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 9.60109 1.377976 6.981334 0.0000 X 0.09138 0.0063 14.45436 0.0000 Z -0.514351 0.051565-9.97486 0.0000 R-squred 0.987846 Men dependent vr 16.05000 Adjusted R-squred 0.987189 S.D. dependent vr 4.96391 S.E. of regression 0.48697 Akike info criterion 1.468044 Sum squred resid 8.749938 Schwrz criterion 1.594710 Log likelihood -6.36089 F-sttistic 1503.585 Durbin-Wtson stt.0355 Prob(F-sttistic) 0.000000
. 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 -7.375 7.39798-3.68113 0.0007 LOG(X) 5.011914 1.518478 3.300616 0.001 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 4.46136.176007.0505 0.0473 LOG(Z) -3.099118 0.915730-3.38431 0.0017 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 -13.97406 3.09650-4.518473 0.0001 LOG(YHAT) 4.06473 1.1886 3.617887 0.0009 H : α= 0 0 H : α 0 reject null nd ccept lterntive given t-sttistic for log(yht) bove
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 -.99438 14.71831-0.0344 0.8417 X 0.178338 0.095361 1.87016 0.085 Z -0.301694 0.96575-1.01760 0.363 R-squred 0.950805 Men dependent vr 1.17647 Adjusted R-squred 0.943777 S.D. dependent vr 1.550617 S.E. of regression 0.36767 Akike info criterion 0.995533 Sum squred resid 1.89556 Schwrz criterion 1.14571 Log likelihood -5.46033 F-sttistic 135.91 Durbin-Wtson stt.09639 Prob(F-sttistic) 0.000000 Dependent Vrible: Y Dte: 10/7/09 Time: 1:00 Smple: 4 40 Included observtions: 17 C 4.60156 5.444699 0.845139 0.41 X 0.107481 0.018347 5.858353 0.0000 Z -0.198560 0.337396-0.588507 0.5656 R-squred 0.959505 Men dependent vr 0.11765 Adjusted R-squred 0.95370 S.D. dependent vr.97665 S.E. of regression 0.64035 Akike info criterion.105187 Sum squred resid 5.740707 Schwrz criterion.55 Log likelihood -14.89409 F-sttistic 165.865 Durbin-Wtson stt.3469 Prob(F-sttistic) 0.000000 H : σ =σ 0 c H : σ σ c Fstt= 5.741/1.893 = 3.033 --- Fcrit.53 --- therefore reject H 0
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 9.983704 Prob. F(5,34) 0.000006 Obs*R-squred 3.79380 Prob. Chi-Squre(5) 0.00038 Test Eqution: Dependent Vrible: RESID^ Dte: 10/7/09 Time: 1:09 C -9.7380 16.60657-5.556463 0.0000 X 0.847981 0.149054 5.689071 0.0000 X^ -0.00186 0.00030-5.707107 0.0000 X*Z -0.035449 0.006641-5.33770 0.0000 Z 7.10441 1.344603 5.83656 0.0000 Z^ -0.119795 0.03987-4.99455 0.0000 R-squred 0.594845 Men dependent vr 0.18748 Adjusted R-squred 0.53564 S.D. dependent vr 0.330958 S.E. of regression 0.560 Akike info criterion -0.0045 Sum squred resid 1.730743 Schwrz criterion 0.50880 Log likelihood 6.049037 F-sttistic 9.983704 Durbin-Wtson stt.98364 Prob(F-sttistic) 0.000006 H : α = 0 0 i H : α 0 i χ =nr χ = 40*.594845 = 3.7938 stt χ = 5.99 crit Reject Ho
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) 9.9553 1.360391 7.96078 0.0000 X/SQR(YHAT) 0.09006 0.006516 13.817 0.0000 Z/SQR(YHAT) -0.56117 0.047675-11.03539 0.0000 R-squred 0.956631 Men dependent vr 3.97430 Adjusted R-squred 0.95486 S.D. dependent vr 0.53785 S.E. of regression 0.114997 Akike info criterion -1.415787 Sum squred resid 0.48997 Schwrz criterion -1.8911 Log likelihood 31.31575 Durbin-Wtson stt.5576
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 9.60109 1.141966 8.4416 0.0000 X 0.09138 0.00593 15.40606 0.0000 Z -0.514351 0.036538-14.07716 0.0000 R-squred 0.987846 Men dependent vr 16.05000 Adjusted R-squred 0.987189 S.D. dependent vr 4.96391 S.E. of regression 0.48697 Akike info criterion 1.468044 Sum squred resid 8.749938 Schwrz criterion 1.594710 Log likelihood -6.36089 F-sttistic 1503.585 Durbin-Wtson stt.0355 Prob(F-sttistic) 0.000000
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