Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard
14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th disincion bwn nominal and ral inrs ras Prsn discound valus calculaions Adjusing h IS-LM modl o accoun for disincion bwn nominal and ral inrs ras 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 2 of 32
14-1 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Inrs Ras xprssd in rms of dollars (or, mor gnrally, in unis of h naional currncy) ar calld nominal inrs ras Inrs ras xprssd in rms of a bask of goods ar calld ral inrs ras. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 3 of 32
Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Figur 14-1 Dfiniion and Drivaion of h Ral Inrs Ra i = nominal inrs ra for yar. r = ral inrs ra for yar. (1+ i ): Lnding on dollar his yar yilds (1+ i ) dollars nx yar. P = pric his yar. P +1 = xpcd pric nx yar. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 4 of 32
Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic P W hav: 1 + r = ( 1 + i ) P + 1 W can dfin xpcd inflaion as: Hnc: π + 1 P P Subsiuing back in: P = + 1 ( 1 + r ) = + 1 P 1 P ( 1 + π ) 1 + i 1 + π + 1 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 5 of 32
Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic If h nominal inrs ra and h xpcd ra of inflaion ar no oo larg, a simplr xprssion is: r = i + π 1 Th ral inrs ra is (approximaly) qual o h nominal inrs ra minus h xpcd ra of inflaion. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 6 of 32
Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Hr ar som of h implicaions of h rlaion abov: If If if = 0 i = r π π > 0 i > r i r π = i π r 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 7 of 32
Nominal and Ral Inrs Ras in h Unid Sas Sinc 1978 Chapr 14:Expcaions: Th Basic Figur 14-2 Nominal and Ral On-Yar T-bill Ras in h Unid Sas sinc 1978 Alhough h nominal inrs ra has dclind considrably sinc h arly 1980s, h ral inrs ra was acually highr in 2001 han in 1981. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 8 of 32
14-2 Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic Figur 14-2 Compuing Prsn Discound Valus Th xpcd prsn discound valu of a squnc of fuur paymns is h valu oday of his xpcd squnc of paymns. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 9 of 32
Compuing Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic (a) On dollar his yar is worh 1+i dollars nx yar. (b) On dollar nx yar is worh 1 his yar 1 + i So, h prsn discound valu of a dollar nx yar is qual o 1 1 + i 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 10 of 32
Compuing Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic Th word discound coms from h fac ha h valu nx yar is discound, wih (1+i ) bing h discoun facor. (Th 1-yar nominal inrs ra, i, is somims calld h discoun ra. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 11 of 32
A Gnral Formula Chapr 14:Expcaions: Th Basic Th prsn discound valu of a squnc of paymns, or valu in oday s dollars quals: $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = + + 1 + z + 2 + 1 + 1 + 1 + Whn fuur paymns or inrs ras ar uncrain, hn: $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = + + 1 + z + 1 + 1 + 1 + Prsn discound valu, or prsn valu ar anohr way of saying xpcd prsn discound valu. + 1 + 1 2 + 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 12 of 32
Using Prsn Valus: Exampls Chapr 14:Expcaions: Th Basic $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = + + 1 + z 1 + 1 + 1 + This formula has hs implicaions: Prsn valu dpnds posiivly on oday s acual paymn and xpcd fuur paymns. Prsn valu dpnds ngaivly on currn and xpcd fuur inrs ras Applicaion: ysrday was in h nws ha xpcaions of (inrs) ra cus by h ECB drov up sock prics + 1 + 2 + 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 13 of 32
Consan Inrs Ras Chapr 14:Expcaions: Th Basic To focus on h ffcs of h squnc of paymns on h prsn valu, assum ha inrs ras ar xpcd o b consan ovr im, hn: $ V = $ z + 1 ( ) $ 1 z + 1 + i ( 1 + i) $ z + 1 2 + 2 + 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14 of 32
Consan Inrs Ras and Paymns Chapr 14:Expcaions: Th Basic Whn h squnc of paymns is qual call hm $z, h prsn valu formula simplifis o: $ V = $ z 1 + 1 1 + + ( 1 + i) ( 1 + i) n 1 Th rms in h xprssion in bracks rprsn a gomric sris. Compuing h sum of h sris, w g: n 1 [ 1/ ( 1 + i) ] $ V = $ z 1 [ 1/ ( 1 + i)] 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 15 of 32
Zro Inrs Ras Chapr 14:Expcaions: Th Basic If i = 0, hn 1/(1+i) quals on, and so dos (1/(1+i) n ) for any powr n. For ha rason, h prsn discound valu of a squnc of xpcd paymns is jus h sum of hos xpcd paymns. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 16 of 32
Consan Inrs Ras and Paymns, Forvr Chapr 14:Expcaions: Th Basic Assuming ha paymns sar nx yar and go on forvr, hn: $ V = 1 ( ) $ 1 z + 1 + i ( 1 + i) $ z + = 1 1 + ( + i) 1 1 ( 1 + i) Using h propry of gomric sums, h prsn valu formula abov is: Which simplifis o: 2 $ V 1 1 i ( ( / ( i)) $ = z 1 + 1 1 1 + $ V = + $ z 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 17 of 32 $ z i
Nominal Vrsus Ral Inrs Ras, and Prsn Valus Chapr 14:Expcaions: Th Basic $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = + + 1 + z 1 + 1 + 1 + Rplacing nominal inrs wih ral inrs ras o obain h prsn valu of a squnc of ral paymns, w g: V = z + Which can b simplifid o: 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 18 of 32 + 1 1 1 z + 1 + z ( 1 + r ) ( 1 + r )( 1 + r ) $V P + 1 = V + 2 + 2 + + Hnc: prsn discound valus in rms of nominal valus using nominal inrs ras o discoun or in ral valus using ral inrs ras gnra h sam ral PDV
14-3 Nominal and Ral Inrs Ras, and h IS-LM Modl Chapr 14:Expcaions: Th Basic Whn dciding how much invsmn o undrak, firms car abou ral inrs ras. Thn, h IS rlaion mus rad: Y = C( Y T) + I( Y, r) + G Th inrs ra dircly affcd by monary policy h on ha nrs h LM rlaion is h nominal inrs ra, hn: M P = YL( i) Wih h ral inrs ra: r = i π 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 19 of 32
Nominal and Ral Inrs Ras, and h IS-LM Modl Chapr 14:Expcaions: Th Basic Th nominal inrs ra appars in mony dmand In dciding how much mony o hold an individual compars h nominal ra of rurn on mony, which is zro, wih h nominal ra of rurn on bonds, which is h nominal inrs ra Th ral inrs ra appars in h IS curv Th inrs ra affcs invsmn. In dciding abou invsmn firms compar h ral cos of capial goods wih h ral payoffs from ha invsmn 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 20 of 32
14-4 Mony Growh, Inflaion, Nominal and Ral Inrs Ras Chapr 14:Expcaions: Th Basic This scion focuss on h following assrions: Highr mony growh lads o lowr nominal inrs ras in h shor run, bu o highr nominal inrs ras in h mdium run. Highr mony growh lads o lowr ral inrs ras in h shor run, bu has no ffc on ral inrs ras in h mdium run. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 21 of 32
Rvisiing h IS-LM Modl Chapr 14:Expcaions: Th Basic Rducing h IS rlaion, LM rlaion and rlaion bwn h ral and nominal inrs ra givs us: IS LM Y = C( Y T) + I( Y, i π ) + G ( ) M = YL i Th IS curv is sill downward sloping. Th LM curv is upward sloping. Th quilibrium is a h inrscion of h IS curv and h LM curv. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 22 of 32
Rvisiing h IS-LM Modl Chapr 14:Expcaions: Th Basic Figur 14-4 Equilibrium Oupu and Inrs Ras Th quilibrium lvl of oupu and h quilibrium nominal inrs ra ar givn by h inrscion of h IS curv and h LM curv. Th ral inrs ra quals h nominal inrs ra minus xpcd inflaion. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 23 of 32
Nominal and Ral Inrs Ras in h Shor Run Chapr 14:Expcaions: Th Basic Figur 14-5 Th Shor-run Effcs of an Incras in Mony Growh An incras in mony growh incrass h ral mony sock in h shor run. This incras in ral mony lads o an incras in oupu and a dcras in boh h nominal and h ral inrs ra as prics ar sicky in h shor run. If r = i π r = i π If π is consan, π = 0 r = i 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 24 of 32
Nominal and Ral Inrs Ras in h Mdium Run Chapr 14:Expcaions: Th Basic In h mdium run, Y =, hn: Y n Y = C( Y T) + I( Y, r) + G n n n Th rlaion bwn h nominal inrs ra and h ral inrs ra is: i = r + π In h mdium run, h ral inrs ra quals h naural inrs ra, r n, hn: i = r n + π In h mdium run, xpcd inflaion is qual o acual inflaion, so: i = r n + π Finally, in h mdium run, inflaion is qual o mony growh: i = r + g n m 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 25 of 32
Nominal and Ral Inrs Ras in h Mdium Run Chapr 14:Expcaions: Th Basic i = r + g n So, in h mdium run, h nominal inrs ra incrass on for on wih inflaion o bring h ral inrs ra back o is quilibrium lvl. This rsul is known as h Fishr ffc, or h Fishr Hypohsis. For xampl, an incras in nominal mony growh of 10% is vnually rflcd by a 10% incras in h ra of inflaion, a 10% incras in h nominal inrs ra, and no chang in h ral inrs ra. m 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 26 of 32
A Monary Expansion: From h Shor Run o h Mdium Run Chapr 14:Expcaions: Th Basic So long as h ral inrs ra is blow h naural ral inrs ra, oupu is highr han h naural lvl of oupu, and unmploymn is blow is naural ra. From h Phillips curv rlaion, w know ha as long as unmploymn is blow h naural ra of unmploymn, inflaion incrass. As inflaion incrass, i bcoms highr han nominal mony growh, lading o ngaiv ral mony growh, h LM curv shifs back In h mdium run, h ral inrs ra incrass back o is iniial valu, bcaus h conomy rurns back o is naural lvl 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 27 of 32
From h Shor Run o h Mdium Run Chapr 14:Expcaions: Th Basic Figur 14-6 Th Adjusmn of h Ral and h Nominal Inrs Ra o an Incras in Mony Growh An incras in mony growh lads iniially o a dcras in boh h ral and h nominal inrs ra. Ovr im, h ral inrs ra rurns o is iniial valu. Th nominal inrs ra convrgs o a nw highr valu, qual o h iniial valu plus h incras in mony growh. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 28 of 32
Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic To s if incrass in inflaion lad o on-foron incrass in nominal inrs ras, conomiss look a: Nominal inrs ras and inflaion across counris. Th vidnc of h arly 1990s finds subsanial suppor for h Fishr hypohsis. Swings in inflaion, which should vnually b rflcd in similar swings in h nominal inrs ra. Again, h daa appars o fi h hypohsis qui wll. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 29 of 32
Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic Figur 14-7 Th 3-Monh Trasury Bill Ra and Inflaion sinc 1927 Th incras in inflaion from h arly 1960s o h arly 1980s was associad wih an incras in h nominal inrs ra. Th dcras in inflaion sinc h mid-1980s has bn associad wih a dcras in h nominal inrs ra. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 30 of 32
Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic Figur 14-7 has a las hr inrsing faurs: Th sady incras in inflaion from h arly 1960s o h arly 1980s was associad wih a roughly paralll incras in h nominal inrs ra. Th nominal inrs ra laggd bhind h incras in inflaion in h 1970s, whil h disinflaion of h arly 1980s was associad wih an iniial incras in h nominal inrs ra. Th rlaion during WWII undrscors h imporanc of h mdium-run qualifir in h Fishr hypohsis. 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 31 of 32
Nominal Inrs Ras and Inflaion Across Lain Amrica in h Early 1990s Chapr 14:Expcaions: Th Basic Figur 1 Nominal Inrs Ras and Inflaion: Lain Amrica, 1992-1993 Across counris, h rlaion bwn nominal inrs ras and inflaion is pry srong 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 32 of 32