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703Assignment6

703Assignment6 - Res E c 703 Assignment N umber 6 S.4 t...

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Res Ec 703, Assignment Number 6 Heteroscedastlclty S.4 tn·Table .".3 d\«e arc tillleseriC\$ data on toW cost (C') .nd output (Q) foe . . two 'linnl'; It lshypoth~b:cd that both 'firms" co,t functions «IC cubic and can be written as . Table Ill.B· Time Series Data ot,. Total 'Cost (0) a.nd Output (Q) .for Two Finns. , finn t: C II =/JI +/J,d211 +/J,Q:' +P4Q~, + eu C, Q. CI' a. 232 3.6S 353 6.99 finn 2: C ll = 11 + 1':2Q2. + rJa:1 + r 4Q~ +e , 293 4.32 240 4:43 564 ·9.02 271 4.78 where S49. 8.79 323 HI 313 S.II 332 S.39 2t7 2.38 256 U;8. 420 7.19 140 1.35 and ell and.e u are independent of each other and.Qver time. ". . 204 2.08 221 3.17 (a> BsUmate each function using least squares. Report ed eomrneRt.oa. the 733 9.87 418 7.02 . results:. . . 2 169 1.30 292 4.33 (b) Test the hypoti'!esis that H.o: a: = o'~ against tlle alternative th~t HI: 0'1 "" 5S0 9.09 " S82 9.34 o}. Use ~ 10% significance level and note that this is a two-tatled test. 221 1.75 193 1.51 (c) . Estimate -both equaUons jointly &ssumi", that PI ::0 y.. fJz. = 1i; iJJ. = lJ. and 278 4.93 '282 3.68 /1" ::')'4. Oct two sets of estimates, 01lC assuming O'~= 0':. and one 374 6.53 163 1.04 assuming u~ '" u:: Report and comment on the results. 491 8:2.8 326 :4.89 234 2.12 163 9.93 (4) Test the hypothesi~ . 326 5.36 464 7.81 252. 3.14 3S0 S.84 H,:PI·=rl. P2=r2 p,=y, p"=.r,, 183 2.09 212 4.33, agaiust 10~ 3.10 208 t.93 280 4.70. 192 1.-41 HI: at least one of the equalities in H' .does not hold SA9 4S9 ~.04 262 214 2.32 2:19 3.30· 313 6.78 2<;18 2.34 Do ~s test f.wi~. Fint asS\fl1ling u~ == 0': and then assuming u: '" 0-;. 393. 1.4~ 289 4.13 Comment on the test o~~mes. 237 3.23 340 6.82 44S 7.44 132 1.48 482 . 7!Y.J 434 .7A9 l TG6k 11M Data for BK~ Iii.' 15.7 Table.1S.4 ~ntalils C)bscrvatioBS ali food..cxppnditurc (y,) •. ~come·(xJ. and T. ... .. . Q"fK I ~I' n~bcr of persoBS.in each household (,y.from a ~dom 'sample of 38 cz:H4 . \$ KASl , ho·u.seholds in. a large U.·S. city. Food ~penditure and blcomc acc.measw:cd ·21.1011 'Mm , '1.431 . 19.1\$1 iti terms of thousands of dollars. CoBSider the statistical model . S 11.481 «:nc 13.\$41 l 14.1&4 19.40( 1Un l lUll .cult (15.5.2.) 2 1 21.141 IUSI i.,.w. J (a) . Test for hcteros~city in the. en"OlS#It usipg. 9.Qt JCS6l 1 14.O(IS , 'UII' 2 (II a Ooldfcld-Quaadt tat with the ObscrvatiOBS ordered accordiDg to -- I t:'fI.I' 2fM2. decreasing valuesofz,,'~ .' . IUS! f'U2S S "~I 'UC . {ill the 8rcuscWagan _ wtih equation 15.5.2 as the altcrQaCtvc. ·4 " nm 4',.,,0, hJpothcals .. '. . . i UN n»c 1 \$ 21.fi.14 IUn . 'COmment-on Chcoutcomes. ' , IItHG !U.\$OG 6 2 Wit . "l\$9 (b) lJi part (a)(lI) Jou would faa\'Oob~c({lClSt squares estima~ al~ att and "~I 2 lo.IU , ci,. What soca .WfOqlf JOu tly 10 compute estim.a.ted ~~ a: froui I• .HI UM9 ' . 1.IAlt 4U11S. 2 ,. 1IMJ -4tM'l a: rita. +ci,z,,'+a,n,. . S IC"" lS.tIS IU9~ 1'U2t . ) Dkcus. this probl~m. ' IS.'" nA". ' \$ 6 1U" (c)P'uid ~ 1_ squires eStimates of P .. /Ja. and lis updct the . 11.169 :i" .Il S IUIlI- C2.OC usumptlon that tI: .O~2S{O.OlJ:;+O.25n, +O.lJ:,n,)and compare the ·4 ,( uso .. un ~ults v4tti those ~m.leat ,\uam~ ".. ' U~ 4(.112 ., ..",,... 6 14."~1 (15.5.1) l4."~' 23~ CAn 4 11.tM' ~ 14.". .~ ,~ U1S "'" .2 n.ni·. .,

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Several Things To Consider In Assignment 6 This handout is intended to provide you with detailed explanations relating to different parts of each problem. In the process, you may find that it provides an overall perspective about correction procedures that deal with heteroscedasticity and how they relate to each other.
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