tailieunhanh - Lecture Advanced Econometrics (Part II) - Chapter 8: Heteroskedasticity

Lecture "Advanced Econometrics (Part II) - Chapter 8: Heteroskedasticity" presentation of content: Proterties of ols in rpesence of heteroskedasticity, teesting for heteroskedasticity, treatment for heteroskedasticity. | Advanced Econometrics Chapter 8 Heteroskedasticity Chapter 8 HETEROSKEDASTICITY r Problem of non-constant error variances Var Sị ơf ơị violated assumption E sể Ơ2I E ss E diagonal matrix with non-constant elements on diagonal ơi . flx1 I. PROPERTIES OF OLS IN PRESENCE OF HETEROSKEDASTICITY 1. 3ols is still unbiased still consistent if X is stochastic . 2. jjOLS is not best efficient because GLS estimators are best jjOLS has variance which are large than jGLS s variances. 3. The standard errors of jj s are biased because they are based on incorrect formula. Wrong OLS formula VarCov jjOLS Ơ2 X X -1 Correct OLS formula VarCov jOLS X X -1X EX X X -1 with E E Note VarCov OLS E j - j j - j E X X -1X ss YX X X -1 X X -1X EX X X -1 If we know the form of the heteroskedasticity that is Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 8 Heteroskedasticity E Ơ2 0 0 0 ơ 0 known. 00 2 n ơ we can apply Weighted Least Squares Í f P2 Pk t X Ì l ơ f f 8 í Generally however form of heteroskedasticity is unknown. Usually sources of heteroskedasticity are differences in some scale factor independent variables . EX C P1 P21 8 Ci . ith individual expenditures of clothes I ith individual income. II. TESTING FOR HETEROSKEDASTICITY Because OLS estimator of p is still consistent if there is heteroskedasticity we can use the OLS residuals to construct at least asymptotically valid test for this problem. 1. Goldfeld - Quandt test Y P1 P2 X P3Z 8 Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 8 Heteroskedasticity Ha f Xi f . 8 Xi suspected scale factor H0 ơf ơl Constant Ha ơf is not a constant. order the observations by size of Xi Divide sample into 3 parts a . 1 observations the 1st 40 of the observations. b . n2 observations the last 40 of the observations. Apply OLS to n1 get ESS1. Apply OLS to n2 get ESS2. ESS 2 F 1- a 2 ESS 2 F n_kn - if 1