1a kuliah sem intro00
TRANSCRIPT
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Model Persamaan Simultan
(Pendahuluan)
Dr. Mahyus Ekananda
Finance Economic Course
Bank Indonesia
27 kto!er sd " #o$em!er 2%%&
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Apa itu Persamaan Simultan ?
Merupakan himpunan persamaan (sistem)dimana variabel tak bebas dalam satu atau lebih
persamaan juga merupakan variabel bebas didalam beberapa persamaan lainnya sebuahvariabel mempunyai dua peran sekaligus
Hubungan antar variabel bersifat dua arah:mempengaruhi dan dipengaruhi
Beberapa pengertian: endogenous, exogenous,predetermine, structural model, reduced form,structural or behavioral eq., technical eq.,identity eq., dan definition eq..
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CONTOH (DASAR)
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Simultaneous Equations Models
11.1 A Supply and Demand Model
11.2 The Reduced Form Equations
11.3 The Failure of east Squares
11.! The "dentification #ro$lem
11.% T&o'Sta(e east Squares Estimation
11.) An E*ample of T&o'Sta(e east Squares Estimation
11.+ Supply and Demand at the Fulton Fish Mar,et
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Simultan ?
Merupakan himpunan persamaan (sistem)dimana variabel tak bebas dalam satu ataulebih persamaan juga merupakan variabel
bebas di dalam beberapa persamaan lainnya sebuah variabel mempunyai dua peransekaligusHubungan antar variabel bersifat dua arah:
mempengaruhi dan dipengaruhiBeberapa pengertian: endogenous, exogenous,predetermine, structural model, reduced form,structural or behavioral eq., technical eq.,identity eq., dan denition eq..
Pemahaman
Ekonometrika
A P
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Apa tu PersamaanSimultan ?A Supply and Demand Model Pemahaman Grafis
1Supply- sQ P e= +
1 2Demand- dQ P X e= + +
2
2
/ 0 ar /
/ 0 ar /
co / 0
d d d
s s s
d s
E e e
E e e
e e
= =
= =
=
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Apa itu Persamaan Simultan ?Pemahaman Diagram Alir(Path Diagram)
Dalam keadaan seimbang
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Bagaimana PersamaanSimultan ditulis ?
Cara Pertama
Persamaan ditulis dalam persamaan keseimbangan
Persamaan ditulis tidak menurut posisi ariabel endogen ! eksogen
Predikat ariabel Eksogen dan endogen didefinisikan dilyar model
1 2Demand- dQ P X e= + +
1Supply- sQ P e= +
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Bagaimana PersamaanSimultan ditulis ?
Cara Pertama
Persamaan ditulis dalam persamaan keseimbangan
Persamaan ditulis tidak menurut posisi ariabel endogen ! eksogenPredikat ariabel Eksogen dan endogen didefinisikan dilyar model
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"he #edu$ed %orm Equations
( ) ( )
( ) ( )
1
2
1
1 1 1 1
1 2 1 1
1 1 1 1
2 2
s
d s
s
d s
Q P e
e eX e
e eX
X v
= +
= + +
= +
= +
1 1 2s dP e P X e + = + +
( ) ( )2
1 1 1 1
1 1
d se e
P X
X v
= +
= +
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"he *dentifi$ation Problem
The effect of chan(in( income
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"he *dentifi$ation Problem
A Necessary Condition for Identification: "n a system of M
simultaneous equations &hich ointly determine the alues of M
endo(enous aria$les at least M41 aria$les must $e a$sent froman equation for estimation of its parameters to $e possi$le. 5hen
estimation of an equation6s parameters is possi$le then the
equation is said to $e identified and its parameters can $e
estimated consistently. "f less than M41aria$les are omitted from
an equation then it is said to $e unidentified and its parameters
can not $e consistently estimated.
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"he *dentifi$ation Problem
Remark- The t&o'sta(e least squares estimation procedure is
deeloped in 7hapter 10 and sho&n to $e an instrumental
aria$les estimator. The num$er of instrumental aria$les requiredfor estimation of an equation &ithin a simultaneous equations
model is equal to the num$er of ri(ht'hand'side endo(enous
aria$les. 7onsequently identification requires that the num$er of
e*cluded e*o(enous aria$les in an equation $e at least as lar(e as
the num$er of included ri(ht'hand'side endo(enous aria$les. This
ensures an adequate num$er of instrumental aria$les.
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''+ ",o-Stage &east Squares
Estimation
1 1 1 /P E P v X v= + = +
( )
( ) ( )
( )
1 1
1 1 1
1 8
s
s
Q E P v e
E P v e
E P e
= + +
= + +
= +
19 9 P X=
1 89 9Q P e= +
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''+ ",o-Stage &east Squares
EstimationEstimatin( the 11.:/ $y least squares (enerates the so'called two-
stage least squaresestimator of ;1 &hich is consistent and
asymptotically normal. To summari
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''+' "he General ",o-Stage &east Squares
Estimation Pro$edure
1. Estimate the parameters of the reduced form equations
$y least squares and o$tain the predicted alues.
1 2 2 3 3 1 1 2 2 1y y y x x e= + + + +
2 12 1 22 2 2 2
3 13 1 23 2 3 3
K K
K K
y x x x v
y x x x v
= + + + +
= + + + +
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''+. "he Properties of the ",o-Stage &east
Squares Estimator
The 2SLSestimator is a $iased estimator $ut it is consistent.
"n lar(e samples the 2SLSestimator is appro*imately normally
distri$uted.
Prini!les of Eono"etris# $rd Edition Slide 11-%&
The ariances and coariances of the 2SLSestimator are un,no&n in
small samples $ut for lar(e samples &e hae e*pressions for them&hich &e can use as appro*imations. These formulas are $uilt into
econometric soft&are pac,a(es &hich report standard errors and t'
alues ust li,e an ordinary least squares re(ression pro(ram.
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''+. "he Properties of the ",o-Stage &east
Squares Estimator
"f you o$tain 2SLS estimates $y applyin( t&o least squares
re(ressions usin( ordinary least squares re(ression soft&are the
standard errors and t-alues reported in theseondre(ression are not
correct for the 2SLSestimator. Al&ays use speciali
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An E/ample of ",o-Stage &east
Squares Estimation
Prini!les of Eono"etris# $rd Edition Slide11-%%
"he #edu$ed %orm Equations
1 2 3 !Demand-d
i i i i iQ P PS '( e= + + + +
1 2 3Supply-s
i i i iQ P P) e= + + +
11 21 31 !1 1
12 22 32 !2 2
i i i i i
i i i i i
Q PS '( P) v
P PS '( P) v
= + + + +
= + + + +
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*dentifi$ation
The rule for identifyin( an equation is that in a system of M
equations at leastM 1 aria$les must $e omitted from each
equation in order for it to $e identified. "n the demand equation the
aria$leP)is not included and thus the necessaryM 1 > 1 aria$le
is omitted. "n the supply equation $othPSand'(are a$sent? more
than enou(h to satisfy the identification condition.
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"he #edu$ed %orm Equations
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"he #edu$ed %orm Equations
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''0. "he #edu$ed %orm Equations
12 22 32 !2
9 9 9 9 9
32.%12 1.+0: +.)02 1.3%!
i i i i
i i i
P PS '( P)
PS '( P)
= + + +
= + + +
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Supply and Demand at the %ulton %ish
Market
( ) ( )1 2 3 ! % )ln ln d
t t t t t t t Q*+, P-(.E M/, 0*E 1E' 02* e= + + + + + +
( ) ( )t 1 2 3ln ln s
t t tQ*+, P-(.E S0/-M3 e= + + +
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*dentifi$ation
The necessary condition for an equation to $e identified is that in this
system ofM> 2 equations it must $e true that at leastM4 1 > 1
aria$le must $e omitted from each equation. "n the demand equation
the &eather aria$le S0/M3is omitted &hile it does appear in the
supply equation. "n the supply equation the four daily dummy
aria$les that are included in the demand equation are omitted.
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"he #edu$ed %orm Equations
( ) 11 21 31 !1 %1 )1 1ln t t t t t t t Q*+, M/, 0*E 1E' 02* S0/-M3 v= + + + + + +
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"he #edu$ed %orm Equations
( ) 12 22 32 !2 %2 )2 2ln t t t t t t t P-(.E M/, 0*E 1E' 02* S0/-M3 v= + + + + + +
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"he #edu$ed %orm Equations To identify the supply cure the daily dummy aria$les
must $e ointly si(nificant. This implies that at least one
of their coefficients is statistically different from
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"he #edu$ed %orm Equations
( )! 12 22 32 !2 %2 )29 9 9 9 9 9ln t t t t t tP-(.E M/, 0*E 1E' 02* S0/-M3= + + + + +
( )
!
12 )29 9ln t tP-(.E S0/-M3= +
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