Fal Eam Appled Ecoomercs. 0 Sppose we have he followg regresso resl: Depede Varable: SAT Sample: 437 Iclded observaos: 437 Whe heeroskedasc-cosse sadard errors & covarace Varable Coeffce Sd. Error -Sasc Prob. C 08.097 6.35965 6.6594 0.0000 HSIE 9.9706 3.8663 5.056069 0.0000 HSIE^ -.9488 0.5400-4.87009 0.0000 FEMALE -45.0945 4.9533-0.660 0.0000 BLACK -69.86 5.4340 -.0049 0.0000 FEMALE*BLACK 6.30636 9.395 3.5048 0.003 R-sqared 0.085783 Mea depede var 030.33 Adjsed R-sqared 0.084677 S.D. depede var 39.404 S.E. of regresso 33.3688 Akake fo crero.6556 Sm sqared resd 73479 Schwar crero.63474 Log lkelhood -609.98 Haa-Q crer..688 F-sasc 77.5436 Drb-Waso sa.96399 ProbF-sasc 0.000000 Here, Score s he combed SAT score, Hse s se of he sde s hgh school gradag class, hdreds, Female s a geder dmm varable, ad Black s a race dmm varable. Is here srog evdece ha Hse^ shold be clded he model? Compe he opmal hgh school se. 3 Holdg oher varables fed, wha s he esmaed dfferece SAT score bewee oblack females ad oblack males? How sascall sgfca hs esmaed dfferece? 4 Wha s he esmaed dfferece SAT score bewee black females ad oblack females? Wha wold o eed o do o es wheher he dfferece s sgfca?
. 0 We are eresed esmag he hedoc prcg model of hose as follows: logprce α + * Sqrf + γ * Bdrms +, where Prce s he hose prce, Sqrf sqare fooage, ad Bdrms he mber of bedrooms. Depede Varable: LOGPRICE Mehod: Leas Sqares Sample: 88 Iclded observaos: 88 Varable Coeffce Sd. Error -Sasc Prob. C 4.76607 0.097044 49.78 0.0000 SQRFT 0.000379 4.3E-05 8.7808 0.0000 BDRMS 0.08884 0.09643 0.974403 0.336 R-sqared 0.58895 Mea depede var 5.63380 Adjsed R-sqared 0.578608 S.D. depede var 0.303573 S.E. of regresso 0.97063 Akake fo crero -0.377086 Sm sqared resd 3.300889 Schwar crero -0.963 Log lkelhood 9.5978 F-sasc 60.79 Drb-Waso sa.806794 ProbF-sasc 0.000000 How well does he model epla he acal daa of hose prce? Evalae he regresso erms of dvdal ad overall sgfcace. How ca we mprove he relevac of he model? Predc he perceage chage prce whe a 50-sqare-foo bedroom s added o a hose. 3 Le θ 50 + γ deoe he perceage chage prce whe a 50-sqare-foo bedroom s added o a hose. Show ha or model ca be wre as follows: logpr ce α + * Sqrf 50* Bdrms + θ * Bdrms +. 4 Usg he followg able, provde a 95% cofdece erval of θ. Depede Varable: LOGPRICE Mehod: Leas Sqares Sample: 88 Iclded observaos: 88 Varable Coeffce Sd. Error -Sasc Prob. C 4.76607 0.097044 49.78 0.0000 SQRFT-50*BDRMS 0.000379 4.3E-05 8.7808 0.0000
BDRMS 0.08580 0.06768 3.0549 0.009 R-sqared 0.58895 Mea depede var 5.63380 Adjsed R-sqared 0.578608 S.D. depede var 0.303573 S.E. of regresso 0.97063 Akake fo crero -0.377086 Sm sqared resd 3.300889 Schwar crero -0.963 Log lkelhood 9.5978 F-sasc 60.79 Drb-Waso sa.806794 ProbF-sasc 0.000000 3. 0 We wa o compare wo models. Model U ses he cosa,, ad as regressors whle Model R s based o he cosa ad. Model U + + + γ α,,...,, Sppose we have he followg: 00, 00, 00, 90, 0, 0, ad. Esmae he parameers ad γ from Model U. H: ] [ ] [ Calclae he resdal sm of sqares e RSS. H: e γ γ 3 Calclae he R-sqared coeffce R. Sppose we om he varable ad esmae Model R. Model R + + α,,...,,
4 Esmae he parameer from Model R. How s dffere from he former? How come do we have hs resl? H: e 5 Calclae he resdal sm of sqares? H: e RSS. How s dffere from he former 6 Calclae he R-sqared coeffce R r. How s dffere from he former 3? Epla wha cases hs dfferece. 7 Calclae he F-sasc ad es he ll hpohess H 0 : γ 0 a he 5% se. RSSr RSS / q H: F RSS / r 8 Show ha he same resl comes from he followg: R Rr / q F. R / r r 4. 0 Le UNRATE deoe he emplome rae ad le GRATE deoe he perceage chage gross domesc prodc. Cosder a damc relaoshp bewee he growh rae ad he emplome rae: UNRATE + α + * UNRATE + γ * GRATE + δ * GRATE where UNRATE ad GRATE are he lagged varables. Depede Varable: UNRATE Sample: 960Q 999Q4 Iclded observaos: 60 Varable Coeffce Sd. Error -Sasc Prob. C 0.560337 0.08678 6.494567 0.0000 UNRATE- 0.963759 0.083 79.0673 0.0000 GRATE -0.580 0.04336-0.54576 0.0000 GRATE- 0.047346 0.0498 3.60346 0.009 R-sqared 0.98076 Mea depede var 6.00797 Adjsed R-sqared 0.980356 S.D. depede var.496805
S.E. of regresso 0.09790 Akake fo crero -0.6074 Sm sqared resd 6.8658 Schwar crero -0.8386 Log lkelhood 4.8599 F-sasc 645.979 Drb-Waso sa.5390 ProbF-sasc 0.000000 The shor-r margal effec of he growh rae o he emplome rae s defed as γ. From he Table above, es he sgfcace of he esmae of he shor-r margal effec. How does he emplome rae respod o he chage growh rae he shor r? γ + δ 3 The log-r margal effec s defed as. Compe he log-r margal effec. 4 We wa o es f here s o dfferece he shor-r ad he log-r margal effecs. Se p he ll hpohess ad epla he procedre of hpohess esg. 5. 0 To es he effecveess of a job rag program o he sbseqe wages of workers, we specf he model log Wage α + Tra + γedc + δeper +, where Tra s a bar varable eqal o f a worker parcpaed he program. Sppose he error erm coas observed worker abl. Assme less able workers have a greaer chace of beg seleced for he program. Wha do o epec abo he basedess of he OLS esmaor of? Wha ca o sa abo he lkel bas he OLS esmaor of? 6. 0 Cosder he hosehold cosmpo fco: α + + where, deoes he cosmpo ad come of hosehold, respecvel. Sppose ε, where E ε 0, Var ε, ad ε s depede of. Show ha E 0, so ha eogee holds. Oba Var. Does he error sasf he whe ose error codo? 3 Epla he coseqeces of he OLS esmaor erms of basedess ad effcec. 4 Epla he bes opo ad he secod-bes opo o deal wh.