47 1.24961489 -------------+------------------------------------------+----------------------------Total | 59.0199978 48 1.22958329
Number of obs F( 1, 47) Prob > F R-squared Adj R-squared Root MSE
= 48 = 0.23 = 0.6333 = 0.0049 = -0.0163 = 1.1179
---------------------------------------------------------------------------------------------------------------------------------------------------------cunem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-----------------------------------------------------+------------------------------------------------------------------------------------unem_1 | -.0130067 .0270885 -0.48 0.633 -.0675017 .0414883 --------------------------------------------------------------------------------------------------------------------------------------------------------. dfuller unem, regres nocon Dickey-Fuller test for unit root
Number of obs
=
48
---------- Interpolated Dickey-Fuller --------Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --------------------------------------------------------------------------------------------------------------------------------------------------------Z(t) -0.480 -2.623 -1.950 -1.609 ---------------------------------------------------------------------------------------------------------------------------------------------------------D.unem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------+-------------------------------------------------------------------------------------unem | L1. | -.0130067 .0270885 -0.48 0.633 -.0675017 .0414883 --------------------------------------------------------------------------------------------------------------------------------------------------------. * diketahui dyt = b0 + q yt-1 + e . reg cunem unem_1 Source | SS df MS -------------+------------------------------------------+-----------------------------Model | 8.38981516 1 8.38981516 Residual | 50.5768493 46 1.09949672 -------------+------------------------------------------+----------------------------Total | 58.9666644 47 1.25460988
Number of obs F( 1, 46) Prob > F R-squared Adj R-squared Root MSE
= = = = = =
48 7.63 0.0082 0.1423 0.1236 1.0486
---------------------------------------------------------------------------------------------------------------------------------------------------------cunem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------+-------------------------------------------------------------------------------------unem_1 | -.2676462 .0968906 -2.76 0.008 -.4626769 -.0726154 _cons | 1.571741 .5771181 2.72 0.009 .4100628 2.73342 --------------------------------------------------------------------------------------------------------------------------------------------------------. dfuller unem, regres Dickey-Fuller test for unit root
Number of obs
=
48
---------- Interpolated Dickey-Fuller --------Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --------------------------------------------------------------------------------------------------------------------------------------------------------Z(t) -2.762 -3.594 -2.936 -2.602 --------------------------------------------------------------------------------------------------------------------------------------------------------MacKinnon approximate p-value for Z(t) = 0.0639 ---------------------------------------------------------------------------------------------------------------------------------------------------------D.unem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------+--------------------------------------------------------------------------------------
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unem | L1. | -.2676462 .0968906 -2.76 0.008 -.462677 -.0726155 | _cons | 1.571741 .5771181 2.72 0.009 .4100629 2.73342 ---------------------------------------------------------------------------------------------------------------------------------------------------------
. * diketahui dyt = b0 + q yt-1 + b1 year + e . reg cunem unem_1 year Source | SS df MS -------------+------------------------------------------+-----------------------------Model | 10.074198 2 5.03709899 Residual | 48.8924664 45 1.08649925 -------------+------------------------------------------+----------------------------Total | 58.9666644 47 1.25460988
Number of obs F( 2, 45) Prob > F R-squared Adj R-squared Root MSE
= = = = = =
48 4.64 0.0148 0.1708 0.1340 1.0424
---------------------------------------------------------------------------------------------------------------------------------------------------------cunem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-----------------------------------------------------+------------------------------------------------------------------------------------unem_1 | -.3507137 .1171655 -2.99 0.004 -.5866972 -.1147303 year | .0164492 .0132111 1.25 0.220 -.0101593 .0430576 _cons | -30.39676 25.68177 -1.18 0.243 -82.12249 21.32898 --------------------------------------------------------------------------------------------------------------------------------------------------------. dfuller unem, regres trend Dickey-Fuller test for unit root
Number of obs
=
48
---------- Interpolated Dickey-Fuller --------Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --------------------------------------------------------------------------------------------------------------------------------------------------------Z(t) -2.993 -4.168 -3.508 -3.185 --------------------------------------------------------------------------------------------------------------------------------------------------------MacKinnon approximate p-value for Z(t) = 0.1340 --------------------------------------------------------------------------------------------------------------------------------------------------------D.unem | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------+-------------------------------------------------------------------------------------unem | L1. | -.3507138 .1171655 -2.99 0.004 -.5866972 -.1147303 _trend | .0164492 .0132111 1.25 0.220 -.0101593 .0430576 _cons | 1.646202 .5768054 2.85 0.007 .4844567 2.807948 --------------------------------------------------------------------------------------------------------------------------------------------------------. * Kesimpulannya: unem random walk dengan drift
Bandingkan R-squares pada hasil hasil estimasi estimasi persamaan persamaan (2) dan (3) pada soal soal A, manakah yang lebih tinggi? Apakah hal ini terkait dengan adanya first order autocorrelation dari unem? Jelaskan . estimates table cinf cinf2 , stat(N r2 r2_a aic bic)
b(%7.4f) stfmt(%7.4g)
star(0.1 0.05 0.01) ---------------------------------------Variable | cinf cinf2 -------------+-------------------------unem | -0.5426** cunem | -0.8422**
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_cons | 3.0306** -0.0782 -------------+-------------------------N | 48 48 r2 | .1078 .135 r2_a | .0884 .1162 aic | 224.2 222.7 bic | 228 226.5 ---------------------------------------legend: * p<.1; ** p<.05; *** p<.01 . * cek serial correlation . * Persamaan ke dua (2) . quietly reg cinf unem . dwstat Durbin-Watson d-statistic(
2,
48) =
1.769648
. bgodfrey Breusch-Godfrey LM test for autocorrelation --------------------------------------------------------------------------------------------------------------------------------------------------lags(p) | chi2 df Prob > chi2 -------------+------------------------------------------------------------1 | 0.062 1 0.8039 --------------------------------------------------------------------------------------------------------------------------------------------------H0: no serial correlation . * Persamaan ke dua (3) . quietly reg cinf cunem . dwstat Durbin-Watson d-statistic(
2,
48) =
1.849401
. bgodfrey Breusch-Godfrey LM test for autocorrelation --------------------------------------------------------------------------------------------------------------------------------------------------lags(p) | chi2 df Prob > chi2 -------------+----------------------------------------------------+-------------------------------------------------------------------------------1 | 0.042 1 0.8385 --------------------------------------------------------------------------------------------------------------------------------------------------H0: no serial correlation
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