docAnaliza reakcji wybranych modeli długookresowego wzrostu
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Analiza reakcji wybranych modeli długookresowego wzrostu
Ba n k i K r ed yt 43 ( 4 ), 2012, 85–118
www.bankikredyt.nbp.pl
www.bankandcredit.nbp.pl
Analiza reakcji wybranych modeli
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+6&76-5">4&36H";05C$&/"5$;"3/,H6<&`/5,;7;,5">D"&7";"C,5;$&!"D,-5&A?4EA"/"&A&76C4";,C&"?,;-D4&+6&
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TR;"55&:e@_WNF;"&D,-5&436;"A,C&+;$H4,D&76>G6+/,D&7;A,A&74,;?-AE&76>G6+/EN&?A4L5E&A,&A/"#4,C&
C4/$-N&C6J/"&-5?4,;+A4(N&J,&?4,3#6S(&5"&/4,&A"3,J0&6+&?4,3#6S>4/-$C7>D4N&"&?4L>&5,J&6+&>A"-$N&
4&D,-5&;F?/"&7";"C,5;6?4&!<&R6/"+56&C4";"&;,3"50?/,H6&;0A0#"&j;;6?"&4&R;"55"&D,-5&?&50C&7;A07"+#$& ;F?/"& ,3"-50>A/6S>4& #;"h>6?,D& $J05,>A/6S>4<& B6& ?4L>,DN& 6+?;65/6S(& 76?0J-A,H6& ?0;"J,/4"&
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?<;<+B%!(6+($,%$(120,1($%+*,'%)-#+C/A)(4/D+E/))/+2+F%%.A/1)/
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A"7;676/6?"/,D& 7;A,A& M"C-,0"& T:e8iWN& "& /"-5L7/4,& ;6A?4/4L5,D& 7;A,A& B"--"& T:e@fW& 4& O667C"/-"&
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∞
max
Σ β t u (ct )
c
t
T]W
t=0
R";"C,5;&#"D,-5&$56J-"C4"/0&A,&-567E&+0-#6/56?EN&"&?4L>&>,/EN&A"&D"#E&;,7;,A,/5"50?/"&D,+/6-5#"&D,-5&?&-5"/4,&7;A,/4,S(&o+A4-4,D-AEp/-$C7>DL&/"&oD$5;6p<&*"&76+-5"?4,&?A6;$&T]W&C6J/"&
-5?4,;+A4(N&J,&7;6%3,C&6750C"34A">0D/0&D,-5&;6A?"J"/0&?&/4,-#6h>A6/0C&G6;0A6/>4,&>A"-6?0C<&
:& &X&+"3-A,D&>ALS>4&";50#$.$&C6+,3&5,/&%L+A4,&/"A0?"/0&C6+,3,C&M"C-,0"<
89
Analiza reakcji wybranych modeli...
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?05?F;>A0>G&UVR1
&T_W
At +1 = At (1 + g )
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η
6+>G03"DE>&H6&6+&76A46C$&$-5"36/,H6&/"&S>4,J>,&A;F?/6?"J6/,H6&?A;6-5$<
R;6>,-&7;6+$#>D4&A6-5"/4,&674-"/0&A"&76C6>E&I$/#>D4&B6%%"&4&Y6$H3"-"<&="H;,H6?"/0&7;6+$#5&
Yt &?&C6C,/>4,& t D,-5&I$/#>DE&#"745".$&I4A0>A/,H6& Kt 6;"A&A"-6%$&7;">0& Lt 4&76A46C$&5,>G/636H4>A/,H6&At TfW<&Z#$5#4,C&&7;6>,-$&?05?F;>A,H6&D,-5&7,?/"&436S(&G6C6H,/4>A/,H6&+6%;"<&X&A"7;676/6?"/,D&-7,>0I4#">D4&?0-5L7$D,&5,J&-#."+/4#&6+76?4,+A4"3/0&A"&-A6#4&-56>G"-50>A/,N&>A034& η1, tNF;0&
?&5,D&>ALS>4&";50#$.$&A6-5".&$A/"/0&A"&-5".0&4&;F?/0&D,+/6S>48<
α
Yt = η1,t K t ( Lt At ) γ &
&
&
&
&&&&&&TfW
α γ 1
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η
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6;"A&&kt N&C6HE&A6-5"(&674-"/,&D"#6&&?";56S>4&AC4,//0>G&A"H;,H6?"/0>G&7;A,34>A6/0>G&/"&D,+/6-5#L&
,I,#50?/,D&7;">0]<
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α γ
α
yt = η1,t kt &
η
&
&
&
&
&&&&&&T@W
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y t = s t + c t = it + c t
T2W
8& =
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]& &X&7;A07"+#$N&H+0
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&
&
α
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&
&
&
&&&&&&TiW
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6;"A&7;A0;6-5&A"-6%$&7;">0<
1
(
(
1 + n + g – β (1 – δ)
k =
α βA
–
&
&
)
)
α –1
1
α
(
& 1 + n &+ g – β&(1 – δ) &α – 1
&
& 1 + n +& g – β (1& – δ)
c=
– (n + g + δ )
αβA
α βA
)
&
α –1
&&&&&&TeW
η =1
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?<?<+B%!(6+(1!%$(120,1($%+*,'%)-#+G,/*4+2+:#0/)/
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91
Analiza reakcji wybranych modeli...
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∞
T:9W
max Σ β t u (ct )
ct ,ut t = 0
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+A4"."3/6S(&7;6+$#>0D/E<
T::W
ht +1 = η 2,t ht B (1 – u t ) + (1 – δt )ht
U"#&-#6/-5;$6?"/0&&7;6>,-&"#$C$3">D4&ht ;FJ/4&-4L&6+&A"7;676/6?"/,D&7;A,A&PA"?L&T:e@_W&>A0&
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76+>A"-&+A4"."3/6S>4&?05?F;>A,DN&/7<&learning by doing&TO3,/6?N&M6+;4H$,AcB3";,&899_W1
α
yt = η1,t Ak t u t
1– α
ht
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&
&
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Lt = L y, t + L A, t
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