Economcs 435 Menze D. Cnn Fall 6 Socal Scences 748 Unversty of Wsconsn-Madson. Standard IS-LM Transactons and ortfolo Crowdng Out Transactons crowdng out of nvestment s te reducton n nvestment attrbutable to ger nterest rates arsng from a fscal expanson (assumng te money supply s eld constant). Note tat gven te nvestment functon, actual nvestment mgt be ger or lower tan t started out. In te standard IS-LM model, wen te margnal tax rate s zero, t=, te IS scedule s gven by: c b () Y <IS curve> Te LM scedule s gven by M () Y <LM curve> Rewrtng n terms of money base, wc te central bank actually controls: (a) MB m Y <LM curve > Were M m MB ; m s te monetary multpler, wc lnks te money stock to money base. Solvng for Y yelds: b m MB (3) Y ˆ <Equlbrum ncome> Were ˆ c b Consder wat s assumed n ts case, so tat one obtans ts soluton. Startng from an ntal budget surplus of zero, wen government spendng s ncreased, te budget defct wdens. Te resultng defct as to be fnanced someow. One way s va bond fnancng, tat s te government sells bonds to fnance te sortfall. If bond demand rses dollar for dollar wt wealt [were wealt/ = (MB/) + (B/)], ten te followng occurs n te money and bond markets, and to te LM scedule (remember te bond market s te mrror mage of te money market). See anel A.
. ortfolo Crowdng Out If on te oter and, money demand rses wt wealt, vz., (4) M d wealt Y j Were j as te nterpretaton of (M d /)/ (wealt/) (and s equal to - (B d /)/ (wealt/) ), ten a budget defct tat ncreases te stock of bonds outstandng wll cause te followng stuaton, llustrated n anel B. Notce tat now nterest rates rse n response to te government defct tat ncreases te stock of bonds outstandng, and te LM sfts n response to a budget defct. Ts wll occur wenever (B d /)/ (wealt/) < (or equvalently (M d /)/ (wealt/) > ). anel A M s / B s / (B s /) B d / (B d /) M d / LM MB, M/ B/ Y anel B R M s / B s / (B s /) LM MB,,B B d / (B d /) LM MB,,B (M d /) M d / Fgure : Money and Bond Markets M/ B/ Y
Note: Te LM s poston, wt ts new money demand functon, depends upon te amount of wealt, and ence amount of bonds, outstandng. To see ts, algebracally solve for te LM to obtan: mmb j MB B (5) Y You wll observe tat te vertcal ntercept depends upon stocks of bot money and bonds. Substtutng ts revsed LM curve nto te IS curve yelds: b mmb j MB B (6) Y ˆ Notce tat te stock of bonds now enters nto te determnaton of equlbrum ncome. Te lnkage to fscal polcy becomes obvous wen one consders ow budget defcts are fnanced. (7) BuS T G Recall, for smplcty, we ave set t=; now work wt te budget defct, BuD, (8) BuS BuD G T t ( B / ) Ts budget defct as to be fnanced someow; ts constrant s reflected n te last term on te rgt and sde of (8). In oter words, f te government spends more tan t takes n n terms of revenue, ten t must borrow by ssung new debt. So f one consders an ncrease n government spendng on goods and servces, Δ, startng from an ntal budget defct of zero, ten: (9) ( B / ) Now consder te total dfferental of (6): m MB j MB B () Y ˆ And zero out tose terms tat are constant wen only government spendng s canged. Assume monetary polcy olds te money base constant. MB And substtute (9) n: j () Y ˆ Ts mples te multpler for government spendng on goods and servces s: Y j () ˆ ˆ c b Tus te cange n output for a cange n government spendng wll be te same as n te standard case, as long as money demand does not depend upon wealt (j = ). Te larger eter b or j, te smaller te multpler. Ts quanttatve result sould pont te way to te economc ntuton. Te ntal output ncrease s mtgated by te fact tat wen te government as to bond fnance te resultng budget defct, t as to offer ger nterest rates to nduce te publc to old te addtonal bonds. 3
Ts means tat n ts model, output can actually fall n response to an ncrease n government spendng (tat s, notng rules out Y endng up less tan Y). Te dfference between Y and Y s called portfolo crowdng out of ncome, to dfferentate t from transactons crowdng out of ncome, wc s te dfference between Y and Y. Transactons crowdng out (wat s dscussed n te textbook) arses because ger ncome spurred by ger government spendng rases money demand and, gven te fxed money supply, ger equlbrum nterest rates. ortfolo crowdng out arses because ger government spendng (n te absence of a fully offsettng ncrease n tax revenues) s assocated wt ger bond sales, ence ger wealt, and ence ger demand for money wc, gven te fxed money supply, results n ger nterest rates for all ncome levels. Tat s wy n te fgure below, as te IS curve sfts out (wte arrow), te ncreased bond ssuance assocated wt te resultng budget defct nduces an upward sft n te LM curve (lgt gray arrow). LM MB, B LM MB, B,, μ b j ˆ ˆ c b IS Λ Y Y Fgure : Crowdng Out: Transactons and ortfolo Motvatons Y Y Notce tat n prncple Y b j ˆ could be greater or less tan zero. In partcular, f j s very large (.e., as wealt goes up, ouseolds want to old a lot of ter ncremental wealt n te form of money, rater tan bonds), ten te more lkely portfolo crowdng out s to occur. 3. Wen Monetary olcy Is Accommodatve, or te Economy Is n a Lqudty Trap IS Λ Y In te above analyss, te money supply s eld fxed. In oter words, monetary polcy s not accommodatve. Consder wat appens f te central bank monetzes te new debt tat arses from te fscal polcy, so tat te cange n government spendng equals te real cange n te money base; ten equaton () becomes: 4
Y Y m MB ˆ j MB m j ˆ Y ( m ˆ j) In ts case, te cange n ncome s unambguously postve, snce j s bounded between and, and, m s usually larger tan one. Fnally, f te central bank completely accommodates, by commttng to keepng te nterest rate constant, ten one recovers te standard smple Keynesan concluson regardng te multpler. LM MB, B LM MB, B LM MB, B c b IS Λ IS Λ Y Y Y Y Y Fgure 3: ortfolo Crowdng Out wt Interest Rate Targetng Wen te central bank commts to keep te nterest rate constant ( n ts case), ten te LM must be sfted downward (dark gray arrow). Hence, n ts case, portfolo crowdng out s rrelevant, except nsofar as te central bank takes on more government debt on ts balance seet. To conclude, note tat f te economy s n a lqudty trap to begn wt, ten te same result apples: te multpler s te same as n te smple Keynesan model. E435_portfolocrowd_f6.doc,.9.6 5