Y i = β 0 + β 1 X i + β 2 Z i + ε i
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1 Homework Exercise #7 Economics 4340 Fll 009 Dr. W. Ken Frr Nme Instructions: Answer the questions given below on lined sheets of pper (or they my be typed) nd provide ll the necessry printouts of informtion needed to support your nswers. Stple your ppers together. Be net so it cn be red!! Assume the following model: Y i = β 0 + β 1 X i + β Z i + ε i 1. Estimte the bove regression eqution using OLS nd print the results. Dependent Vrible: Y Dte: 10/7/09 Time: 11:3 C X Z R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion Log likelihood F-sttistic Durbin-Wtson stt.0355 Prob(F-sttistic)
2 . Test for heteroscedsticity in the error terms using the Prk Test (use the functionl form described in the text). Test X, Z, nd Yht. (α =.05) nd include the null nd lterntive hypotheses. Dependent Vrible: LOG(EHAT^) Dte: 10/7/09 Time: 11:4 C LOG(X) H : α= 0 0 H : α 0 reject null nd ccept lterntive given t-sttistic for log(x) bove Dependent Vrible: LOG(EHAT^) Dte: 10/7/09 Time: 11:5 C LOG(Z) H : α= 0 0 H : α 0 reject null nd ccept lterntive given t-sttistic for log(z) bove Dependent Vrible: LOG(EHAT^) Dte: 10/7/09 Time: 11:6 C LOG(YHAT) H : α= 0 0 H : α 0 reject null nd ccept lterntive given t-sttistic for log(yht) bove
3 3. Test for heteroscedsticity in the error terms using the Goldfeld-Qundt Test with the observtions ordered ccording to incresing vlues of X i (leve out the middle 6 observtions) (α =.05) nd include the null nd lterntive hypotheses. Dependent Vrible: Y Dte: 10/7/09 Time: 11:59 Smple: 1 17 Included observtions: 17 C X Z R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion Log likelihood F-sttistic Durbin-Wtson stt Prob(F-sttistic) Dependent Vrible: Y Dte: 10/7/09 Time: 1:00 Smple: 4 40 Included observtions: 17 C X Z R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion.55 Log likelihood F-sttistic Durbin-Wtson stt.3469 Prob(F-sttistic) H : σ =σ 0 c H : σ σ c Fstt= 5.741/1.893 = Fcrit therefore reject H 0
4 4. Test for heteroscedsticity in the error terms using White s Generl Heteroscedsticity Test (include the cross-product term). (α =.05) nd include the null nd lterntive hypotheses. White Heteroskedsticity Test: F-sttistic Prob. F(5,34) Obs*R-squred Prob. Chi-Squre(5) Test Eqution: Dependent Vrible: RESID^ Dte: 10/7/09 Time: 1:09 C X X^ X*Z Z Z^ R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion Log likelihood F-sttistic Durbin-Wtson stt Prob(F-sttistic) H : α = 0 0 i H : α 0 i χ =nr χ = 40* = stt χ = 5.99 crit Reject Ho
5 5. Assume tht heteroscedsticity hs been detected such tht: Vr(ε i ) = Ε(ε ) = σ i Yht i Re-estimte the bove eqution correcting for heteroscedsticity under these circumstnces using weighted lest squres (WLS). Dependent Vrible: Y/SQR(YHAT) Dte: 10/7/09 Time: 1: 1/SQR(YHAT) X/SQR(YHAT) Z/SQR(YHAT) R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion Log likelihood Durbin-Wtson stt.5576
6 6. Re-estimte the eqution in number 1 bove correcting for heteroscedsticity using the procedure vilble in the Eviews softwre tht increses the efficiency of the stndrd error estimtes using the White-Heteroscedsticity-Consistent Stndrd Errors nd Covrince procedure. Dependent Vrible: Y Dte: 10/7/09 Time: 1:4 White Heteroskedsticity-Consistent Stndrd Errors & Covrince C X Z R-squred Men dependent vr Adjusted R-squred S.D. dependent vr S.E. of regression Akike info criterion Sum squred resid Schwrz criterion Log likelihood F-sttistic Durbin-Wtson stt.0355 Prob(F-sttistic)
7 Y X Z
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