SINGAPORE MANAGEMENT UNIVERSITY
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1 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 w (8.9 ( p ( (.09 a 4 (
2 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$, whou reesmang he model, wha are he new esmaed coeffcens? (7 marks The followng resuls are obaned based on he same daa: C p (.67 (0.0..( 0.8 (g Whch model, ( or (, do you prefer? Gve your reasonng. (6 marks 3. Consder he followng model: 0 D 3D 4D D (3 where
3 annual salary of a junor college eacher (n housand S$ 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 A A D.36.0 A3 A6 D A4 0.0 D*D 0.65 A squared Mean dependen var Adjused squared S.D. dependen var S.E. of regresson Akake nfo creron Sum squared resd Schwarz creron Log lkelhood Fsasc DurbnWason sa Prob(Fsasc
4 (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
5 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.
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