Please type your name in the output above the first. regression you run.

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1 Name Department of Economics Ohio Wesleyan University Delaware, Ohio Robert J. Gitter Econometrics Economics 355 Spring, 2004 Exam II You have 75 minutes hour for this exam. The exam is worth 20 percent of your grade. The exam is closed book, but calculators are p(1rmitted. Please do all your work carefully and check your calculations before handing.)1our work in. PLEASE SHOW ALL YOUR WORK TO AID IN THE A W ARDING <t>f P AR TIAL CREDIT WHERE APPLICABLE. Go to Minitab From the File Menu at the top go to Open Worksheet Look in Shared on w2kdocl(h:) Open Econ355 OK Select ExarnData OK And you should have the data Please type your name in the output above the first. regression you run. Please either print your results or save them so they can be turned in and printed. Go to the File Menu at the top and go to Save Project as: Save it ON THE A: drive, i.e., to disk. Make sure you update it before you sign off anu hand the disk in with it. POINTS WILL BE TAKEN OFF IF YOu DON'T PRINT OR SA YE THE RESULTS!!! PLEASE PERFORM FORMAL TESTS AND No1 QUICK AND DIRTY ONES.

2 I. (24 points) Data are given in columns C I-C3 Cl = C2= C3= GDP Receipts Year = Gross Domestic Product in Billions of Dollars (Nominal) = Federal Government Tax Receipts in Billions ofdollars =Year a. Please run a regression to detemline: the effect hat the level of GDP has on the federal government's tax receipts. Write the equation below. ) b. When we test for autocorrelation, what is the null and alternate hypotheses? State them below..4...to'''.'uj"'f.:-0,/16 e-(...,): c. viol' ".$ H.4-:..Ov u c),h.+ tt(()..,.v,.., "... T ) :/tj Please run a formal test for autocorrelation at the.05 level. Show all your work in doing the test and reaching your conclusion. > /11:-1' d =.q 2.f/""1)A, /'1"".6 A 1:-# 1jJ V4/'J :- J dl.-j. yji.ql-:: d 01- /1,) 4vh -(,... c,.cij c!u,.,-", ffj >,+ 1{0 Ctd d. 2.t""' j:> I" s,h "". w ould a first difference or generalized difference regression be more appropriate here? Discuss why. ")... TIle.,e;? ',l a',#,0/i'al'f. d.:;-,q:<. $" :;-1-, q.2./ ry e. Please do a first difference regression on the data and write the equation below. ).:l/rlj (problem continues next page)

3 f. In tenus of the variables, what does the slope tell you? wa.e", c--op II. j.fj 'y r I Jj,11IoJ" I Lvf -- fj/i',(,(.j- } Ty (rijj h /'II 1. 'll \ 11,'11",., g. In tenns of the variables, what does the constant tell you? 1+ JJ,.f, e f/j".'j. [;"v'/\ 1-/- C;:IJf' do.pj Ao;L? CA 4;1t' Il.ecellk Jv 1"'1 J 1" 6y w.e /J/elri!lc"l.. pe..1i'/' I IK h When auto-correlation exists what does it do tq the slope? '2 When auto-correlation exists what does it do tqe standard error of the slope? ")... J+ 6tq Jt'J ( oi,t:" '..'4// ;f' a. -c ) M '0 /I) 1: 2. (6 points) Data on the Median Family Income of Blacks (in 2002 dollars) are given in Column 11 with the year in Column 12. Please run a regression to determine the annual percentage change in Median Family Income. Write the annual percentage y.:- -lfl. / -+ 2

4 3. (25 points) I gathered data on 26 states in terms cpftheir spending on education. C21 = State C22 = Income C23 = Popl C24 = South C25 = Totsp = State Name = State Income in Milliohs ofdollars = State Population = 1 if state in South; O iflnot = Total Spending on edubation in the state (kindergarten through 12th grade) illions of dollars 1 1 a. Please run a regression of Totsp on Income, Popl and South. Write the equation below r..v Tc)SP= (!),O/Or,,(Cl4'9 O,I.1V I)pl -jcj.)i:), b..in tenus of the variables, explain what the slop on South tells you. C"+/,,,JI;9....;..,(!('vel 0+" 1'1\t:;4J",,1" Q"e( fjo,,/.,(i..fro"1) w-e J>H.,{.c..J..rDtJ.181)e.rJ-e1,L., ("IJ tl If'J/ 0'1 ed""".:fh,,,1.? c. Which variables are statistically significant at the.05 level? Show what you base your answer on. ()"IV f>c)i'ij,.5 shrj. SIS/.+. c>.11ly ;> s.."s- Ah\-lf :;;/.2' A2J.t>.I- A(.s- Vtilv9 o-r ;t ::-.2.)1>,4;", fi.1"j. d. Perform an F Test to see if you can drop ths'viriables that are not statistically '-'AIr I significant above. Show your work. 5!!!:!.:.-,'1"1 Ctr 17.'Ct'tYI')::'..u, U" \ 131. rfiv-=o Jr-lr' -i1...- vs /v9.1,,""..J HA H.,.s "'I-f "'"' -'-r ) /r)"f'..' o...i -r::;if \ < v '-:. }- -T?""" F ).:>.JJ> - - I rl J.," )).).,,)--.'3. VI?f.;- "."JPc.te. Does multicollinearity exists here? Explain. s:f J"c (.s rs'..jjn v-., I"'I.J t >oij/') d2. ;;- er. r.- i f>"i'.',j ",95..."S"J ".' J"J\(;. (,,J.. Il J..:: &j '1..I S:1.> rnv l.j.j c..., e4"",7 ey {,).t..) f. Suppose multicollinearlity exists. How might rou correct for it? You need not run the regression but state what you would doiin detail. b -II '.."S".J.}-'..y h h"..1 h ",J d.j.. ;.-<1' V1t'1 " 6/,) J/i.j- ei..-,<, l1"f /'f IlIA 'C./ II..I'H"' ) I f K YIf/?/p I",Pt".1'"' ;(!; c, /-' / J ;;'""1Jo1 6'1,;?01,J)vl"J1,, fro 1- D J 7.;"; eo" 1,!,,- I) ).. d 4 V4/,lciL,. -I)..,("',1 c;d { fr ) 1 ]1-13 L ) -H..J. )'IP- d;. Iy r; /J ft:: f ---I, C 4...S "., t'/"'...j -1),-1{ "" f"t eiri.; fk. 1v5-11/Je

5 4. (25 points) I put some data on age and producti\1ity of miners in the worksheet. C31 = Age C32 = Prod = Worker's Age = Tons of Coal Mined a. Run a regression to determine the effect of a worker's age on the tons of coal they mine. b. Run a reciprocal fom1 of the regression. c. d. Run a quadratic fonn of the regression, i.e., adding a square tenn to part a. f /'lj tit =- >.7+ A-e f e. At what age is production predicted to be at a peak? Show your work.,,\ f. =- I /{, e.:-(,) 1 '1, 6 Lf =-, I 6Af' )., "...,,4--(' Run a logarithmic regression of production on age. Interpret the slope in tenns of the variables. An a /'1 le J 611 1'2 ;.7 rl,/,(1- ft; Gv I'//)v(h c/ Pc.JA e 'J, r) '2 I"')

6 5 16 points.) I put some data on shipping for 30 firms in columns 41 & 42 C41 = SHIPM C42 = WORKERS = Value of Products ShiwPed (dollars) = Number of Workers i, the Firm a. Run a regression to determine how the value of the shipments depends on the number of workers.! 5 J-I If;YI =-,y 6 Ull 2 r r:j. I fj2 v/,j b. IF heteroscedasticity existed, what would it do Ito the slope of the regression? 11 v Jt, ;1') c, IF heteroscedasticity existed, what would it do Ito the value of the standard errors? b ( Ci J ;- Je,..."J, (J d. Please run the Park Test to determine whether heteroscedasticity would exist Does it exist here. (Use a.05 level.) e--l' 1. J.,. r -+ "'1 2 'i IJ, / t:.r /.., rj,."...j ;:- I V.l.S- '>.6 J.A- :- I '(J.A-2.r-- 2t""r f." '.'1.1, 111,,() A.,..1, (,1, 6. (4 points) a. Spring has arrived, which reminds me there are four seasons. Suppose we define Winter to be the first three months of the year, Spqng to be the next three, etc. If we gathered quarterly data on income (INC) and expe1iditures (EXP) for 40 quarters, what regression would you run to see if expenditues depended on both income and the season of the year? No need to run the regression. just write down the variables, " but how would you see if the b. Once again, no need to run the actual regressio effect of income on expenditure was different in t e Summer quarter, compared to all of the other quarters? - l;; f'j.11- ::- i,