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Adaptive learning and the cyclical behavior of output and inflation

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Academic year: 2021

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(56) o. H ,^*Mh@ | 54T*i +i}hittL?t @?_ |i t?itt )U*i At tiU|L? t|_it |i ThLTih|it Lu L_i*  @?_ L_i* 2 i^*Mh@ @?_ UL4T@hit |i4 | |i ThLTih|it Lu N5 _@|@ Thiti?|i_ ? tiU|L? 2. H |T| @?_ W?@|L? ? L_i*  ,^*Mh4 6hL4 Ef | uL**Lt |@| L|T| @?_ ?@|L? ? L_i*  i^*Mh4 @hi }i? M) |. +|. +|3 + r n |3 ' ' +r +r ' + r n | 22.

(57) Output-Lagged Output. Output-Lagged Inflation 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0. 0. 1. 2. 3. 4. 5. 6. 0. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. -0,8. 1. 2. Inflation-Lagged Output. 3. 4. 5. 6. 4. 5. 6. Inflation-Lagged Inflation. 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0 0. 1. 2. 3. 4. 5. 6. 0. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. -0,8. 1. 2. 3. 6}hi SG |L @?_ UhLttULhhi*@|L?t | h@|L?@* i TiU|@|L?t W?@|L? @?_ L|T| @hi |i ?Lti M|c _i |L t|U!) ThUitc ?@|L? _i@|L?t *@} L|T| _i@|L?t M) L?i TihL_  }Lih?4i?| _i4@?_ tLU! | |i4TLh@h*) ?Uhi@tit L|T| @?_ 4L?i) L*_?}t Ai ?Uhi@ti_ 4L?i) t|LU! EULhhiU|*) U@tit ?@|L? i TiU|@|L?t |L ?Uhi@ti M) @? @4L?| |@| 4T*it |@| |i ?Uhi@ti_ 4L?i) t|LU! ** Mi _i@*@|i_ M) |i ?i | TihL_ Ai ?Uhi@ti_ ? @|L? i TiU|@|L?t |i? U@tit i?|hiThi?iht |L ?Uhi@ti |ih ThUit M) i @U|*) @? @4L?| |@| 4@!it |iti i TiU|@|L?t MiUL4i |hic tii E 5LU!tc |ihiuLhic tL ?L Tihtt|i?Ui 6}hi S _iTU|t |i @|L @?_ UhLttULhhi*@|L?t Lu L|T| @?_ ? @|L? ? L_i*  ,^*Mh4 W| TihuLh4t h@|ih i@! i? UL4T@hi_ | €}hi 2 uLh N5 _@|@ Ai h@|L?@* i TiU|@|L?t i^*Mh4 Tih uLh4t hi@tL?@M*) i** L?*) @*L?} L?i _4i?tL?G Uhhi?| i Uitt L|T| *i@_t |L ?@|L? ? |i tMti^i?| TihL_c U t _i |L |i t|U!) ThUi @tt4T|L? 2

(58).

(59) Output-Lagged Output. Output- Lagged Inflation 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0 0. 1. 2. 3. 4. 5. 0. 6. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. 1. 2. 3. 4. 5. 6. -0,8. Inflation- Lagged Output. Inflation-Lagged Inflation. 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0 0. 1. 2. 3. 4. 5. 6. 0. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. -0,8. 1. 2. 3. 4. 5. 6. 6}hi .G |L @?_ UhLttULhhi*@|L?t ? L_i* 2 ,^. H2 |T| @?_ W?@|L? ? L_i* 2 ,^*Mh4 At tiU|L? Thiti?|t |i ThLTih|it Lu L_i* 2 ,^*Mh4 AhL}L| |i tiU|L? | t @tt4i_ |@| |i i*@t|U|) Lu *@MLh tTT*) t }i? M) 0?c ' Hc U t @| |i *Lih i?_ Lu |i h@?}i uLh U L_i* 2 ,^*Mh@ i t|  *L i*@t|U|) @*i @t Mii? ULti? MiU@ti }ih L?it L*_ }i?ih@|i ii? 4Lhi Tihtt|i?Uic @t t @h}i_ |L@h_t |i i?_ Lu |t tiU|L? 6}hi . _iTU|t |i @|L @?_ UhLtt ULhhi*@|L?t Lu L|T| @?_ ?@|L? ? L_i* 2 ,^*Mh4 Ai _@|@ t tL? uLh S TihL_tc U ULhhitTL?_t |L 2e ^@h|iht Lu N5 _@|@ u i@U 4L_i* TihL_ t ?|ihThi|i_ @t  )i@h Ai t@Tit Lu |i @|L @?_ UhLttULhhi*@|L?t ULhhitTL?_ hi4@h!@M*) i** | |i ULhhi*@|L? ? |i _@|@ |T| @?_ ?@|L? @hi Tihtt|i?| Ai) @hi TLt|i*) ULhhi*@|i_ uLh tLh| *@}t @?_ ?i}@|i*) uLh *L?}ih *@}t |T| t @ TLt|i *i@_?} ?_U@|Lh uLh ?@|L? @?_c 4Lhi 4TLh|@?|*)c ?@|L? tLU!t @hi @ *i@_?} ?_U@|Lh uLh _iUhi@t?} 2e.

(60) L|T| t ? |i _@|@c |i *@} *i?}| @| U ULhhi*@|L? Lu L|T| | T@t| L|T| t 3ihL hL}*) ULhhitTL?_t | |i *@} *i?}| @| U |i ULhhi*@|L? Lu ?@|L? | T@t| ?@|L? t 3ihL 6h|ih4Lhic @| |t *@} *i?}| |i UhLttULhhi*@|L?t Lu L|T| @?_ ?@|L? @i |ih hitTiU|i 4@ 44 @?_ 4?44 AL ?_iht|@?_ L |i @MLi hit*| i4ih}it UL?t_ih @}i?|t< it| 4@|it Lu |i |L uLhiU@t| 4L_i*t ? L_i* 2 ,^*Mh4G feS. + + r |3 L_i* 2 G | ' E  fSHH n fSHH|3. L_i*  G | ' E  feS. n. Ai it|4@|i Lu |i +ULiUi?| Lu L_i*  tLt |@| ?@|L? ? @ L_i* 2 i^*Mh4 t hi@U|?} 4U i@!ih |L @? L|T| _i@|L? |@? ? L_i*  ,^*Mh4 ihi |i t@4i ULiUi?| t }i? M) +r c tii Ef At hi*@|i*) i@! hi@U|L? Lu ?@|L? |L @ _i4@?_ tLU! t _i |L @? i*@t|U *@MLh tTT*) @?_ |i ti Lu L_i* 2 @t @ uLhiU@t| 4L_i* +i 4i4Mih |i i^@|L? _itUhM?} €h4t< ThUi ti||?} Mi@Lhc hiThL_Ui_ ihi uLh UL?i?i?UiG. | '. . j. .|3 E| |. W? |i TihL_ @u|ih @ _i4@?_ tLU!c €h4t ?Uhi@ti |ih ThUit MiU@ti |i) i TiU| @}it |L ?Uhi@tiH OLiihc t?Ui |i) UL?_|L? |ih ?@|L? i TiU|@|L?t L? T@t| ?@|L? @?_ ?L| L? T@t| L|T|c |ih ? @|L? i TiU|@|L?t _L ?L| TU! T ? hitTL?ti |L @ _i4@?_ tLU! `| @? i*@t|U *@MLh tTT*)c ULt|t ?Uhi@ti L?*) t*}|*) @?_ ThUit |ihiuLhi hitTL?_ t*}}t*) t @ hit*| |i _i4@?_ tLU! Tihtt|t ?|L |i tiUL?_ TihL_ @u|ih |i tLU! @?_ U@tit @}it @}@? |L Mi @MLi i^*Mh4 5?Ui ?@|L? 4; Lq wkh shulrg ri wkh vkrfn sulfhv duh douhdg| vhw dqg fdqqrw uhdfw1. 2D.

(61) Output. Inflation 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 1. 16. 2. 3. 4. 5. 6. 7. 8. 9. 10. 9. 10. 11. 12. 13. 14. 15. 16. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. -0,8. Output. Inflation. 1,2. 1,2. 1. 1. 0,8. 0,8. 0,6. 0,6. 0,4. 0,4. 0,2. 0,2. 0. 0 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 1. -0,2. -0,2. -0,4. -0,4. -0,6. -0,6. -0,8. -0,8. -1. -1. 2. 3. 4. 5. 6. 7. 8. 11. 12. 13. 14. 15. 16. 6}hi HG W4T*ti +itTL?tit ? L_i* 2 ,^*Mh4 ? |i €ht| TihL_ @u|ih |i tLU! @t @MLi i^*Mh4c ?@|L? i TiU |@|L?t ?L TU! Tc hit*|?} ? @__|L?@* ?@|L? At @__|L?@* ?@|L? _i@*@|it _i4@?_ Mi*L |t i^*Mh4 @*i @?_ U@tit @ _i 4@?_ tLh|u@** @?_ @? ?@|L? _iUhi@ti ? |i uL**L?} TihL_t ?|* |i tLU! t*L*) u@_it L| Ai €ht| hL Lu €}hi H tLt |i 4T*ti hitTL?tit Lu L|T| @?_ ?@|L? |@| uL**L @ _i4@?_ tLU! |@| |t |i iUL?L4) ? TihL_  Ai 4T*ti hitTL?tit }h@TU@**) **t|h@|i |i 4iU@?t4 _itUhMi_ @MLiG |i ?|@**) t*}}t ThUi hitTL?ti ? TihL_ 2 U@tit L|T| |L hi4@? @MLi i^*Mh4 ? |i TihL_ @u|ih |i tLU! `i? ?@|L? i TiU|@|L?t TU! T ? TihL_

(62) c ?@|L? t tL } |@| | U@tit @ _i4@?_ t*4T ? |i tMti^i?| TihL_tc @?_ @ ULhhitTL?_?} _hLT ? 2S.

(63) ?@|L? Ai igiU|t |i? t*L*) u@_i L| 6Lh UL4T*i|i?ittc |i tiUL?_ hL Lu €}hi H tLt |i 4T*ti hitTL?tit |L @ E?L?4L_i*i_ ?@|L? tLU! Ai ?||L? uLh |ih t@Tit t @?@*L}Lt |L |i L?i @MLi L|i |@| |i 4T*ti hitTL?tit Lu €}hi H ?Ui*) 4@|U |i it| 4@|i_ 4T*ti hitTL?tit uLh N5 _@|@ tL? ? €}hi

(64)  Ai 4T*ti hitTL?tit hii@* |@| L|T| ? L_i* 2 ,^*Mh4 _tT*@)t @ }ih @h@?Ui |@? ? L_i*  ,^*Mh4 uLh |i t@4i ti^i?Ui Lu ?_ih*)?} tLU!t | G W? L_i* 2 ,^*Mh4 _i4@?_ tLU!t Uhi@|i L|T| @h@|L?t ii? @ *L?} |4i @u|ih |ih LUUhhi?Ui | |i t@4i |4ic |i ?|@* L|T| hi@U|L? |L @ _i4@?_ tLU! t |i t@4i ? ML| i^*Mh@ `i|ih ?@|L? ? L_i* 2 ,^*Mh4 t 4Lhi L*@|*i @t i** t ?U*i@h MiU@ti ?@|L? ?|@**) hi@U|t *itt |L @? L|T| tLU! i? UL4T@hi_ |L |t hi@U|L? ? L_i*  ,^*Mh4 OLiihc t4*@|L?t tLi_ |@|c @| *i@t| uLh 0?c ' Hc ?@|L? t @*tL 4Lhi L*@|*i ? L_i* 2 ,^*Mh4 6Lh }ih @*it Lu |i i*@t|U|) Lu *@MLh tTT*)c |i 4T*ti hi tTL?tit @?_ |i Tihtt|i?Ui Lu L|T| @?_ ?@|L? _i@|L?t MiUL4i ii? t|hL?}ih |@? tL? ? |i €}hit @MLi #i4@?_ tLU!t |i? *i@_ |L @? ii? 4Lhi t*}}t hitTL?ti ? ULt|t @?_ ThUitc U }i?ih@|it ?Uhi@ti_ Tihtt|i?Ui 6Lh *Lih @*itc i} uLh 0?c ' .Dc |i hit*|t @hi @*4Lt| ?_t|?}t@M*i uhL4 |i L?it Thiti?|i_ @MLi. b L_i* LUi @?_ <N?t|@M*i< +@|L?@* , TiU|@|L?t ,^*Mh@ W? |i ThiLt tiU|L?t | @t Mii? tL? |@| @}i?|t 4}| Thiuih ti uLhiU@t| 4L_i*t |@| }i?ih@|i ?iUi?| uLhiU@t|t Ai ThTLti |t tiU|L? t |L tL |@| |t U@? U@ti |i iUL?L4) |L Mi U*Lti @ h@|L?@* i TiU|@|L?t i^*Mh4 |@| t ?t|@M*i ?_ih *i@h??} UL?tt|i?| uLhiU@t| 4L_i*t 2.. |L Lu |L Lu.

(65) At TL?| t Lu ?|ihit| MiU@ti |i ?t|@M*|) Lu @ T@h|U*@h h@|L ?@* i TiU|@|L?t i^*Mh@ ?_ih @_@T|i *i@h??} Lu UL?tt|i?| 4L_i*t @t |)TU@**) Mii? ?|ihThi|i_ @t tU i^*Mh@ Mi?} ?*!i*) iUL?L4U L|UL4itc i} ,@?t @?_ OL?!@TL@ dfo At tiU|L? tLt |@| tU <?t|@M*i< i^*Mh@ U@? ?iih|i*itt }i E? @ih@}i |ih4t }LL_ Thi_U|L?t Lu |i iUL?L4U L|UL4it W €ht| UL?t|hU| @ h@|L?@* i TiU|@|L?t i^*Mh4 |@| t ?t|@M*i ?_ih *i@t| t^@hit *i@h??} Lu UL?tt|i?| uLhiU@t| 4L_i*t. AL |t ThTLti @tt4i |@| |ihi i t|t @? ?@|L? |@ 4@ 4 @MLi U @}i?|t _iU_i ?L| |L tTT*) @?) *@MLh i? |i @}i t }i? M)  '   jb At 4T*it |@| |i _i|ih4?t|U ihtL? Lu |i 4L_i* TLttittit @ tiUL?_ t|@|L?@h) h@|L?@* i TiU|@|L?t i^*Mh4 ihi L|T| + rr t U*Lti |L 3ihL @?_ ?@|L? rr t U*Lti |L 4@ 2f u|ih *?i@h3?} ES @?_ E. @hL?_ |t t|i@_) t|@|i L?i €?_t |L h@|L?@* i TiU|@|L?t tL*|L?t }@?c |ihi t @ t|@|L?@h) tL*|L? rr @?_ @ ?L?t|@|L?@h) tL*|L? | ?@|L? uL**L?} | ' +rr +|3 @?_ | ' rr  2 +|3 c hitTiU|i*) L|i |@| L_i*  t @ UL?tt|i?| 4L_i* uLh |iti h@|L?@* i TiU|@|L?t i^*Mh@ W| t i@t) |L tL |@| ML| h@|L?@* i TiU|@|L?t tL*|L?t @hi ?t|@M*i ?_ih *i@t| t^@hit *i@h??} Lu L_i*  iih|i*ittc |ihi i t| L_i* 2 i^*Mh@ |@| @hi U*Lti |L |i } ?@|L? h@|L?@* i TiU|@|L?t i^*Mh4 AL tL i t|i?Ui Lu tU i^*Mh@c @tt4i |@| |i *@MLh tTT*) u?U|L? t }i? M)2  k. ?| '.  .|d |no |. 4< D vxflhqw frqglwlrq iru wklv lv x3 +3, ? 41 53 Wkh ghwdlov ri wklv dqg wkh iroorzlqj dujxphqwv fdq eh irxqg lq Dgdp ^4`1 54 Vxfk d oderu vxsso| ixqfwlrq fdq eh ghulyhg iurp djhqwv wkdw pd{lpl}h wkh. orzlqj olihwlph remhfwlyh=. pd{ H3. %4 [ w@3. orj+4 . fw ,  qw. vxemhfw wr fw  p4 dqg pw @ p4  fw . qwzw 1 w. w. w. w. 2H. &. iro0.

(66) 0,75. 0,73. 0,71. alpha. 0,69. 0,67. 0,65. 0,63. 0,61 0. 0,025. 0,05. 0,075. 0,1. 0,125. 0,15. 0,175. 0,2. 0,225. sigma. 6}hi bG L_i* 2 ,^*Mh@ @| |i O} W?@|L? 5|i@_) 5|@|i Ai 4L_i* t |i? _itUhMi_ M) |L T@h@4i|ihtc |i 4@h}?@* _t|*|) Lu *@MLh k @?_ |i _i}hii Lu 4TihuiU| UL4Ti||L? j  Nt?} UL4T|@|L?@* 4i|L_tc @ }h_ ti@hU @t 4@_i |L UiU! uLh |i i t|i?Ui Lu L_i* 2 i^*Mh@ @UhLtt |i hi*i@?| Ekc j tT@Ui22 c 2

(67) Ai t@_i_ @hi@ ? €}hi b ?_U@|it tL4i T@h| Lu |i T@h@4i|ih tT@Ui uLh U L_i* 2 ,^*Mh@ i t|2e *|L} |i @hi@ t h@|ih t4@**c |i }h@T hii@*t |@| | @t TLt|i 4@tt 55 Wkh rwkhu sdudphwhuv zhuh vhw wr j @ 3=35 dqg yw  X ^3=338> .3=338`1 56 Ohw djhqwv hvwlpdwh dqg xvh Prgho 5 wr iruhfdvw lqdwlrq1 Fdofxodwh qhz lqdwlrq. udwhv dqg rxwsxw ohyhov dffruglqj wr wkh olqhdul}hg yhuvlrq ri +9, dqg +:,1 Djhqwv xsgdwh wkhlu hvwlpdwhv xqwlo wkh| kdyh frqyhujhg wr vrph ydoxh +>  ,1 Wkh frqyhujhg ydoxhv duh d srwhqwldo fdqglgdwh iru d Prgho 5 htxloleulxp1 Vlpxodwh wkh hfrqrp| zlwk Prgho 5 dqg +> , dqg fdofxodwh wkh phdq vtxduhg iruhfdvw huuruv1 Ilw Prgho 4 wr wkh vlpxodwhg gdwd dqg fdofxodwh wkh iruhfdvw huuruv1 Li wkhvh duh kljkhu wkdq zlwk Prgho 5/ d Prgho 5 htxloleulxp kdv ehhq irxqg1 57 Prgho 5 Htxloleuld h{lvw dovr iru  A 3=558 dqg  ? 3=94= 2b.

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(69) f.

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(130)

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