Abschlußklausur Advanced Macroeconomics

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1 Prof. Dr. Olivr Landmann WS 2006/07 Abschlußlausur Advancd Macroconomics 20. Fbruar 2007 Aufgab (40%) Im Ramsy-Cass-Koopmans Modll sind di Bwgungsglichungn von Konsum c und Kapital (jwils pro fftivm Arbitsinput) ggbn durch c f '( ) ρ θg () = c θ (2) = f ( ) c ( n + g) 2 Output pro Effizinzinhit ist ggbn durch f ( ) = 2. a) Bstimmn Si di stady-stat Wrt von c und. b) Was ist das goldn Rgl -Nivau ds Kapitals ()? Dfinirn Si diss Konzpt und litn Si dssn Wrt mit dr ggbnn Spzifiation hr. Wi hoch ist dr damit vrbundn Wrt ds Konsums (c)? Illustrirn Si Ihr Antwort mit Hilf ins Diagramms im (,c)-raum. c) Btrachtn Si in Ausgangssituation, in dr di Kapitalausstattung dr Volswirtschaft halb so hoch wi ihr stady-stat-nivau (gmäss a) und das Konsumnivau dopplt so hoch wi das goldn Rgl -Nivau (gmäss b) sind. Erlärn Si, warum dr Konsum von dism Ausgangspunt aus nicht dr Eulr- Glichung () ghorcht, wnn di Konsumntn rational sind und übr prft Voraussicht vrfügn. d) Analysirn Si di Auswirungn inr Bschlunigung ds tchnischn Fortschritts auf di Lag ds stady stat (grafisch Analys). Aufgab 2 (30%) Wi untrschidn sich di Efft inr antizipirtn und inr unantizipirtn Erhöhung dr Wachstumsrat ds Gldangbots in jdm dr folgndn vir Modll? a) Lucas Modll mit vollommnr Information; b) Lucas Modll mit unvollommnr Information; c) Modll unvollständign Wttbwrbs ohn nominal Starrhitn; d) Modll unvollständign Wttbwrbs mit übrlappndn Vrträgn. Ein formal Darstllung odr Hrlitung dr Modll ist nicht rfordrlich. Achtn Si jdoch auf in sorgfältig Bgründung Ihrr Antwortn. Sit von 2

2 Advancd Macroconomics WS 2006/07 Aufgab 3: Montary Policy (30%) Ein Volswirtschaft lass sich durch di folgndn dri Glichungn bschribn: ) () y = α α 0 i π y: Output; i: Nominalzins; (2) π = π + β ( y y) π: Inflation; π : rwartt Inflation (3) i = γ T + π + γ ( π π ) + γ (y y) π T : Inflationszil dr Zntralban 0 2 All Koffizintn sind positiv und xogn. a) Gbn Si in öonomisch Intrprtation dr Glichungn () - (3) und rlärn Si di Bdutung von α 0 und y. b) Bstimmn Si di langfristign Glichgwichtswrt ds Output, dr Inflation und ds Ralzinss. c) Edmund S. Phlps, Noblpristrägr ds Jahrs 2006, gab ürzlich folgnd Warnung ggn di Vrwndung von Zinsrgln in dr Gldpoliti ab: Th main shortcoming of a fixd intrst rat rul is that it rquirs th cntral ban to st th short-trm intrst rat in rlation to a variabl, namly th natural intrst rat, that is not obsrvabl and, owing to its potntial for shifts and swings, oftn sriously unnown Should th cntral ban undrrstimat for a long strtch of tim th natural ral rat of intrst, thr will rsult a tndncy for th ban to st th short-trm ral intrst rat too low in viw of initial inflation xpctations and initial unmploymnt lowr than it would dsir wr its stimat of th natural rat corrct. [Hinwis: Dr natürlich Zins ist dr langfristig glichgwichtig Ralzins.] Disutirn Si dis Kriti untr Vrwndung ds obign Modlls. Erläutrn Si insbsondr, warum s für di Zntralban wichtig ist, dn natürlichn Zins orrt zu schätzn. Wi würdn Si als Zntralbanr Ihr Politi ändrn, wnn Si bmrn, dass Si dn natürlichn Zins bishr untrschätzt habn? Sit 2 von 2

3 Prof. Dr. Olivr Landmann WS 2006/07 Final Exam Advancd Macroconomics Fbruary 20, 2007 Qustion (40%) In th Ramsy-Cass-Koopmans modl, th dynamics of consumption c and capital (pr ffctiv worr) ar givn by th following quations: c f '( ) ρ θg () = c θ (2) = f ( ) c ( n + g) 2 Assum that output pr ffctiv worr is givn by f ( ) = 2. a) Dtrmin th stady-stat valus of c and. b) What is th goldn-rul lvl of capital? Dfin this concpt and driv th valu with th givn spcification. What is th associatd goldn-rul lvl of consumption? Illustrat your answr with a diagram in (,c)-spac. c) Assum that th conomy starts with half th stady-stat valu of capital pr ffctiv worr (calculatd in a) and with twic th goldn-rul lvl of consumption pr ffctiv worr (calculatd in b). Explain why consumption dos not follow th path implid by th Eulr quation () from this starting point if consumrs ar rational and hav prfct forsight. d) How dos an acclration of tchnical progrss affct th stady stat? Giv a graphical analysis. Qustion 2 (30%) How do th ffcts of an anticipatd and an unanticipatd incras in th growth rat of th mony supply diffr in ach of th following four modls? a) Th Lucas modl with prfct information; b) Th Lucas modl with imprfct information; c) Th imprfct-comptition modl without nominal rigiditis; d) Th imprfct-comptition modl with ovrlapping contracts. You ar not xpctd giv a formal xposition or drivation of ths modls. But b sur you carfully xplain your answrs.

4 Advancd Macroconomics 2 WS 2006/07 ) Qustion 3: Montary Policy (30%) Considr an conomy rprsntd by th following thr-quation systm: () y = α α 0 i π y: output; i: nominal intrst rat; (2) π = π + β ( y y) π: inflation; π : xpctd inflation (3) i = γ T + π + γ ( π π ) + γ (y y) π T : inflation targt of th cntral ban 0 2 All cofficints ar positiv and xognous. a) Giv an conomic intrprtation of quations () - (3) and xplain th maning of α 0 and y. b) Dtrmin th long-run quilibrium valus of output, inflation and th ral intrst rat. c) 2006 Nobl Laurat Edmund S. Phlps rcntly issud th following warning against th us of intrst-rat ruls in montary policy: Th main shortcoming of a fixd intrst rat rul is that it rquirs th cntral ban to st th short-trm intrst rat in rlation to a variabl, namly th natural intrst rat, that is not obsrvabl and, owing to its potntial for shifts and swings, oftn sriously unnown Should th cntral ban undrstimat for a long strtch of tim th natural ral rat of intrst, thr will rsult a tndncy for th ban to st th short-trm ral intrst rat too low in viw of initial inflation xpctations and initial unmploymnt lowr than it would dsir wr its stimat of th natural rat corrct. [Hint: Th natural intrst rat is th long-run quilibrium lvl of th ral intrst rat]. Us th abov modl to discuss this criticism. In particular, xplain why it is important for th cntral ban to hav a corrct stimat of th natural intrst rat. As a cntral banr, how would you chang policy if you found out that you had undrstimatd th natural intrst rat hithrto?

5 Prof. Dr. Olivr Landmann WS 2006/07 Final Exam Advancd Macroconomics (Fbruary 20, 2007) Outlin of Solution Qustion a) Stady-Stat valus of c and : ' 0 = c& = f () ( ) ρ θ g * = ( ρ + θ g) 2 (2) 0 = = f ( ) c ( n g) & c * 2 n + g = ρ + θ g + ( ρ θ g) 2 b) Goldn-rul of capital is th stady-stat lvl of capital which maximizs consumption (i.. th valu of associatd with th pa of th ( & = 0) -curv). d ( 2) '! c d f ' c * GR = ( ) f ( ) ( n + g) = 0 = n + g = n + g c * GR = ( n + g) 2 c & = 0 * c GR E & = 0 * * GR Sit von 4

6 Advancd Macroconomics WS 2006/07 c c) A c & = 0 E & = 0 B Th starting point of th conomy is in A. As thr is prfct forsight on th part of th consumrs, th consumrs now that thy don t satisfy thir intrtmporal optimality condition. Hnc, thy lowr c for th givn to jump onto th saddl path to point B. Th conomy thn convrgs along th saddl path to its stady stat. d) In diagram: ( c & = 0)-lin movs to lft. ( & = 0) -curv shifts down. In th old quilibrium A, starts to fall ( & < 0) and c starts to fall as wll ( c & < 0). Th conomy movs along th saddl path towards th nw stady stat whr * * th nw stady stat lvls of and c ar lss than th old valus. As drawn, point A is on th saddl path convrging to B. But th saddl path could as wll pass abov or blow point A. c ( c & = 0) ' c & = 0 A & = 0 B ( & = 0) ' Sit 2 von 4

7 Advancd Macroconomics WS 2006/07 Qustion 2 (30%) a) Lucas modl with prfct information: Prfct information mans that agnts hav no difficulty idntifying this chang as an aggrgat macroconomic disturbanc. As a consqunc, th acclration of mony growth, whthr anticipatd or unanticipatd, is fully rflctd in th inflation rat at onc. Thr is no ffct on ral output. b) Lucas modl with imprfct information: Impact of anticipatd acclration is th sam as in a). Unanticipatd acclration is only partially rflctd in th inflation rat and, thrfor, dos hav an ffct on ral output. c) Imprfct-comptition modl without nominal rigiditis: In th absnc of nominal rigiditis, imprfct comptition dos not imply any non-nutrality of mony. As a consqunc, th acclration of mony growth, whthr anticipatd or unanticipatd, is fully rflctd in th inflation rat at onc. Thr is no ffct on ral output. d) Imprfct-comptition modl with ovrlapping contracts: If th acclration of mony growth was anticipatd at th tim whn th oldst of th contracts currntly in forc wr ngotiatd, it is fully mbodid in all currnt prics and hnc dos not hav an ffct on ral output. If som or all of th currntly prvailing prics wr ngotiatd bfor th chang in th bhaviour of mony growth was forsn, th acclration is only partially rflctd in th inflation rat or not at all and, thrfor, dos hav an ffct on ral output. Qustion 3: Montary Policy (30%) a) Equation (): Th IS Curv spcifis dmand-dtrmind output as a function of th ral intrst rat. All othr dmand-sid factors that might affct output ar capturd by α 0. Equation (2): Th Phillips Curv rlats (unanticipatd) inflation to th output gap. Hr, y rprsnts natural output. Equation (3): Th Taylor Rul spcifis th intrst-rat rul followd by th cntral ban. According to this rul, th ral intrst rat should rspond to dviations of th inflation rat from targt as wll as to th output gap. b) Th long run is dfind by π = π, which implis ( y y) = 0 (vrtical long-run Phillips α 0 y Curv). Equation () thn implis that th natural ral intrst rat is r n =. α Using th information on output and th intrst rat, q. (3) can b solvd for th T long-run inflation rat: π = π + ( r n γ 0 ). Th cntral ban mts its inflation targt γ if (and only if) it sts th paramtr γ 0 qual to r n. Sit 3 von 4

8 Advancd Macroconomics WS 2006/07 c) Phlps is clarly right. Th natural intrst rat, bing an quilibrium concpt, is not obsrvabl. It rflcts all th shifts and swings of α 0 and y which can b stimatd only imprcisly. Morovr, an stimat of α is rquird. Errors in th stimat of r n ar invitabl and quit possibly larg. As shown abov, thy caus th cntral ban to miss its inflation targt. If A cntral ban which uss q. (3) as a guidlin finds out that it is missing its inflation targt systmatically (inflation will ovrshoot th targt if th cntral ban undrstimats r n ), it will adjust th intrst rat accordingly for any givn lvl of (actual and xpctd) inflation and output. This amounts to a chang of γ 0 in th dirction of th natural rat of ral intrst. Sit 4 von 4