Expectations Traps and Monetary Policy with Limited Commitment

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Economics Department

Discussion Papers Series

ISSN 1473 – 3307

Expectations Traps and Monetary Policy with

Limited Commitment

Christoph Himmels and Tatiana Kirsanova

Paper number 11/02

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dqg Zuhq0Ohzlv +5344,/ exw suhvhqw uhvxowv d wkh irup frqyhqlhqw iru rxu sxusrvhv1

(8)

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614 Glvfuhwlrqdu| Srolf|

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lw iroorzv wkdw wkh sulydwh vhfwru*v ghflvlrq fdq dovr eh zulwwhq dv

w @ +e.,ew. +e,fw= +44,

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;

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(9)

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Ogw @ 4 5 2w .f2w .4 5Ve 2 wn.wn+ewfwewn,.!wn+wfweweewn,= +46,

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fw@++ e., +e,V,

+e,2..2V

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fulwhulrq +45,= V@ ++e., . +e,fe, 2 .f2 e 4+fe,2 = +53, Khqfh wkh uvw rughu frqglwlrqv +44,/ +4<, dqg +53, ghqhfe> e dqgV=

wkh sdlu +4<, dqg +53,1 Jlyhqfe wkh rswlpdo uhvsrqvh We ri wkh sulydwh vhfwru lv jlyhq e| +44,1

Wkhuhiruh/ iru hyhu| qrw qhfhvvdulo| rswlpdo e zh fdq frpsxwh d xqltxh We dqg sorw wkh

(10)

ghshqghqfhW

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glvfuhwlrqdu| sureohp1

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e=Wklv frpsohphqwdulw| hqvxuhv

vwhhsqhvv riW

e+e,dqg wkuhh htxloleuld dulvh1 615 Frpplwphqw Srolf|

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Of@ " [ w'f w 4 5 2w .f2w .wn+ewfwewn, .!wn+wfwewwn, =

Wkh fruuhvsrqglqj uvw rughu frqglwlrqv duh=

3 @ w.wn!wn> +54,

3 @ w.!wn!w> +55,

3 @ fwwn!wn> +56,

3 @ ewfwewn> +57,

3 @ wn.fw.eww> +58,

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4=

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(11)

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e=D vroxwlrq wr wkh frpplwphqw sureohp lpsolhvWe @e1 Wkh judsk

riW

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(12)

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r, +4,@+r++4r,r,,/ wkh hfrqrp|

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714 Srolf| Htxloleuld

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+5344,1

(13)

Otf _@ " [ w'f ++4,,w 4 5 2w .f2w .Ve2wn .wn+ewfwewn, +63, .!wn+wfwew+4,wneewn,

iru3 ?41 Wkh uvw rughu frqglwlrqv duh

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3 @ w.!wn!w> +65,

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3 @ ewfwewn> +67,

3 @ +4,wn.eewn.fw.eww> +68,

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Wkhvh uvw rughu frqglwlrqv duh vlplodu wr wkrvh iru frpplwphqw/ exw ghshqg rq sdudphwhuv/

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e= Vroxwlrqv wr wkh v|vwhp

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(14)

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(20)

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(21)

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(22)

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(23)

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(24)

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(25)

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−0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π_b πb * III: QUASI−COMMITMENT, α = 1/2 −0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π_b πb * V: QUASI−COMMITMENT, α = 1/4 −0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π_b πb * II: COMMITMENT −0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π b πb * I: DISCRETION −0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π_b πb * IV: QUASI−COMMITMENT, α→ 1 −0.1 0 0.1 0.2 0.3 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 π_b πb * VI: QUASI−COMMITMENT, α = 1/8 B C A A B C A A A A B C

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2 4 6 8 10 −0.5 0 0.5 1 Inflation 2 4 6 8 10 0 0.5 1 LM 2 4 6 8 10 0 1 2 Debt 2 4 6 8 10 −5 0 5 Consumption

IRF type (i)

2 4 6 8 10 −0.5 0 0.5 1 Inflation 2 4 6 8 10 0 1 2 LM 2 4 6 8 10 0 0.5 1 1.5 Debt 2 4 6 8 10 −5 0 5 Consumption IRF type(ii) 2 4 6 8 10 0 0.5 1 1.5 Debt 2 4 6 8 10 −5 0 5 Consumption

IRF type (iii)

2 4 6 8 10 −0.5 0 0.5 1 Inflation 2 4 6 8 10 0 0.5 1 LM Commitment Discretion Best (A) Discretion Worst (C) Quasi−Commitment Best (A) Quasi−Commitment Worst (C)

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0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 Probability of default, α (L−L c )/(L d −L c )

PANEL II: EXPECTED LOSS for given µ=0.015 0 10 20 30 40 0 0.5 1 1.5 2 2.5 3

PANEL III: EXPECTED LOSS for given µ=0.015

Average regime duration, 1/α

(L−L c )/(L d −L c ) 0 0.05 0.075 0.1 0 0.5 1 1.5 2 2.5 3 Fiscal feedback, µ (L−L c )/(L d −L c )

PANEL I: EXPECTED LOSS

discretion commitment quasi−commitment (best) quasi−commitment (worst) quasi−commitment (best) quasi−commitment quasi−commitment (worst) Ac Aqc Bd Bqc Cd Cqc α=0, commitment α=1/2 α=1/8 α=1/100 α=1, discretion Ad Worst Best

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