Chapter8多重共线性 Multicollinearity
Chapter 8 多重共线性 Multicollinearity
1.何谓 Multicollinearity Y=Ⅹb+ Y=:,X 12 k2 n One of the conditions for ols: rank(X=k +l<n
1. 何谓 Multicollinearity One of the conditions for OLS: 11 1 0 1 1 12 2 1 2 1 1 1 , , , 1 k k n n kn k n X X b Y X X b Y X X b = + = = = = Y Xb ε Y X b ε rank( )= 1 X k n +
oLSE for the CMlrM: b=(XXXY 若干个自变量存在较高程度的近似线性关系。即有 XX≈0 或者,有 X≈a0+a1X1+…+a1X1+a11+…+ a,x a不全为零
OLSE for the CMLRM: 若干个自变量存在较高程度的近似线性关系。即有 或者，有 X X 0 1 ˆ ( − b X X) X Y = 0 1 1 1 1 1 1 1 , , i i i i i k k k X a a X a X a X a X a a − − + + + + + + + + 不全为零
2. Causes for multicollinearity 有关经济变量(因素)是线性或近似线性相关的 样本原因(碰巧是线性或近似线性相关的) 模型误设 3. Aftermath var(b)=El(b-b(b-b)=0(XX) Ⅴar(b,)变得很大,工检验失灵
2. Causes for multicollinearity 有关经济变量（因素）是线性或近似线性相关的. 样本原因（碰巧是线性或近似线性相关的） 模型误设 3. Aftermath 变得很大。T-检验失灵。 2 1 ˆ ˆ ˆ var( ) E[( )( ) ] ( ) − b b b b b X X = − − = ˆ var( )j b
4. Testing for multicollinearity 1)Correlation Matrix 2)R-sq, F-statistic and t-statistics 3)Regress X1=a+a1A1+…+a1X1+a1X1+…+ a, x R-sq R X Variance inflation factor (IF) VIF()=-1
4. Testing for multicollinearity 1) Correlation Matrix 2) R-sq, F-statistic and t-statistics 3) Regress R-sq: Variance inflation factor (VIF): X a a X a X a X a X i i i i i k k 0 1 1 1 1 1 1 − − + + = + + + + + + 2 Xi R 2 1 VIF( ) ˆ 1 i i X b R = −