Ekonometrika ilustrasi permasalah multiple regression dengan software
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Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software. Pendugaan Model Cobb Douglas. Data pada file Excell Tugas , sheet CobbDouglas

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Ekonometrika ilustrasi permasalah multiple regression dengan software

Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software

Dr. Rahma Fitriani, S.Si., M.Sc


Pendugaan model cobb douglas
Pendugaan Model Cobb Douglas

  • Data pada file ExcellTugas, sheet CobbDouglas

  • Dari 51 perusahaandiamatiproduktivitas (OUTPUT dalam $), investasiuntuk modal (CAPITAL dalam $) daninvestasitenagakerja (LABOR dalam $)

  • Dilakukan pendugaan model

Dr. Rahma Fitriani, S.Si., M.Sc


Uji keberartian model secara simultan
UjiKeberartian Model secaraSimultan

  • Menggunakanujihipotesis

  • Model unrestricted:

  • Model restricted

  • Hipotesis

Dr. Rahma Fitriani, S.Si., M.Sc


Output untuk unrestricted model
Output untuk Unrestricted Model

  • Model 1: OLS, using observations 1-51

  • Dependent variable: l_output

  • coefficient std. error t-ratio p-value

  • ----------------------------------------------------------

  • const 3.88760 0.396228 9.812 4.70e-013 ***

  • l_labor 0.468332 0.0989259 4.734 1.98e-05 ***

  • l_capital 0.521279 0.0968871 5.380 2.18e-06 ***

  • Mean dependent var 16.94139 S.D. dependent var 1.380870

  • Sum squared resid 3.415520 S.E. of regression 0.266752

  • R-squared 0.964175 Adjusted R-squared 0.962683

  • F(2, 48) 645.9311 P-value(F) 2.00e-35

  • Log-likelihood -3.426721 Akaike criterion 12.85344

  • Schwarz criterion 18.64892 Hannan-Quinn 15.06807

  • Log-likelihood for output = -867.437

JKGU= 3.4155

Dr. Rahma Fitriani, S.Si., M.Sc


Output untuk restricted model
Output Untuk Restricted Model

  • Model 2: OLS, using observations 1-51

  • Dependent variable: l_output

  • coefficient std. error t-ratio p-value

  • ---------------------------------------------------------

  • const 16.9414 0.193361 87.62 2.12e-056 ***

  • Mean dependent var 16.94139 S.D. dependent var 1.380870

  • Sum squared resid 95.34013 S.E. of regression 1.380870

  • R-squared 0.000000 Adjusted R-squared 0.000000

  • Log-likelihood -88.31931 Akaike criterion 178.6386

  • Schwarz criterion 180.5704 Hannan-Quinn 179.3768

  • Log-likelihood for output = -952.33

JKGR= 95.34

Dr. Rahma Fitriani, S.Si., M.Sc


Output omitted variable test
Output Omitted variable Test

Samadengan output sebelumnya Restricted Model

  • Model 3: OLS, using observations 1-51

  • Dependent variable: l_output

  • coefficient std. error t-ratio p-value

  • ---------------------------------------------------------

  • const 16.9414 0.193361 87.62 2.12e-056 ***

  • Mean dependent var 16.94139 S.D. dependent var 1.380870

  • Sum squared resid 95.34013 S.E. of regression 1.380870

  • R-squared 0.000000 Adjusted R-squared 0.000000

  • Log-likelihood -88.31931 Akaike criterion 178.6386

  • Schwarz criterion 180.5704 Hannan-Quinn 179.3768

  • Log-likelihood for output = -952.33

  • Comparison of Model 1 and Model 3:

  • Null hypothesis: the regression parameters are zero for the variables

  • l_labor, l_capital

  • Test statistic: F(2, 48) = 645.931, with p-value = 1.99686e-035

  • Of the 3 model selection statistics, 0 have improved.

Statistikuji F

Dr. Rahma Fitriani, S.Si., M.Sc


  • Karena p-value relatifkecil, menujunol

    • Cukupbuktiuntukmenolak H0

  • Koefisienbagipeubah Labour dan Capital tidaksamadengannol

  • Unrestricted model berbedanyatadengan restricted model

  • Unrestricted model lebihbaikmenjelaskankeragamanOutput produksi

Dr. Rahma Fitriani, S.Si., M.Sc


Uji linear restriction
UjiLinear Restriction

  • Menggunakanujihipotesis

  • Model unrestricted:

  • Restritcionpadahipotesis:

  • Model restricted:

Dr. Rahma Fitriani, S.Si., M.Sc


Output untuk unrestricted model1
Output untuk Unrestricted Model

  • Model 1: OLS, using observations 1-51

  • Dependent variable: l_output

  • coefficient std. error t-ratio p-value

  • ----------------------------------------------------------

  • const 3.88760 0.396228 9.812 4.70e-013 ***

  • l_labor 0.468332 0.0989259 4.734 1.98e-05 ***

  • l_capital 0.521279 0.0968871 5.380 2.18e-06 ***

  • Mean dependent var 16.94139 S.D. dependent var 1.380870

  • Sum squared resid 3.415520 S.E. of regression 0.266752

  • R-squared 0.964175 Adjusted R-squared 0.962683

  • F(2, 48) 645.9311 P-value(F) 2.00e-35

  • Log-likelihood -3.426721 Akaike criterion 12.85344

  • Schwarz criterion 18.64892 Hannan-Quinn 15.06807

  • Log-likelihood for output = -867.437

JKGU= 3.4155

Dr. Rahma Fitriani, S.Si., M.Sc


Output linear restricted model
Output Linear Restricted Model

  • Model 4: OLS, using observations 1-51

  • Dependent variable: l_Out_Labor

  • coefficient std. error t-ratio p-value

  • --------------------------------------------------------------

  • const 3.75624 0.185368 20.26 1.82e-025 ***

  • l_Capital_Lab 0.523756 0.0958122 5.466 1.54e-06 ***

  • Mean dependent var 4.749135 S.D. dependent var 0.332104

  • Sum squared resid 3.425582 S.E. of regression 0.264405

  • R-squared 0.378823 Adjusted R-squared 0.366146

  • F(1, 49) 29.88247 P-value(F) 1.54e-06

  • Log-likelihood -3.501733 Akaike criterion 11.00347

  • Schwarz criterion 14.86712 Hannan-Quinn 12.47988

  • Log-likelihood for Out_Labor = -245.708

JKGR= 3.4255

Dr. Rahma Fitriani, S.Si., M.Sc


Output linear restriction test
Output Linear Restriction Test

  • Restriction:

  • b[l_labor] + b[l_capital] = 1

  • Test statistic: F(1, 48) = 0.141406, with p-value = 0.708544

  • Restricted estimates:

  • coefficient std. error t-ratio p-value

  • ----------------------------------------------------------

  • const 3.75624 0.185368 20.26 1.82e-025 ***

  • l_labor 0.476244 0.0958122 4.971 8.56e-06 ***

  • l_capital 0.523756 0.0958122 5.466 1.54e-06 ***

  • Standard error of the regression = 0.264405

Dr. Rahma Fitriani, S.Si., M.Sc


  • Karena p-value yang cukupbesar, tidakcukupbuktiuntukmenolak H0

  • Restricted dan unrestricted model tidakberbedanyata

  • Jumlahdarikedua parameter = 1

  • Penduga model:

^l_output = 3.89 + 0.468*l_labor + 0.521*l_capital

(0.396)(0.0989) (0.0969)

n = 51, R-squared = 0.964

(standard errors in parentheses)

Dr. Rahma Fitriani, S.Si., M.Sc


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