January Examinations 2012

Transcription

1 Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons o canddaes Answer FOUR quesons. Make sure ha you answer TWO quesons from Secon A and TWO quesons from Secon B. Equal marks are gven o each queson. SECTION A: MATHEMATICS (Answer TWO quesons). (a) Evaluae (calculae) he followng: () () () (v) (v) [%] Usng any mehod, fnd he nverse of he followng marx. A [%]

2 EC79 (c) Express he followng equaons n marx form and solve hem by marx nverson. Also solve hem by Cramer s rule or by he Gauss-Jordan elmnaon mehod. 6x ( x x x ) x x x x ( x x x x ) [%]. Fnd saonary values, f any, of he followng funcons, usng he second order condons o classfy hem: () () z w w x x y y [5%] z w w x x y y [5%] () z wx w 8w x [%] (v) [%] (v) z w 8w x x [%]. (a) Fnd saonary values for he followng funcon subjec o he consran ndcaed and ndcae wheher s a maxmum, mnmum or oherwse. Subjec o: [8%] If an addonal consran ha w + x = 6 s added o he problem n (a) wha effec does hs have? [%]. (a) A Bank makes hree sors of loans. The value of hgh rsk loans s H, of medum rsk loans s M and of low rsk loans s L. Toal profs from he nvesmens are log H log M log L. Reurns o each sor of loan are, β, γ. The Bank has I o nves n all loans. Wha s he value of each ype of loan f he Bank maxmses s profs? Check he second order condons. [75%] How do he proporons of he nvesmen n each ype of loan change as he reurns and he oal avalable for nvesmen change? [5%] Page of 5

3 EC79 SECTION B: ECONOMETRICS (Answer TWO quesons). (a) Explan he hree dfferen mehods of esmang parameers of a regressons funcon [5%] Wha s heeroscedascy? How can be addressed? Gve Example(s) [5%]. A researcher has esmaed he followng earnngs funcon on 5 ndvduals. The dependen varable s log of wages(lnwage) whch s regressed on a se of explanaory varables such as years (.e. years of schoolng compleed by he ndvdual), lnage (.e. log of age of he ndvdual) and male (.e. a bnary varable whch assumes a value of f he ndvdual s male and oherwse). Hence, he esmang equaon can be gven as: ln wage ( years ) (ln age ) ( male) The E-Vews oupu of he esmaon s gven below. Followng he resuls able here are quesons ha you are requred o answer. Dependen Varable: LNWAGE Mehod: Leas Squares Dae: //9 Tme: :6 Sample: 7 Included observaons: 5 Varable Coeffcen Sd. Error -Sasc Prob. C YEARS LNAGE MALE R-squared.5968 Mean dependen var Adjused R-squared.5695 S.D. dependen var.97 S.E. of regresson.886 Akake nfo creron.5776 Sum squared resd Schwarz creron.695 Log lkelhood -.67 Hannan-Qunn crer F-sasc.669 Durbn-Wason sa.985 Prob(F-sasc). a. Tes he hypohess a % level of sgnfcance. Inerpre he es resuls. [%] b. Inerpre each of he slope coeffcens. [%] Page of 5

4 EC79 c. Tes he hypohess ha all he coeffcens are equal o zero. Inerpre your resul. [%] d. Sugges how he specfcaon of he wage funcon can be mproved. [%]. Consder he process y.y.y. 5 where s a whe nose process. a. Show wheher y s a saonary or a non-saonary process. [%] b. Show ha y y y follows an ARMA process. [%] c. Show ha y follows an AR process of nfne order. [%] d. Show ha y follows an MA process of nfne order.[%]. () Wha s a saonary seres? Explan he dfferen mehods of esng for un roos. [5%] () An economercan has esmaed he followng model for he reurns for he FTSE ndex, r w var(,,...) where r s he reurn for FTSE ndex and esmaed oupu from Evews s as follows: s an unobserved whe nose process. The Dependen Varable: RET_FTSE Mehod: ML - ARCH (Marquard) - Normal dsrbuon Dae: //9 Tme: :5 Sample (adjused): 57 Included observaons: 57 afer adjusmens Convergence acheved afer eraons Bollerslev-Wooldrdge robus sandard errors & covarance Presample varance: backcas (parameer =.7) GARCH = C() + C()RESID(-)^ + C()GARCH(-) Varable Coeffcen Sd. Error z-sasc Prob. C Varance Equaon C.86E-6.7E RESID(-)^ GARCH(-) R-squared -.57 Mean dependen var.9 Adjused R-squared -.57 S.D. dependen var.89 S.E. of regresson.9 Akake nfo creron Sum squared resd.665 Schwarz creron Log lkelhood Hannan-Qunn crer Durbn-Wason sa.958 Page of 5

5 EC79 (a) Inerpre he esmaed values for and. Is here here evdence of hgh perssence n volaly? [%] Show ha model above can be wren as an ARCH model of nfne order. [%] END OF PAPER Page 5 of 5