GMM Estimation of Dynamic Panel Data Models with Persistent Data
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(176) Eo K fc @?_ 2 f 6?@**)c i ** i @4?i i|ih Ko2 2Ko 2o n K U@? i^@* fG. Kn 2 `i? K : fc i U@? h|i Ko2 2Ko 2o n K ' KEo2 2E Kn K o n 5?Ui eE K e : fc Ko2 2Ko 2o n K ' f ** @i |L hi@* tL*|L?t L| tL*|L?t ** Mi TLt|ic | L?i tL*|L? Mi?} t4@**ih |@? @?_ |i L|ih tL*|L? Mi?} *@h}ih |@? `i? K ' fc Ko2 2Ko 2o n K ' 2o Lc 2o ' f g o ' f `i UL?U*_i |@| T @oEe oC
(177) : T @oEe ouC ?*itt Ko2 2Ko 2o n K ' f 2 2E3KnKo2 3 E n o EeKo o
(178) eK c
(179) 2 @oEe oC
(180) ' 2EKo2 n2Ko 323
(181) K E n o EKo .Ko n 2o DKo n S n Eo3 e oC 2 ' 2 E n o 2 K2 EKo2n2Ko323
(182) @oEe oC
(183) T @oEe K E3KnKo2 3 2. 5?Ui T @oEe oC 2 ' T T. K c i ?_ |@|. 6ht| i ** tL |@| EKo n 2Ko 2
(184) K f G. Ko2 n 2Ko
(185) K ' Eo n
(186) Eo K f @?_ 2 f i | i ** tL |@| EK n Ko2 f G K n Ko2 ' K Eo E n o f @?_ f oC
(187) ?*itt K ' f E>2 ' f ; 5 ic c j `i UL?U*_i |@| T @oEe oC 2 : T @oEe L|Ui |@| |i |h_ 4L4i?| UL?_|L?c .E6
(188) Eo ' fc _Lit ?L| _i?|u) o i? o L?i|i*itt ?U*_?} .E6
(189) Eo ' f ? |i ti| Lu 4L4i?| UL?_|L?t }i?ih@**) *i@_t |L 4Lhi iUi?| it|4@|Lht wi| oeC Mi |i B it|4@|Lh |@| t M@ti_ L? |i hhi*@?LL?_ 4L4i?| UL?_ |L? .E62 Eo ' .E+c {0c
(190) ' f Ai? T @oEe oC ' E n o 2 2K n 32o2 c. T @oEe oC 2 '. 2E3KnKo2 3 . E n o EeKo2 o
(191) eK c @?_. T @oEe oC 2 T @oEe oC ' 2 E n o
(192) `i ** ht| tL |@| EK n Ko2 f G. E2oK32K3 2 E3KnKo2 3 Eo3 . K n Ko2 ' Eo E n o K f @?_ f i | i ** tL |@| 2oK 2K f G 2oK 2K ' 2Eo K f @?_ f `i UL?U*_i |@| T @oEe oC : T @oEe oC 2 2S.
(193) . iNNu Nu |j ijt,|t A tjW|NA g hLLut Lu hit*|t ? tiU|L? e V@hLt hit*|tG. 6Eo ' 6 ' E6 Eo 62 Eo 6
(194) Eo 6e Eo c ihi 6 Eo c 62 Eo c 6
(195) Eo c @?_ 6e Eo @i @*hi@_) Mii? _i?i_ ? tiU|L? e E@?_ @*tL ? @TTi?_ hLTih|it Lu .E6Eo 6Eo G. 5. o n o ne o no 2E3o o 9 2K n 2 9 no 3o2 2K n 3o no `i? mom c .E6Eo 6Eo ' 9 o 2o 2 2K n 3o o e n 2K n 3 2 7 no 2 o eE3fon
(196) o2 o 2 ne o 2E3 no Eno 2 2 no. 5. je 9 f .E6E 6E m +c c c +c ' 9 7 je 2je hLTih|it Lu .E _6_oEo G. f S 2 2j2 ' +c S 2j2 ' +c2 f. 5. 6 5 2 n o j 2 2j 2 2 : 9 9 no j : ' 9 2j *4o .E _6_oEo ' *4o 9 7 8 7 f f 2 2 j2 no j. 6 : :c 8. 6 : : e :j 8 6 2je : f : e 8 2j ej e. je S 2 2j2 c ' +S 2 Dje n 2j2 ' +c 2je. 5. 6 j2 9 f : : .E _6_oEo mo' ' 9 7 j2 8 j2. +i4i4Mih |@| 6Eo h ' E62 Eo 6
(197) Eo 6e Eo 6D Eo hLTih|it Lu .E6Eo h 6Eo h @?_ d.E6Eo h 6Eo h o3 G 5 nKo2 3 2Ko32K3o 3 2 3K3n 2 on 2 no o 2 o3 o 2 2 9 2Ko32Ko3o o 3K2nKo 9 2 32n3n 2 n2 o o 3 o 9 2 wi| T Eoc K ' .E6Eo h 6Eo h '9 o3 3fon
(198) o
(199) 3eono2 2 2 e 2 2 n o En o Eno 2 7 2 no o. n2 o. @?_ ` Eoc K ' T 3 Eoc K . 2.. o no 2
(200) 3e Eno 2. 2. o no 2
(201) 3e Eno 2. 2. 6 : : e :j c : 8.
(202) 5. e. e. b ef. ef. 9 e `i ?_ |@| *4o ` Eoc K ' 9 7 H. H. e H. b ef ef D S. H D S D S. 5. : 3e :j 8. 4. e. e. b ef. ef. 9 e 6Lh o *LU@* |L ?|) i @i ` Eoc K 9 7 H. 6. e H. H. H D S D S. b ef ef D S DE3o . 6 : 3e :j 8. iEoc K ' E` Eoc K n `22 Eoc K n `
(203)
(204) Eoc K n `ee Eoc K 3 ` Eoc K #i?i ` 5 6 f f f f 9 : i Eoc K ' 9 f f f f : Ai? *4o ` 7 f f f f 8 f f f 5. S S 2j2 +c2 2j2 +c2 ' ' S S 9 2j2 + 2 Dje n 2j2 +2 ' c ' c L .E6E h 6E h m +c c c +c ' 9 7 f 2je f f 5 f f f 9 f f f i Ec K ' 9 tL i? o ' |i ?Lh4@*ti_ LT|4@* i}|?} 4@|h ` 7 f f f f f f i Eoc K ' ` iEc K `i UL?U*_i |@| *4o `. 2H. f 2je ej e f 6 f f : : f 8 . 6 f f : :c f 8 f.
(205) 2. hLLu Lu |iLhi4 D E*LU@*|L?|) @t)4T|L|Utc A '
(206) G. +c| ' o+c|3 n E o > n 0c| @?_ i @tt4i t|@|L?@h|) `i ** _ihi |i *LU@*|L?|) @t)4T|L|U _t|hM|L?t Lu |i uL**L?} it|4@|LhtG S + {+ S E0 n> {+ c2 ' c
(207) oe-T ' S ' +c
(208) {+c2 ' o n S ' c2 c2 S S ' +c2 {+c2 + {+ + {0 oe-( ' S ' +c{+c
(209) ' o n S ' +c{+c
(210) ' c c2 ' c c2 S " r Nt?} | ' r'f o 0|3r c i LM|@? |i uL**L?} hit*|tG. 2 j2 c .dE{c2 2o ' 2j2 c .E2c ' 3j o2 c .Ec {c2 ' n o no S S S S" oer " " "
(211) je e 2 .Eec ' .E r'f oer 0ec3r n S r'f |'rn o2Ern| 02c3r 02c3| ' 3 oe n Sj o r'f 3o2 '.
(212) je 3oe. n. Sje o2 E3o2 E3oe . '.
(213) j e E3o2 2 c. .dE{c2 e o ' .dEo e ec n SEo 2 2c 02c2 n 0ec2 o '
(214) E3o 2 nSE3o Eno n
(215) Eno 2 e j Eno 2. '. 2je Eno 2 c.
(216) E3o 2 je Eno 2. n. SE3o je no. n
(217) j e '. o je
(218) je ' Sje c .dc E{c2
(219) o ' .dEo
(220) ec n
(221) Eo 2c 02c2 o '
(222) E3 Eno 2 no Eno 2 .d2c E{c2 2 o ' .dEo 2 ec n 2c 02c2 o '.
(223) je Eno 2. e n 3j o2 '. 2E23o je Eno 2 E3o c. .E+c {0c
(224) ' fc .dE0c
(225) n E o > {+c2 o ' .dE0c
(226) n E o > {c2 o ' fc. j c .E+c {+c2 ' .dEc n > {c2 o ' n o 2. j2 c .E+c2 {+c2 ' .E{+c2 {+c2 n +c {+c2 o ' .E{c2 {c2 n +c {+c2 o ' n o. 2j2 dj2 n>2 E3o2 o 2j e 2 2 n 2> j ' c T @oE+c {0c
(227) ' .dE+c {0c
(228) 2 o ' .idEc n > {0c
(229) o2 j ' 3 2 o Eno E3o 2j2 dj2 n>2 E3o 2 o c no 2j2 >2 2je .dEc {c2 2 En o 2 n no. T @odE0c
(230) n E o > {+c2 o ' .idE0c
(231) n E o > {c2 o2 j '. j2 2o ' T @oE+c {+c2 ' .dEc {c2 n > {c2 n n o 2E23o je Eno 2 E3o . n. j2 E2>2 Eno 3j2 ' j2E2>2 E3o2 nE
(232) 3o j2 c Eno 2 Eno 2 E3o . j2 2 o ' T @oE+c2 {+c2 ' .dEc {c2 n E{c2 2 n > {c2 n o. e n Enj o 2 o '. 2j 2j 2 .dEc {c2 2 n E{c2 e n E> {c2 2 n Enj o 2 n 2c E{c2
(233) n o Ec{c2 no E{c2 o ' e. 2j2 >2 2E23o je 2je n n 2 2 Eno E3o Eno no j2dE
(234) 3o j2 n2>2 E3o2 o c Eno 2 E3o . n. je 2je 2je eje Eno 2 Eno 2 n Eno 2 Eno 2 '. 2. 2E23o je Eno 2 E3o . 2. n. j2 d2>2 Eno 3o ' Eno 2. JE+c {0c
(235) c +c {+c2 ' JE+c {0c
(236) c +c {c2 ' JE+c {0c
(237) c c {c2 n JE+c {0c
(238) c > {c2 ' JEc {0c
(239) c c {c2 n JE> {0c
(240) c > {c2 ' 2b.
(241) .E2c {0c
(242) {c2 n >2 .E{0c
(243) {c2 ' .E2c 02c2 >2 .E02c2 ' . j2 dj2 n>2 E3o2 o c @?_ E3o Eno . JdE0c
(244) n E o > {+c2 c +c2 {+c2 o ' JE0c
(245) {c2 c +c2 {c2 n JdE o > {c2 c +c2 {c2 o ' .dE o E> {c2 2 o ' S wi| t _i?i f ' ' +c {0c
(246) c S f2 ' ' +c{+c2 c S f
(247) ' 3fD 'dE0c
(248) n E o > {+c2oc @?_ S fe ' ' +c2{+c2 . 2j2 >2 E3o no. wi| t UL?t_ih |i ti^i?Ui o ' b *i !iiT?} |i > r i_ e e _ Ai? *4 <" T @oEf ' jb ( f $ Efc jb c. e 2 e _ *4 <" T @oEf2 ' j2b ( f2 $ E j2 c j2b c. *4 <" JEf c f2 ' j2b c e. S T*4 <" 3fD f
(249) ' T*4 <" ' dE0c
(250) n E o > {+c2o ' fc _ *4 <" T @oEf
(251) ' j e ( f
(252) $ Efc je c e 2 e _ *4 <" T @oEfe ' j2b ( fe $ E j2 c j2b c @?_. *4 <" JEf
(253) c fe ' f. W| uL**Lt |@| T*4 <" oe-T ' oc. _. oe-( $ o n f f2 c ihi 2 e f f 2 j j c 2b c @?_ 2 2 f s _
(254) Ee o-T o $ f fe c ihi e
(255) j f 2 f f j c e e 2 f j2b f. . *|ih?@|i*)c *i| t UL?t_ih |i 4L_i* +c| ' o+c|3 n # n 0c| | t|@|L?@h|)c @?_ |i. ti^i?Ui o ' E b fD c @?_ *i| t ?L !iiT |i # r i_ 6Lh UL?i?i?Ui i @tt4i |@| S 2 2 *4 <" ' # ' # S #i?i t
(256) ' 3fD 'dE0c
(257) n # {+c2oc @?_ t ' f c ' c 2c e Ai? i @i 2 2 2 2 _ *4 <" T @oEt ' 2jb# ( t $ Efc 2jb# c 2 2 2 2 2 _ *4 <" T @oEt2 ' j b# ( t2 $ E j2 c j b# c. *4 <" JEt c t2 ' j b# c 2 2.
(258) f.
(259) S T*4 <" 3fD t
(260) ' T*4 <" 'dE0c
(261) n # {+c2o ' fc _ *4 <" T @oEt
(262) ' j 2 Ej2 n # 2 ( t
(263) $ Efc j2 dj 2 n # 2 o c. 2 2 2 2 2 _ *4 <" T @oEte ' j b# ( te $ E j2 c j b# c @?_ *4 <" JEt
(264) c te ' *4 <" j2 # 2 b3fD . W| uL**Lt |@| T*4 <" oe-T ' oc. _. oe-( $ o n tt c ihi 2 2 #2 2 f 2 t j j 2 c b c @?_ t2 s _ Ee o-T o $ tt
(265) c ihi e 2 2 j dj n # 2 o j 2 #2 b3fD 2 t
(266) f j 2 c j 2 #2 te j 2 # 2 b3fD b
(267). . hLLu Lu |iLhi4 S E*LU@*|L?|) @t)4T|L|Utc A :
(268) G. `i ** _ihi |i *LU@*|L?|) @t)4T|L|U _t|hM|L? Lu |i LT|4@* hi**@?LL?_ B it|4@|Lh uLh @hM|h@h) A :
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