the value of inside and outside money: expanded verssion · wrrfhqwudol}hg1 wkxv/...

WORKING PAPER SERIES

The Value of Inside and Outside Money: Expanded Version

James Bullard and Bruce D. Smith

Working Paper 2001-011Ahttp://research.stlouisfed.org/wp/2001/2001-011.pdf

September 2001

FEDERAL RESERVE BANK OF ST. LOUISResearch Division411 Locust Street

St. Louis, MO 63102

______________________________________________________________________________________

The views expressed are those of the individual authors and do not necessarily reflect official positions ofthe Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.

Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulatediscussion and critical comment. References in publications to Federal Reserve Bank of St. Louis WorkingPapers (other than an acknowledgment that the writer has had access to unpublished material) should becleared with the author or authors.

Photo courtesy of The Gateway Arch, St. Louis, MO. www.gatewayarch.com

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djhqwv pxvw lvvxh oldelolwlhv zlwk d pdwxulw| ri wzr shulrgv wr plggoh0djhg

djhqwv1 Wkh odwwhu wkhq fduu| wkhvh oldelolwlhv wr d orfdwlrq zkhuh wkh|

zloo eh vhsdudwhg iurp wkhlu lvvxhuv1 Wkh wzr0shulrg oldelolwlhv khog e|

djhqwv zkr duh qrz rog dw w . 4 zloo wkhq eh vrog wr qhzo| plggoh0djhg

djhqwv lq orfdwlrq l�

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oldelolwlhv zlwk d pdwxulw| ri wzr shulrgv qhfhvvdulo| flufxodwh1 Lq idfw/

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ri irxu w|shv ri oldelolwlhv= rxwvlgh prqh|/ rqh0shulrg +qrq0flufxodwlqj, sul0

ydwh oldelolwlhv/ qhzo|0lvvxhg wzr0shulrg +flufxodwlqj, sulydwh oldelolwlhv/ dqg

suhylrxvo|0lvvxhg wzr0shulrg +flufxodwlqj, sulydwh oldelolwlhv1 Qhzo|0lvvxhg

flufxodwlqj oldelolwlhv zloo eh vrog qh{w shulrg> suhylrxvo|0lvvxhg flufxodwlqj

oldelolwlhv zloo eh sxufkdvhg dqg suhvhqwhg wr wkhlu lvvxhu iru uhghpswlrq1 Lw

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zloo�lq wkh ixwxuh�phhw qhz djhqwv zkr wkhpvhoyhv zloo�hyhq ixuwkhu

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wlrqv fdq eh phgldwhg wkurxjk wkh xvh ri sulydwh flufxodwlqj oldelolwlhv1

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duh qrw idfwruv1 Khuh zh frqvlghu rqo| wkh hfrqrp| zlwk rxwvlgh prqh|

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dq djhqw*v sdwwhuq ri pryhphqw1 Ru/ lq rwkhu zrugv/ doo djhqwv idfh wkh

frpprq jurvv udwh ri lqwhuhvw U +w, ehwzhhq w dqg w . 4= Pruhryhu/ vlqfh

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v|vwhp frqvlvwlqj ri +45,0+47, e|

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prqhwdu| vwhdg| vwdwh1

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wkh prqhwdu| vwhdg| vwdwh lv ghwhuplqdwh/ dqg sdwkv dssurdfklqj lw glvsod|

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518141 Duelwudjh frqglwlrqv

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frqglwlrqv iru djhqwv eruq lq orfdwlrq 5 duh jlyhq e|

U � � +w,U � � +w. 4, @ U � � +w,U � � +w. 4, +53,

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U � � +w,U � � +w. 4, @ U � � +w,U � � +w. 4, +55,

iru doo w � 3 iru djhqwv iroorzlqj wkh lwlqhudu| +5> 4> 4, > dqg �qdoo|

U � � +w,U � � +w. 4, @ U � � +w,U � � +w. 4, +56,

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s � +w,s +w. 4,

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D � .E � .F � @ H � > +58,

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D � .E � .F � @ H � +63,

zkhuh D � lv wkh ghvluhg frqvxpswlrq ri wkh |rxqj lq orfdwlrq 5 dw gdwh w>

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E � lv wkh ghvluhg frqvxpswlrq ri wkh plggoh0djhg lq orfdwlrq 5 dw gdwh w/

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+66,

dqg H � lv wkh dydlodeoh hqgrzphqw lq orfdwlrq 5 dw gdwh w> jlyhq e|

H � � +� � � � . � � � � . � � � � . � � � � , h � .

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pdunhw fohdulqj frqglwlrqv +58, dqg +63,/ frqvwlwxwh wkh htxloleulxp odzv

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fkrrvh � � � � > � � � � > � � � � > dqg � � � � frqvlvwhqw zlwk wkh vdwlvidfwlrq ri +H1;,

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Wkhq lw iroorzv wkdw v � +U � � , A +?, 3 dqg v � +U � � , A +?, 3 krog xqghu

wkhvh dvvxpswlrqv li +J1<, lv vdwlv�hg/ dqg li +J17, dqg +J19, erwk krog

+idlo,1

Xqghu wkh dvvxpswlrqv pdgh wkxv idu +J17, krogv +idlov, li

+4 . �, h � +� � � � . � � � � ,� +� � � � . � � � � , +�h � � h � ,. +J143,

+� � � � . � � � � , h � ? +A, 3=

Frqglwlrq +J19, krogv +idlov, li

+4 . �, h � +� � � � . � � � � ,� +� � � � . � � � � , +�h � � h � ,. +J144,

+� � � � . � � � � , h � A +?, 3=

Lw lv vwudljkwiruzdug wr fkrrvh sdudphwhu ydoxhv vr wkdw +J1<, krogv/ dqg vr

wkdw +J143, dqg +J144, hlwkhu erwk krog ru erwk idlo1 Wkxv wkh ghfhqwudol}hg

hfrqrp| fdq kdyh hlwkhu v � +U � � , A 3 dqg v � +U � � , A 3> ru v � +U � � , ? 3

dqg v � +U � � , ? 3= Wklv lv wuxh hyhq wkrxjk wkh dqdorj fhqwudol}hg hfrqrp|

lv qhlwkhu fodvvlfdo qru Vdpxhovrqldq1

Lw lv wkhuhiruh dssduhqw wkdw/ e| vpdoo yduldwlrqv lq sdudphwhuv/ zh fdq

vhw wkh whup ^h � . h � � +4 . �, i +4> 4,` . ^h � � i +4> 4,` hlwkhu voljkwo| srv0

lwlyh ru voljkwo| qhjdwlyh zlwkrxw dowhulqj wkh suhylrxv dujxphqw1 Wklv

hvwdeolvkhv Fodlpv 714 dqg 7151

the value of inside and outside money: expanded verssion · wrrfhqwudol}hg1 wkxv/...

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