Introduc tion to E c onome tric s Cha pte r 6 E ze quie l Urie l - PowerPoint PPT Presentation

Introduc tion to E c onome tric s Cha pte r 6 E ze quie l Urie l Jimé ne z Unive rsity of Va le nc ia Va le nc ia , Se pte mbe r 2013

6 Re la xing the a ssumptions in the line a r c la ssic a l mode l 6.1 Re la xing the a ssumptions in the line a r c la ssic a l mode l: a n ove rvie w 6.2 Misspe c ific a tion 6.3 Multic olline a rity 6.4 Norma lity te st 6.5 He te roske da stic ity 6.6 Autoc orre la tion E xe rc ise s Appe ndix

6.2 Misspe c ific a tion 6 Relaxing the assumptions in the linear classical   T ABL E 6.1. Summa ry of bia s in whe n x 2 is omitte d in e stima ting e qua tion. 2 Corr(x 2 , x 3 )>0 Corr(x 2 , x 3 )<0  3 >0 Positive bias Negative bias model  3 <0 Negative bias Positive bias [3]

6.2 Misspe c ific a tion E XAMPL E 6.1 Misspe c ific a tion in a mode l for de te rmina tion of wa g e s 6 Relaxing the assumptions in the linear classical (file wa g e 06sp) = b + b + b + Initial model wage educ tenure u 1 2 3  = + + wage 4.679 0.681 educ 0.293 tenure i i i (1.55) (0.146) (0.071) model = = 2 R 0.249 n 150 init   2 3 = b + b + b + a + a + Augmented model wage educ tenure wage wage u 1 2 3 1 1 = 2 R 0.289 augm  2 2 ( R R ) / r   augm init F 4.18   2 (1 R ) / ( n h ) augm [4]

6.3 Multic olline a rity E XAMPL E 6.2 Ana lyzing multic olline a rity in the c a se of la bor a bse nte e ism 6 Relaxing the assumptions in the linear classical (file a bse nt) ole ra nc e a nd VIF T ABL E 6.2. T . Collinearity statistics model VIF Tolerance age 0.2346 42.634 tenure 0.2104 47.532 wage 0.7891 12.673 [5]

6.3 Multic olline a rity E XAMPL E 6.3 Ana lyzing the multic olline a rity of fa c tors de te rmining time 6 Relaxing the assumptions in the linear classical de vote d to house work (file timuse 03)            houswork educ hhinc age paidwork u 1 2 3 4 5  542.14     max 8782   7.06 E 06 min model T ABL E 6.3. E ig e nva lue s a nd va ria nc e de c omposition proportions. Eigenvalues 7.03E-06 0.000498 0.025701 1.861396 542.1400 Va ria nc e de c omposition proportions Associated Eigenvalue Variable 1 2 3 4 5 C 0.999995 4.72E-06 8.36E-09 1.23E-13 1.90E-15 EDUC 0.295742 0.704216 4.22E-05 2.32E-09 3.72E-11 HHINC 0.064857 0.385022 0.209016 0.100193 0.240913 AGE 0.651909 0.084285 0.263805 5.85E-07 1.86E-08 PAIDWORK 0.015405 0.031823 0.007178 0.945516 7.80E-05 [6]

6.4 Norma lity te st 6 Relaxing the assumptions in the linear classical E XAMPL E 6.4 Is the hypothe sis of norma lity a c c e pta ble in the mode l to a na lyze the e ffic ie nc y of the Ma drid Stoc k E xc ha ng e ? (file bolma de f) n =247 model T ABL E 6.4. Norma lity te st in the mode l on the Ma drid Stoc k E xc ha ng e . skewness Bera and Jarque kurtosis coefficient coefficient statistic -0.0421 4.4268 21.0232 [7]

6.5 He te roske da stic ity 6 Relaxing the assumptions in the linear classical  y y                                                             model                        x x F IGURE 6.1. Sc a tte r dia g ra m F IGURE 6.2. Sc a tte r dia g ra m c orre sponding to a mode l with c orre sponding to a mode l with homoske da stic disturba nc e s. he te roske da stic disturba nc e s. [8]

6.5 He te roske da stic ity E XAMPL E 6.5 Applic a tion of the Bre usc h- Pa g a n- Godfre y te st 6 Relaxing the assumptions in the linear classical 6.5. Hoste l a nd inc da ta . T ABL E i hostel inc 1 17 500 2 24 700 3 7 250 4 17 430 5 31 810 6 3 200 7 8 300 model 8 42 760 9 30 650 10 9 320  b + b + hostel inc u S te p 1. Applying OL S to the mo de l, 1 2 using data fro m table 6.5, the fo llo wing e stimate d mo de l is o btaine d:  = - + hostel 7.427 0.0533 inc i i (3.48) (0.0065) T he re siduals c o rre spo nding to this fitte d mo de l appe ar in table 6.6 . [9]

6.5 He te roske da stic ity E XAMPL E 6.5 Applic a tion of the Bre usc h- Pa g a n- Godfre y te st. (Cont.) 6 Relaxing the assumptions in the linear classical 6.6. Re sidua ls of the re g re ssion of hoste l on inc . T ABL E i 1 2 3 4 5 6 7 8 9 10 ˆ i u -2.226 -5.888 1.1 1.505 -4.751 -0.234 -0.565 8.913 2.777 -0.631 S te p 2. T he auxiliary re gre ssio n model       2 ˆ u inc i 1 2 i i     2 2 ˆ u 23.93 0.0799 inc R 0. 0 5 45 i S te p 3. T he BPG statistic s is: ( ) = = = 2 BPG nR 10 0.56 5.05 ar  2(0.05) S te p 4. Give n that =3.84, the null hypo the sis o f ho mo ske dastic ity is 1 re je c te d fo r a signific anc e le ve l o f 5%, but no t fo r the signific anc e le ve l o f 1%. [10]

6.5 He te roske da stic ity 6.6 Applic a tion of the White te st E XAMPL E 6 Relaxing the assumptions in the linear classical S te p 1. T his ste p is the same as in the Bre usc h-Pagan-Go dfre y te st. S te p 2. T he re gre sso rs o f the auxiliary re gre ssio n will be    1 i 1 i    1 inc 2 i i   2 inc 3 i i model         2 2 ˆ u inc inc i 1 2 i 3 i i     2 2 2 ˆ u 14.29 0.10 inc 0.00018 inc R 0. 56 i i i S te p 3. T he W statistic : ( ) = = = 2 W nR 10 0.56 5.60  2(0.10) S te p 4. Give n that =4.61, the null hypo the sis o f ho mo ske dastic ity is 2 re je c te d fo r a 10% signific anc e le ve l be c ause W=nR 2 >4.61, but no t fo r signific anc e le ve ls o f 5% and 1%. [11]

6.5 He te roske da stic ity E XAMPL E 6.7 He te roske da stic ity te sts in mode ls e xpla ining the ma rke t va lue of the Spa nish ba nks (file bolma d95) 6 Relaxing the assumptions in the linear classical e te ro ske dastic ity in the line ar mo de l  H  = b + b + + = marktval bookval u marktval 29.42 1.219 bookval n 20 1 2 (30.85) (0.127) 400 350 Residuals in absolute value 300 250 200 150 100 model 50 0 0 100 200 300 400 500 600 700 bookval GRAPHIC 6.1. Sc a tte r plot be twe e n the re sidua ls in a bsolute va lue a nd the va ria ble bookval in the line a r mode l.     2 BPG nR 20 0.5220 10.44 ar  2(0.01) As =6.64<10.44, the null hypo the sis o f ho mo ske dastic ity is re je c te d 1 fo r a signific anc e le ve l o f 1%, and the re fo re fo r  =0.05 and fo r  =0.10.l     2 W nR 20 0.6017 12.03 ar  2(0.01) As =9.21<12.03, the null hypo the sis o f ho mo ske dastic ity is re je c te d fo r 2 [12] a signific anc e le ve l o f 1%.

6.5 He te roske da stic ity E XAMPL E 6.7 He te roske da stic ity te sts in mode ls e xpla ining the ma rke t va lue of the Spa nish ba nks (Cont.) 6 Relaxing the assumptions in the linear classical H e te ro ske dastic ity in the lo g-lo g mo de l   + ln( marktval ) 0.676 0.9384ln( bookval ) (0.265) (0.062) 1.0 0.9 0.8 Residuals in absolute value 0.7 0.6 0.5 0.4 0.3 model 0.2 0.1 0.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 ln(bookval) GRAPHIC 6.2. Sc a tte r plot be twe e n the re sidua ls in a bsolute va lue a nd the va ria ble bookval in the log - log mode l. T ABL E 6.7. T e sts of he te roske da stic ity on the log -log mode l to e xpla in the ma rke t va lue of Spa nish ba nks. Test Statistic Table values  2(0.10) 2 nR Breusch-Pagan BP = =1.05 =4.61 2 ra  2 2(0.10) nR White W = =2.64 =4.61 [13] ra 2

6.5 He te roske da stic ity E XAMPL E 6.8 Is the re he te roske da stic ity in de ma nd of hoste l se rvic e s? (file hoste l) ( )  b + b + b + b + b + 6 Relaxing the assumptions in the linear classical ln hostel ln( inc ) secstud terstud hhsize u 1 2 3 4 5   - + + + - ln( hostel ) 16.37 2.732ln( inc ) 1.398 secstud 2.972 terstud 0.444 hhsize i i i i i (2.26) (0.324) (0.258) (0.088) (0.333) = = 2 R 0.921 n 40 1.6 1.4 Residuals in absolute value 1.2 1 model 0.8 0.6 0.4 0.2 0 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 ln (inc) GRAPHIC 6.3. Sc a tte r plot be twe e n the re sidua ls in a bsolute va lue a nd the va ria ble ln( inc ) in the hoste l mode l. T ABL E 6.8. T e sts of he te roske da stic ity in the mode l of de ma nd for hoste l se rvic e s. Test Statistic Table values Breusch-Pagan-  2(0.05) 2 nR BPG = =7.83 =5.99 2 Godfrey ra  2 2(0.01) nR White W = =12.24 =9.21 [14] ra 2