Lecture 8 Application of VAR Model

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


2/22

SEEQ5133 APPLIED

ECONOMETRICS

INTROD#CTION

Some analysis using VAR model: Impulse response functions

(IRFs) Variance decomposition Granger causality

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ECONOMETRICS

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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SEEQ5133 APPLIED

ECONOMETRICS

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

SEEQ5133 APPLIED

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6/22

IMP#LSE RESPONSEF#NCTION ) VECM

SEEQ5133 APPLIED

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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$

SEEQ5133 APPLIED

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8/22

SEEQ5133 APPLIED

ECONOMETRICS

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

SEEQ5133 APPLIED

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10/22

FORECAST ERRORVARIANCE DECOMPOSITION) VECM

SEEQ5133 APPLIED

10

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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SEEQ5133 APPLIED

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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12/22

SEEQ5133 APPLIED

ECONOMETRICS

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$

SEEQ5133 APPLIED

ECONOMETRICS

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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$

SEEQ5133 APPLIED

ECONOMETRICS

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CA#SALIT*

SEEQ5133 APPLIED

ECONOMETRICS

15

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$

SEEQ5133 APPLIED

ECONOMETRICS

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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$

SEEQ5133 APPLIED

ECONOMETRICS

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ECONOMETRICS

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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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ECONOMETRICS

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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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SEEQ5133 APPLIED

ECONOMETRICS

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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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SEEQ5133 APPLIED

ECONOMETRICS

+RAN+ER CA#SALIT*TEST21


22/22

SEEQ5133 APPLIED

ECONOMETRICS

+RAN+ER CA#SALIT*TEST22

Lecture 8 Application of VAR Model

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