You may need to consider 2 plotting jbi j against xji

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
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