1A Kuliah SEM Intro00

8/9/2019 1A Kuliah SEM Intro00

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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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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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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-%%


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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''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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( ) 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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( ) 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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( )! 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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