Download - Lecture 8 Application of VAR Model
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8/17/2019 Lecture 8 Application of VAR Model
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TOPIC 8:
APPLICATION OF VAR
MODEL
By:
Assoc. Prof. Dr. Sallahudd! "assa!
SEEQ5133 Applied Econometrics
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SEEQ5133 APPLIED
ECONOMETRICS
INTROD#CTION
Some analysis using VAR model: Impulse response functions
(IRFs) Variance decomposition Granger causality
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IMP#LSE RESPONSE
F#NCTION Impulse response function (IRF)shows the eects of shocs on thead!ustment path of the "aria#le$
%&amines the response of thedependent "aria#le to shocs in theerror term or e&ogenous shoc:
nominal and real shoc domestic and e&ternal shocs
permanent and transitory shocs
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IMP#LSE RESPONSE
F#NCTION 'attern of coecients are IRFs$ IRFs depict:
how the shoc spread up o"er time$ the response of each "aria#le taen in le"el
to a * shoc as well as the con+denceinter"al$
%"iews implementation: Select V$%&I'(uls$ and in impulse
de+nition ta# choose residuals,one std$de"iation
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IMP#LSE RESPONSEF#NCTION ) VECM
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IMP#LSE RESPONSEF#NCTION ) VECM
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FORECAST ERRORVARIANCE DECOMPOSITION Forecast error "ariance decomposition
(F%V-) e&plains the proportion of themo"ements in a se.uence due to its own
shocs "ersus shocs to other "aria#le$ F%-V:
ena#les to determine the most /uctuationsources of the endogenous "aria#les for the
period of study permits to measure the part of the anticipated
"ariance of each endogenous "aria#le e&plained#y the dierent shocs for the dierent hori0ons$
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FORECAST ERRORVARIANCE DECOMPOSITION Varia#le that is e&pected to ha"e any
predicti"e "alue for other "aria#lesshould #e put last$
1he percentage of "ariation dependson: 2orrelation #etween the residuals of a
"aria#le and the residuals of "aria#lethat appear #efore it in the ordering$
2orrelation among inno"ation$
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FORECAST ERRORVARIANCE DECOMPOSITION) VECM
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FORECAST ERRORVARIANCE DECOMPOSITION) VECM
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Variance Decomposition of REP!M"
Perio### S#E# REP!M R$DI!M R%DP!M
1 &1'()(5' 1((#(((( (#(((((( (#((((((
* ''(&+'') '5#','35 *#3)1),& 1#&&'1&( 3 1#31E-(, '5#+)(35 *#5)155* 1#+1,('3
) 1#5'E-(, '('&'1 *#1,(,&1 1#+***3*
5 1#,)E-(, '&3)' 1#+15((1 1#+*151*
& *#(+E-(, ''*5)5 1#3&33+3 1#+111,*
+ *#*,E-(, '+#(3,&( 1#*&+*,) 1#&')11*
, *#),E-(, ',('1( 1#5*(,'3 1#&+(((5
' *#&+E-(, '+33) *#1,,*+* 1#&3,3'1
1( *#,+E-(, '5#('('* 3#31(()3 1#5''()1
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ECONOMETRICS
RES#LT OF ANAL*SIS
In the short run3 impulse ofinno"ation or shoc to R%4'
account for 55 percent"ariation of the /uctuation inR%4' (own shoc)$
Shoc to RF-I and RG-' cancause 5$55 percent in the +rstperiod$
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RES#LT OF ANAL*SIS
In the long run3 impulse ofinno"ation or shoc to R%4'
account for 67$56 percent"ariation of the /uctuation inR%4' (own shoc)$
Shoc to RF-I and RG-' cancause 8$8* and $76*$
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CA#SALIT*
Refers to the a#ility of one"aria#le to predict (and
therefore cause) the other$ Suppose 9t and 4t aect each
other with distri#uted lags$
1his relationship can #ecaptured #y a VAR model$
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CA#SALIT*
Granger (66) de"elopedcausality test:
A "aria#le 9t is said to Granger,
causes 4t 3
if 4t can #e predicted with greater
accuracy #y using past "alues of the
9t rather than not using such past"alues3 all other terms remainingunchanged$
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CA#SALIT*
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CA#SALIT*
∑∑=
−
=
− +++=
M
j
t jt j
N
i
it it Y X Y 1
1
1
1 ε γ β α
∑∑ =−
=
− +++=
M
j
t jt j
N
i
it it Y X X 1
2
1
1 ε φ θ α
∑∑=
−−
=
− ++++=
M
j
t t jt j
N
i
it it ECT Y X X
1
212
1
1 ε π φ θ α
∑∑=
−−
=
− ++++= M
j
t t jt j
N
i
it it ECT Y X Y 1
111
1
1 ε π γ β α
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DIRECTION OFCA#SALIT* ;nidirectional causality from 9t to 4t$ 1he estimated coecients on the lagged 4 in %.uation
is statistically signi+cant$ Varia#le 4 (Granger) causes 9$
1he estimated coecients on the lagged 9 in %.uation< is not statistically signi+cant$
;nidirectional causality from 4t to 9t$ 1he estimated coecients on the lagged 4 in %.uation
is not statistically signi+cant$ 1he estimated coecients on the lagged 9 in %.uation
< is statistically signi+cant$ Varia#le 9 (Granger) causes4$
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DIRECTION OFCA#SALIT* =ilateral causality of Feed#ac$
1he set of lagged 9 and 4 coecientsare statistically signi+cant dierent
from 0ero in #oth regression$ Independence$
1he set of lagged 9 and 4 coecients
are not statistically signi+cantdierent from 0ero in #oth regression$
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+RAN+ER CA#SALIT* TEST
1wo tests: Granger causality test
Sim causality test 2ase two stationary "aria#les
9t and 4t$ Standard>reduced form:
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t t t t
t t t t
x y x
x y y
212212120
111211110
µ φ φ α
µ φ φ α
+++=
+++=
−−
−−
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+RAN+ER CA#SALIT*TEST does not G,cause if do not help
in prediction of 3 controlling for allother rele"ant information a"aila#le at
t ? $ ( does not G,cause ) Single e.uation tests implemented as
@ald tests (F,statistic or ,statistic)$
y x: H ≠>0
x y 0120 =φ : H ⇔
x y 1−t x
t y
2
χ
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+RAN+ER CA#SALIT*
TEST %,"iews implementation: V$%&La, S-ruc-ur$&+ra!,$r
causal-y)loc/ $0o,$!$-y-$s-s (in VAR) or
1uc/&+rou(
s-a-s-cs&+ra!,$r causal-y-$s-&S$r$s Ls-&O2&La,S($c3ca-o!&O2
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+RAN+ER CA#SALIT*TEST21
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