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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 BreuschPagan test
Disadvantage: Including all squ...
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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.
 Two '13
 strachan

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