KULIAH 12 1

 Nature of the problem: X’X matrix must not be singular  why?  Ada hubungan linier antar beberapa (atau semua) variabel bebas.  Perfect:  Not perfect: 2

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 Metode pengumpulan data, sampel diambil dari populasi dgn lingkup terbatas  Keterbatasan model/populasi, ex: Y= konsumsi listrik, X1 = pendapatan ruta, X2 = luas rumah  Spesifikasi model, ex: menambahkan variabel polinomial pada data X yg terbatas  Overdetermined model: #paramater > # obs  Common trend, ex: income, poupulation, wealth growing over time at more or less the same rate 4

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Apa komentar Anda ? 7

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 Estimasi parameter tidak stabil 9

 1. High R 2 but few significant t ratios.  2. High pair-wise correlations among regressors. (tapi kdg terjadi juga meski r ij rendah)  3. Examination of partial correlations. Misal:  = 1  if r ij = 0.5  R 2 tinggi tapi partial-R 2 rendah 10

 4. Auxiliary regressions.  to regress each X i on the remaining X variables and compute the corresponding R 2 (R 2 i )  F i sig  X i collinearity with other X  Rule of thumb: R 2 i > R 2  multicollinearity problem 11

 5. Eigenvalues and condition index. (SAS)  CI  6. Tolerance (TOL) and variance inflation factor (VIF). moderatestrong severe low 12

 r 23 = koef. korelasi antara X2 dan X3   r 23  ,,    r 23 = 1 ? 13

 Kecepatan kenaikan var-covar  variance inflation factor (VIF) 14

  VIF   prob. multikolinierity   Rule of thumb: VIF > 10  high multicollinearity  0 ≤ TOL j ≤ 1 15

 Do nothing ??!  1. Apriori information: berdasar teori or pengalaman sebelumnya  didapat  didapat dari hubungan 16

 2. Combining cross-sectional and time series data.  Time series view: Price & income sgt berkorelasi  multikolinieriti   estimate regresi (time series)  Dimana (regresi cross section) 17

 3. Dropping a variable(s) and specification bias.  Ex: consumption = f (income, wealth) (cth sebelumnya)   income & wealth berkorelasi  hapus wealth dari model  Tapi jika teori menyatakan bhw fungsi diatas berlaku, maka menghapus wealth dari model akan mengakibatkan bias spesifikasi.  True model:  Estimated by:   b 32 = koef regresi b 3 atas b 2  Jika > 0  b12 over estimate dari β 2 (bias +)  Jika < 0  b12 under estimate dari β 2 (bias -) 18

 4. Transformasi variabel  First differencing  Ratio transformation  Y = konsumsi, X2 = PDB, X3 = Jml Pddk   PDB & Jml Pddk “grow over time”  berkorelasi  Regresi per kapita penduduk: Be careful of new problem: serially correlated error, heteroscedasticity, 19

 5. Menambah jumlah data (observasi)  n = 10   n = 40   6. Reducing collinearity in polynomial regressions. Transform variables in deviation form.  7. Other methods of remedying multicollinearity, ex: factor analysis, ridge regression, principal component regression 20