Suden Name: Economcs 0C Sprng 009 Suden ID: Name of Suden o your rgh: Name of Suden o your lef: Insrucons: Economcs 0C Fnal Examnaon Sprng Quarer June h, 009 Verson A a. You have 3 hours o fnsh your exam. Wre your name and suden ID number on he upper lef corner of hs page, as well as he names of he sudens seaed nex o you. And, n case you wsh o do so, please sgn he Buckley Waver. STUDENT CONSENT FOR RELEASE OF STUDENT INFORMATION (Buckley Waver) I hereby auhorze he UCSD Economcs Deparmen o reurn my graded fnal examnaon/research paper by placng n a locaon accessble o all sudens n he course. I undersand ha he reurn of my examnaon/ research paper as descrbed above may resul n dsclosure of personally denfable nformaon, ha s no publc nformaon as defned n UCSD PPM 60-, and I hereby consen o he dsclosure of such nformaon. Sgnaure b. Confrm ha your es has 3 pages. Make sure you fnd a shee wh wo ables of crcal values, n he pages of your exam. The las page can be used as scrach paper. c. There are wo pars o hs exam mulple-choce quesons (Par I) and longer quesons (Par II). You do no need o jusfy your answers for he mulple-choce quesons. Show ALL your work for he longer quesons. d. Use a pen o wre your answers. You gve up your rgh o a regrade f you use a pencl. e. The able below ndcaes how pons wll be allocaed on he exam. You can answer he quesons n any order you lke. Use your me carefully and effcenly. Queson Pons Par I 4 Par II. 8. 5 3 8 4 5 5 6 7 6 Exam Toal 00 f. Wh you, you should only have a pen, and a basc calculaor. g. You wll NOT be allowed o leave he room durng he exam. Turn off your cell phone and your IPod, and good luck!
PART I: Mulple-Choce Quesons (.5 pons each, 4 pons oal) Economcs 0C Sprng 009 ) You have esmaed he followng equaon: TesScore ˆ 607.3 + 3.85Income 0.043Income where TesScore s he average of he readng and mah scores on he Sanford 9 sandardzed es admnsered o 5 h grade sudens n 40 Calforna school dsrcs n 998. Income s he average annual per capa ncome n he school dsrc, measured n housands of 998 dollars. The equaon a. suggess a seeper effec of ncome on es scores a low values of ncome han a hgher values of ncome. b. shows a negave relaonshp unl a ceran value of ncome and hen a posve relaonshp afer. c. does no make much sense snce he square of ncome s enered. d. suggess a posve relaonshp beween es scores and ncome for all he sample. ) In a model wh a bnary dependen varable, a predced value of 0.6 means ha a. he mos lkely value he dependen varable wll ake s 60 percen. b. gven he values for he explanaory varables, here s a 60 percen probably ha he dependen varable wll equal one. c. he model makes lle sense, snce he dependen varable can only be 0 or. d. gven he values for he explanaory varables, here s a 40 percen probably ha he dependen varable wll equal one. 3) For he polynomal regresson model, a. you need new esmaon echnques snce he OLS assumpons do no apply any longer. b. he echnques for esmaon and nference developed for mulple regresson can be appled. c. you can sll use OLS esmaon echnques, bu he -sascs do no have an asympoc normal dsrbuon. d. he crcal values from he normal dsrbuon have o be changed o.96,.96 3, ec. 4) Havng more relevan nsrumens a. s a problem because nsead of beng jus denfed, he regresson now becomes overdenfed. b. s lke havng a larger sample sze n ha he more nformaon s avalable for use n he IV regressons. c. ypcally resuls n larger sandard errors for he TSLS esmaor. d. s no as mporan for nference as havng he same number of endogenous varables as nsrumens. 5) The log margnal effec of ncreasng he value of an explanaory varable a. s consan for all values of he explanaory varables. b. depends on he sandard normal probably densy funcon. c. can poenally ake a value ousde he range 0 o. d. none of he above. 6) In he regresson model Y β 0 + β X + β D + β 3 ( X D ) + u where X s a connuous varable and D s a bnary varable, o es ha he wo regressons (one for D 0 and he oher for D ) are dencal, you mus use he a. -sasc separaely for β 0, β 3 0. b. F-sasc for he jon hypohess ha β 0 0, β 0. c. -sasc separaely for β 3 0. d. F-sasc for he jon hypohess ha β 0, β 3 0. 7) The followng ools from mulple regresson analyss carry over n a meanngful manner o he lnear probably model, wh he excepon of he a. F-sasc. b. sgnfcance es usng he -sasc. c. 95% confdence nerval usng ±. 96 mes he sandard error. d. regresson R.
Economcs 0C Sprng 009 8) In he fxed effecs regresson model, usng (n ) bnary varables for he enes (he dummy for he frs eny s lef ou), he coeffcen of he bnary varable a. ndcaes he level of he fxed effec of he h eny. b. wll be eher 0 or. c. ndcaes he dfference n fxed effecs beween he h and he frs eny. d. ndcaes he response n he dependen varable o a percenage change n he bnary varable. 9) Negave frs auocorrelaon n he change of a varable mples ha a. he varable conans only negave values. b. he seres s no sable. c. an ncrease n he varable n one perod s, on average, assocaed wh a decrease n he nex. d. he daa s negavely rended. 0) Wh panel daa, regresson sofware ypcally uses an eny-demeaned algorhm because a. he OLS formula for he slope n he lnear regresson model conans devaons from means already. b. here are ypcally oo many me perods for he regresson package o handle. c. he number of esmaes o calculae can become exremely large when here are a large number of enes. d. devaons from means sum up o zero. ) Weak nsrumens are a problem because a. he TSLS esmaor may no be normally dsrbued, even n large samples. b. hey resul n he nsrumens no beng exogenous. c. he TSLS esmaor canno be compued. d. you canno predc he endogenous varables any longer n he frs sage. ) The forecas s a. made for some dae beyond he daa se used o esmae he regresson. b. anoher word for he OLS predced value. c. equal o he resdual plus he OLS predced value. d. close o.96 mes he sandard devaon of Y n he sample. 3) Tme fxed effecs regresson are useful n dealng wh omed varables a. even f you only have a cross-secon of daa avalable. b. f hese omed varables are consan over me bu vary across enes. c. when here are more han 00 observaons. d. f hese omed varables are consan across enes bu no over me. 4) The dsrbued lag model assumpons nclude all of he followng wh he excepon of a. here s no perfec mulcollneary. b. X s srcly exogenous. c. E u X, X, X, K) 0. ( d. The random varables X and Y have a saonary dsrbuon. 5) In he case of exac denfcaon a. you can use he J-sasc n a es of overdenfyng resrcons. b. you canno use TSLS for esmaon purposes. c. you mus rely on your personal knowledge of he emprcal problem a hand o assess wheher he nsrumens are exogenous. d. OLS and TSLS yeld he same esmae. 6) Saonary means ha he a. error erms are no correlaed. b. probably dsrbuon of he me seres varable does no change over me. c. random varables become ndependenly dsrbued when he me separang hem ges larger. d. he error erm has condonal mean zero, gven all he regressors and addonal lags of he regressors beyond he lags ncluded n he regresson. 3
Economcs 0C Sprng 009 PART II: Problems (76 pons oal) Noe: Assume hrough he end of he exam, ha he sgnfcance level for any hypohess esng s 5%. ) (8 pons) A recen arcle suded he effecs of aendng a Caholc Hgh School on he probably of aendng college. Le college be a bnary varable ha akes a value of one f a suden aends college, and zero oherwse. Le CahHS be a bnary varable equal o one f he suden aends a Caholc hgh school, and zero oherwse. A lnear probably model s college β + CahHS + oherfacors + u, 0 β where he oher facors nclude gender, race, famly ncome and parens educaon. a. Why mgh CahHS be correlaed wh u? (Hn: hnk of facors ha are mos lkely ncluded n he error erm). b. Le CahRel be a bnary varable ha akes he value one f he suden s a Caholc. Dscuss he wo requremens needed for hs o be a vald nsrumen for CahHS n he precedng equaon. Whch of he wo can be esed, and how? 4
Economcs 0C Sprng 009 ) (5 pons) Are rens nfluenced by suden populaon n a college own? Le ren be he average monhly ren pad on renal uns n a college own n he Uned Saes. Le pop denoe he oal cy populaon, avgnc he average cy ncome, and pcsu he suden populaon as a percenage of he oal populaon. We have daa for he years 980 and 990 for 64 ces n he US. a. You decde he pool all he observaons for he wo years, and you esmae he followng model whch ncludes a dummy varable D90 ndcang he year ( f year 990 and zero oherwse): loĝ( ren ) 0.569 + 0.6 D90 + 0.04log( pop (0.85) (0.058) (0.0) n 8 R 0.86 SER 0.6 ) + 0.57log( avgnc (0.098) ) + 0.0050 pcsu (0.00) where n parenhess you fnd he heeroskedascy-robus sandard errors. Wha does he esmae on he year dummy varable D90 ells you? Inerpre he esmae on pcsu. b. You hnk more n deph abou he problem and conclude ha here are unobserved varables ha deermne he renal raes n cy, bu ha are consan over he 0-year perod (cy fxed effecs). If n fac ha s he case, and f some of hose unobserved varables are correlaed wh pcsu, can you rely on he esmae you obaned n a.? Explan. 5
Economcs 0C Sprng 009 c. To ake no accoun he cy fxed effecs you decde o esmae he model usng changes (dfference beween he varable n 990 and he varable n 980). The resuls of ha esmaon are as follows: Δ loĝ( ren ) 0.386 + 0.07 Δ log( pop ) + 0.30 Δ log( avgnc ) + 0.0 Δpcsu (0.049) n 64 (0.070) R 0.3 (0.089) SER 0.090 (0.009) Compare your esmae on pcsu wh ha from par a. Does he relave sze of he suden populaon appear o affec renal raes? d. Fnally compare he sandard error of he esmaor of pcsu you obaned n c. wh he one obaned n a. How do you explan he hgher sandard error of he regresson n par c.? 6
Economcs 0C Sprng 009 3) (8 pons) We have annual daa from 948 o 003 on he hree-monh T-bll rae (3 ), he nflaon rae based on he consumer prce ndex (nf ), and he federal budge defc as a percenage of GDP (def ). The esmaed equaon s: 3ˆ.73 + 0.606 nf + 0.53 def n 56 R 0.60 SER.843 (0.38) (0.093) (0.60) Assume ha saonary s respeced. a. In order for us o say ha he nflaon rae or he defc are exogenous, wha do we need o make sure abou he effec of lagged values of hose varables? b. We decde o add a sngle lag of he nflaon rae and of he defc o he equaon. The resuls are: 3ˆ.6+ 0.343 nf + 0.38 nf 0.90 def + 0.569 def n 55 R 0.685 SER.660 (0.35) (0.30) (0.6) (0.36) (0.85) Wha s he mpac effec of nflaon on he hree-monh T-bll rae? Wha s he long-run cumulave dynamc mulpler of he nflaon rae? c. The F-sasc for sgnfcance of nf - and def - s abou 5.. Are hose varables jonly sgnfcan a he 5% sgnfcance level? 7
Economcs 0C Sprng 009 4) (5 pons) You have daa on wages for 85 workng men, as well as nformaon on oher ndvdual and famly characerscs. You are neresed n fndng he reurns from educaon (educ), bu you know ha an OLS esmaon of log(wage) on educaon alone suffers from omed varable bas. You decde o ry o do nsrumenal varables esmaon o oban a conssen esmae of he reurns from educaon. a. The varable brhord s brh order (brhord s one for a frs-born chld, wo for a second-born chld, and so on). Explan why educ and brhord mgh be negavely correlaed. b. You use wo-sage leas squares o esmae he reurns from educaon. The resuls are as follows: loĝ( wage ) 5.03 + 0.3educ (0.4) (0.03) Inerpre he esmae of he coeffcen on educaon. c. Now, suppose you nclude number of sblngs (sbs) as an explanaory varable n he wage equaon; hs conrols for famly background, o some exen: log( wage ) β 0 + β educ + β sbs + u Suppose ha you wan o use he varable brhord as an IV for educaon, assumng ha sbs s exogenous. Wre down he frs sage leas squares equaon, and ell how you would es he relevance of he nsrumen. d. The resuls of he wo-sage leas squares regresson are: loĝ( wage ) 4.94 + 0.37 educ + 0.00sbs (.08) (0.077) (0.079) Commen on he sandard errors of he esmaor on educaon. (In parcular, I wan you o answer he quesons: Is he sandard error larger? Why?) 8
Economcs 0C Sprng 009 5) ( pons) We have a panel daa on school dsrcs n Mchgan for he years 99 hrough 998. The dependen varable n hs queson s mah4, he percenage of fourh graders n a dsrc recevng a passng score on a sandardzed mah es. The key explanaory varable s rexpp, whch s real expendure per pupl n he dsrc. The amouns are n 997 dollars. The spendng varable wll appear n logarhm form. a. We pool all he observaons of all he years and regress he followng model, usng OLS: Lnear regresson Number of obs 3300 F( 9, 390) 39.44 Prob > F 0.0000 R-squared 0.5053 Roo MSE.04 Robus mah4 Coef. Sd. Err. P> [95% Conf. Inerval] y94 6.377355.7833 8.96 0.000 4.98676 7.773034 y95 8.650.7388 5.77 0.000 7.3 0.0694 y96 8.03336.7697507 3.43 0.000 6.54 9.546 y97 5.34006.793434 9.33 0.000 3.7844 6.8957 y98 30.39788.773735 39.4 0.000 8.88546 3.903 lrexpp.533934.5555 0. 0.834-4.46877 5.5364 lrexpp_ 9.04975.45608 3.69 0.000 4.4343 3.8560 lenrol.59679.94533.0 0.044.05887.7055 lunch -.4067083.06589-5.7 0.000 -.4383908 -.375058 _cons -3.6656.35386 -.56 0.00-55.88358-7.439533 where lrexpp_ s he log of he frs lag of real expendure per pupl, lenrol s he log of oal dsrc enrollmen and lunch s he percenage of sudens n he dsrc elgble for he school lunch program (lunch s a prey good measure of he dsrc-wde povery rae). The frs avalable year (he base year) s 993. Is he sgn of he lunch coeffcen wha you expeced? Inerpre he magnude of he coeffcen. Would you say ha he dsrc povery has a bg effec on es pass raes? b. We re-esmae he model, assumng ha here are dsrc fxed effecs. The resuls are as follows: Lnear regresson, absorbng ndcaors Number of obs 3300 F( 9, 74) 459.6 Prob > F 0.0000 R-squared 0.7700 Adj R-squared 0.73 Roo MSE 8.996 Robus mah4 Coef. Sd. Err. P> [95% Conf. Inerval] y94 6.7736.6064 0. 0.000 4.980697 7.373935 y95 8.0967.866857.00 0.000 6.40305 9.789 y96 7.9404.0377 7.7 0.000 5.95353 9.976 y97 5.984.0999 3.90 0.000 3.04867 7.3350 y98 9.8839.95098 5.00 0.000 7.5398 3.657 lrexpp -.4804 3.873469-0. 0.95-8.006393 7.84033 lrexpp_ 7.00988 3.480938.0 0.044.7746 3.885 lenrol.450874.05097 0.0 0.839 -.7903.608078 lunch.0657.096777 0.64 0.55 -.879.588 _cons -6.0809 35.7383-0.45 0.653-86.5765 53.99583 dsd absorbed (550 caegores) 9
Economcs 0C Sprng 009 Wha happened o he esmaed coeffcen of he lagged spendng varable. Is sll sgnfcan? c. The F-sasc for he es of jon sgnfcance of he enrollmen and lunch varables s 0. (pvalue of 0.807). Why do you hnk, n he fxed effecs esmaon, he enrollmen and lunch program varables are jonly nsgnfcan? 6) ( pons) You have me seres of monhly daa on he ndex of ndusral producon (IP) from January of 947 o June of 993.You compue annualzed raes of monhly percenage changes of he ndex of ndusral producon and call pcp. (Noe: pcp s n percenage pons) a. You esmae a AR(3) model for pcp. You convnce yourself ha you have ncluded he correc number of lags (n parcular, when you add a fourh lag you verfy ha s very nsgnfcan). Here are he resuls of he AR(3) regresson: pcp.80 + 0.349 pcp (0.64) (0.06) + 0.07 pcp (0.488) + 0.067 pcp (0.45) n 554 0.66 3 R SER.5 Forecas he value of pcp for July of 993, usng he followng nformaon for he values of he ndex of ndusral producon: Dae Jan93 Feb 93 Mar 93 Apr 93 May 93 Jun 93 IP 09.3 09.9 0. 0.4 0.3 0. Hn: pcp 00 [ln( IP ) ln( IP )] b. If much of he forecas error arses as a resul of fuure error erms (and ha source of error domnaes he error resulng from esmang he unknown coeffcens, snce he number of observaons s large), hen wha s your bes guess of he RMSFE here? 0
Economcs 0C Sprng 009 c. You add hree lags of he varable pcsp o your AR(3) model of par a. pcsp s he annualzed rae of monhly percenage changes n he S&P500 ndex. How do you es wheher pcsp Granger causes pcp? (Sae he hypohess). If he F-sa of ha es s 5.7, wha s your concluson? 7) (6 pons) We are ryng o explan he sandardzed score on a fnal exam (sndfnl) n erms of he percenage of classes aended (andre), pror college grade pon average (prgpa), and ACT score (ACT). Usng observaons on a random sample of 680 sudens n mcroeconomcs prncples, we esmae he followng model: Lnear regresson Number of obs 680 F( 6, 673) 39.70 Prob > F 0.0000 R-squared 0.87 Roo MSE.8787 Robus sndfnl Coef. Sd. Err. P> [95% Conf. Inerval] andre -.00679.0099434-0.68 0.500 -.06367.0809 prgpa -.6854.504699-3.3 0.00 -.6950 -.637578 ACT -.80394.038536 -.3 0.8 -.339554.0758766 prgpa_sq.959046.0363.87 0.004.09348.498663 ACT_sq.0045334.00945.98 0.049.00008.0090386 GPA_andre.0055859.0040768.37 0.7 -.00489.035907 _cons.05093.39686.47 0.43 -.693489 4.79935 where prgpa_sq s he square of prgpa, ACT_sq s he square of ACT, and GPA_andre s an neracon erm prgpa*andre. A F-es on he coeffcens of andre and GPA_andre s 0.4 (so, he wo varables are jonly sgnfcan). a. Wha was he dea behnd nroducng he neracon coeffcen? b. The mean value for prgpa n hs sample s.59. Wha s he esmaed effec of 0 percenage pon ncrease n aendance on he suden s performance n he fnal, when prgpa s a s mean. Explan n words wha he esmaed effec means.
Appendx: Tables and Formulas Economcs 0C Sprng 009 Large Sample Crcal Values for he -sasc from he Sandard Normal Dsrbuon Sgnfcance Level 0% 5% % -Sded Tes.64.96.58 -Sded Tes (>).8.64.33 -Sded Tes (<) -.8 -.64 -.33 Large Sample Crcal Values for he F-sasc from he F q, Dsrbuon Some formulas: Sgnfcance Level Degrees of Freedom (q) 0% 5% %.7 3.84 6.63.30 3.00 4.6 3.08.60 3.78 4.94.37 3.3 5.85. 3.0 6.77.0.80 7.7.0.64 8.67.94.5 R ESS TSS n n ( Yˆ Y ) ( Y Y ) SSR TSS n u ˆ n ( Y Y ) and SER s ), where u s ) u SSR n k Δx ln( x + Δx) ln( x), when x Δx x s small. ) TSLS Y β 0 + β X + u and Z s a vald nsrumen, hen β T s ZY s ZX j h sample auocovarance cov (ˆ Y, Y j ) ( Y Y j +, T )( Y j Y, T j ), where Y j +, T denoes he sample T + j average of Y compued over observaons j+,., T. cov(ˆ Y, Y ) j h j sample auocorrelaon ˆ ρ j Var( Y ) RMSFE ˆ [( Y T Y T T ) ] E + +
SCRATCH PAPER: Economcs 0C Sprng 009 3