EMET2007 Lecture 7

# You may need to consider 2 plotting jbi j against xji

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Unformatted text preview: r. You may need to consider 2 plotting jbi j against xji or ln xji or ... ε Note that the relationship may be over many xji . You may need to consider plotting jbi j against x1i and x2i and ... or against yi ε Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 10 / 34 An example: Explaining wages wage = [ 3.96 + 0.595educ + 0.268exper b = wage ε 0.005exper 2 wage the residuals [ We plot the bi against educi and then we plot the jbi j against educi ε ε Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 11 / 34 15 10 Residuals 5 0 -5 0 Lecture 7 (heteroscedasticity) 5 10 years of education EMET2007/6007 15 20 24 th April 2013 12 / 34 15 10 arr 5 0 0 Lecture 7 (heteroscedasticity) 5 10 years of education EMET2007/6007 15 20 24 th April 2013 13 / 34 How can I tell if I have it? Formal evidence from Testing for heteroscedasticity It is important to know whether there is heteroscedasticity because then OLS may not be the most e¢ cient linear estimator anymore Breusch-Pagan test for heteroscedasticity H0 : Var (εi jx1 , x2 , , xk ) = Var (εi jxi ) = σ2 That is, the null hypothesis states that Var (εi jxi ) = Var (εi ) is not a function of xi Under MLR.4: Var (εi jxi ) = E ε2 jxi [E (εi jxi )]2 = E ε2 jxi i i ) E ε2 jxi = E ε2 = σ2 i i The mean of ε2 must not vary with x1 , x2 , i Lecture 7 (heteroscedasticity) EMET2007/6007 , xk 24 th April 2013 14 / 34 Breusch-Pagan test for heteroscedasticity (cont.) The alternative hypothesis: H1 H1 : Var (εi jx1 , x2 , , xk ) = Var (εi jxi ) = f (xi ) That is, the alternative hypothesis states that the variance changes with xi (or Var (εi jxi ) 6= Var (εi )) The mean of ε2 may vary with x1 , x2 , i Lecture 7 (heteroscedasticity) EMET2007/6007 , xk 24 th April 2013 15 / 34 Breusch-Pagan test for heteroscedasticity (cont.) S...
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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.

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