WORKING PAPER NO A SHORT-TERM MODEL OF THE FED S PORTFOLIO CHOICE. Dean Croushore Federal Reserve Bank of Philadelphia

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1 WORKING PAPERS RESEARCH DEPARTMENT WORKING PAPER NO A SHORT-TERM MODEL OF THE FED S PORTFOLIO CHOICE Dean Crouhore Feeral Reerve Bank o Philaelphia Octoer 2000, Revie April 2003 FEDERALRESERVE BANK OF PHILADELPHIA Ten Inepenence Mall, Philaelphia, PA (215)

2 WORKING PAPER NO A SHORT-TERM MODEL OF THE FED S PORTFOLIO CHOICE Dean Crouhore Feeral Reerve Bank o Philaelphia Octoer 2000 revie, April 2003 The view expree in thi paper o not necearily repreent the view o the Feeral Reerve Bank o Philaelphia or the Feeral Reerve Sytem. Thi paper wa prepare uner the irection o Rick Lang or the Feeral Reerve Sytem tuy that wa pulihe a: Alternative Intrument or Open Market an Dicount Winow Operation, Boar o Governor, Decemer Thi paper i reerence in ootnote 3, on page 3-47 in Appenix 3.C, The Potential Eect on Financial Market an Intitution o Replacing the SOMA Treaury Securitie with Avance o Feeral Reerve Creit.

3 A SHORT-TERM MODEL OF THE FED S PORTFOLIO CHOICE ABSTRACT What woul happen i the Feeral Reerve were to change the aet in it portolio? Suppoe that intea o uing open-market operation in Treaury ecuritie to increae the monetary ae, the Fe were to engage in open-market operation in private ecuritie or to ue icount loan via a mechanim that allowe ank to orrow a much a they woul like at a ixe icount rate. The analyi in thi paper how the impact on the economy in a tatic general-equilirium moel.

4 A SHORT-TERM MODEL OF THE FED S PORTFOLIO CHOICE What woul happen i the Feeral Reerve were to change the aet in it portolio? Suppoe that intea o uing open-market operation in Treaury ecuritie to increae the monetary ae, the Fe were to engage in open-market operation in private ecuritie or to ue icount loan via a mechanim that allowe ank to orrow a much a they woul like at a ixe icount rate. The analyi in thi paper how the impact on the economy in a tatic general-equilirium moel. Thi moel ollow Santomero (1983), aapte to evaluate a change in the Fe portolio an how that aect the economy general equilirium at a point in time. The nature o the exercie one here i completely tatic in nature an oe not evaluate the economy repone to a iappearance o government et, analyi o which woul require a more complete moel that ynamic in nature an incorporate real eect. The preent moel ocue on the more narrow iue o the irection o portolio change with no real-ie economic eect. But the moel i general equilirium in nature an thu perorm a reaonale comparative-tatic exercie. In what ollow, we irt ecrie the moel in Section I. Next, we moel a ituation in which the Fe change it portolio in uch a way a to keep the interet rate on epoit rom changing (Section II). Section III generate reult uner a pecial et o aumption that lock mot interet rate together. Section IV attempt to generalize the reult to a ituation in which the monetary ae i unchange. Section V ummarize the reult.

5 I. The Moel Framework There are 5 agent in the moel, ank (), the Fe (), the Treaury (t), houehol (h), an irm (m). There are 5 inancial intrument in the moel: (1) epoit at ank (D); (2) high-powere money (H), in the orm o currency (C) an reerve (R); (3) government on (G); (4) private on (V) [you can think o private on hel y houehol a corporate et an private on hel y ank a corporate loan]; an (5) icount winow loan (W). Figure 1 how the alance heet o the agent. Note that all inancial intrument are liailitie o at leat one agent an aet o at leat one agent, an the total amount o aet hel y all agent mut equal the total amount o liailitie or each intrument. Notation in thi moel ollow the convention o Santomero, uing lower-cae areviation or agent an upper-cae or intrument. For intrument I, the eman y agent j will e enote I j ; or example, the eman or government on y ank i G. A upercript enote upply. We ll alo aume there only one o each agent to keep thing imple. The net worth o each agent i i NW i. Following Santomero, the uget contraint (rom the alance heet in Figure 1) are: Bank: R G V D W NW Fe: G V W H NW Houehol: D C G V NW h h h h h Firm: K V NW (K i irm capital.) m m Treaury: D G NW t t t 2

6 Now, i we look at the eman an upply o each aet an equate them to in equilirium, we get: Depoit: Dh Dt D interet rate i r D High-powere money: R C H interet rate i 0 h Government on: G G G G interet rate i r G h t Private on: V V V V interet rate i r V h m Dicount winow loan: W W interet rate i r W Equilirium come aout y change in interet rate an quantitie o aet. It a hort-run moel, o we aren t worrie aout igger iue. Imagine an equilirium an we ll look at ome comparative-tatic exercie. Since we won t e allowing income or wealth to change in thee experiment, we won t inclue thoe in the moel. The Fe can increae the amount o high-powere money either y increaing the amount o non-orrowe reerve via open-market operation (uying either government on or private on in the open market) an via icount winow loan (lening irectly to ank). Note that we re taking an aggregate view, thu not moeling the interank (e un) market; o any hortage o reerve that ank want mut e met y change in interet rate to reuce the eman or reerve. Now or each o the eman an upply term in the moel, we nee to in how they are relate to the variou interet rate (an other actor that won t change in thi hort-run moel). 3

7 Bank: Deman or reerve: R D o reerve requirement are ining an no exce reerve are hel. Deman or government on: G G ( r, r, r, r ) G V D W + where the ign inicate the partial repone o the variale to an increae in the argument aove. Here the eman or government on y ank rie when the interet rate on government on rie (higher own return), ut all when the interet rate on private on rie (ank uy more private on an ewer government on) or when the ank mut pay higher interet rate on epoit or icount loan (ince then the cot o un i higher, o the ank want a maller portolio). Deman or private on: V V ( r, r, r, r )-- imilar to the cae o government G V D W + on. Supply o epoit: D D ( r, r, r, r )-- when return to ank aet rie, the ank G V D W will want more epoit; when the interet rate on epoit rie it will want ewer epoit; when the interet rate on icount loan rie, it will want more epoit to replace icount loan, i it ha any outtaning. Deman or icount loan: W W ( r, r, r, r )-- ame actor a upply o epoit, G V D W ut with oppoite eect ue to change in rate on epoit or icount rate. 4

8 Fe: Houehol: Firm: Treaury: We take Fe action to e exogenou; given ome equilirium, we re going to ee what happen in a comparative-tatic ene when the Fe change it aet an liailitie, auming monetary policy target an interet rate, a icue elow. Houehol utitute etween epoit, currency, government on, an private on, epening on the relative return to each. A higher own return increae eman, while a higher return on an alternative aet ecreae eman. So the eman or each are: Deman or epoit: Dh Dh ( rg, rv, rd) + Deman or currency: Ch Ch ( rg, rv, rd) Deman or government on: Gh Gh ( rg, rv, rd) + Deman or private on: Vh Vh ( rg, rv, rd) + For now, we take capital an the amount o private on iue a exogenou. I we conier more complicate iue, uch a the iuance y government-ponore enterprie o aitional on when their relative return ecline, thi aumption mut e change. But or now, V m i taken to e exogenou. We aume that Treaury iuance o government on, G t, i exogenou. An earlier verion o thi moel aume that any change in on iue mut e oet y an equal 5

9 change in epoit, D t. But that not really appropriate. The ecline in government et occur ecaue the government ha eentially receive a urprie increae in net wealth (i.e., tax receipt an unexpectely higher an expeniture unexpectely lower than they were eore). However, thi act mut e relecte in real economic activity (i.e., houehol or irm mut have higher capital or net wealth than eore) a well, analyi o which i going to require a more complete moel o real activity. Thu, it make ene at thi point to imply o a ierential analyi on the Fe portolio. In thi verion, in orer to examine jut the ierential eect rom the Fe portolio eciion, we ll take the upply o government on a exogenou. Equilirium: We aume that an equilirium exit in which all the equation ecriing eman an upply are etermine, all the uget contraint are atiie, an there a unique equilirium in the return variale, r D, r G, r V, an r W. Monetary Policy: Conier the ollowing comparative tatic experiment: The Fe reuce it holing o government on y the amount G 0. What happen in equilirium epen on what ele the Fe oe to it portolio. We aume or now that, in the hort run, monetary policy target the interet rate on epoit, o rd 0. Thu, any change that occur to r D are oet y the Fe to return the interet rate to it initial level. Why i it thi interet rate that targete? Since we aren t 6

10 moeling ank iniviually or complicating the moel y introucing uncertainty aout withinmaintenance-perio hock, we on t moel a eeral un market explicitly. Intea, thinking o the uual upply an eman iagram or reerve, which i conitent with our moel, ince reerve eman epen only on epoit eman, we aume the Fe target the interet rate on epoit in the hort run. How can the Fe hit it interet-rate target? Conier two poile metho y which thi happen: (1) The Fe oe open-market operation in private on to hit it interet-rate target. (2) The Fe utitute a new icount loan mechanim y which icount loan utitute or government on on the Fe alance heet an are upplie to ank elatically at the interet rate r W. The Dicount Winow: To keep thing imple, we aume that cae (1) involve mechanim in place toay, an that the icount winow i prohiitively expenive or ank. Thu there i no icount winow orrowing. In cae (2), we aume the Fe ha in place a imple icount winow mechanim allowing ank to orrow all they want at the icount rate (the NACF, nonaminitere creit acility). Spell it out in the moel: Now, let think aout what goe on in each market: Depoit: D ( r, r, r ) D D ( r, r, r, r ) h G V D t G V D W An increae in the return to government or private on ecreae houehol eman or epoit an increae ank upply o epoit, o exce eman or epoit ecreae. A higher interet rate on epoit increae houehol 7

11 eman or epoit an ecreae the ank upply o epoit, o the exce eman or epoit rie. An increae in Treaury epoit increae exce eman. Thu, we can ummarize the epoit market with the exce eman unction (ignoring the eect o change in the icount rate): Dr (, r, r, D, r ) 0. G V D t W + + High-powere money: R C H h D ( r, r, r, r ) C ( r, r, r ) H G V D W h G V D The eman or high-powere money i plit into two part: currency eman y houehol an reerve eman y ank. The Fe operate y aecting the upply o high-powere money, thu inluencing interet rate. In the market or high-powere money, the exce eman i given y: Hr (, r, r, r, H) 0. G V D W?? + Note that higher return to government or private on lea ank to earn a higher return on their aet, o they want to attract more epoit, o they eman more reerve, hence more high-powere money, ut houehol eman le currency an epoit, hence le high-powere money; o the ign o the irt two argument are amiguou. Higher epoit interet rate lea ank to oer ewer epoit, o they nee ewer reerve, an houehol want to hol le currency, o the eman or high-powere money i lower. An, o coure, when the Fe upplie more reerve, exce eman or reerve ecline. 8

12 Government on: G ( r, r, r, r ) G G ( r, r, r ) G G V D W h G V D t + + Higher return to government on will increae the eman y oth ank an houehol or the on. Higher return to private on will have the oppoite eect. When the return to epoit rie, houehol an ank want to hol ewer government on. Thu the exce eman or government on i: Gr (, r, r, G, G, r) 0 G V D t W + + Private on: V ( r, r, r, r ) V V ( r, r, r ) V G V D W h G V D m + + Higher return to private on will increae the eman y oth ank an houehol or the on. Higher return to government on will have the oppoite eect. When the return to epoit rie, houehol an ank want to hol ewer private on. Thu the exce eman or private on i: V( r, r, r, V, V, r ) 0. G V D m W + + What we have i really a ytem o 4 exce eman equation [D=0, H=0, G=0, an V=0] in 3 enogenou variale [r D, r G, an r V ]. But i three o the exce eman are zero, the ourth mut alo e zero ecaue uget contraint hol (Walra Law). That mean one exce eman equation i reunant. 9

13 Solving: In all three cae, the Fe reuction in eman or government et i moele a: 0. Thi change in the Fe alance heet i oet y a Fe action to keep the interet rate on epoit unchange: G (1) Open-market operation in private ecuritie: V H or (2) Dicount winow loan: W H Metho: In oth cae, we ll totally ierentiate the exce eman equation an ee i we can olve or a eterminitic equilirium. Totally ierentiate the unction G, D, an V: D r D r D r D D D r 0 1 G 2 V 3 D 4 t 5 W G r G r G r G G G G G r 0 1 G 2 V 3 D 4 5 t 6 W V r V r V r V V V r 0 1 G 2 V 3 D 4 5 W Note that the exce eman unction are aecte one-or-one y change in upply or eman, o D 4 = 1, G 4 = 1, G 5 = 1, an V 4 = 1. 10

14 II. Fe Portolio Shit with No Change in Interet Rate on Depoit In thi ection, we moel the reult when the Fe portolio hit in uch a way that the epoit interet rate i unchange. Cae 1: Open-Market Operation in Private Securitie 0, V, H, uch that r D = 0. G Sytem o 3 equation in 3 unknown: Dr 1 G Dr 2 V Gr 1 G Gr 2 V 0 0 Vr Vr 0 1 G 2 V Ue the irt equation to in r G in term o r V, then ue that in the econ equation to olve or r V. Ue that in the thir equation to olve or, to ee which irection monetary policy goe. Reult o erivation: r D /( D G D G ) 0 V r D /( D G D G ) 0 G ( DV DV )/( DG DG) D1( G2 V2) D2( G1V1) DG DG The ign o i unclear, ince it epen on the relative ize o ierent eect. Thu we on t know i high-powere money increae or ecreae. But we o know that the Fe uy private on an ell government on; we jut on t know which quantity i larger. Overall eect: The remaining eect can e oun rom the irection o change o r G an r V, an the agent uget contraint. Since r G an r V move in oppoite irection, ome thing can t e igne. 11

15 Depoit: D?, D?, r 0 h High-powere money: R?, C?, H? D h Government on: G >0, G <0, G >0, r 0 h Private on: V <0, V >0, V <0, r 0 h V G Cae 2: Dicount Winow Loan NACF In thi cae, the Fe open the icount winow an let ank orrow all they want at the icount rate, with no aminitrative cot. Monetary policy i conucte y changing the icount rate a the Fe change it portolio. Dicount winow loan an high-powere money upply clear the market uch that the Fe alance contraint i atiie an the interet rate on epoit oen t change. G 0, rw, uch that r D = 0. Let W H. Becaue there one more market now (icount winow loan), the ytem grow y an orer o magnitue. The exce eman unction or icount loan i: Sytem o 4 equation in 4 unknown: Dr 1 G Dr 2 V D5 0 Gr 1 G Gr 2 V G6 0 Vr Vr V 0 W r W r W W 0 1 G 2 V 5 1 G 2 V 5 W( rg, rv; rd; W ; rw)

16 Solve the irt 3 equation imultaneouly to in, r G, an r V, then ue thoe in the ourth equation to olve or Reult o erivation: W. Xr D ( DV DV), 1 G where X DD( GV GV) D ( GV GV ) DD( GV GV) I we aume that GV 1 2 GV 2 1, then X1 0, o r 0. G r V D5( DV 5 1 DV 1 5) X 1 D5( DV 2 1 DV 1 2) 0. X 1 The term r V can t e igne, o we on t know i the return to private on will rie or all. W W r W r W 1 G 2 V 5 [ ( ) ( ) ( )], X D5 W 1 DV 2 5 DV 5 2 W 2 DV 5 1 DV 1 5 W 5 DV 2 1 DV which i poitive i the main eect i rom the W 5 term. Other eect: 1. I rv 0 : Depoit: D <0, D <0, r 0 h High-powere money: R <0, C <0, H <0 D h Government on: G >0, G <0, G >0, r 0 Private on: V >0, V <0 h Dicount loan: W W 0, r 0 h W G 13

17 2. I rv 0 : 3. I rv 0 : Depoit: D?, D?, r 0 h High-powere money: R?, C?, H? D h Government on: G >0, G <0, G >0, r 0 Private on: V >0, V <0 h Dicount loan: W W 0, r 0 h W Depoit: D <0, D <0, r 0 h High-powere money: R <0, C <0, H <0 D h Government on: G >0 (proaly), G <0, G >0 (proaly), r 0 Private on: V?, V? h h Dicount loan: W W 0 (proaly), r 0 G W G 14

18 III. Special Aumption Locking Interet Rate Together Uner one cenario uner conieration, the return to mot aet are locke together. That cenario involve a ituation in which ank view icount loan an epoit a perect utitute, o r W r. Bank are willing to loan a much a irm eire to orrow rom them at D a contant prea, o r m r. Given thee aumption, all our olution metho are change D V omewhat, ecaue now quantitie upplie an emane, rather than interet rate, will change to achieve equilirium. Letting r rw rd, the analyi can e retructure o that eman an upplie epen jut on r G an r, with ome eman or upplie ajuting completely, when there are perect utitute. Depoit: Dh ( rg, r) Dt D, where Dt i exogenou an D i enogenou ut ank + upply all the epoit account that are opene at a given epoit rate. High-powere money: R C H h o [ D ( r, r) D ] C ( r, r) H + h G t h G Government on: G G Gh ( rg, r) Gt. + Private on: (, ) V V Vh rg r Vm, where V i etermine paively uch that the return on epoit plu a contant equal the return on private on.. Dicount loan: W W, where W ajut paively uch that r W r. D Inclue in the pecial aumption are that G 0. 15

19 Cae 1a: OMO in Private Securitie With the pecial aumption in place, when the Fe reuce it eman or government on an increae it eman or private on, oing o in a way that leave the interet rate on private on unchange (ecaue r r 0 ), the ollowing reult are otaine: The change in the uget contraint o the agent are: V D Bank: Fe: R V D G V H Reult: Houehol: D C G V 0 h h h h Government on: G ( r, r) G 0 h G Since G 0, G 0, o r 0. h G Since r 0, D 0, C 0, V 0. G h h h Depoit: D D 0, o R 0. h High-powere money: Since R 0 an C 0, then H 0. h Private on: From the ank uget contraint, ince reerve ecline le than epoit, ank mut hol ewer private on, o V 0. Thu the ank portolio hrink. Aitional Retriction: Uner another et o aumption coniere, eman y houehol or currency an epoit i exogenou. Impoing thoe conition here woul mean that H 0 an V G 0. 16

20 Cae 2a: Dicount Winow Loan NACF The experiment i one in which the Fe reuce it holing o government on, with an NACF in place, an the Fe upplie however many avance ank want at a ixe icount rate, which in thi cae equal r. The change in the uget contraint o the agent are: Bank: Fe: R V D W G W H Houehol: D C G V 0 h h h h Reult: Government on: G ( r, r) G 0 h G Since G 0, G 0, o r 0. h G Since r 0, D 0, C 0, V 0. G h h h Depoit: D D 0, o R 0. h High-powere money: Since R 0 an C 0, then H 0. Private on: V V 0, o V 0. h h In thi ituation, the anking ytem expan. Dicount loan: Auming the irect eect rom the Fe reuction in eman or government on excee the impact on the monetary ae (a very likely event), then W W 0. 17

21 18

22 Aitional Retriction: Uner another et o aumption, eman y houehol currency an epoit i exogenou. Impoing thoe conition here woul mean that H 0 an W G 0. 19

23 IV. Generalizing the Prolem with an Unchange Monetary Bae Suppoe we now wih to get ri o the retriction that rd 0. Thi make the prolem much more iicult to olve algeraically, ecaue now there one more term to olve or. However, we then ue a new aumption aout Fe policy, which put another retriction on the ytem either we aume the Fe oe not allow the monetary ae to change, or we aume that the icount rate oen t change. We conier 3 new cae, relate to the 2 previou cae: Cae 1: Private on cae: 0, V, H = 0. G In thi cae, the Fe eman ewer government on an replace them with private on, with no change in the monetary ae an no icount winow in operation. Cae 2: Dicount winow NACF cae: 0, W, r 0, H. G W Cae 2c: Dicount winow ACF cae (ACF = auction creit acility): 0, W, H 0. G 20

24 Cae 1: Private on cae: 0, V, r 0, H = 0. G W Sytem o 3 equation in 3 unknown: Dr 1 G Dr 2 V Dr 3 D 0 Gr 1 G Gr 2 V Gr 3 D 0 Vr Vr Vr 0 1 G 2 V 3 D Reult o erivation: r G [ D2( G3 V3) D3( G2 V2)] D ( GV GV ) D ( GV GV) D( GV GV) The ign o thi i har to igure out, ecaue the term point in oppoite irection. The V numerator i poitive i V2 G2, which eem likely ince V 2 i an own eect ( r V ), while G2 G i a cro eect ( ). The enominator i much more complicate, coniting o ix thir-orer r V term. O thee 6, 5 are negative an 1 i poitive. However, the one term that poitive i the D G V only own eect ( DGV ), o thi may e larger in value then all the other cro r r r D G V eect, in which cae the enominator i poitive. Thi type o aumption i one that we oten make in comparative tatic exercie uing graphical analyi. But we houl e careul ecaue thoe cro partial here mut alo relect uget contraint, o juging their magnitue can e iicult. Nonethele, i thee aumption hol, then rg 0. Other reult: r V [ D3( G1V1) D1( G3 V3)] D ( GV GV ) D ( GV GV) D( GV GV)

25 I we make the ame aumption that we mae aove, an i we urther aume that G1 V1 an that D3G1 DV 3 1D1( G3 V3), which again may e reaonale i the own eect are much larger in magnitue than the cro eect, then rv 0. Thi i intuitive ince the eman or private on i increaing. r D [ D1( G2 V2) D2( G1V1)] D ( GV GV ) D ( GV GV) D( GV GV) Unortunately, there no intuition on the ign o the change in the interet rate on epoit. Dierent eect point in ierent irection, an the ign epen on relative magnitue. Bank utitute ome government on or ome private on, given the irection o change o return, ut it impoile to tell whether ank aet overall increae or ecline, ince we can t tell i epoit increae or ecreae. 22

26 Cae 2: Dicount winow NACF cae: 0, W, r 0, H. G W Sytem o 4 equation in 4 unknown: Dr 1 G Dr 2 V Dr 3 D 0 Gr 1 G Gr 2 V Gr 3 D 0 Vr 1 G Vr 2 V Vr 3 D 0 Wr Wr Wr 0 1 G 2 V 3 D Reult o erivation: r G ( DV 2 3 DV 3 2) D ( GV GV ) D ( GV GV) D( GV GV) Compare to cae 1 aove, ining ign i a it eaier. The numerator i proaly poitive, which occur i D3V2 DV 2 3. Again, thi woul occur i the own eect are igger than cro eect. The enominator i the ame a in cae 1, o uner the ame aumption, then rg 0. r V ( DV 3 1 DV 1 3) D ( GV GV ) D ( GV GV) D( GV GV) r D ( DV 1 2 DV 2 1) D ( GV GV ) D ( GV GV) D( GV GV) Both r V an r D are poitive, uner the aumption mae aove. People eman or epoit account coul rie or all, epening on how they repon in comparing the higher yiel on government on an private on to the higher yiel on epoit. [ D1( VW 2 3 VW 3 2) D2( VW 3 1VW 1 3) D3( VW 1 2 VW 2 1)] D ( GV GV ) D ( GV GV ) D ( GV GV ) Thi term i mot likely poitive, though not einitively (5 o the 6 term in the numerator have the ame ign). But to know whether the monetary ae rie or all, we nee to know whether i poitive or negative, which i impoile to tell. 23

27 With return on government on, private on, an epoit all riing, people will hol le currency. But we on t know i the monetary ae rie or all. I it rie, then given that there le currency hel, there mut e more reerve hel againt more epoit. In that cae, the anking ytem mut get igger. But i the monetary ae ecline, which happen i epoit ecline uiciently, then we wouln t e ale to tell i the anking ytem aet woul increae or ecreae. 24

28 Cae 2c: Dicount winow ACF cae: 0, W, H 0. G Sytem o 4 equation in 4 unknown: D1rG D2rV D3rD D5rW 0 G1rG G2rV G3rD G6rW 0 V1rG V2rV V3rD V5rW 0 W r W r W r W r 0 1 G 2 V 3 D 5 W Reult o erivation: r G ( DX 2 1DX 3 2 DX 5 3) D X D X D X D X , X1 V3( W5 G6) V5( G3 W3) X2 V2( G6 W5) V5( W2 G2) X3 V2( W3 G3) V3( G2 W2) X4 G2( VW 3 5 VW 5 3) G3( VW 5 2 VW 2 5) G6( VW 2 3VW 3 2) X5 G1( VW 3 5 VW 5 3) G3( VW 5 1VW 1 5) G6( VW 1 3VW 3 1) X6 G1( VW 2 5 VW 5 2) G2( VW 5 1VW 1 5) G6( VW 1 2 VW 2 1) X G ( VW VW ) G ( VW VW ) G ( VW VW ) Thi i quite a complicate ytem. I we aume that the own eect ominate, a we i earlier, then it ugget that oth numerator an enominator are negative, o rg 0. r V ( DX 1 8 DX 3 9 DX 5 10) D X D X D X D X , X V ( W G ) V ( G W ) X V ( G W ) V ( W G ) X V ( W G ) V ( G W ) Thi i clearly not ignale, an there are no own eect, o it impoile to ign r V. 25

29 r D ( DX 1 11DX 2 12 DX 5 13) D X D X D X D X , X V ( W G ) V ( G W ) X V ( G W ) V ( W G ) X V ( W G ) V ( G W ) Again, there are no own eect in the numerator, o it can t e igne. r W ( DX 1 14 DX 2 15 DX 3 16) D X D X D X D X , X V ( W G ) V ( G W ) X V ( G W ) V ( W G ) X V ( W G ) V ( G W ) Here, there an own eect, an i it ominate the other term, then rw 0. All the reult here are quite tentative, or they epen on omewhat uiou aumption. Whether the anking ytem expan or contract here i har to ay. We know that the anking ytem take out more icount loan, equal to the ecreae in the eman or government on y the Fe. But o thoe icount loan iplace more or ewer epoit? Since uning i ecoming more expenive, ank may wih to reuce the ize o their portolio; on the other han, return are higher, o they may wih to expan. Houehol may utitute government on or epoit account, a well. 26

30 V. SUMMARY Thi paper evelop a tatic general-equilirium moel o the Fe portolio choice in the hort run. Fining the reult o a Fe portolio hit require a numer o aumption, which may not hol in all cae. The reult reporte elow make ue o thoe aumption. When the Fe change it portolio y reucing it ownerhip o government on an keep the interet rate on epoit rom changing, the reult epen on what the Fe utitute to replace government on. I the Fe uy private ecuritie, the interet rate on uch ecuritie ecline while the interet rate on government on rie. I the Fe ue a nonaminitere creit acility (NACF), the interet rate on government on rie an the icount rate all. When the Fe change it portolio y reucing it ownerhip o government on an interet rate are locke together, the reult alo epen on what the Fe utitute to replace government on. I the Fe uy private ecuritie, the interet rate on government on rie an ank hol ewer private on an ank hrink in ize. I the Fe ue an NACF, the interet rate on government on rie an the anking ytem expan. When the Fe change it portolio y reucing it ownerhip o government on ut oe not ix the epoit rate an interet rate are not locke together, we in the ollowing reult. I the Fe uy private on an oe not allow the monetary ae to change, then the interet rate on private on ecline while the interet rate on government on rie. I the Fe ue an NACF an oe not allow the icount rate to change, then the interet rate on government on, private on, an epoit all rie an the eman or currency ecline. I the Fe ue an auction creit acility (ACF) an oe not allow the monetary ae to change, then the interet rate on government on an private on rie. 27

31 REFERENCES Feeral Reerve Sytem Stuy Group on Alternative Intrument or Sytem Operation. Alternative Intrument or Open Market an Dicount Winow Operation. Wahington, D.C.: Feeral Reerve Boar o Governor, Santomero, Anthony M. Controlling Monetary Aggregate: The Dicount Winow. Journal o Finance 38 (June 1983), pp

32 Figure 1 Balance Sheet Bank () Aet Liailitie + Net Worth Reerve R D Depoit Account Government Bon G W Dicount Loan Private Bon V NW Net Worth Houehol (h) Aet Liailitie + Net Worth Depoit D h Currency C h Government Bon G h Private Bon Vh NWh Net Worth Feeral Reerve () Aet Liailitie + Net Worth Government Bon G H High-Powere Money Private Bon V Dicount Loan W NW Net Worth 29

33 Figure 1 (continue) Balance Sheet Treaury (t) Aet Liailitie + Net Worth Depoit D t Gt Government Bon NWt Net Worth Firm (m) Aet Liailitie + Net Worth Capital K Vm Private Bon NWm Net Worth 30