speeches · October 9, 2008
Regional President Speech
James Bullard · President
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THE OPTIMAL INFLATION TARGET IN AN
ECONOMY WITH LIMITED ENFORCEMENT
GaetanoAntinolfi
WashingtonUniversity
CostasAzariadis
WashingtonUniversityandFRB-St. Louis
JamesBullard*
FederalReserveBankofSt. Louis
NewPerspectivesonMonetaryPolicyDesign
Barcelona,Spain
10October2008
ViewsexpressedarethoseoftheauthoranddonotnecessarilyreflectofficialpositionsoftheFOMCortheFederalReserveSystem.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
COMFORT ZONES
TypicalFOMCmemberstatements: 1to2percentinflation
wouldbeideal.
“Smallpositiveinflationisthebestinflationtarget.”
Associatedwithshort-termnominalinterestratesnear5percent.
Economictheory: nominalinterestratesshouldbezero.
Whythedifference?
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THEORY AND REALITY: WHY THE DIFFERENCE?
Japan.
Summers(1991): Zeroboundonnominalinterestratesinterferes
withstabilizationpolicy.
AdamandBilli(2006).
Smith(2002). Deflationcausesdisintermediation,harmingthe
operationofcreditmarkets.
Westudyaversionofthelatter:
Asmallamountofinflation“deepensfinancialmarkets”inaway
wemakeprecise.
Acontinuumofinfinitely-livedhouseholds.
Endowmentsfluctuate.
Twoassets: currencyandconsumptionloans.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
WHAT WE DO
Endowmenteconomywithconstantaggregateincome.
Endowmentsfluctuate.
Twoassets: currencyandconsumptionloans.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
WHAT WE DO
Endowmenteconomywithconstantaggregateincome.
Acontinuumofinfinitely-livedhouseholds.
Twoassets: currencyandconsumptionloans.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
WHAT WE DO
Endowmenteconomywithconstantaggregateincome.
Acontinuumofinfinitely-livedhouseholds.
Endowmentsfluctuate.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
WHAT WE DO
Endowmenteconomywithconstantaggregateincome.
Acontinuumofinfinitely-livedhouseholds.
Endowmentsfluctuate.
Twoassets: currencyandconsumptionloans.
“Townsend-Bewley-type”orcashagentscanonlyusecurrencyin
nonnegativeamountstosmoothconsumption.
“Kehoe-Levine-type”orcreditagentscanparticipateineither
assetmarketsubjecttoendogenousdebtconstraints.
Defaultispunishedbyperpetualexclusionfromtheloanmarket
butstillpermitsdefaultinghouseholdstoholdnonnegative
currency.
Inflationwillmakedefaultlessattractive,loosening
participationconstraintsandstrengtheningthecreditmarket.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
AGENT TYPES
Householdsaredividedintotwotypes.
“Kehoe-Levine-type”orcreditagentscanparticipateineither
assetmarketsubjecttoendogenousdebtconstraints.
Defaultispunishedbyperpetualexclusionfromtheloanmarket
butstillpermitsdefaultinghouseholdstoholdnonnegative
currency.
Inflationwillmakedefaultlessattractive,loosening
participationconstraintsandstrengtheningthecreditmarket.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
AGENT TYPES
Householdsaredividedintotwotypes.
“Townsend-Bewley-type”orcashagentscanonlyusecurrencyin
nonnegativeamountstosmoothconsumption.
Defaultispunishedbyperpetualexclusionfromtheloanmarket
butstillpermitsdefaultinghouseholdstoholdnonnegative
currency.
Inflationwillmakedefaultlessattractive,loosening
participationconstraintsandstrengtheningthecreditmarket.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
AGENT TYPES
Householdsaredividedintotwotypes.
“Townsend-Bewley-type”orcashagentscanonlyusecurrencyin
nonnegativeamountstosmoothconsumption.
“Kehoe-Levine-type”orcreditagentscanparticipateineither
assetmarketsubjecttoendogenousdebtconstraints.
Inflationwillmakedefaultlessattractive,loosening
participationconstraintsandstrengtheningthecreditmarket.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
AGENT TYPES
Householdsaredividedintotwotypes.
“Townsend-Bewley-type”orcashagentscanonlyusecurrencyin
nonnegativeamountstosmoothconsumption.
“Kehoe-Levine-type”orcreditagentscanparticipateineither
assetmarketsubjecttoendogenousdebtconstraints.
Defaultispunishedbyperpetualexclusionfromtheloanmarket
butstillpermitsdefaultinghouseholdstoholdnonnegative
currency.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
AGENT TYPES
Householdsaredividedintotwotypes.
“Townsend-Bewley-type”orcashagentscanonlyusecurrencyin
nonnegativeamountstosmoothconsumption.
“Kehoe-Levine-type”orcreditagentscanparticipateineither
assetmarketsubjecttoendogenousdebtconstraints.
Defaultispunishedbyperpetualexclusionfromtheloanmarket
butstillpermitsdefaultinghouseholdstoholdnonnegative
currency.
Inflationwillmakedefaultlessattractive,loosening
participationconstraintsandstrengtheningthecreditmarket.
Deflationisinfeasibleiftheplannerassignspositiveweightto
credithouseholds.
Inflationhigherthanthelevelrequiredtoslackendebt
constraintswillnotbechoseniftheplannerassignssufficient
weighttocashhouseholds.
Iftheplannerputsarelativeweightgreaterthanzerobutless
thanthepopulationweightoncredithouseholds,theoptimum
inflationrateispositive.
Conclude: Independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
PREVIEW OF MAIN FINDINGS
Westudyaparticularsocialplanningproblem,madeprecise
below.
Inflationhigherthanthelevelrequiredtoslackendebt
constraintswillnotbechoseniftheplannerassignssufficient
weighttocashhouseholds.
Iftheplannerputsarelativeweightgreaterthanzerobutless
thanthepopulationweightoncredithouseholds,theoptimum
inflationrateispositive.
Conclude: Independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
PREVIEW OF MAIN FINDINGS
Westudyaparticularsocialplanningproblem,madeprecise
below.
Deflationisinfeasibleiftheplannerassignspositiveweightto
credithouseholds.
Iftheplannerputsarelativeweightgreaterthanzerobutless
thanthepopulationweightoncredithouseholds,theoptimum
inflationrateispositive.
Conclude: Independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
PREVIEW OF MAIN FINDINGS
Westudyaparticularsocialplanningproblem,madeprecise
below.
Deflationisinfeasibleiftheplannerassignspositiveweightto
credithouseholds.
Inflationhigherthanthelevelrequiredtoslackendebt
constraintswillnotbechoseniftheplannerassignssufficient
weighttocashhouseholds.
Conclude: Independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
PREVIEW OF MAIN FINDINGS
Westudyaparticularsocialplanningproblem,madeprecise
below.
Deflationisinfeasibleiftheplannerassignspositiveweightto
credithouseholds.
Inflationhigherthanthelevelrequiredtoslackendebt
constraintswillnotbechoseniftheplannerassignssufficient
weighttocashhouseholds.
Iftheplannerputsarelativeweightgreaterthanzerobutless
thanthepopulationweightoncredithouseholds,theoptimum
inflationrateispositive.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
PREVIEW OF MAIN FINDINGS
Westudyaparticularsocialplanningproblem,madeprecise
below.
Deflationisinfeasibleiftheplannerassignspositiveweightto
credithouseholds.
Inflationhigherthanthelevelrequiredtoslackendebt
constraintswillnotbechoseniftheplannerassignssufficient
weighttocashhouseholds.
Iftheplannerputsarelativeweightgreaterthanzerobutless
thanthepopulationweightoncredithouseholds,theoptimum
inflationrateispositive.
Conclude: Independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
RECENT RELATED LITERATURE
AiyagariandWilliamson(2000JET).
Relatedenvironment,randomendowments,outsideoptionis
Bewley,emphasisonfinancialintermediation,positiveinflation
detersdefault,computational.
Berentsen,CameraandWaller(2007JET).
Relatedenvironment,Lagos-Wright,emphasisonfinancial
intermediation,positiveinflationdetersdefault.
Ragot(2007). OLGframework.
Andolfatto(2007).
Antinolfi,Azariadis,andBullard(2007).
Moneyistheonlyasset,emphasisondynamicsandequilibrium
selection.
Sanchez,Williamson,andWright(2007). Blackboardversion.
λ“Kehoe-Levine”orcredittypeagents.
1 λ“Townsend-Bewley”orcashtypeagents.
(cid:0)
Alltypeshaveidenticalpreferences
∞
∑ βtu ci (1)
t
t=0
(cid:16) (cid:17)
withdiscountfactor0< β <1,u(c)standard,andi=0,1,2,3.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENVIRONMENT
Continuumofinfinitely-livedhouseholds.
1 λ“Townsend-Bewley”orcashtypeagents.
(cid:0)
Alltypeshaveidenticalpreferences
∞
∑ βtu ci (1)
t
t=0
(cid:16) (cid:17)
withdiscountfactor0< β <1,u(c)standard,andi=0,1,2,3.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENVIRONMENT
Continuumofinfinitely-livedhouseholds.
λ“Kehoe-Levine”orcredittypeagents.
Alltypeshaveidenticalpreferences
∞
∑ βtu ci (1)
t
t=0
(cid:16) (cid:17)
withdiscountfactor0< β <1,u(c)standard,andi=0,1,2,3.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENVIRONMENT
Continuumofinfinitely-livedhouseholds.
λ“Kehoe-Levine”orcredittypeagents.
1 λ“Townsend-Bewley”orcashtypeagents.
(cid:0)
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENVIRONMENT
Continuumofinfinitely-livedhouseholds.
λ“Kehoe-Levine”orcredittypeagents.
1 λ“Townsend-Bewley”orcashtypeagents.
(cid:0)
Alltypeshaveidenticalpreferences
∞
∑ βtu ci (1)
t
t=0
(cid:16) (cid:17)
withdiscountfactor0< β <1,u(c)standard,andi=0,1,2,3.
Cashhouseholdsaredividedintotwosub-types,2and3,with
mass1 λ/2each.
(cid:0)
Endowments,interpretedasincomeshares,areperiodic:
(1+α,1 α) ift=0,2,...
ω0,ω1 = ω2,ω3 = (cid:0) (2)
t t t t (1 α,1+α) ift=1,3,...
(cid:16) (cid:17) (cid:16) (cid:17) (cid:26) (cid:0)
α (0,1)indexesthedegreeofincomevolatility.
2
Aggregateincomeisconstant.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENDOWMENTS
Credithouseholdsaredividedintotwosub-types,0and1,with
massλ/2each.
Endowments,interpretedasincomeshares,areperiodic:
(1+α,1 α) ift=0,2,...
ω0,ω1 = ω2,ω3 = (cid:0) (2)
t t t t (1 α,1+α) ift=1,3,...
(cid:16) (cid:17) (cid:16) (cid:17) (cid:26) (cid:0)
α (0,1)indexesthedegreeofincomevolatility.
2
Aggregateincomeisconstant.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENDOWMENTS
Credithouseholdsaredividedintotwosub-types,0and1,with
massλ/2each.
Cashhouseholdsaredividedintotwosub-types,2and3,with
mass1 λ/2each.
(cid:0)
α (0,1)indexesthedegreeofincomevolatility.
2
Aggregateincomeisconstant.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENDOWMENTS
Credithouseholdsaredividedintotwosub-types,0and1,with
massλ/2each.
Cashhouseholdsaredividedintotwosub-types,2and3,with
mass1 λ/2each.
(cid:0)
Endowments,interpretedasincomeshares,areperiodic:
(1+α,1 α) ift=0,2,...
ω0,ω1 = ω2,ω3 = (cid:0) (2)
t t t t (1 α,1+α) ift=1,3,...
(cid:16) (cid:17) (cid:16) (cid:17) (cid:26) (cid:0)
Aggregateincomeisconstant.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENDOWMENTS
Credithouseholdsaredividedintotwosub-types,0and1,with
massλ/2each.
Cashhouseholdsaredividedintotwosub-types,2and3,with
mass1 λ/2each.
(cid:0)
Endowments,interpretedasincomeshares,areperiodic:
(1+α,1 α) ift=0,2,...
ω0,ω1 = ω2,ω3 = (cid:0) (2)
t t t t (1 α,1+α) ift=1,3,...
(cid:16) (cid:17) (cid:16) (cid:17) (cid:26) (cid:0)
α (0,1)indexesthedegreeofincomevolatility.
2
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
ENDOWMENTS
Credithouseholdsaredividedintotwosub-types,0and1,with
massλ/2each.
Cashhouseholdsaredividedintotwosub-types,2and3,with
mass1 λ/2each.
(cid:0)
Endowments,interpretedasincomeshares,areperiodic:
(1+α,1 α) ift=0,2,...
ω0,ω1 = ω2,ω3 = (cid:0) (2)
t t t t (1 α,1+α) ift=1,3,...
(cid:16) (cid:17) (cid:16) (cid:17) (cid:26) (cid:0)
α (0,1)indexesthedegreeofincomevolatility.
2
Aggregateincomeisconstant.
The“unbanked.”
Noclaimscanbeenforcedonthemorbythem.
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
Futureinflationrateswillimpactthepayofftodefault.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
The“unbanked.”
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
Futureinflationrateswillimpactthepayofftodefault.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
Noclaimscanbeenforcedonthemorbythem.
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
Futureinflationrateswillimpactthepayofftodefault.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
Noclaimscanbeenforcedonthemorbythem.
The“unbanked.”
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
Futureinflationrateswillimpactthepayofftodefault.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
Noclaimscanbeenforcedonthemorbythem.
The“unbanked.”
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Futureinflationrateswillimpactthepayofftodefault.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
Noclaimscanbeenforcedonthemorbythem.
The“unbanked.”
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
NATURE OF THE ENVIRONMENT
Cashagentsareanonymoushouseholdswhomayonlyuse
currencytosmoothincomefluctuations,asinBewley(1980).
Noclaimscanbeenforcedonthemorbythem.
The“unbanked.”
Creditagentsmayenterintoloanarrangementstosmooth
consumptionsubjecttoendogenousdebtlimits,asinKehoeand
Levine(1993).
Creditagentswhodefaultareforeverexcludedfromtheloan
marketandmustinsteadusecurrency.
Futureinflationrateswillimpactthepayofftodefault.
... anddirectlyselectsconsumptionvectorsforcreditagentswho
mayeitheraccepttheirallocationsorbehavelikecashagentsin
perpetuity.
Theinflationtargetinthiseconomyissimilartoanoptimaltax
subjecttoanincentiveconstraintasunderstoodbyMirrlees
(1971).
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THE MONETARY AUTHORITY, BRIEF VERSION
Benevolentsocialplannerchoosesaconstantinflationrateat
whichcashagentscantrade...
Theinflationtargetinthiseconomyissimilartoanoptimaltax
subjecttoanincentiveconstraintasunderstoodbyMirrlees
(1971).
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THE MONETARY AUTHORITY, BRIEF VERSION
Benevolentsocialplannerchoosesaconstantinflationrateat
whichcashagentscantrade...
... anddirectlyselectsconsumptionvectorsforcreditagentswho
mayeitheraccepttheirallocationsorbehavelikecashagentsin
perpetuity.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THE MONETARY AUTHORITY, BRIEF VERSION
Benevolentsocialplannerchoosesaconstantinflationrateat
whichcashagentscantrade...
... anddirectlyselectsconsumptionvectorsforcreditagentswho
mayeitheraccepttheirallocationsorbehavelikecashagentsin
perpetuity.
Theinflationtargetinthiseconomyissimilartoanoptimaltax
subjecttoanincentiveconstraintasunderstoodbyMirrlees
(1971).
atransferofresourcesfromthecashsector,and
areductioninthedefaultpayoffwhichbringsabouthigherdebt
limits.
... andconfertwobenefitsoncreditagents:
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
COSTS AND BENEFITS OF POSITIVE INFLATION
Positiveratesofinflationimposeataxoncashagents...
atransferofresourcesfromthecashsector,and
areductioninthedefaultpayoffwhichbringsabouthigherdebt
limits.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
COSTS AND BENEFITS OF POSITIVE INFLATION
Positiveratesofinflationimposeataxoncashagents...
... andconfertwobenefitsoncreditagents:
areductioninthedefaultpayoffwhichbringsabouthigherdebt
limits.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
COSTS AND BENEFITS OF POSITIVE INFLATION
Positiveratesofinflationimposeataxoncashagents...
... andconfertwobenefitsoncreditagents:
atransferofresourcesfromthecashsector,and
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
COSTS AND BENEFITS OF POSITIVE INFLATION
Positiveratesofinflationimposeataxoncashagents...
... andconfertwobenefitsoncreditagents:
atransferofresourcesfromthecashsector,and
areductioninthedefaultpayoffwhichbringsabouthigherdebt
limits.
Itwouldassign(c ,c )tohighincomeandlowincomecredit
H L
agents,andconsumption(x ,x )tothecorrespondingcash
H L
agents.
Equivalenttolump-sumtaxesonsomeagentsandlump-sum
subsidiestoothers.
Becauseinflationisadistortionarytax,wedefineamodified
planningproblem.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
INFLATION TARGETING AS A PLANNING PROBLEM
Pureequal-treatmentplanningproblemwouldchooseaperiodic
consumptionsequenceforeachagent.
Equivalenttolump-sumtaxesonsomeagentsandlump-sum
subsidiestoothers.
Becauseinflationisadistortionarytax,wedefineamodified
planningproblem.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
INFLATION TARGETING AS A PLANNING PROBLEM
Pureequal-treatmentplanningproblemwouldchooseaperiodic
consumptionsequenceforeachagent.
Itwouldassign(c ,c )tohighincomeandlowincomecredit
H L
agents,andconsumption(x ,x )tothecorrespondingcash
H L
agents.
Becauseinflationisadistortionarytax,wedefineamodified
planningproblem.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
INFLATION TARGETING AS A PLANNING PROBLEM
Pureequal-treatmentplanningproblemwouldchooseaperiodic
consumptionsequenceforeachagent.
Itwouldassign(c ,c )tohighincomeandlowincomecredit
H L
agents,andconsumption(x ,x )tothecorrespondingcash
H L
agents.
Equivalenttolump-sumtaxesonsomeagentsandlump-sum
subsidiestoothers.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
INFLATION TARGETING AS A PLANNING PROBLEM
Pureequal-treatmentplanningproblemwouldchooseaperiodic
consumptionsequenceforeachagent.
Itwouldassign(c ,c )tohighincomeandlowincomecredit
H L
agents,andconsumption(x ,x )tothecorrespondingcash
H L
agents.
Equivalenttolump-sumtaxesonsomeagentsandlump-sum
subsidiestoothers.
Becauseinflationisadistortionarytax,wedefineamodified
planningproblem.
Next,givenπ,highincomecashagentschooseaperiodic
consumptionvector(x ,x ) 0tomaximizestationary
H L
(cid:21)
discountedutility
1
[u(x )+βu(x )] (3)
1 β2 H L
(cid:0)
subjectto
x 1+α, (4)
H
(cid:20)
x +πx =1+α+π(1 α), (5)
H L
(cid:0)
u(x )+βu(x ) u(1+α)+βu(1 α) (6)
H L
(cid:21) (cid:0)
(1)nonnegativecurrency;(2)moneybalancesareusedupto
smoothconsumptioninlowincomedates;(3)agentscan
renouncemoneyandconsumeendowments.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MODIFIED PLANNING PROBLEM
First,themonetaryauthoritysetsaconstantinflationfactorπ.
(1)nonnegativecurrency;(2)moneybalancesareusedupto
smoothconsumptioninlowincomedates;(3)agentscan
renouncemoneyandconsumeendowments.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MODIFIED PLANNING PROBLEM
First,themonetaryauthoritysetsaconstantinflationfactorπ.
Next,givenπ,highincomecashagentschooseaperiodic
consumptionvector(x ,x ) 0tomaximizestationary
H L
(cid:21)
discountedutility
1
[u(x )+βu(x )] (3)
1 β2 H L
(cid:0)
subjectto
x 1+α, (4)
H
(cid:20)
x +πx =1+α+π(1 α), (5)
H L
(cid:0)
u(x )+βu(x ) u(1+α)+βu(1 α) (6)
H L
(cid:21) (cid:0)
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MODIFIED PLANNING PROBLEM
First,themonetaryauthoritysetsaconstantinflationfactorπ.
Next,givenπ,highincomecashagentschooseaperiodic
consumptionvector(x ,x ) 0tomaximizestationary
H L
(cid:21)
discountedutility
1
[u(x )+βu(x )] (3)
1 β2 H L
(cid:0)
subjectto
x 1+α, (4)
H
(cid:20)
x +πx =1+α+π(1 α), (5)
H L
(cid:0)
u(x )+βu(x ) u(1+α)+βu(1 α) (6)
H L
(cid:21) (cid:0)
(1)nonnegativecurrency;(2)moneybalancesareusedupto
smoothconsumptioninlowincomedates;(3)agentscan
renouncemoneyandconsumeendowments.
Equaltreatmentofhighincomeandlowincomehouseholds
meansthatthediscountedutilitiesareweightedequally. This
givesthewelfarefunctionabove.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON THE MODIFIED PLANNING PROBLEM
Letx (π)andx (π)solvethepreviousproblem. Givenπ,the
H L
plannernowchoosesconsumptionvalues(c ,c ) 0forcredit
H L
(cid:21)
householdstomaximizetheequal-treatmentwelfarefunction
1
[u(c )+u(c )] (7)
1 β2 H L
(cid:0)
subjecttotheresourceconstraint
λ(c +c )+(1 λ)[x (π)+x (π)] =2, (8)
H L H L
(cid:0)
andtheparticipationconstraint
u(c )+βu(c ) u[x (π)]+βu[x (π)]. (9)
H L H L
(cid:21)
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON THE MODIFIED PLANNING PROBLEM
Letx (π)andx (π)solvethepreviousproblem. Givenπ,the
H L
plannernowchoosesconsumptionvalues(c ,c ) 0forcredit
H L
(cid:21)
householdstomaximizetheequal-treatmentwelfarefunction
1
[u(c )+u(c )] (7)
1 β2 H L
(cid:0)
subjecttotheresourceconstraint
λ(c +c )+(1 λ)[x (π)+x (π)] =2, (8)
H L H L
(cid:0)
andtheparticipationconstraint
u(c )+βu(c ) u[x (π)]+βu[x (π)]. (9)
H L H L
(cid:21)
Equaltreatmentofhighincomeandlowincomehouseholds
meansthatthediscountedutilitiesareweightedequally. This
givesthewelfarefunctionabove.
ThisSWFassignsequalweightstomembersofthesamegroup
butpotentiallydifferentweightstodifferentgroups.
AstrictlyutilitarianSWFwouldhaveequalweightsforall,that
is,δ = λ.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON THE MODIFIED PLANNING PROBLEM
Ifc (π)andc (π)solvethepreviousproblemforagiven
H L
π >0,theplannerselectsthestationaryinflationfactorπto
maximizethesocialwelfarefunction
(π,δ) = δ u[c (π)]+u[c (π)]
H L
W f g
+(1 δ) u[x (π)]+u[x (π)] . (10)
H L
(cid:0) f g
AstrictlyutilitarianSWFwouldhaveequalweightsforall,that
is,δ = λ.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON THE MODIFIED PLANNING PROBLEM
Ifc (π)andc (π)solvethepreviousproblemforagiven
H L
π >0,theplannerselectsthestationaryinflationfactorπto
maximizethesocialwelfarefunction
(π,δ) = δ u[c (π)]+u[c (π)]
H L
W f g
+(1 δ) u[x (π)]+u[x (π)] . (10)
H L
(cid:0) f g
ThisSWFassignsequalweightstomembersofthesamegroup
butpotentiallydifferentweightstodifferentgroups.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON THE MODIFIED PLANNING PROBLEM
Ifc (π)andc (π)solvethepreviousproblemforagiven
H L
π >0,theplannerselectsthestationaryinflationfactorπto
maximizethesocialwelfarefunction
(π,δ) = δ u[c (π)]+u[c (π)]
H L
W f g
+(1 δ) u[x (π)]+u[x (π)] . (10)
H L
(cid:0) f g
ThisSWFassignsequalweightstomembersofthesamegroup
butpotentiallydifferentweightstodifferentgroups.
AstrictlyutilitarianSWFwouldhaveequalweightsforall,that
is,δ = λ.
Weallowlump-sumincometransfers.
TheplannerthenmaximizestheSWFsubjecttotheeconomy’s
resourceconstraint.
Thisgivesafirstbestsolutionwithπ = β,RN =1,andsmooth
consumptionforbothgroupsofagents.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
OPTIMUM INFLATION WITHOUT INCENTIVE
CONSTRAINTS
Tobuildupintuition,wefirstsolvetheplanner’sproblem
ignoringforthemomenttheincentiveconstraints.
TheplannerthenmaximizestheSWFsubjecttotheeconomy’s
resourceconstraint.
Thisgivesafirstbestsolutionwithπ = β,RN =1,andsmooth
consumptionforbothgroupsofagents.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
OPTIMUM INFLATION WITHOUT INCENTIVE
CONSTRAINTS
Tobuildupintuition,wefirstsolvetheplanner’sproblem
ignoringforthemomenttheincentiveconstraints.
Weallowlump-sumincometransfers.
Thisgivesafirstbestsolutionwithπ = β,RN =1,andsmooth
consumptionforbothgroupsofagents.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
OPTIMUM INFLATION WITHOUT INCENTIVE
CONSTRAINTS
Tobuildupintuition,wefirstsolvetheplanner’sproblem
ignoringforthemomenttheincentiveconstraints.
Weallowlump-sumincometransfers.
TheplannerthenmaximizestheSWFsubjecttotheeconomy’s
resourceconstraint.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
OPTIMUM INFLATION WITHOUT INCENTIVE
CONSTRAINTS
Tobuildupintuition,wefirstsolvetheplanner’sproblem
ignoringforthemomenttheincentiveconstraints.
Weallowlump-sumincometransfers.
TheplannerthenmaximizestheSWFsubjecttotheeconomy’s
resourceconstraint.
Thisgivesafirstbestsolutionwithπ = β,RN =1,andsmooth
consumptionforbothgroupsofagents.
Theplannermustnowchoose(π,c ,c )tosolvethemodified
H L
planningproblem,butstillignoringtheincentiveconstraints.
Supposeδ =1,nowelfareweightonthecashcommunity. Then
theplannerchoosesmaximalseigniorageπ˜ andsmoothsthe
consumptionofthecreditcommunitycompletely.
Supposeδ =0,nowelfareweightonthecreditcommunity. Then
theplannerwillpushtheinflationfactorasclosetozeroas
possible.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
SECOND BEST
Supposethattheplannercannotimposealump-sumtaxonany
agentbutmustinsteaduseinflationordeflationandredistribute
theresultingseignoragefromonegrouptoanother.
Supposeδ =1,nowelfareweightonthecashcommunity. Then
theplannerchoosesmaximalseigniorageπ˜ andsmoothsthe
consumptionofthecreditcommunitycompletely.
Supposeδ =0,nowelfareweightonthecreditcommunity. Then
theplannerwillpushtheinflationfactorasclosetozeroas
possible.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
SECOND BEST
Supposethattheplannercannotimposealump-sumtaxonany
agentbutmustinsteaduseinflationordeflationandredistribute
theresultingseignoragefromonegrouptoanother.
Theplannermustnowchoose(π,c ,c )tosolvethemodified
H L
planningproblem,butstillignoringtheincentiveconstraints.
Supposeδ =0,nowelfareweightonthecreditcommunity. Then
theplannerwillpushtheinflationfactorasclosetozeroas
possible.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
SECOND BEST
Supposethattheplannercannotimposealump-sumtaxonany
agentbutmustinsteaduseinflationordeflationandredistribute
theresultingseignoragefromonegrouptoanother.
Theplannermustnowchoose(π,c ,c )tosolvethemodified
H L
planningproblem,butstillignoringtheincentiveconstraints.
Supposeδ =1,nowelfareweightonthecashcommunity. Then
theplannerchoosesmaximalseigniorageπ˜ andsmoothsthe
consumptionofthecreditcommunitycompletely.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
SECOND BEST
Supposethattheplannercannotimposealump-sumtaxonany
agentbutmustinsteaduseinflationordeflationandredistribute
theresultingseignoragefromonegrouptoanother.
Theplannermustnowchoose(π,c ,c )tosolvethemodified
H L
planningproblem,butstillignoringtheincentiveconstraints.
Supposeδ =1,nowelfareweightonthecashcommunity. Then
theplannerchoosesmaximalseigniorageπ˜ andsmoothsthe
consumptionofthecreditcommunitycompletely.
Supposeδ =0,nowelfareweightonthecreditcommunity. Then
theplannerwillpushtheinflationfactorasclosetozeroas
possible.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
MORE ON SECOND BEST
Thesecondbesttradesoffthesetwoextremecases.
THEOREM
Thesecondbestoptimumallocationunderautilitariansocialwelfare
functionsatisfies(c ,c ,x ,x ) = (c ,c ,x (π ),x (π )). Itis
H L H L (cid:3)(cid:3) (cid:3)(cid:3) H (cid:3)(cid:3) L (cid:3)(cid:3)
supportedbya“modifiedFriedmanrule”forsomeinflationfactor
π (β,1),andanominalyieldsuchthatRN = π /β >1.
(cid:3)(cid:3) (cid:3)(cid:3)
2
PROOF.
Seetheappendix.
Calltheassociatedinflationfactorπ¯.
Perhapsmorecontroversial?
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
A2. Incomesharescannotbe“toosmooth.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
Calltheassociatedinflationfactorπ¯.
Perhapsmorecontroversial?
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
A2. Incomesharescannotbe“toosmooth.”
Calltheassociatedinflationfactorπ¯.
Perhapsmorecontroversial?
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
A2. Incomesharescannotbe“toosmooth.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
Perhapsmorecontroversial?
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
A2. Incomesharescannotbe“toosmooth.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
Calltheassociatedinflationfactorπ¯.
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
A2. Incomesharescannotbe“toosmooth.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
Calltheassociatedinflationfactorπ¯.
Perhapsmorecontroversial?
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
KEY ASSUMPTIONS
A1. Incomesharescannotbe“toovariable.”
A2. Incomesharescannotbe“toosmooth.”
A3. Itiswithinthepowerofthecentralplannertolowertherate
ofreturnfacingusersofcashtothepointwheretheincentive
constraintoncreditusersbecomesslack.
Calltheassociatedinflationfactorπ¯.
Perhapsmorecontroversial?
“Themarketforunsecuredcreditcanbemadetoworkperfectly.”
Part(b)intuition. Asmallincreaseintheinflationtaxcreatesa
creditmarketwhereonewouldotherwisenotexist.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
LEMMA 2
LEMMA
Define (π,δ) = ∂ /∂π.Then(a) (π,δ) <0
π π
(π,δ) W [π¯,π˜] [0, W λ],and(b)lim W (π,δ) = +∞whenπ
π 1 π
8 2 (cid:2) ! W
convergesfromabove.
Part(a)intuition. Toraiseπaboveπ¯ doesnotimprovetheability
oftheplannertosmooththeconsumptionofthecredit
communityanyfurther. Doingsomerelytransfersincomefrom
thecashcommunity. Thistransferwillreducesocialwelfare
exceptwhenδ > λ.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
LEMMA 2
LEMMA
Define (π,δ) = ∂ /∂π.Then(a) (π,δ) <0
π π
(π,δ) W [π¯,π˜] [0, W λ],and(b)lim W (π,δ) = +∞whenπ
π 1 π
8 2 (cid:2) ! W
convergesfromabove.
Part(a)intuition. Toraiseπaboveπ¯ doesnotimprovetheability
oftheplannertosmooththeconsumptionofthecredit
communityanyfurther. Doingsomerelytransfersincomefrom
thecashcommunity. Thistransferwillreducesocialwelfare
exceptwhenδ > λ.
Part(b)intuition. Asmallincreaseintheinflationtaxcreatesa
creditmarketwhereonewouldotherwisenotexist.
Theoutcomeofanydeflationisthatmoneyhasahigherpayoff
thancredit.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
LEMMA 3
LEMMA
(π,δ)isnotdefinedforπ <1.Itisdecreasinginπforπ (π˜,1/R¯)
a W ndconstantforπ 1/R¯. 2
(cid:21)
Deflationviolatestheparticipationconstraintforhighincome
credithouseholds.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
LEMMA 3
LEMMA
(π,δ)isnotdefinedforπ <1.Itisdecreasinginπforπ (π˜,1/R¯)
a W ndconstantforπ 1/R¯. 2
(cid:21)
Deflationviolatestheparticipationconstraintforhighincome
credithouseholds.
Theoutcomeofanydeflationisthatmoneyhasahigherpayoff
thancredit.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
THEOREM 4
THEOREM
SupposeassumptionsA1,A2,andA3hold,and0< δ λ.Thenthe
optimuminflationfactorisπ?(δ) >1andtheassociate (cid:20) dnominalinterest
yield,RN (π?(δ),π?(δ)/β),isevenhigher.
2
U.S.A.:Onetotwopercent.
RepublicofSouthAfrica:Threetosixpercent.
Mainconclusion: independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
Soundslike“comfortzones”articulatedbycentralbankers.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
CONCLUSIONS AND EXTENSIONS
Inthispaper,theoptimalinflationtargetshouldstrikeabalance
betweenthedeadweightlossfrominflationandthepotential
improvementincreditmarketconditions.
U.S.A.:Onetotwopercent.
RepublicofSouthAfrica:Threetosixpercent.
Soundslike“comfortzones”articulatedbycentralbankers.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
CONCLUSIONS AND EXTENSIONS
Inthispaper,theoptimalinflationtargetshouldstrikeabalance
betweenthedeadweightlossfrominflationandthepotential
improvementincreditmarketconditions.
Mainconclusion: independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
RepublicofSouthAfrica:Threetosixpercent.
Soundslike“comfortzones”articulatedbycentralbankers.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
CONCLUSIONS AND EXTENSIONS
Inthispaper,theoptimalinflationtargetshouldstrikeabalance
betweenthedeadweightlossfrominflationandthepotential
improvementincreditmarketconditions.
Mainconclusion: independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
U.S.A.:Onetotwopercent.
Soundslike“comfortzones”articulatedbycentralbankers.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
CONCLUSIONS AND EXTENSIONS
Inthispaper,theoptimalinflationtargetshouldstrikeabalance
betweenthedeadweightlossfrominflationandthepotential
improvementincreditmarketconditions.
Mainconclusion: independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
U.S.A.:Onetotwopercent.
RepublicofSouthAfrica:Threetosixpercent.
INTRODUCTION MAINIDEAS ENVIRONMENT PLANNINGPROBLEMS OPTIMUMINFLATION THEROLEOFINCENTIVECONSTRAINTS CONCLUSIONS
CONCLUSIONS AND EXTENSIONS
Inthispaper,theoptimalinflationtargetshouldstrikeabalance
betweenthedeadweightlossfrominflationandthepotential
improvementincreditmarketconditions.
Mainconclusion: independentcentralbankswillsetlowpositive
inflationtargetsineconomiesthatpossesshighlydeveloped
financialmarkets.
U.S.A.:Onetotwopercent.
RepublicofSouthAfrica:Threetosixpercent.
Soundslike“comfortzones”articulatedbycentralbankers.
Cite this document
APA
James Bullard (2008, October 9). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20081010_james_bullard
BibTeX
@misc{wtfs_regional_speeche_20081010_james_bullard,
author = {James Bullard},
title = {Regional President Speech},
year = {2008},
month = {Oct},
howpublished = {Speeches, Federal Reserve},
url = {https://whenthefedspeaks.com/doc/regional_speeche_20081010_james_bullard},
note = {Retrieved via When the Fed Speaks corpus}
}