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Unformatted text preview: ares and interactions leads to a large
number of estimated parameters (e.g. k = 6 leads to 27 parameters
to be estimated)
Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 19 / 34 Alternative form of the White test
b2 = δ0 + δ1 y + δ2 y 2 + ν
b save 2
ε This regression indirectly tests the dependence of the squared residuals on
the explanatory variables, their squares, and interactions, because the
predicted value of y and its square implicitly contain all of these terms.
H0 : Var (εi jx1 , x2 ,
LM : , xk ) = Var (εi jxi ) = σ2 δ1 = δ2 = 0 2
= nRb2 s χ2
ε Example: Heteroscedasticity in (log) housing price equations
Rb2 = 0.0392 LM = 88 (0.0392) t 3.45 p
Lecture 7 (heteroscedasticity) EMET2007/6007 value = 0.178 24 th April 2013 20 / 34 What can I do about it (I)?
Adjust the data to remove it - Weighted least squares (WLS)
To use this form of WLS, we …rst assume that the form of the
heteroscedasticity is known up to a multiplicative constant
Var (εi jx1 , x2 , , xk ) = σ2 h (xi ) , h (xi ) = hi > 0 That is, The functional form of the heteroscedasticity, hi , is known
The transformation we apply will result in an error with a constant
variance, σ2 Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 21 / 34 With this function we transform the variables as follows.
yi where εi = β0 + β1 x1,i + β2 x2,i +
+ βk xk ,i + εi
s N 0, σ h (xi )
= β0 p + β1 p + β2 p +
+ β k p ,i + p
= β0 x0,i + β1 x1,i + β2 x2,i +
+ βk xk ,i + εi
s N 0, σ The Transformed model (Note that this regression model has no intercept)
yi = β0 x0,i + β1 x1,i + β2 x2,i + + βk xk ,i + εi has the new regressand yi and the regressors xj ,i
Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 22 / 34 Example: Savings and income
savi = β0 + β1 inci + εi
Var (εi jinci ) = σ2 inci
) hi = inci ) hi = inci Transform (Note that this regression mod...
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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