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Research Unit for Statistical
and Empirical Analysis in Social Sciences (Hi-Stat)
Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp
Global COE Hi-Stat Discussion Paper Series
Research Unit for Statistical
and Empirical Analysis in Social Sciences (Hi-Stat)
July 2011
Bayesian Analysis of Time-Varying Parameter Vector
Autoregressive Model with
the Ordering of Variables for
the Japanese Economy and Monetary Policy
Jouchi Nakajima
Toshiaki Watanabe
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) & & &
£ £ & " £ $ " £ £ £ $ > ( £" $( £ &( £ >( £ '" $?'"$>'" £ £$?'" £ $ 7" $" £ £ £$ .3 && ) " £ $>* *> &" £ £ £$$" £ £ £ $$" £ $" £ $" £ £ £ $ &" $$" $$"$" £ $" $ + "I$ + >," £ £ £ $," $ &
( ( "+$ " ' "$ 6 "$ $ " £ £ £ $ > " $ '" $ > '" £ $ '" £ £$ > '"$ " £ $>" £ $ " £ £ £ £ $>" £ $ & & " £ $ " £ $ & ././ 9 ././ & 4 & & & 9Æ* ././ '(')* 9 & & & ! & 4 9& & 9* ././& '( ')* 5Æ* ././: ( " £ £ £$ "$ ( £ &&" £ $ "&$ ( " $ " £ £ £$ & > " £ £ £ £ $ £ >"$ + > & " £ £ £ £ $ > " £ J J $J " £ £ J K $J " £ £ £ J $J " £ £ £ £ $ AB# /A!9CCC);/!$''$) ! *)#
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& & &
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1980
1985
1990
1995
2000
2005
0.0
0.5
1.0
Inflation (p)
1980
1985
1990
1995
2000
2005
−5.0
−2.5
0.0
2.5
Industrial production (y)
1980
1985
1990
1995
2000
2005
−1
0
1
Call rate (r)
1980
1985
1990
1995
2000
2005
−10
0
10
Monetary base (m)
7E "#ILM IL<M$ ! " " " * ././ '(')* 4#ILMIL<M9& '(')*E
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&& $"$ > * ././ - £ " > £ $&&" £ $> "#$" $ && "$># #0 7 # >< & . .3 * ././ E "+$ ! ""=$ ! ""=$ 7 "$ "$ "+$ 9 1 > & & 7 & * ././ 7 "$ & 4 .3 && #HN & 7"$ ! && * ././ * ././ 7 "$&&") )$ & * ././ & & '( ')* 7 & E "$ #ILM ##+L=M "$ ##DLM IL<M & !##: #!$''')=01!$''9)) 1 1 E ! @')# 2 B 1 B * 1 1 0 ** ! ') 1 1 * # +BJ#'!30!$''())#
0
20000
40000
60000
80000
100000
4
8
12
16
20
24
(i) Model trace
0
20000
40000
60000
80000
100000
0.05
0.10
(ii) Average model probability
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0.02
0.04
0.06
(iii) Posterior model probability
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1985
1990
1995
2000
2005
0.1
0.2
(p)
1985
1990
1995
2000
2005
0.1
0.2
1985
1990
1995
2000
2005
1
2
(y)
1985
1990
1995
2000
2005
1
2
1985
1990
1995
2000
2005
0.5
1.0
(r)
1985
1990
1995
2000
2005
0.5
1.0
1985
1990
1995
2000
2005
2.5
5.0
7.5
(m)
1985
1990
1995
2000
2005
2.5
5.0
7.5
7 <E O > " $ "$ * ././ "$ "&$ "$ ( "$ &"$ 7 + S #IILM ##+L=M +L=M & & & ! "#$ & : : 7 + & & " $ & +L=M 4 Æ # Æ #1990
2000
0.00
0.25
ε
y
↑
→
y
1 year
2 years
3 years
1990
2000
−0.25
0.00
0.25
ε
y
↑
→
m
1990
2000
−0.1
0.0
0.1
0.2
ε
y
↑
→
p
1990
2000
0.0
0.1
0.2
ε
y
↑
→
r
1990
2000
−0.1
0.0
0.1
0.2
ε
m
↑
→
y
1990
2000
−0.1
0.0
0.1
0.2
ε
m
↑
→
m
1990
2000
−0.1
0.0
0.1
ε
m
↑
→
p
1990
2000
−0.05
0.00
0.05
0.10
ε
m
↑
→
r
1990
2000
−0.02
−0.01
0.00
ε
p
↑
→
y
1990
2000
−0.04
−0.02
0.00
ε
p
↑
→
m
1990
2000
0.00
0.01
0.02
ε
p
↑
→
p
1990
2000
−0.01
0.00
ε
p
↑
→
r
1990
2000
−0.02
0.00
ε
r
↑
→
y
1990
2000
−0.02
0.00
0.02
ε
r
↑
→
m
1990
2000
0.00
0.01
0.02
ε
r
↑
→
p
1990
2000
−0.01
0.00
0.01
ε
r
↑
→
r
7=E '(')* "./$ "$ "$ "$ :0
10
0.0
0.5
1.0
1.5
ε
y
↑
→
y
1988/2Q
1995/4Q
2005/4Q
0
10
−0.25
0.00
0.25
ε
y
↑
→
m
0
10
−0.05
0.00
0.05
0.10
ε
y
↑
→
p
0
10
0.0
0.1
0.2
ε
y
↑
→
r
0
10
0.0
0.1
ε
m
↑
→
y
0
10
0.00
0.25
0.50
0.75
ε
m
↑
→
m
0
10
−0.05
0.00
0.05
ε
m
↑
→
p
0
10
0.00
0.05
0.10
ε
m
↑
→
r
0
10
0.00
0.02
ε
p
↑
→
y
0
10
−0.02
0.00
ε
p
↑
→
m
0
10
0.000
0.025
0.050
ε
p
↑
→
p
0
10
0.00
0.01
ε
p
↑
→
r
0
10
−0.025
0.000
0.025
ε
r
↑
→
y
0
10
−0.025
0.000
0.025
ε
r
↑
→
m
0
10
0.000
0.005
0.010
ε
r
↑
→
p
0
10
0.00
0.05
0.10
ε
r
↑
→
r
7+E '(')* "./$ #IILM ##+L=M +L=MÆ * ././ '(')* & #II & & : 7% '(')*,;"I$, , "$ 7 "$ 7 ! "&$ : & '(')* ! 9 "$ 4 : * . /./
5 "./$ "./$ < "./$ = "./$ + "./$ D "./$ H "./$ I "./$ # "/.$ "/.$ "./$ "/.$ < "/.$ = "/.$ + "/.$ D "/.$ H "/.$ I "/.$ # "./$ "./$ "./$ "/.$ < "/.$ = "/.$
&<E . ".E F
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0.02
0.04
0.06
(i) First subsample
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0.02
0.04
0.06
0.08
(ii) Second subsample
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