Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

' -

!""# $ % &

() *

+

, ) . / / ,#

1), 2

3

, 0)

+4

%% % %

&

(
01 %
"""+ ,,

""*+ ,, & ! /01$&
1 %%

3 4/ %

&
5 36, 5(

%% &%
&'

! ""#$ %'

) .

&
%% ! .$
%

% % &. %

%
% /
2 ""*+ ""#

!, -

)

ρ

%%

%%
% %
% &6

%

&/

! ""#$ % )

7 &

ρ

% '%

&0

%&

%

%

&0

7%

%

%%

&%

%'

%8

8

%

&

! ""*+ ,, $ %

%

&2 %

% %

+ %

& %
/ '
& >
& &

%

% )
%

! ""#$

& &

8 & ! ,,*$ &

Available online at http://eaces.liuc.it

17
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

%
( 0 1 ! /01$ %

.

& ! .$

& %

&0 %

8

% !C(/1$

2 33%

% %

'

%

1 &'

% ""9 % %8

,, & .

%&

& % 4 − 6%
%
%+
& 2%

% &2

2*

&

2 &2 6 &2 9

/ 8
2 %
%

% % &

)

&

% % x5

%X

xt = log( X t ) − log( X t−1)

≈ Xt −1 X t−1

%

% F (x) % %

%&

% G(x)

F (x) %

0%



%)

%0

% &ρ

D%

D !C(/1$& 0 %

F ( x) > G ( x) x < 0. 4

f (x)
>

&

> x = 0 g(x)

% 7&

Available online at http://eaces.liuc.it

18
EJCE, vol. 3, n. 1 (2006)

% &
% (

! ,,9$ %
5 %
% .?(F
&

& % E D%

!E .?(F
!E

% )

D$& D$&

1 if x < 0 I(x) =
0 else
%%
I (x)ρF (x) = g(x) − f (x) =η

% C 5-

x %0 > x =0&
%

Observed G(x)

Counterfactual F(x)

Density 0 2 4 6 8 10
Density 0 2 4 6 8 10

-0.2 -0.1 0.0 0.1 0.2 0.3 wage change (%)

C x=0 %
(r = 1,..., R) gr

'
G(x) F (x)
r0

-0.2 -0.1 0.0 0.1 0.2 0.3 wage change (%)

% > η.

C

%%

& )r

x=0

fr

r%

Available online at http://eaces.liuc.it

19
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

? r = r0 −1.
dzr :

fr < gr for r < r0

fr=gr for r>r0

r0 −1
fr0 + gr − fr
r =1

r0 −1

= fr0 +ρ

f

r

=

g r

0

r =1

ρ

>

1 if r < r0 dnr = 0 else
1 if r = r0 dzr = 0 else

%

%

r =1 dnr

>)
' fr
r0 −1
gr = fr − ρ frdnr + dzr ρ frdnr + εrt
r =1

gr ρ:
for r = 1,..., R

ε rt
> % r > r0
& ρ

&/ r0 +1
%)
> %

% rt0 rmax &

rt0

r0 t ! t = 1, ...,T $

>
>& fr = gr &

frt = frs
' ) &.
t. (

&

% x−

&

& 4 r min

%

) x− 0

> r min )

Available online at http://eaces.liuc.it

20
EJCE, vol. 3, n. 1 (2006)

rmin −1

r max

R

frt = 1 −

frt −

g rt

r =1

r = r min

r=rmax +1

RR
fr = gr = 1
r=1 r=1

RR

fr = gr

r=rmax +1

r =rmax +1

> grt = frt − ρ frtdnrt + dzrt ρ

)

rmax −1

rmin −1

frtdnrt +

f rt

r =rmin

r =1

D ! ""#$

'

%

%&

'

%%

xhigh − xlow.

%>

! & & xlow = x0.5 $

xlow > 0,

%>

%

t %+

&

%

xlow = 0.5

xhigh = 0.9 &

- %8

'

0%

rt0 t.

0%

rt0 ' %

&+

0 rt0 %

T,

% rt0.

% > %
% %
%

&2
& (
4 4
%

' /
2> 2> ! (42 $&

&(
% )

% 5

&( '

% %

4 2> ! (42 $
%

!42F$

&%

)=

)

&

%

%

Available online at http://eaces.liuc.it

21
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

x unr it

N

(

µt

,

σ

t

)

µtU (0.02, 0.10)

σ tU (0.2, 0.3)

xobs = xunr if xunr ≥ 0 I ⋅ xunr if xunr < 0

1 with Pr = 1 − ρ I=
0 with Pr = ρ

ρ = 0.2

i = 1,.., nt ; t = 1,..., 7 nt = 1000

C

%%

+ (T = 7) % %

&( ' %&

% & ( i (i = 1,..., nt )

&9 C ρ& % %

%%

σˆ ρ G G ρ &*

σρ

)

52
binwidth 0.005
0.01
0.015
0.02

ρ σˆ ρ σρ ρ σˆ ρ
σρ ρ σˆ ρ σρ ρ σˆ ρ
σρ

LS 0.1990
0.0053
0.0115 0.1990
0.0083
0.0102 0.1990
0.0112
0.0100 0.1991
0.0143
0.0093

IWLSI 0.1992
0.0090
0.0104 0.1996
0.0070
0.0091 0.1998
0.0063
0.0085 0.1998
0.0061
0.0087

IWLSII 0.1988
0.0090
0.0104 0.1991
0.0070
0.0091 0.1993
0.0062
0.0086 0.1994
0.0060
0.0087

4(
n = 500
5?

n = 2000.

n = 1000
*,&

%

%

Available online at http://eaces.liuc.it

22
EJCE, vol. 3, n. 1 (2006)

%&

4 2>

&

%8

5

% &C

%%

& % &(
% 2> &
%& &
4 2>

%% 54% % %

% 4

% ,&,

4 2> %
2>
t+ %

& 7
4
&

,

/01

! $& .

+

' /01

+%

&

/ 7 /01& (

'

'&

/01

D %+

&

1 ! ,, $

/01

'

&%

/01

""9 6, ,,, = =, ,,,

&%

%5

. 8C

;;

4)

? 12

&

(8

%%

""* C

""=&

%

%%

)&

? %%

; 4)

>

% % /01

&

""# %

%

/01

)

&;

2

1 !;2- 1$ 4 )

D2

1 !12 44$

0

1 2 ! 012$&

/01

.

/01

4 ) &2

7

'% %

% ""9 ,, %

; !;2- 1$

! 012$

&

,,9

/01 .

%

: % ""9 ,, &

%

%8

:% 5;

.8

C

Available online at http://eaces.liuc.it

23
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

;2

1

F ! ,,*$

'

&

/

G7

G

%

%

7&

: =* % 8

% 6,,B

7

%

%
& '

&=1 ! ,, $ ( ! ,,6$
> F ! ,,9$
! & & ""#$ % %
%%

% %

% % 8&
% %

%

&

/01&

7 %%
%

% %8 % % H#*B %

&

%,

/ ) ), 2

3

&

,, 8&
4 5.

&

%
%'
,, & C &

""*+ ,,

/) ) , 4

% %

,, '%
,

Germany Denmark Belgium France UK Ireland Italy Greece Spain Portugal

n 4260 1830 1634 3108 3320 1340 3573 1919 3209 3757

median 0.032 0.042 0.045 0.044 0.069 0.108 0.029 0.037 0.056 0.053

IQR x ≤ 0 (%) x = 0 (%)

0.172

0.403

0.066

0.111

0.31

0.086

0.163

0.367

0.061

0.183

0.356

0.04

0.227

0.322

0.025

0.273

0.251

0.011

0.167

0.448

0.161

0.143

0.39

0.164

0.309

0.381

0.009

0.131

0.234

0.091

6.

%?

&

Available online at http://eaces.liuc.it

24
EJCE, vol. 3, n. 1 (2006)

% ,, &

)

'%

xts

=

xt − x0.5,t x0.9,t − x0.5,t

% %

. 8; 2 &C ,%

1 ;%
=B
%

%
6% 2 % ,&, &

&'

%

)%

%%

%

""*+ ""#

"""+ ,, & /

%%

%&

9&

4 %5

, ), 2

&,

period Germany 1995-1997
1999-2001 Denmark 1995-1997
1999-2001 Belgium 1995-1997
1999-2001 France 1995-1997
1999-2001 UK 1995-1997
1999-2001 Ireland 1995-1997
1999-2001 Italy 1995-1997
1999-2001 Greece 1995-1997
1999-2001 Spain 1995-1997
1999-2001 Portugal 1995-1997
1999-2001

binwidth 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

ρ 0.133 0.159 0.309 0.27 0.209 0.175 0.028 0.105 0.052 0.058 0.051 0.071 0.261 0.331 0.152 0.109 0.046 0.025 0.25 0.422

x0.9,t − x0.5,t = 1 & 4 2>
%
%

sd(ρ) 0.024 0.028 0.029 0.036 0.026 0.024 0.019 0.033 0.035 0.029 0.029 0.042 0.022 0.025 0.032 0.025 0.025 0.031 0.039 0.037

t(ρ) 5.52 5.68 10.74 7.43 8.07 7.14 1.44 3.18 1.49 2.02 1.77 1.71 11.66 13.37 4.74 4.32 1.81 0.82 6.45 11.5

Available online at http://eaces.liuc.it

25
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

%
C 68 % 1%
&

% %

% %

2& % %%

&

6) 5. / / ,

/ ) ), 2 / 4 ,

& 1
%; %

)
. C
)

8

1995-1997 1999-2001

ρ 0.0 0.1 0.2 0.3 0.4 0.5 Germany Denmark Belgium France UK Ireland Italy Greece Spain Portugal

6& . % %

%

(

7%

%

% !ρ$&

%

%% %

&)

%

%

C(/1

&C 9

""*+ ,,

C(/1

"""+ ,, &

8
C(/1 % ) % &
% ""*+ ""#

Available online at http://eaces.liuc.it

26
EJCE, vol. 3, n. 1 (2006)

6 ) %5 !

,, / / ,/ ) ), 2

inflation rate (%)

10

Inflation rate

8

ρ, 1995-1997 ρ, 1999-2001

6

4

2

0

0.5
0.4
0.3
ρ
0.2
0.1
0

Germany Denmark Belgium
France UK
Ireland Italy
Greece Spain
Portugal

( % C
,,
6) 5

*% ,&,"
,& & ( &
, ), 2

; %
% ""*+ ""#&
"""+ ,, %

& C(/1 &(

;

&
C* %
"""+ ρ

1995-2001 0.5

1995-1997 0.5

1999-2001 0.5

0.4

r = 0.14

0.4

r = 0.09

0.4

r = 0.12

0.3 0.3 0.3

0.2 0.2 0.2

ρ ρ ρ

0.1 0.1 0.1

0.0
02 46 8
inf lation rate (%)
. )
&

0.0 0 24 68 inf lation rate (%)
%%

0.0 0 246 8 inf lation rate (%)
% %

Available online at http://eaces.liuc.it

27
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

ρ ""* ,, &

&

6) 5( )

/) ) , 4

Germ any

% %8

%

Denm ark

Density 05

Density 04

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Be lgium

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Fr ance

Density 04

Density 04

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
UK

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Ir e land

Density 0.0 3.5

Density 03

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Italy

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Gr e e ce

Density 08

Density 08

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Spain

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)
Por tu gal

Density 06

Density 0.0

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)

-0.5 -0.3 -0.1 0.1 0.3 0.5 ∆log(w)

Available online at http://eaces.liuc.it

28
EJCE, vol. 3, n. 1 (2006)

(% F%

&( 8 σˆ ρ
&

45

, ), 2

Germany Denmark Belgium France UK Ireland Italy Greece Spain Portugal

2 C

& &.

ρ2

binwidth 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

ρ 0.151 0.286 0.185 0.059 0.054 0.061 0.294 0.155 0.041 0.347

1
%
sd(ρ) 0.015 0.019 0.014 0.013 0.019 0.019 0.013 0.015 0.018 0.023

.
GG
t(ρ) 9.85 15.27 13.16 4.57 2.83 3.26 22.00 9.99 2.25 15.35

8& +

( &%

'&

%%

%&

&

-

)%

66B 1

&(

""*+ ""#

"""+ ,, %

;%

%

% % % &(

%

% %
%

9+=B

% C
%

1

%8

%% % ""*

/
+
2 % &
) %
% ,, &

1
3& 4 "", D

1& ! ,,6$ E2

% *+ "&

5 2%

Available online at http://eaces.liuc.it

29
Andreas Behr, Properties of the histogram location approach and the extent and change of downward nominal wage rigidity in the EU

8 ;& . 8 (& 1 (& ! ""=$ E ? & +#=&

%D

/& & ! ,,*$ E D

% 85

+ 6=&

& /

&F 0

& ! ,,*$ E ) 1D

.

1 9:"+* &

& "#*+ ""*D

8 /& ! ,, $ E. % % 6:*+9 #&

( +;

/

4& ?& 4

& & ! ,,6$ E?

%

D & = "+=6:&

5

/%

&

&

0

& ! ""#$ E

%%

%

&(&4& ! ,,9$ E D&

%% %

0 2& (

C& ! ,,9$ E. % %

! ""##&

%

D

0 2& (

C& ! ,,*$ E. % %

%

- /.D

&

& & ! ,,9$ E0 % ) 96 +9*,&

%

ID $ %

2& ! ""#$ E $& ""6+ ,,:&

? ( 28

D&

8 /& ;

& ! ,,6$ E0 % F D

? (I $ = "+=9 &

8 /&

& ! ,,*$ E. % % ?

(F

5

.

/01 ""9+ ,, D ' (

%)

! *+,&

2& A

& ! ,,6$ E

5>

%% 3 D -. )

% / ! ,++0 ",&

? 8 2& @

;& ! ,,6$ E?

(F

F

D

#= +#: &

1 C& ! ,, $ E & =6+",&

/ 0 1 5 F %D

2 3& /& ! ,,,$ E? / "*&

%

D / #=+

( .& ! ,,6$ E2 0 1D

%(

*

6= +6#:&

/

Available online at http://eaces.liuc.it

Documento similar