Lecture Notes in Economics and Mathematical Systems
593
Founding Editors: M. Beckmann H.P. Künzi Managing Editors: Pr...
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Lecture Notes in Economics and Mathematical Systems
593
Founding Editors: M. Beckmann H.P. Künzi Managing Editors: Prof. Dr. G. Fandel Fachbereich Wirtschaftswissenschaften Fernuniversität Hagen Feithstr. 140/AVZ II, 58084 Hagen, Germany Prof. Dr. W. Trockel Institut für Mathematische Wirtschaftsforschung (IMW) Universität Bielefeld Universitätsstr. 25, 33615 Bielefeld, Germany Editorial Board: A. Basile, A. Drexl, H. Dawid, K. Inderfurth, W. Kürsten, U. Schittko
Jens Rubart
The Employment Effects of Technological Change Heterogenous Labor, Wage Inequality and Unemployment
With 54 Figures and 21 Tables
123
Jens Rubart Darmstadt University of Technology Institute of Economics Residenzschloss 64283 Darmstadt Germany
Library of Congress Control Number: 2007923239
ISSN 0075-8442 ISBN 978-3-540-69955-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production: LE-TEX Jelonek, Schmidt & V¨ ockler GbR, Leipzig Cover-design: WMX Design GmbH, Heidelberg SPIN 11979166
88/3100YL - 5 4 3 2 1 0
Printed on acid-free paper
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0,0025 skill augmenting low skill augmenting neutral
0,50
% dev. from steady state
0,0020
0,40 0,0015 0,30 0,0010 0,20
0,0005 0,10
0,00
% dev. from steady state (neutral shock)
0,60
0,0000 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Quarters
' ' = $ *) $ - 3
%
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0,12 low skill augm. (flex) low skill augm. (minw) neutral (flex) neutral (minw)
% dev. from steady state
0,08
0,04
0,00
-0,04 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Quarters
4 3 - &' )& , 3 - *& * $ 3
*) $ -
0 )
4! ( 2 < 5 * > )
"
%>
6
) ' ' $ &
0 % & &
' # 6 # # J#0 J # # ! 0 % & & D ++ 8 ++ - 8 - +8 - - 4 4 D
% >
3
Æ G
%&' )& %= && .*
7) & ' # ! P P P ) 8 G@
H
1
B
Q Q
' 2
P G
524 5 P
1 2
5
2" 5
5Q)
2" 95
Q
24
P 24 Æ5 Q P 24 % 5 Q
P 24 % 5 Q
2" E5 24 5 2" = ( 2" 52" "5 &
%>
G P
1 2
Q5
Q
5 24
5Q)
' 2 524 5 2" 75
Q 24 % 5 24 5
Q 24 % 5 24 5
> 1 25 P 5
' 2 55 P ' 2 55 P
P 5 24 Q ) Æ5
P 1 25 5 Q ' 2
Q 24 % 5
P 1 25 5 Q ' 2
Q 24 % 5
5
2" D5 2" C5 2" 4!5 2" 445
2" 4 5
2" 495
>8
( 28 > > 9
P & 25
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$ %
4 "
2" 4E5
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$
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G
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2" 4 G ( > ( H
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2" E5
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' 6 8 G@ ( 2" D52" 495 (
%&' )& 4*
1 2 5
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Q ' 2 55Q
1 2 5 Q 5 2
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24 %
' 1 2 5 Q 5 2
' 2 5 5
Q ' 2
24 %
5 2 55 P ! 2" 75
55Q
' 2
5 55 P ! 2" D5
6 5 & 8 @ 0 > >8 ( 2" 4C52" 95 (
5 4 5 (
& 25 )
P!
2" C5
Q ( 4 24 % 5 P !
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5 4
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$
Q ( 4 24 % 5 P !
2" 945
( > 8 >8 ( 2" "52" 945 ( 2 1,40 neutral skill augmenting low skill aug. firing costs = 0.5 x respective wage
1,20
% dev. from steady state
1,00
0,80
0,60
0,40
0,20
0,00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Quarters
' ' 2 *
0 >
>
) 2 5
"
%>
(
" < " " ( ) ) > > 8 >8 O
B
B OG
)
%>
0,007
firing cost=1 x a_s firing cost=2 x a_s firing cost=0.5 x wage
0,006
% dev. from steady state
0,005 0,004 0,003 0,002 0,001 0,000 -0,001 -0,002 -0,003 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Quarters
4 - &' )& = " 7 > B % ) ( > B > 3 >
B
( 8 = > E 3 > G ( = " ! ) ( 3 G > G ) ( %
%>
.% $ (
G > 2 " 95 = P B B P !E >
> 2 > " 4" 95 % > 2 > " " " C OG
B > 2 ( 5 > )
%>
0,008 Minimum Wages Firing Costs F.Costs+Min. Wage
% dev. from steady state
0,006
0,004
0,002
0,000
-0,002
-0,004
-0,006 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Quarters
4 3 - &' )& 2 *
& && * ' $ & $ 2 *
& && *
0 % & & & &
' # 6 # # J#0 J # # ! 0 % & & & & D 4 - 8 + ++ - 44 + + + 4 -+ 4 8
3 " <
%&' )& && .*
Æ > E 9" 4
> 2 E 5 &' ) & ' # ! P P P % @ > ) > G
) > G B ) > = " 4! " 49 ) > G 3 > " 4! > G C!J 8
0 ) )
!
−3
x 10 6 5
% dev. from steady state
4 3 2 1 0 −1 −2 −3 0 0.5 Firing Tax 1
0
5
10
15
20
25
30
35
40
Quarters
0 ) ) , &' )&
> G G > B > > G
%> −4
x 10
2
% dev. from steady state
0
−2
−4
−6
0 0.2 0.4 0.6 Firing Tax
0.8 1
10
5
0
15
20
25
30
35
40
Quarters
0 ) ) , $ )
0.25
0.2
% dev. from steady state
"
0.15
0.1
0.05
0 0 0.2 0.4 0.6 Firing Tax
0.8 1
0
5
10
15
20
25
30
35
Quarters
0 ) ) , )
40
0 ) )
−3
x 10 5
4
% dev. from steady state
3
2
1
0
−1 0 0.2 0.4 0.6 Firing Tax
0.8 1
0
5
10
15
20
25
30
35
40
Quarters
0 ) ) , ? 5 & $ A ) B
B 0 G 2 5 B
0 ) B % G !
B B ) B > = " 4E " 47 ) −3
x 10 1
0
% dev. from steady state
−1
−2
−3
−4
−5
−6
−7 1
0.8
0.6
Ratio of Minimum Wages
0.4
0.2
0
0
5
10
15
20
25
30
Quarters
0 ) ) , &' )&
35
40
0 ) ) −5
x 10 15
% dev. from steady state
10
5
0
−5 1 Ra tio
0.8 of M in im
0.6 um
0.4 W
ag
0.2
es
0
10
5
0
15
20
25
30
35
40
Quarters
0 ) ) , $ )
0.2
% dev. from steady state
0.15
0.1
0.05
0
−0.05 1 Ra
tio
of
Mi
0.5
nim
um
Wa
ge
s
0
0
5
10
15
20
25
30
35
Quarters
0 ) ) , )
40
%> −4
x 10 8 6
% dev. from steady state
4 2 0 −2 −4 −6 −8 −10 1 0.8
Ra
tio
0.6
of M
inim
um
0.4
Wa
ges
0.2 0
0
5
10
15
20
25
30
35
40
Quarters
0 ) ) , ? 5 & $
.. $ /
% ( )
= > 8 ) G 3 > @
) = " 4D
4 * ) %=
% >
2.8 2.75 2.7 2.65 2.6 2.55 2.5
1.4
2.45
1.2 1
2.4 0.8
2.35 1
S Pa ubs ra titu m ti et on er
Steady State Employment, Low Skilled Workers, hu
2.85
0.6 0.9
0.8
0.4 0.7
Ratio of Minimum Wages
0.6
0.5
0.2 0.4
0.3
0.2
0
%&' )& = * ' 3 - -
A
%
%>
G 2B 7! J5 >
2.2
Employment Skilled Workers, hs
2.15
2.1
2.05
2
1.95
1.9 1.5 1 Substitution Parameter
0.5 0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Ratio of Minimum Wage
%&' )& = * ' - - 0 > G
2 > " ! 5
4 * ) %=
Low Skilled Employment
2.5
2.45
2.4
1
1 0.8
0.8 0.6
0.6 0.4
0.4 0.2
0.2
Substitution Parameter
0
Firing Tax
0
%&' )& = 2 * > 3 - - > 2> " 4C5
8 0 > 8 H C
P 1 2
5 Q 1 2
5
2" 9E5
1 25 8 > ( 2E !5 3 > " 4 >
G D!J 8 = > " 4
%>
60 50 40 30
Welfare
20 10 0 −10 −20 1.5 −30 −40 1
1
0.9
0.8
0.7
0.6
Ratio of Mininum Wage
0.5
0.4
0.3
0.2
ra
n
0
tio
pa
itu
st
b su
er
et
m
0.5
. = & && * 0 G
( ) > G
> G 2> " 5
)
) 3 ) 2 > " " 95 >
4 * ) %=
!
270
265
Welfare
260
255
250
245
240 0
0 0.2
0.5 1
0.4
0.6
Minimum Wage Rate
0.8
1.5 1
Firing Tax
2
. = & && * 2 * > 3
2> " 95 14.7
14.6
14.5
Minimum Wage Model
Steady State Output Level
14.4
14.3
14.2
14.1
14 Firing Tax Model
13.9
13.8
13.7
0
0.1
0.2
0.3
0.4 0.5 0.6 0.7 Firing Tax, Ratio of Minimum Wages
0.8
0.9
&' ) '
1
"
%>
6 )
>
) .0 &
G
> " 4 " " D ) = >
> G B ( % ) > ) 3 ) ) > " E
7
0,016 Search Model Wage Rigidity Firing Costs (1/2xwage) RBC-Model
0,014 0,012
% dev. from steady state
0,010 0,008 0,006 0,004 0,002 0,000 -0,002 -0,004 -0,006 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Quarters
4 3 - &' )& ; &' ) G 8 3 , = " < G ) G
B 2> " 4"5 3 B
> B
%>
= ) 3 ) 2 > " 4 " 95 G >
*
= 2 > ! ! .
Æ
. 1 8???
0 - $
4CCE # ? N
! "
B 8 G , 25 ) G > 4CC! 2 45 G
B , ? 24CCE5 G %
G 3 6 " - 8+
24CCD5 / ;
; 24CCD5 3 2 !! 5
% A B G ( G
=@ 24CCC5 * 6 2 !! 5 # 2 !! G 3, G = 2 > " E5 0 > > )
8 3 ;0* G )
0
> B >
"
> B
% O
0 ) G = 8 G B 8 )
B OG > = > G
> B
B OG = " " )
>
A ) ( 0 "
3
@
-
% (
B G = $? % -
0 > ) > O , = 3
; 0 * G ) % (
0B 6 , 6 Y ) &!, 2 !!"5H $F , ; - * 0 ' # , 6 """ = I/ 3 $ % & 24CCC5H : 2 ! 5 ; 2 2 : 5 # . % 2 !! 5H $ , G
/ % ' - "C 4+E! ! ' 2 !!95H # # # 3 ; = ,@ / ' 9
!
( 24CC45H 9 - ' 9 * 2 4 ' ? "
6 Y
AG # AG
( , 24CD"5H $ ; = -
6 * ; 0 ; & , 6 4C7+ 47 AG 6 Y 0 0 (% ( 24CC # # # 3 ; = ,@ / ' 9CE+E94 # 6 # # + 24CDC5H @ +,A, A* # # 24CC95H @ +,,B A* # # 24CC"5H @ +,,3 A* # #
!!
24CC75H $A* , ? & # / A* & / , # A # 6 C # 2 !!!5H @ 1%%% A* # # 2 !!95H 5 1%%B A* # # 2 !!E5H @ 1%%0 A* # # 2 !!"5H @ 1%%3 A* # # & ( ( 24CCC5H $, / A* * - "" 4D4+ !7 & 2 !!45H $& 0 0GH 3 , / = - 4 9C 9C!+E94 1 / 2 !!45H $, 0 - ( 4"29 5 D 0-35 $ * $ *, , , , , , ! 0 , , 0 ) , , , ! #$ *) $ -, , ! 4 3 - 5 , !, , , ! .3; > , 4C7D 44CCD E 4C7 4E" " 4! , 4EC " 44 , 4 G 4
