SINGAPOE MANAGEMENT UNIVESIT School of Economcs Econ07 Inroducon o Economercs Sample Quesons (Tme allowed: hours Consder he varable regresson model 0 ( Denoe o be he OLS esmaor of and se( o be. For each of he followng saemens ndcae wheher s jusfed and eplan your reasons. (a Mulcollneary rases he sandard error of and hence he es based on and se s nvald. (6 marks ( (b Heeroskedascy leads o an unbased esmaor of and hence he es based on and se ( s vald. (6 marks (c Seral correlaon leads o an unbased esmaor of bu he es based on s always nvald. (6 marks (d Msspecfcaon of he funconal form leads o an unbased esmaor of bu he es based on and se( s nvald. (6 marks (e If s a dummy varable, he lnear probably model allows for an unresrced range of probably, hence he es based on s always nvald. (6 marks. Suppose you are gven he followng resuls for a me seres of 3 annual Ausralan aggregae economc daa (sandard errors n parenheses: C 8.33 0.95w (8.9 (0.95 0.45 p (0.66 0.95 0. (.09 a 4 (
where C annual Ausralan domesc consumpon (n bllons of A$; w annual Ausralan wage ncome (n bllons of A$; p annual Ausralan nowagenofarm ncome (n bllons of A$; a annual Ausralan farm ncome (n bllons of A$. (a How would you nerpre he coeffcens of w, p, a? (6 marks (b Tes he null hypoheses ha he coeffcens of w, p, a are ndvdually ndfferen from zero respecvely a a 5% sgnfcance level usng a onesded es. (6 marks (c Inerpre. Specfy he hypohess o es he overall sgnfcance of he regresson model. Use he value of o es hs hypohess. (7 marks (d Wha can you conclude from (b and (c? In hs case, wha are he properes of he OLS esmaor? Do you need o be concerned wh he problem from he perspecve of hypohess esng? Why or why no? (7 marks (e Eplan how o use an aulary regresson o deec he problem you denfed n (d. Sugges a way o solve he problem. (7 marks (f If we now measure he dependen varable and all he ndependen varables by mllons of A$ nsead of by bllons of A$, whou reesmang he model, wha are he new esmaed coeffcens? (7 marks The followng resuls are obaned based on he same daa: C 8.94 0. 6p (.67 (0.0..( 0.8 (g Whch model, ( or (, do you prefer? Gve your reasonng. (6 marks 3. Consder he followng model: 0 D 3D 4D D (3 where
annual salary of a junor college eacher (n housand S$ years of eachng eperence D 0 f female oherwse D 0 f nonchnese oherwse (a The erm represens he neracon effec. Is hs erm a dummy varable? If so, wha does hs erm means? (4 marks (b (c (d (e Show how equaon (3 can be used o fnd he mean salary for a nonchnese female. ( marks Show how equaon (3 can be used o fnd he mean salary for a Chnese female. ( marks Show how equaon (3 can be used o fnd he mean salary for a nonchnese male. ( marks Show how equaon (3 can be used o fnd he mean salary for a Chnese male. ( marks (f Usng he resuls obaned from (b(e o nerpre 4. (5 marks Evews s used o produce he followng regresson resuls (wh four sascs, one sandard error and one pvalue removed based on crossseconal daa on 000 junor college eachers n Sngapore: Dependen Varable: Mehod: Leas Squares Dae: 0/5/05 Tme: :40 Sample: 000 Included observaons: 000 Varable Coeffcen Sd. Error Sasc Prob. C 3.0 4.0 A 0.000. 0. A 0.000 D.36.0 A3 A6 D.645.0 A4 0.0 D*D 0.65 A5 6.5 0.000 squared 0.68608 Mean dependen var 03.738 Adjused squared 0.68480 S.D. dependen var 8.9560 S.E. of regresson 5.0550 Akake nfo creron 6.0798 Sum squared resd 59.47 Schwarz creron 6.096457 Log lkelhood 3030.959 Fsasc 543.6556 DurbnWason sa.06098 Prob(Fsasc 0.000000
(g Fnd he numercal values for AA6 n he above Evews oupu. (4 marks (h Consruc he 95% confdence nerval for he slope parameer of and nerpre. (4 marks ( If we now measure by S$ nsead of by housands of S$, whou rerunnng he regresson, wha are he new esmaed coeffcens? (5 marks
Seleced Formulae ] se( + se( Prob[ ] n[var( n d ( h K (n / ( /K F n TSS K n SS TSS ESS SS + ESS TSS se( n se( K n e + n n y y y / /, /( /(,, 0 0 Seleced Sascal Tables. Table for he Normal dsrbuon.. Table for he dsrbuon. 3. Table for he F dsrbuon 4. Table for he DurbnWason es sasc.