Chapter5异方差 Heteroskedasticity
Chapter 5 异方差 Heteroskedasticity
1. Recall the assumption for the cmlrm var(;)=σ= const.i=1l,…,n (Homoskedasticity) 2. Counterexamples 1)rich family and poor family expenditures 2)large company and small company sales There exists heteroskedasticity in lots of econometric problems
1. Recall the assumption for the CMLRM: (Homoskedasticity) 2. Counterexamples 1) rich family and poor family expenditures; 2) large company and small company sales. There exists heteroskedasticity in lots of econometric problems. 2 var( ) const. 1, , i = = =i n
3. What happens if there is heteroske dasticity in an econometric problem? 1) The Ols estimators are maybe not blues( they are not efficient 2) The hypothesis tests for the parameters do not hold good though they is very important and so on
3. What happens if there is heteroskedasticity in an econometric problem? 1) The OLS estimators are maybe not Blues (they are not efficient ). 2) The hypothesis tests for the parameters do not hold good though they is very important. and so on
4. Tests for Heteroskedasticity 1) Goldfeld-Quandt Test Given a sample with size n (1) Sort it by the order of an independent variable and then portion it into three parts Sub-sample 1 with size n1 Sub-sample 2 with size n2 Sub-sample 3 with size n3 1 tn<n
4. Tests for Heteroskedasticity 1) Goldfeld-Quandt Test: Given a sample with size n (1) Sort it by the order of an independent variable and then portion it into three parts. Sub-sample 1 with size n1 Sub-sample 2 with size n2 Sub-sample 3 with size n3 1 3 n n n +
(2)Estimate the regression equation with sub-sample 1 and 3 respectively (3)let k-1 (4)Test H0:=G3wH1:≠σ
(2) Estimate the regression equation with sub-sample 1 and 3 respectively. (3) let (4) Test 2 2 1 1 1 ˆ 1 e n k = − − 2 2 3 3 3 ˆ 1 e n k = − − 2 2 2 2 0 1 3 1 1 3 H H : vs : =