藉由分期MS模型分析臺灣經濟景氣狀態

(1)

29 : 3 (2001), 297319

) * + , MS - . + / 0 1 2 3 4 5 6 7 8 9 : < = > ? @ A

∗

% & & ' ( ( ) * + , - . / 0 1 2 3 4 5

Markov-switching models

6 7 8 9 :

MS

3 4 ; 6 < =

19701998

> ? @ B C D E F G H I J K L M D E N O

(GDP)

> P Q R L M S , -

MS

3 4 * + T U V H I W X Y Z V [ \ ] 6 ^ _ ` a b c L d e f g T U h i j k 6 T U 5 E C ; l m / n f g 6 o p W X Y Z E D l m q V r s t R u v w x 6 ) \ y - < z

MS

3 4 6 {

MS

3 4 | } ~ > P Q z I V H 7 6 7 h L d e f g T U h i j k 6 F V H W X Y Z [ R ( ( J l h b ~ ? @ e T U l m V 5

1987

> ; 6 T U W X Y Z l m V ~

GDP

¡ F V H 6 ¢ £ J K ~ I [ < = 6

1987

> 6 q P 6 [ } f 8 R 2 6 T U [ ¡ b R ~ T U | ) 6

MS

3 4 < = / ! W X [ R w h L d | ? @ I " # 6 7 $ % & ' | T U l m 1 V ( ) 6 * y ) \ + , m < z

MS

3 4 R - . / < z

MS

3 4 ~

MS

3 4 ~ W X Y Z ~ T U l m ~ J K L M D E N O ~ B C D E G H ∗ _B _C _D _E _F _G _H _I _J _K _L _M _N _I _O _P _Q _R _{S T} _U _V _M _N _I _W _P _R _S _X _I _J _Y _Z _I _½ _M _N _\ _] _^

_ N P ` a R S b D E c d e

Professor James D. Hamilton

T f g h T i ^ j X k C l m n o p q r s t u v ( w x y z { | b } ~ D E â ã ä

(2)

1.& 0 & 1

2 2 3 4 5 6 7 8 9 : ; < = > ?

Markov-switching model

@ A B C D

MS

= > E @

F G H I J K L M N O P Q ? R S T U P V W X Y

GDP

Z [ \ E ] ^ _ J K `

V L M N O a 4 5 @ b c ^ d e f g h i j k W l m n

(1998)

A H I X Y

GNP

Z [ \ o 4 5 p q @ r 7 s t u v

MS

= > @ w x H I L M N O ; y z {

Huang

(1999)

| A } t u v

MS

= > F G H I L M u v {

Lin and Chen (1999)

| F G W

~ >

MS

= > p H I L M u v F @ 4 5 P @ } t u v W ` V ? X Y

GDP

h Z [ \ E x @ p H I L M N O 9 ] 2 2 4 5 H I b o J K @ H I J K ¡ ¢ m @ £ ^ ¤ ¥ ; ¦ m § ¥ a J K ? U S E ¨ © ª

(structural shift)

? «

1

E ] F G X Y

GDP

W R S T U P V Z [ \ @

1990

Z ¬ ® ¯ ° ± F ² ³ ´

9.7%

W

6.8%

@

1990

Z ¬ A µ | o

6.0%

W

4.4%

{ ¶ · µ ¸ ¹ º » ¼ ® ¸ @ · ½ ¾ ¿ À Á µ ¸ a L M Â Ã ¢ § x Ä » ¼ ® ¸ @ Å o ¿ Æ Ç È @ É Ê H I J K ¥ Ë µ a U S W Ì ¨ @ Í Î ¡ Ï a Ð Ñ 3 h Ð Ò Ó h Ð Ô Ò Õ Ö § U × o Ø @ Ù f ¤ Ñ 3 h ¤ Ò Ó h ¤ Ô Ò Õ Ö § U × o Ø ] < Ú @ U S ¨ ¹ º Û ` Ü Ý B @ ¡ Ï H I J K a ¤ ¥ Þ ß à ¿ 9 á â T @ ã ä å A æ ç 3 è é a Z [ \ ¤ h Ð Q ê @ ë ì J K L M u v @ í î á ï ð w x L M Â Ã ñ ò ó a ô q õ ö ÷ ø ù @ F G X Y

GDP

W R S T U P V Z [ \ Q ê ú @

1990

Z ¬ ® µ F ² o

4.8%

h

13.1%

W

1.0%

h

4.0%

@ û ü H I L M ý þ ÿ § ¹ º Ð @ J K L M N O a ¨ ` o ÷ 4 5 a = > x í î 9 A p ø A ÷ 2 2 3 ¾ z @ p

MS

= > A ï @

MS

= > a V @ d ¤ h Ð Z [ \ ± W ` V 9 A Û ` @ ø 9 A U T s ñ s A ¤ h Ð ± ñ ` V @ ¿ Æ J K È J K ` V L M N O ý þ Ü @ ; < \ x h 9 ` 8 9 : ; <

-VAR

MS

= > F H I L M u v ] 2 2 Æ Ç @ l m n

(2000)

r W 3 Æ ! z @ " Ñ # F $ È @ F ² %

7 ¿ Æ Ç È Ñ # è é = > @ % 7

Gibbs Sampling

& A è é @ Ñ # V ¡ ' ( U T a ) Î § ¿ * ] s + , T - a í @ . h H I Î / m b 0 ;

(3)

< o Í / b 0 @ 1 ¿ Æ J K È @ H I L M N O ¡ ¢ T ` @ 2 H I J K L M N O ¨ ` a c 3 @ W 1 Û ` a Ø 4 5 Å o ÷ . $ h 6 7 8 9 : = > a x ¿ Æ a b 0 í î 8 9 7 ÷ < Ú @ / ¢ § : a b W ; 3 @ / ¢ § < a = > W H I @ L M ý þ ¡ ¢ í î 8 ÷ ã î @ ú - o ÷ o ? @ 3 @ A F G B ~ X Y

GDP

Ø 4 ¨ C D @ E F 1 H I L M ý þ ¨ Û ` a Ø Å @ Æ Ç 4 5 W ~ ; h > h H b J K L M N O ¡ ¢ ú ] 2 2 3 4 5 G F H I { . $ I o = > x ] . } I o H I L M u v F G @ ~

MS

= > W 3 J ¨ F

MS

= > @ p J K ` V L M u v F ] 4 5 p q d H I R S T U K P V W X Y

GDP

Z [ \ ] . L I o H I J K L M N O ¨ ` F G @ ¤ h Ð ¥ u v F @ W F G H I X Y

GDP

Ø 4 ¨ C D d X Y M Ñ h X Y N O W X Y Ì ý þ ¡ ¢ @ E F 1 H I ¿ Æ J K È @ J K L M ý þ ¡ ¢ Û ` 5 Å { . H I o = > P Q - R x @ S Î F G ; h > b L M N O ¡ ¢ @ o 3 T z U V W { . X I o T ] 2.& Y Z [ \ ] ^ _ 2.1` a b c d

2.1.1 MS

e f 2 2

y

_t

o L M N O K J K ` V Z [ \ @

Hamilton (1989) MS(Y)

= > x B d

(y

t

− u

s

t

) = φ

1

(y

t−

1

− u

s

t− 1

) + φ

2

(y

t−

2

− u

s

t− 2

) + · · · + φ

q

(y

t−q

− u

s

t−q

) + e

t

g m

e

_t

o h ú C @

e

_t

∼ i.i.d.N(

0 , σ

2

)

@

q

o Z [ \

y

_t

) i j k l m µ n @

s

_t

o ¿ 9 ! o ´ a u v ` V @ V ± o d

1

h

2

h

3 · · ·

K

@ ã p F T u v + V o

2

a Ü Ý @

s

_t

=

1

Ç ¬ Þ J K q ¼ Ð ¥ u v @

y

_t

± o

u

1{ û @

s

t

=

2

Ç ¬ Þ J K q ¼ ¤ ¥ u v @

y

_t

± o

u

2{ ø Ç u v ; < \ 9 C B d

p

(s

_t

=

1 |s

_t−

1

=

1 ) = p

11

, p

(s

t

=

2 |s

t−

1

=

1 ) = p

12

(4)

p

(s

_t

=

2 |s

_t−

1

=

2 ) = p

22

, p

(s

t

=

1 |s

t−

1

=

2 ) = p

21 2 2 g m

p

11

+ p

12

= p

21

+ p

22

=

1

@ þ v ¡ ¢

s

t

r ¼ s x

(strictly stationary)

¡ ¢ a ó t o d

0 < p

11 W

p

22

<

1

] 2 2 u v ` V

s

_t

¶ o ¿ 9 ! o @ 2 u 9 v T w À Ç z

t

@ u v a \ ± ? «

2

E ] ã 7 A v T a Ñ x í y z { Ç z

t

Ç @ D o ¡ | \

(ltering probability):

p

(s

_t

|y

_t

, y

_t−

1

,

· · ·)

{ U ù } 9 7 æ ~ Ñ # v T Ç z

t

a u v d

p

(s

t

|y

T

, y

T −

1

,

· · ·)

@ D o ¯ \

(smoothing probability)

] ® ½ Ú @ A z {

(t −

1 )

a Ñ x v T Ç @ | D o \

(predicting probability):

p

(s

_t

|y

_t−

1

, y

t−

2

)

] 2 2 o ~ = > L M u v w x Þ ß @ 3 A J K J Ä ? A B C D J J Ä E L M O o ê @ é = > w x ; y z ú ?

turning point

error

@ A B C D

TPE

E { S Î ® W µ ! ö @ 9 F o

predicting-TPE

W

smoothing-TPE

d

predicting

− T P E = T

−

1

T

S

t=

1

[P (s

t

=

1 |y

t−

1

, y

_t−

2

,

· · · , y

1

) − d

t

]

2

smoothing

− T P E = T

−

1

T

S

t=

1

[P (s

t

=

1 |y

T

, y

T −

1

,

· · · , y

1

) − d

t

]

2 g m @

d

_t

=

0

ñ

1

]

d

_t

=

1

¬ Þ J J Ä Ç z

t

r L M O { û @

d

_t

=

0

o L M O ] 2 2 Z [ \

y

_t

) i j k l m µ n

(q)

a @ 3

q

=

0 ,

1 ,

2 · · · ,

6

x F ² A è é @ L M u v F @ A

q

=

0

W

q

=

1

a

Smoothing-TPE

W

Predicting-TPE

» ? Þ

1

E ] 2 2 Z [ \

y

_t

) i j k l m µ n

q

=

0

a x B @ = > C B d

y

_t

= u

_s

_t

+ e

_t

g m Z [ \ Ñ # @ " Ñ # p V µ @ â A p Z Æ ú F é ] R S T U P V o Ñ # @ Z [ \ é í A ® h µ

12

Ñ # p V µ ½ @ l Þ B d

(5)

¡ 1¢ MS(Y) £ ¤ ¥ ¦ § ¨ © ª

(A)

« ¬

GDP

® ¯

° ± ² ³ 2 2

0

1

2

3

4

5

6 Predicting-TPE

2 2

0.362* 0.374 0.513 0.444 0.454 0.432 0.446

Smoothing-TPE

2 2

0.344* 0.417 0.549 0.449 0.469 0.494 0.513

(B)

´ µ ¶ · ¸ ¹

(Industrial Production Index)

® ¯

° ± ² ³ 2 2

0

1

2

3

4

5

6 Predicting-TPE

2 2

0.353* 0.367 0.563 0.558 0.475 0.518 0.512

Smoothing-TPE

2 2

0.345* 0.396 0.567 0.560 0.502 0.533 0.529

º » ¼

*

½ ¾ ¿ À Á Â Ã

y

_t

=

log

Y

_t

−

log

Y

_t−

12 Ä Å Æ Ç

GDP

È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø

4

Ù Ê Ë Ú Û Ü Ö × Ý Þ ß Ì à á â ã ä å æ

y

_t

=

log

Y

_t

−

log

Y

_t−

4 ç ç è Û é ê ë ì í î ï ð ñ ò Ì ó ô õ ö Ö ÷ ø ù ú û Ì Û ü ý þ ÿ â Þ î Ì È Ê Ë Ç Ê Ë Ù Õ × ê Ì ì Ù Ð Ñ ù Ï Ì é ê Í Î Ï Ê Ë Ì Ê Ë Ú Û Ü Ö Ì Ó Í Ù Ð Ñ Í Ï Ì ! " # Ý $ Ê Ë % ù & ' ( ) * Õ é ê ë í Ê Ë + , Ù È

1970

Í - Ä

1998

Í . Ì ü ý / 0 1 2 3 Ü Æ Ç

GDP

Í Î Ï Ì

1970

Í Ö ù 4 5 6 & ' ( ) î

1970

Í Ô ï 7 8 Ì ! ì

AR

ö Ö ÷ ø î 9 ù : ; Ó < = Ì Ý $ ñ ò % ù ö Ö ÷ ø Ì > ! ? @ A B C Ê Ë Ù 4 Ì * ÷ D

GDP

É Ê Ë 4 E F G Ì Þ H 1 ù ñ ò ( I J Ü ð K L

(over

parameterize the model)

ç ç â

1

M N Ì O P ô õ ö Ö ÷ ø ù ú Q Ì R S T Î ; þ ÿ U ' V Ì > ! W B ö Ö ÷ ø

(q)

X Å

1

Õ

2

Õ

4

Õ

5

6

ù Y Z å Ì [ í \ Ö ] E ^ _ `

(6)

a é b ë c Ð d ù e f g Ï B þ ÿ U ' ù V Ì î [ í \ Ô ] E ^ _ ? a é b ë c Ð d ù h i g Ï È j Ì k l m Ì

Smoothing-TPE

" Å

Predicting-TPE

Ì M N n o × p Ì q r

Hamilton (1989)

ñ ò B ö Ö ÷ ø : Ì F s í Å ü ý ù þ ÿ U ' Ê Ë ^ t u Æ Ç

GDP

Í Î Ï / 0 1 2 3 Ü Í Î Ï b ç ç B

q

X Å

0

4 Ì

Smoothing-TPE

9 Å

Predicting-TPE

Ì r

q

=

0

4 ù : v Ò w x n o ^ y

3

b Ì z Ê Ë { ã Ì

q

=

0

ù : Û ü ý þ ÿ U ' ù V Ì q ! â î Û | ? } ~ ü ý þ ÿ U ' ë ì í ù ñ ò : Ì

Hamilton

(1989)

ù ñ ò F × Ì ñ ò : È B Ø × U ' : é ê c Ð M N Ì B ó ô õ ö Ö ÷ ø ù : å Ì Æ ! < =

1987

Í Ô ù ü ý þ ÿ U ' Ì Þ @ A

1987

Í Ö ü ý ù þ ÿ U ' V Ì > F B ö Ö ÷ ø ù : K L Ì B * ÷ D

GDP

É Ê Ë 4 E F G ù Y Z å Ì é ê ì í ù ñ ò ó ; õ ö Ö ÷ ø :

2.1.2 MS

ç ç È < = W % õ % I M 7 ù W 1 Ì é ê

MS(Y)

ñ ò ; Ó Ì m È Ù

MS(Y)

ñ ò æ

y

_t

= u

_s

_t

+ e

_t

,

for 0

< t

≤ tw

y

_t

= u

∗

_s

t

+ e

∗

t

,

for

tw < t

≤ T

á % Ì

e

_t

∼ i.i.d.N(

0 , σ

2

)

Õ

e

∗

_t

∼ i.i.d.N(

0 , σ

∗

2

)

Ù

MS

ñ ò Ì ! Ó 2 1 ¡ ¢ £ ¡ ¢ Ó Õ $ Ù ¤ ¥ £ ¦ Ü Ì § ¨ F W © ÷ D ¦ Ü þ ÿ ª « ¬ & Y Z Ì Ó ü ý þ ÿ ¬ & ù & ' ( )

ç ç È V M ® ¦ 4 E Ì ¯ x ° ù ± ² ³ Ò Ì ü ý õ % I ù M 7 Ì W 1 B ´ µ ! ¶ k ñ ò S T · þ ÿ ¸ ¹ ¬ & 4 E ù º » Ì é ê B ´ µ ! ¶ k ñ ò S T ¼ ü ý þ ÿ ¸ ¹ ¬ & ù

1987

Í Ô Ö Ì ½ Ú Í ! ¾ W 1 M 7 ù 4 E Ì ¿ c Ð " À R Á Ü ¥ Ì Ú % " ¥ Ì Â í ë Û m M 7 4 E Ä Å È Ã Ä

1990

Í Å + ü ý ¬ & Æ Ç È Ì È ! ¾ É Ê Ï ¦ & Ë Õ 1 2 Ì á ù ® ¦ ^ y

4

b Õ Í Î

(7)

å Ï 2 0 / ù Ð Õ É Ë Ñ Ò 2 Ó Ô Õ ù Ö X F ! × ù Ì ü ý ù Ç È Ì > 8 Ø Ù Ú ù ° 2.2` a b Û Ü

2.2.1

Ý Þ ß à á â ã ä å æ ç 2 2 3 " F

MS

= > F u v ; < \ x W u v ; < \ T ¨ Û ` s è x @ i é " ® ¸ D o F

MS(1)

= > @ µ ¸ | D o F

MS(2)

= > ] s ¸ ú ¼ F

MS(2)

= > í " Ñ # F ¿ Æ Ç È @ â F ² % 7 ¿ Æ Ç È a Ñ # A è é @ g ê z o ë Ñ # X Y

GDP

a F G m @ ì í ¼ . $ È Ñ # ¡ ' @ " î ï ¡ § V @ Ñ # R S T U P V Z [ \ F G m @ Î ¼ ç 3 z ð @ ¿ Ä T ] 2 2 { ¼ F

MS(1)

= > @ u v ; < \ Æ x B @ " æ ç 3 Ñ # Æ Ç è é @ 9 7 A ñ ò ë Ñ # F G m @ µ È Ñ # z ¡ ' , T a ) Î § ¡ Ð ? «

5

E @ F

MS(1)

= > m @ y

tw

´

tw

+

1

@

S

_tw

` ´

S

_tw+

1 Ç @

u

1−

> u

∗

1 a \ ó ·

p

11@ W

t < tw

Ç

u

1−

> u

1

t > tw

Ç @

u

∗

1−

> u

∗

1 Æ ] Æ ô

u

1−

> u

∗

2 @

u

∗

2−

> u

∗

1 @

u

∗

2−

> u

∗

2 a \ F ² o

p

12h

p

21h

p

22 õ

t < t

t > tw

Æ @ ö

u

∗

2

u

1 Ç @ 9 á Ä ^ ÷ ø U ? «

6

E ] á ù ú Ç z a u v ; < \ @ Ä û = > © ü ý õ þ ÿ @ 2 ø @ [ è é V a V D @ û õ è é a § ¤ ]

2.2.2

Ý Þ Ý Þ ç 2 2 3 J ¨ F

MS

= > @ / m b 0 J K z " ¤ h Ð Z [ \ ± x o

u

2 W

u

1@ J K ¨ Û ` o m § ¥ µ @ | x o

u

∗

2 W

u

∗

1 ] @ W L t u v Z [ \ ± x ^ Æ q @ s ¸ ú o ÷ ± @ A E F ] 2 2 L t u v x m @ i é " Z [ \ ± x o d

u

1h

u

2h

u

3 W

u

4 L è ¿ Æ V ± @ ¶ 9 7 A ð > u v ù < ¡ ¢ @ = > ê z o @ Ñ # m ( J K ¨ Û ` a - Y ] < Ú @ Ò Ó ê Ü Ý B @ L t u v Z [ \ Ë µ a L M Â Ã ¢ § @ í î 9 7 ä å a Z [ \ V ± h » A ë x ÷ 3 J ¨ F

MS

= > @ ¡ È a s ¤ h Ð ± x @ | á 9 ù

(8)

J K ¨ Û ` - Y ] 2 2 o L t u v = > u v ù < ¡ ¢ @ r 7

4X4

u v \ @ G é

12

+ ; < \ V d

P

=







p

11

p

21

p

31

p

41

p

12

p

22

p

32

p

42

p

13

p

23

p

33

p

43

p

14

p

24

p

34

p

44







3 J ¨ F

MS(Y)

= > t u v x B @ u v \ o

2X2

@ p

2

+ V ] 1 s ¸ ø a ú ¼ @ F

MS(Y)

= > a x @ & î ¼ i é p L t u v x a u v ; < ¡ ¢ ! " # $ í % ] í % o d

u

1h

u

2 O 9 ; < @

u

3h

u

4 } 9 ; < @

u

1h

u

2 W

u

3h

u

4 O & ù < { ' d (

P

11h

P

12h

P

21h

P

22h

P

33h

P

34h

P

43 W

P

44 ¿ o

0

ù @

P

13h

P

14h

P

23h

P

24h

P

31h

P

32h

P

41 W

P

42 ) o

0

@ o 9 ù / m b 0 J K ¨ a ; ` @ í % ö r * ô + ] , ( @ 3 J ¨ F

MS(Y)

= > L t u v = > @ ¶ · õ ö ^ " @ V x o - C @ 9 . F H I L M u v / Y ] 3.& 0 1 2 3 4 5 6 _ 3.1` 7 8 9 : ; < = > ? @ A B Ü 2 2 3 I 7 Ñ # o H I R S T U P V Ñ # Z [ \

(IP)

@ Ñ # C D O o

1970

Z

1

{

1999

Z

1

] Ñ # E o H I J K F G Ñ # H ] 2 2 J K ¨ © ª Ç z ë x í A

1987

Z

8

o m I ? )

1987

Z

8

A µ @ 8 9 : ; < = > â p R S T U P V Z [ \ ¤ h Ð u v A F E @ ® µ

12

+ ¨ ` þ 9 á T Ç z @ g m A

1987

Z

7

¨ ` þ Ç z a x @ ( p 6 õ V è é ± ? o

−

1,068.5

E @ Å ø i é r 7 Ç z o ¨ -` þ Ç z ? Þ

2

E ]

(9)

¡ 2¢ J K L M N O P Q R S T U V W X Y Z [ \ ¹ ] R S T U V W X Y Z [ \ ¹ ]

1986

8

^

−

1,092.0

1987

8

^

−

1,068.6

1986

9

^

−

1,091.7

1987

9

^

−

1,069.9

1986

10

^

−

1,091.7

1987

10

^

−

1,072.8

1986

11

^

−

1,085.6

1987

11

^

−

1,075.0

1986

12

^

−

1,082.7

1987

12

^

−

1,076.0

1987

1

^

−

1,080.1

1988

1

^

−

1,076.4

1987

2

^

−

1,079.3

1988

2

^

−

1,073.6

1987

3

^

−

1,079.4

1988

3

^

−

1,074.2

1987

4

^

−

1,073.6

1988

4

^

−

1,075.1

1987

5

^

−

1,072.1

1987

5

^

−

1,075.9

1987

6

^

1,069.5

1987

6

^

−

1,076.5

1987

7

^

−

1,068.5*

1987

7

^

−

1,977.3

º » ¼

*

_ ½ ¿ À ` Â Ã ç ç

MS(IP)

ñ ò " À R T ù c Ð M N × a Ð Q 6 ã Å â

3

1

b ^ y

7

b Ì c d M N { ã ½ e f J Ü g a Ð { h Ì i j ì í

MS(IP)

ñ ò ë k m þ ÿ U ' F ° l m

1(b) MS(IP)

ñ ò $ U ' e f g Ï m Z ! n d Ì Ä

1987

Í

8

o Ó Ö Ì

MS(IP)

ñ ò S T Û ü ý þ ÿ ù ¬ & ; Ó k â

3

2

Õ

3

b È Ù

MS(1)(IP)

Ù

MS(2)(IP)

ñ ò c Ð M N p î

MS(IP)

Ù

MS(1)(IP)

Õ Ù

MS(2)(IP)

ñ ò Ì z

LR

q Q Õ

AIC

Õ

Schwarz

value

Ì Ó

predicting-TPE

Õ

smoothing-TPE

Þ l Ì Ö ¡ ~ r { h s t Ä Å

Ù

MS(1)(IP)

Ù

MS(2)(IP)

ñ ò p î u z

LR

q Q Õ

AIC

Schwarz

value

v w Ì Ô ~ â î Ì z é ê ë x þ ÿ U ' V 3 y

(predicting-TPE

z

smoothing-TPE)

Ì w Ö ~ î s t Ì j Ø F { | ë ¨ Ì * 4 D m

Õ $ Í Î Ï Ù ¤ ¥ y v j { h j Ì { ã ü ý Ó } õ % I ~ Ì Þ Ì U ' k g Ï ù ¦ ð × Û î F {

(10)

¡ 3¢ MS M S £ ¤ J

¹

MS(IP)

MS(1)(IP)

MS(2)(IP)

p

22

0.971

0.966

0.978 (0.015)

(0.014)

(0.013)

p

11

0.984

0.945

0.960 (0.008)

(0.021)

u

1

3.799

2.521

2.526 (0.394)

(0.789)

(0.781)

u

2

19.074

18.820

18.820 (0.560)

(0.623)

σ

5.607

6.467

6.470 (0.216)

(0.323)

p

∗

22

0.937 (0.033)

p

∗

11

0.895 (0.049)

u

∗

1

0.757

0.919 (0.573)

(0.559)

u

∗

2

6.247

6.450 (0.396)

(0.437)

σ

∗

2.761

2.686 (0.188)

(0.198)

Log Likelihood

−

1,123.0000000

−

1,068.5.000000

−

1,067.6.000000)

AIC

−

1,128.0000000

−

1,076.5.000000

−

1,077.6.000000)

Schwarz value

−

1,137.6000000

−

1,099.4.000000

−

1,096.9.000000)

Predicting-TPE

00.353 000.200*

000.195**

Smoothing-TPE

00.345 000.187*

000.185**

Number of parameters

500)

800)

100000)

u

2

, u

1

, σ, p

22

, p

11

u

∗ 2

, u

∗ 1

, σ

∗

_{, p}

∗ 22

, p

∗ 11

MS(2)(Y)

¡ ¢ £ ¤ ¥ ¦ § ¦ ¨ © ª « ¬ ® ¯ ° ± ² ¬ ³ ´ µ ¶ · ¸ ¹ º ° »

(11)

(a) ¼ ½ ¾ ¿ À Á Â Ã (IP) Ä Å Æ

(b) MS(IP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

(c) Ò Ó MS(2)(IP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

Ô 1Õ ¼ ½ ¾ ¿ À Á Â Ã Ä Å Æ Ö É Ê Ë Ì Í Î Ï Ð Æ × Ø Ù Ó Ú Û 1970 Ä

(12)

¡ 4¢ MS MS £ ¤ J Þ ß GDP ¹

MS(GDP)

MS(1)(GDP)

MS(2)(GDP)

p

22

0.911

0.923

0.934 (0.045)

(0.031)

(0.038)

p

11

0.948

0.850

0.874 (0.026)

(0.061)

(0.063)

u

1

5.745

4.639

4.856 (0.260)

(0.536)

(0.552)

u

2

11.571

11.435

12.252 (0.354)

(0.405)

(0.420)

σ

2.120

2.424

2.586 (0.147)

(0.217)

(0.231)

p

∗

22

0.884 (0.090)

p

∗

11

0.944 (0.040)

u

∗

1

4.770

5.733 (0.301)

(0.147)

u

∗

2

6.804

7.965 (0.138)

(0.243)

σ

∗

0.771

0.792 (0.088)

(0.089)

Log Likelihood

−

273.1.0000

−

244.2.00000

−

248.0.00000

AIC

−

278.1.0000

−

252.2.00000

−

258.0.00000

Schwarz value

−

285.0.0000

−

263.2.00000

−

271.8.00000

Predicting-TPE

00.362 000.170**

00.306*

Smoothing-TPE

00.344 000.151**

00.298*

Number of parameters

500)

8.00)

100000)

à

3

»

ç ç m

1(a)

Õ

(b)

Õ

(c)

¿ á d ü ý / 0 1 2 Í Î Ï Õ

MS(IP)

Õ Ù

MS(2)(IP)

ñ ò $ U ' e f g Ï p î W Ì Ù

MS(2)(IP)

ñ ò O d

1987

Í Ô ù

3

D $ Ù Ì B

1987

Í Ö Ì q ! d

3

D â ã ù $ Ù Ì þ ÿ U ' V

3 y æ

predicting-TPE

smoothing-TPE

b > ¿

0.350

0.345

ä å È

0.195

(13)

(a) ¼ ½ æ ç G DP Ä Å Æ

(b) MS(GDP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

(c) Ò Ó MS(1)(GDP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

Ô 2Õ ¼ ½ æ ç GDP Ä Å Æ Ö É Ê Ë Ì Í Î Ï Ð Æ × Ø Ù Ó Ú Û 1970 Ä è I

(14)

3.2` 7 8 ê ë GDP ? @ A B Ü

2 2 3 I 7 Ñ # o H I X Y

GDP

Z [ \ ë Ñ # @ Ñ # C D O o

1970

Z

I

ë {

1998

Z

IV

ë ] Ñ # E o H I J K F G Ñ # H ] Þ

4

ì = > V è é W _ 7 é í ]

MS

= > u á

1987

Z A ® a

3

È Ð ¥ O ]

~

MS(GDP)

= > W F

MS(1)(GDP)

F

MS(2)(GDP)

? «

8

E @

LR

R x í h

AIC

h

Schwarz value

h

predicting-TPE

W

smoothing-TPE

= > ë ì P

Q @ ) A µ s ¸ Þ ß ] ± î À a í @ F

MS(2)(GDP)

= > Þ ß ¿ ã F

MS(1)(GDP)

= > @ i é w o ¾ í Å o . $ È ^ ç 3 V ï ' @ 1 F

MS(2)(GDP)

= > ^ ¡ § V ] 2 2 ð

2(a)

h

(b)

h

(c)

F ² ñ H I X Y

GNP

Z [ \ h

MS(GDP)

h F

MS(1)

(GDP)

= > Ð ¥ u v ¯ \ ] ~ ß @ F

MS(1)(GDP)

= > ( w x

1987

Z ® a

3

È Ð ¥ O @

1987

Z µ @ 9 w x

2

È ü ý a Ð ¥ O @ L M u v ë x P Q d

predicting-TPE

W

smoothing-TPE

E } F ² Î

0.362

W

0.344

ò o

0.170

W

0.151

] 4.& 0 1 ó ô 2 3 õ ö ÷ ø ù ú 6 _ 2 2 H I R S K U ± Z [ \ F

MS(IP)

= > a è é d . È ¤ h Ð Z [ \ ± W Q ê ú F o d

u

2

=

18 .

820

h

u

1

=

2 .

521

W

σ

=

6 .

467

{ . $ È ¤ h Ð Z [ \ ± W Q ê ú | F ² o d

u

∗

2

=

6 .

247

h

u

∗

1

=

0 .

757

W

σ

∗

=

2 .

761

] H I X Y

GDP

Z [ \ F

MS(1)(GDP)

= > a è é d . È ¤ h Ð Z [ \ ± W Q ê ú F ² o d

u

2

=

11 .

435

h

u

1

=

4 .

639

W

σ

=

2 .

424

{ . $ È ¤ h Ð Z [ \ ± h W Q ê ú | F ² o d

u

∗

2

=

6 .

804

h

u

∗

1

=

4 .

770

W

σ

∗

=

0 .

771

] ~ s È è é ± @ . È Z [ \ ¤ ¥ u v ± º û ¼ . $ È Æ r ¤ ¥ u v a ± @ û ü ! / m b 0 J K z a ¤ ¥ Þ ß { . $ È Z [ \ Q ê ú ¹ º » ¼ . È Q ê ú @ º H I L M ý þ ÿ § a » ü ] 2 2 F T @ ¿ Æ J K È @ H I L M N O ¡ ¢ T ` @ 1 H I L M ý þ ¡ ¢ Û ` a Ø 4 5 Å o

?

± @ A E F ] ý B i é X Y

GDP

¨ C D A F G @ d X Y N O

(PC)

h X Y N O M Ñ

(IV)

h X Y Ì

(15)

(EX)

W þ

(GC)

] g m X Y N O X Y Ì W X Y

GDP

Æ @

MS

= > ) w x s ` V a ¤ h Ð ¥ u v @ X Y N O M Ñ W þ & @ ' r 7

MS

= > ' 9 w x æ ç 3 O X Y N O M Ñ W þ a ¤ h Ð ¥ u v @ < Ú @ X Y N O M Ñ W þ J K ¨ ; ` µ g ý þ X Y

GDP

^ ÿ ¹ º » ß q ] 2 2 o ¹ ð ~

1987

Z ® h µ @ X Y

GDP

Ø 4 ¨ C D ? d X Y N O h M Ñ h Ì W þ E a ¨ ` @ i é r 7 F

MS

= > è é N O X Y h X Y Ì h X Y N O M Ñ W þ @ è é W _ 7 é í ì ¼ Þ

5

@ 4 5 º N O W Ì J K ¨ ; ` µ ý þ ¹ º » @ ß ¨ - ` @ p ½ Ú X Y N O M Ñ W þ . h $ È ý þ ¡ ¢ ¶ ^ B @ B ~

¿ ã N O W Ì @ ý þ - ¤ ¿ B ] Î ¼

Lin and Chen (1999)

W l m n

(2000)

à W L M N O _ A F T @ ½ þ õ r ù T a ` V @ Å ø 3 " z X Y Ì W N O M Ñ a ~ ] 2 2 F G X Y Ì ý þ @ . È ¤ h Ð Z [ \ ± ú W Q ê ú F ² o

23.8

W

12.9

@ . $ È a ¤ h Ð Z [ \ ± ú W Q ê ú | o

7.2

W

3.5

@ F ² B

70%

W

73%

@ û ü H I J K ; > µ @ X Y Ì ý þ ¹ º ' ] Ì ý þ a B @ 9 á W i b Ì U × ¨ a ¹ º ; ` _ ] )

1980

Z ¬ m A @ û i b U S a @ Ø 4 Ì U × Í Î ¡ Ï Ð Ò Ó h Ð Ñ 3 h Ð Ô Ò Õ Ö § a U × @ ; f ¤ Ò Ó h ¤ Ñ 3 h ¤ Ô Ò Õ Ö § a U × ] H I Ñ 3 Õ Ö h Ò Ó Õ Ö A ¤ Ô Ò U S @ Ì ß x ¥ @ ý þ Å ½ ÿ Ð ] 2 2 F G N O M Ñ ý þ ¡ ¢ @ H I J K ; > µ È @ ý þ ` ¿ ã X Y Ì @ M Ñ ý þ Ê ¤ ¿ B ] N O M Ñ . È ¤ h Ð Z [ \ ± ú W Q ê ú F ² o

26.99

W

11.61

@ . $ È a ¤ h Ð Z [ \ ± ú W Q ê ú | o

17.35

W

7.15

@ F ² B

36%

W

38%

] M Ñ W Ì ý þ ~ @ N O M Ñ ý þ a B ~ p ³ X Y Ì a ] ø ù @ H I J K ¨ ; ` ® @ X Y Ì ¤ h Ð Z [ \ ± ú W Q ê ú » F o

23.8

W

12.9

@ W N O M Ñ a

26.99

W

11.61

ú ¿ @ H I J K ¨ ; ` µ @ X Y Ì a ¤ h Ð Z [ \ ± ú W Q ê ú ÿ ò o

7.2

W

3.5

@ N O M Ñ | p o

17.35

W

7.15

@ F ² o X Y Ì a

2.4

-

2.0

- Ì ¬ & # I . " Å Æ Ç d / Ì k l m Ì Æ Ç 0 1 Ê È 2 3

(16)

¡ 5¢ Þ ß ! " # $ % & ' ! " # $ T ¹

u

1

u

2

σ

u

∗

1

u

∗

2

σ

∗

u

2

− u

1

u

∗

2

− u

∗

1 % &

6.22 11.01 1.60 5.97 8.38 0.68

24.79 22.41

(0.40) (0.33) (0.14) (0.19) (0.17) (0.09)

' (

5.97 29.72 12.89 4.53 11.72 3.50

23.75 27.19

(3.2) (3.09) (1.31) (0.79) (1.44) (0.46)

) *

2.52 29.51 11.61 3.66 21.01 7.15

26.99 17.35

(2.14) (3.12) (1.19) (1.84) (2.38) (0.83)

+ , % &

−

8.33). 7.42 4.31 1.06 8.96 2.71

15.75 27.9

(5.39) (0.62) (0.36) (0.71) (0.63) (0.31)

à

3

» ¬ & Ò × 4 5 ù 6 7 Ë m 5.& 8 9 : ; < = > ? @ A B C 6 _

2 2 3

MS(Y)

= > A ï @ J D F

MS(Y)

X W & @ 6 7 8 9 :

; < p H I L M u v E á a ] # $ W H I Æ r / m b 0 a = > @ " Æ ç î p J K ¨ ; ` a ¡ ¢ @ r F

MS(Y)

= > w x L M ý þ @ J K a ; 3 @ | 6 ¿ r F

MS(Y)

= > ] 3 I 7 b ù Ñ # o ; 3 W = > R S T U P V Z [ \ @ o & F b Ñ # ~ @ i é 7 Æ ç 3 O @ Ñ # E o G H F G Ñ # H ] 2 2 ð

3(a)

W

(b)

F ² o ; 3 R S T U P V Z [ \ I ð W 6 7

MS(Y)

= > è é ; 3 R S T U K P V Z [ \ Ð ¥ u v ¯ \ ] 4 5 ß @ { ç 3 J @

MS(Y)

= > u 9 ; 3 L M ý þ ¡ ¢ @ < Ú @ F

MS(Y)

= > p ; 3 L M u v F { i é w o ¾ í Å o è é ç 3 O c @ ; 3 T / m b 0 Î ¤ ¥ ; ¦ m § ¥ a J K ¨ ; ` ] 2 2 û ! ð

4(a)

= > R S T U P V Z [ \ W ð

4(b)

K 7

MS(Y)

= > è é = > R S T U K P V Z [ \ Ð ¥ u v ¯ \ @ )

1988

Z

4

C @

MS(Y)

= > p = > L M ý þ A F @ Å ø i é N ¦ F

MS(2)(Y)

(17)

(a) L M ¾ ¿ À Á Â Ã (IP) Ä Å Æ (b) MS(IP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ Ô 3Õ L M ¾ ¿ À Á Â Ã Ä Å Æ Ö É Ê Ë Ì Í Î Ï Ð Æ × Ø Ù Ó Ú Û 1970 Ä 1 Ü Ý 1998 Ä 12 Ü

1988

Z

3

? «

9

E ] ð

4(c)

ñ F

MS(2)(Y)

= > ( è é a = > R S T U P V Z [ \ Ð ¥ u v ¯ \ ] ~ ð

4(b)

W

(c)

@ 9 ¹ º ß µ ¸ p = > L M u v ý þ ¡ ¢ u á ^ ]

(18)

¡ 6¢ O % P % J Q R S T

(A)

U V ´ µ ¶ · ¸ ¹ ® ¯ « W R X

p

22

p

11

u

1

u

2

σ

u

2

− u

1 U V

0.974 0.947

−

3.976 6.577 4.513

10.053 (0.011) (0.022) (0.606) (0.358) (0.176)

(B)

Y Z [ \ ] ´ µ ¶ · ¸ ¹ ® ¯ « W R X

(1)

^ _ ` a ² b

(High-growth Stage)

p

22

p

11

u

1

u

2

σ

u

2

− u

1 \ ]

0.978 0.960

2.526 18.820 6.470

16.294 (0.013) (0.021) (0.781) (0.623) (0.323)

Y Z

0.968 0.955

8.017 23.931 6.220

15.914 (0.016) (0.021) (0.694) (0.627) (0.307)

(2)

c _ ` a ² b

(Middle-growth Stage)

p

∗

22

p

∗

11

u

∗

1

u

∗

2

σ

∗

u

∗

2

− u

∗

1 \ ]

0.937 0.895

0.919 6.450 2.686

5.531 (0.033) (0.049) (0.559) (0.437) (0.198)

Y Z

0.982 0.932

−

3.614 8.937 5.809

12.551 (0.013) (0.057) (1.264) (0.527) (0.323)

º » ¼

u

2

, u

1

, σ, p

22

, p

11 d

u

∗ 2

, u

∗ 1

, σ

∗

_{, p}

∗ 22

, p

∗ 11 e f ½ e g

MS(2)

h i j k l m n d m o p q r s t u v w g x Â s y z { d | } ~ w Ã ç ç È p î Õ Õ ü ½ þ ÿ ¬ & ( ) j Ì â

6

â

7

È ½ ñ ò × a Ð Q $ U ' k Æ M N { ã æ Õ p î B ¡ × ÷ D c Ð ¥ Ì ÷ D Í Î Ï U ' Ù ¤ ¥

(23.93)

{ h " Å * ÷ D U ' ù Ù ¤ ¥

(18.94)

(5.81)

9 Å ÷ D y v j

(6.22)

Ì { ã þ ÿ ¬ & # I ù 9 Ç t Ì ü ý × î Ì ¦ ð î 9 ^ y

10

MS(Y)

ñ ò î ¾ < = ¡ þ ÿ ª « ( ) * Õ p î » ø $ Ù Ì é Å

1997

Í

10

o

11

o _ 2 Ì õ ¬ $ Ù Ì ü ý n Ä

1998

Í

10

o õ $ Ù Ì r ü ý Å - Ù ù s â

(19)

(a) ¾ ¿ À Á Â Ã (IP) Ä Å Æ

(b) MS(IP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

(c)Ò Ó MS (2)(IP) Ç È É Ê Ë Ì Í Î Ï Ð Æ Ñ

Ô 4Õ ¾ ¿ À Á Â Ã Ä Å Æ Ö É Ê Ë Ì Í Î Ï Ð Æ × Ø Ù Ó Ú Û 1970 Ä

(20)

¡ 7¢ O % P % " # U V \ ] Y Z

1974:041975:12 1974:011975:06 1974:041975:12

1980:101981:06 1979:041983:04 1980:101981:06

1982:061983:03

1985:111987:05 1984:091986:02 1985:111987:05

1991:081994:08 1989:091991:03 1991:081994:08

1992:091993:05

1997:111998:12 1995:101996:09

1998:101998:12 1997:111998:12

6.& ÷ & 2 2

MS

= > A 4 5 ¿ Æ q ¼ p ( % 7 Ñ # 3 a / - @ 9 è é + Ç z q ¼ ¿ Æ u v a \ @ S A ! F ¤ h Ð ¥ O @ £ ^ é í a À @ ( è é a = > 9 L M a ]

Hamilton (1989)

W

Filardo

(1994)

6 7

MS

= > @ p b a J K N O ! a F @

MS

= > p H I W = > a J K L M N O @ ê ¡ E a á @ ¾ í ¢ Å ¼ H I W = > o a J K ? £ d b h ; 3 E @ H I W = > J K ¡ ¢ m @ £ ^ / m b 0 ; ¦ Í / b 0 J K ¨ Û ` ] F G H I X Y

GDP

W R S T U P V Z [ \ @

1990

Z ¬ ® ¯ ° ± F ² ³ ´

9.7%

W

6.8%

@

1990

Z ¬ A µ | o

6.0%

W

4.4%

@ Z [ \ Q ê ú @ } Î

1990

Z ¬ ® a

4.8%

W

13.1%

@ ò o

1.0%

W

4.0%

] 3 ¾ z @ p

MS

= > A ï @ "

MS

= > a ¤ h Ð Z [ \ ± W ` V x o s ñ s A @ A / m b 0 ¿ Æ J K È @ J K ` V L M N O ý þ Ü ] 2 2 3 4 5 X W o d . h F

MS

= > 9 A

MS

= > F H I ? W = > E J K L M u v @ p J K L M u v ¤ x @ V ¥ - P Q ] . $ h F G ¦ §

GDP

t 4 J K ` V @ £ d X Y M Ñ h N O W Ì ý þ ] X W º

1987

Z A Ì ¨ x @ N O x - [ @ M Ñ ý

(21)

þ u ¤ ¿ B ] < Ú @ M Ñ Í o ¦ § J K ý þ a Ø 4 Å © ] . } h F G B ~ ; h > h H b J K L M N O @ E F ¢ § b 0 a L M N O þ v ¡ ¢ ú @ X W º @ 6 7

MS

= > . F = > W H I Î / m ; ` o Í / J K a L M N O ¡ ¢ @ ¢ Å ¼ b 0 ¥ ¡ ¢ m U T J K ¨ ; ` @ Í r J K a ; 3 @ | ] ª & & «

¬

Kuznets, Simon (1979), Growth and Structural Shifts, in Walter Galenson (ed.),

Economic Growth and Structural Change in Taiwan. Cornell University Press.

p

(s

_t

|y

_t+r

, y

_t+r−

1

,

· · ·)

@ ö

r

=

0

d ¡ | \ @

r <

0

d \ @

r >

0

d ¯

\ ]

®

q

=

3

Ç @

Smoothing-TPE

W

Predicting-TPE

a ú } ¿ º û ]

¯ R ° Ç È J K Ü @ g m ' í b ± i ÿ ² ³ ´ µ _ ¶ · ¸

?

General System of Preference

@ A B C D

GSP

E @ p H I A Ì o Ø a J K

1 ¹ º » @ 9 á Û ` H I U S T U ¨ @

GSP

½ l m n

(2000)

r 7

Gibbs Sampling

è é & @ F

MS(2)

= > ) Î § ¿

* ] 3 X W P @ u v ; < \ ¹ º Û ` a Ü Ý B @ r 7 æ

ç 3 è é a F

MS(1)

= > 9 ^ w x X Y

GDP

ë Ñ # ¤ h Ð ¥ O ]

¾ ¸ Q ¿ À Á a P ï ]

Â è é 8 9 : ; < = > Ç @ ð Ã r ? ê E õ

(approximate

(quasi) maximum likelihood estimation)

è é = > V ] g ¿ ù í % 7

EM-algorithm

ñ í V ± & Ä Å õ V ¹ a è é ± { 3 r 7 µ ¸

? V ± & E è é V @ 6 7

GAUSS

a Æ Ç ¢ l

OPTIMUM

@ 7 ¢ l c J D a

BFGS

¬ V Ä = > È a ç 3 õ V ¹ » ± ]

É

MS(GDP)

= > )

1988

Z

I

ë A µ @ â p H I X Y

GDP

Z [ \ ¤ h Ð u

v A F @ A

1988

Z

I

ë o m I @ ® µ

1

Z ¨ ` þ 9 á T Ç z @ g m A

1987

Z

IV

ë ¨ ` þ Ç z a x @ ( p 6 õ V è é ±

(22)

1988

Z

4

o m I ? )

1988

Z

4

A µ @

MS

= > â p = > L M ¤ h Ð u v A F E @ ® µ

6

+ ¨ ` þ 9 á T Ç z @ g m A

1988

Z

3

¨ ` þ Ç z a x @ ( p 6 õ V è é ± ] Ë H I R S T U ± Z [ \ Q ê ú Î . È a

6.47

ò o . $ È a

2.69

] Ì Í Î Ï Ð Ñ Ò s Ó Ô Õ s Ö ¿ ×

(1998)

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26(4)

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431457

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(23)

EXAMINING TAIWAN'S BUSINESS CYCLE VIA

TWO-PERIOD MS MODELS

Hsiu-Hua Rau, Hsiou-Wei William Lin and Ming-Yuan Leon Li

∗

ABSTRACT

This study adopts Markov-switching models (hereafter MS models) to examine the

annual growth of Taiwan’s industrial product index (hereafter IP) and real gross domestic

products (hereafter real GDP) from 1970 to 1998. Among the contemporary papers

explor-ing business cycles via MS models, few, if any, aim at copexplor-ing with the diminishexplor-ing business

cycle patterns due to economic structural changes. In contrast, we adopt two-period MS

models, which incorporate a specific set of mean and variance parameters for each period,

to control the structural changes in Taiwan’s and South Korea’s economies.

Our empirical findings are consistent with the following notions. First, Taiwan’s

busi-ness cycle patterns changed significantly after 1987. Second, Taiwan’s real exports and

consumptions appear to be less volatile after 1987, whereas real investments replaced real

exports as the primary factor for post-1987 economic movements. Third, for Taiwan and

South Korea, which both experienced substantial economic growth, our two-period MS

settings appear to outperform the conventional settings in modeling the business cycles.

The volatilities for the two nations’ IP and real GDP were significantly lower in the second

period. The result is in contrast with our finding with respect to Japan’s more

devel-oped economy. For Japanese business cycles, conventional single MS models appear to be

descriptive.

Keywords: Markov-switching models, Two-period MS models, Business cycles, Economic

structure, Real GDP, Industrial product index

∗

藉由分期MS模型分析臺灣經濟景氣狀態

29 : 3 (2001), 297 319

∗

Markov-switching models

MS

19701998

(GDP)

MS

MS

MS

1987

GDP

1987

MS

MS

MS

MS

Professor James D. Hamilton

Markov-switching model

MS

GDP

(1998)

GNP

MS

Huang

(1999)

MS

Lin and Chen (1999)

MS

GDP

(structural shift)

1

GDP

1990

9.7%

6.8%

1990

6.0%

4.4%

GDP

1990

4.8%

13.1%

1.0%

4.0%

MS

MS

-VAR

MS

(2000)

Gibbs Sampling

GDP

MS

MS

GDP

GDP

2.1.1 MS

y

t

Hamilton (1989) MS(Y)

(y

t

− u

s

) = φ

(y

t−

− u

s

) + φ

(y

t−

− u

s

) + · · · + φ

q

(y

t−q

− u

s

29 : 3 (2001), 297319

19701998

_t

_t

_t

_t

_t

_t

_t

_t

_t

_t−

_t

_t−