EMET2007 Lecture 7

# EMET2007 Lecture 7

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: peci…cation of the model to be tested b2 = δ0 + δ1 x1,i + δ2 x2,i + εi save + δk xk ,i + νi 2 Rb2 ε Regress squared residuals on all explanatory variables and test whether this regression has explanatory power. H0 : Var (εi jx1 , x2 , becomes H0 : δ 1 = δ 2 = Lecture 7 (heteroscedasticity) , xk ) = Var (εi jxi ) = σ2 = δk = 0 EMET2007/6007 24 th April 2013 16 / 34 The test statistic is F= 1 2 Rb2 /k ε 2 Rb2 / (n ε k 1) s F k ,n k1 2 A large test statistic (= a high Rb2 ) is evidence against the null hypothesis. ε Alternative test statistic (= Lagrange multiplier statistic, LM ) 2 LM = nRb2 s χ2 k ε 2 Again, high values of the test statistic (= high Rb2 ) lead to rejection of the ε null hypothesis that the expected value of ε2 is unrelated to the explanatory variables. Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 17 / 34 Example: Heteroscedasticity in housing price equations [ price = 21.77 + 0.0021lotsize + 0.123 sqrft + 13.85bdrms (29.48 ) 2 Rb2 ε (0.0006 ) = 0.1601 ) p (0.013 ) valueF = 0.002 and p (9.01 ) valueLM = 0.0028 This regression shows clear evidence of Heteroscedasticity \ log (price ) = 1.3 + 0.168 log (lotsize ) + 0.700 log (sqrft ) + 0.037 bdrms (0.65 ) 2 Rb2 ε (0.038 ) = 0.048 ) p (0.093 ) valueF = 0.245 and p (0.028 ) valueLM = 0.2390 In the logarithmic speci…cation, homoscedasticity cannot be rejected Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 18 / 34 White test for heteroscedasticity Speci…cation of the model to be tested 2 2 2 b2 = δ0 + δ1 x1 + δ2 x2 + δ3 x3 + δ4 x1 + δ5 x2 + δ6 x3 ε +δ7 x1 x2 + δ8 x1 x3 + δ9 x2 x3 + ν 2 save Rb2 ε Regress squared residuals on all explanatory variables, their squares, and interactions (here: example for k = 3) H0 : Var (εi jx1 , x2 , becomes H0 : δ 1 = δ 2 = , xk ) = Var (εi jxi ) = σ2 = δ9 = 0 Advantage: The White test detects more general deviations from homoscedasticity than the Breusch-Pagan test Disadvantage: Including all squ...
View Full Document

## This note was uploaded on 06/15/2013 for the course EMET 2007 taught by Professor Strachan during the Two '13 term at Australian National University.

Ask a homework question - tutors are online