OPTIMAL RESEARCH
AND DEVELOPMENT EXPENDITURE:
A GENERAL EQUILIBRIUM APPROACH
Galo Nuño
Documentos de Trabajo
N.º 1009
2010
OPTIMAL RESEARCH AND DEVELOPMENT EXPENDITURE:
A GENERAL EQUILIBRIUM APPROACH
OPTIMAL RESEARCH AND DEVELOPMENT EXPENDITURE:
A GENERAL EQUILIBRIUM APPROACH (*)
Galo Nuño (**)
BANCO DE ESPAÑA
(*) I am grateful for comments and suggestions by Alessio Moro, Anton Nakov and participants at the 2008 EEA
meeting in Milano and the 2009 CEMLA Conference in Salvador de Bahia. The views expressed are those of the
author and do not represent the views of the Bank of Spain or the Eurosystem.
(**) Galo Nuño is at Banco de España, Economía y Asuntos Internacionales, Alcalá 48, 28014 Madrid.
Documentos de Trabajo. N.º 1009
2010
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© BANCO DE ESPAÑA, Madrid, 2010
ISSN: 0213-2710 (print)
ISSN: 1579-8666 (on line)
Depósito legal: M. 14637-2010
Unidad de Publicaciones, Banco de España
Abstract
How much should be spent in research and development (R&D)? How should R&D vary over
the business cycle? In this paper we answer both questions in the context of a calibrated
dynamic general equilibrium model with Schumpeterian endogenous growth. Firstly,
we demonstrate that, although the existence of distortions in a decentralized economy
produces underinvestment in R&D, a simple proportional subsidy to R&D spending alone
cannot restore the first best allocation. The optimal proportional R&D subsidy attains a
second best allocation in which R&D spending exceeds its first best level. Secondly, we
show how the observed procyclicality of R&D is socially inefficient. However, the welfare
loss due to this dynamic inefficiency is much smaller than the loss due to underinvestment
in R&D.
Keywords: Schumpeterian growth, technology adoption, optimal subsidy.
JEL classification: E32, O38, O40.
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DOCUMENTO DE TRABAJO N.º 1009
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DOCUMENTO DE TRABAJO N.º 1009
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DOCUMENTO DE TRABAJO N.º 1009
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>@-50.? ?: B30=0 4> ?30 ,8:@9? :1 2:A0=9809?>@->4/4E0/ & ? 80,9> ?3,? ?30 09?=0;=090@=
8,C484E0> ?30 /4>.:@9?0/ A,7@0 :1 -0.:8492 ?30 49.@8-09? ?30 90C? ;0=4:/ B0423?0/ -D ?30 ;=:-,-474?D
:1 /:492 >: B34.3 4> , 1@9.?4:9 :1 ?30 ,8:@9? :1 & >;09/492 (30 F=>? :=/0= .:9/4?4:9 4> ?3,? ?30
8,=249,7 .:>?> :1 ,9 0C?=, @94? :1 2::/> ,77:.,?0/ ?: =0>0,=.3 0<@,7 ?30 /4>.:@9?0/ 8,=249,7
B30=0 &! 0C;0.?0/ -090F? '49.0 ?30 A,7@0 :1 -0.:8492
4> ?30 >,80 1:= ,77 >0.?:=> ,> ,77 :1 ?308 5@8; ?: ?30
?30 49.@8-09? 49 ?30 90C? ;0=4:/ ?0.39:7:2D 1=:9?40= 41 ,9 499:A,?4:9 3,;;09> ?30 49;@? 49A0>?0/ 49 & 49 0,.3 49?0=80/4,?0 >0.?:= 4>
?30 >,80 ,9/ ' ' -*+*.&/&*) ! !'%- "!" , ' %' (&!&& '(%!")% ' & )! ,
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-**# '00 ;;09/4C =:B?3 49 ?30 70,/4920/20 ;,=,80?0= :..@=> ,> , =0>@7? :1 ?30 69:B70/20 >;477:A0=> ;=:/@.0/ -D
499:A,?4:9> ,> 49 234:9 ,9/ :B4?? ? ,9D 8:809? 49 ?480 ?30 ?0.39:7:2D 1=:9?40= 4> ,A,47,-70
?: ,9D >@..0>>1@7 499:A,?:= ,9/ ?34> ;@-74.7D ,A,47,-70 69:B70/20 2=:B> ,? , =,?0 ;=:;:=?4:9,7 ?: ?30
,22=02,?0 =,?0 :1 499:A,?4:9> (30=01:=0 B0 3,A0
# ' B30=0 4> ?30 >;477:A0= .:0L.409?
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(30 =0;=0>09?,?4A0 3:@>03:7/ >:7A0>
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4> 49A0>?809? 4> ?30 ,8:@9? :1 >?,?0.:9?49209? -:9/> 4> , 2:A0=9
809? ?,C ,9/ "$ ,=0 ?30 /4A4/09/> 1=:8 ,9 49A0>?809? 1@9/ ?3,? F9,9.0>
09?=0;=090@=>I 49A0>?809?> ,9/ .:770.?> ?30 ;=:F?> 1=:8 ?30 :B90=>34; :1 ?30 8:9:;:74>? F=8>
(30 >:7@?4:9 :1 ?30 3:@>03:7/>I ;=:-708 D407/> ?30 >?,9/,=/ @70= 0<@,?4:9> 1:= ?30 =4>61=00 49?0=0>?
=,?0 ,9/ ?30 .:>? :1 .,;4?,7 ,9/ ?30 =07,?4:9>34; :1 B,20> B4?3 ?30 8,=249,7 =,?0 :1 >@->?4?@?4:9 -0?B009
.:9>@8;?4:9 ,9/ 7,-:=
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12
DOCUMENTO DE TRABAJO N.º 1009
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.:8;0?4?4A0 0<@474-=4@8 1:= ?34> 0.:9:8D 4> , >0? :1 ;=4.0> ,9/ ,77:.,?4:9> >: ?3,? 24A09 ;=4.0> 3:@>0
3:7/> F9,7 ,9/ 49?0=80/4,?0 F=8> ,9/ 09?=0;=090@=> >:7A0 ?304= 8,C484E,?4:9 ;=:-708> ,9/ 8,=60?>
.70,= (30 .,;4?,7 =09?,7 8,=60? .70,=> B309 ?30 /08,9/ 1:= .,;4?,7 -D 49?0=80/4,?0 2::/ ;=:/@.0=>
0<@,7> ?30 >@;;7D -D 3:@>03:7/> (30 7,-:= 8,=60? .70,=> B309 F=8>I /08,9/ 1:= 7,-:= 0<@,7> 7,-:= >@;
;7D -D 3:@>03:7/> (30 2:A0=9809? ,7B,D> =@9> , -,7,9.0/ -@/20? >: ?3,? ?,C0> ,=0 0<@,7 ?: 2:A0=9809?
>@->4/40> 49,77D ?30 F9,7 2::/> 8,=60? .70,=> 41 ;=:/@.?4:9 0<@,7> /08,9/ 1:= .:9>@8;?4:9
.,;4?,7 ,..@8@7,?4:9 ,9/ 09?=0;=090@=>34;
9 0<@474-=4@8 ?30 0A:7@?4:9 :1 ?30 ,A0=,20 ;=:/@.?4A4?D :1 ?30 0.:9:8D 4> 24A09 -D ?30 9@8-0= :1
>0.?:=> ?3,? 0C;0=409.0 ,9 499:A,?4:9
' ' "$ ' B34.3 /0>.=4-0> 3:B ?30 ;=:/@.?4A4?D 49.=0,>0> /@0 ?: ?30 /4>?,9.0 ?: ?30 ?0.39:7:2D 1=:9?40= 8@7?4;740/ -D ?30 09?=D =,?0 :1 90B F=8> ' ?30 9@8-0= :1 >0.?:= B30=0 , 90B 49.@8-09? ,;;0,=>
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9 ?30 8:/07 ;=0>09?0/ ,-:A0 ?30 .:8;0?4?4A0 0<@474-=4@8 8,D 9:? -0 >:.4,77D :;?48,7 (34> 4> /@0 ?: ?30
0C4>?09.0 :1 8:9:;:74>?4. .:8;0?4?4:9 49 ?30 49?0=80/4,?0 2::/> >0.?:= ,9/ ?: ?30 >;477:A0=> ,>>:.4,?0/
B4?3 ?30 /0.09?=,74E0/ 499:A,?4:9 ;=:.0>> B34.3 09?=0;=090@=> /: 9:? 49?0=9,74E0 B309 8,6492 ?304=
& /0.4>4:9> (30 0C4>?09.0 :1 ?30>0 /4>?:=?4:9> 8,D ;=:/@.0 ,9 490L.409? ,77:.,?4:9 :1 =0>:@=.0> >:
?3,? ?30 0<@474-=4@8 4> 9:? %,=0?: :;?48,7 ,> /4>.@>>0/ 49 234:9 ,9/ :B4?? (: >00 3:B ?30 0.:9:8D -03,A0> 49 ?30 %,=0?: :;?48,7 .,>0 B0 ,>>@80 ?3,? ?30 0.:9:8D 4> 8,9,20/
-D , -090A:709? >:.4,7 ;7,990= B3: 8,C484E0>
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?4:9 :1 09?=0;=090@=> ?30 0A:7@?4:9 :1 ,22=02,?0 ;=:/@.?4A4?D ,9/ ?30 >;477:A0= 0M0.? :1 499:A,?4:9
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BANCO DE ESPAÑA
13
DOCUMENTO DE TRABAJO N.º 1009
A,=4,-70> ,9/ 2=:B ,? =,?0 # ' B30=0,> ' ) % ,9/ #
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8,60 ?308 >?,?4:9,=D
(30 ;,=,80?0=> :1 ?30 8:/07 ,=0 .,74-=,?0/ ?: 8,?.3 60D 08;4=4.,7 0A4/09.0 49 ?30 )94?0/ '?,?0> 1:=
?30 ;:>?B,= ;0=4:/ 91:=8,?4:9 ,-:@? /,?, >:@=.0> 4> ;=:A4/0/ 49 ;;09/4C (30 A,7@0 :1 4> >0? ?:
>: ?3,? ?30 >3,=0 :1 :@?;@? /0A:?0/ ?: 7,-:= .:8;09>,?4:9 4> (30 ,A0=,20 2=:B?3 :1 % ;0=
B:=6492,20 ;:;@7,?4:9 4> >: ?3,? ,>>@8492 , =0,7 49?0=0>? =,?0 :1 B0 :-?,49 , A,7@0 :1 :1 ,;4?,7 /0;=0.4,?4:9 4> >0? ?: ;0= D0,= ,9/ =4>.3 7,-:= >@;;7D 07,>?4.4?D ?: ,77
>?,9/,=/ A,7@0> 49 ?30 74?0=,?@=0
+0 8,?.3 ?30 A,7@0> :1 -@>490>> ?@=9:A0= ,9/ ;@-74. ,9/ ;=4A,?0 & >;09/492B4?3 ?30 ;,=,80?0=>
,9/ (30 ,A0=,20 -@>490>> ?@=9:A0= :1 )' F=8> ' ?30 =,?0 :1 .=0,?4:9/0>?=@.?4:9 :1 F=8> 49 ?30
0.:9:8D 49 ?30 7,>? ?B: /0.,/0> 3,> -009 > >3:B9 49 42@=0 ?34> A,7@0 4> ,7>: .:9>4>?09? B4?3
?30 08;4=4.,7 0A4/09.0 ,-:@? ,A0=,20 >@=A4A,7 =,?0> 1:= ?30 ,9/ .:3:=?> :1 )' 8,9@1,.?@=492
F=8> (30 ?:?,7 >3,=0 :1 & >;09/492 3,> -009 =:@237D >?,-70 ,? ,-:@? ;0=.09? 1:= 8:>? :1 ?30
;:>?B,= ;0=4:/ :B0A0= ?30 >3,=0> :1 ;=4A,?0 ,9/ ;@-74. & 3,A0 >4294F.,9?7D .3,920/ /@=492 ?34>
;0=4:/ +0 .:9.09?=,?0 :9 ?30 7,>? ?3=00 /0.,/0> >: ?3,? ?30 ,A0=,20 >3,=0 :1 ;@-74. & 4> ,=:@9/ ,9/ ?30=01:=0 B0 >0? ?: 7:2 ?: ,9/ ?: =0>;0.?4A07D 49,77D 24A09 , -@>490>> ?@=9:A0=
:1 ?: =0;74.,?0 ?30 A,7@0 :1 % 2=:B?3 :1 B0 >0? ?30 >;477:A0= .:0L.409? ?: (,-70 /4>;7,D> ?30 .:8;,=4>:9 -0?B009 ?30 -09.38,=6 .,74-=,?4:9 ,9/ ?30 /,?,
-"/*"6 &")/ )1"./(")/
(: ,9,7DE0 0L.409? & 0C;09/4?@=0> B0 >:7A0 ?30 >:.4,7 ;7,990=I> ;=:-708 1:= ?30 >0? :1 .,74-=,?0/
;,=,80?0=> ;=0>09?0/ ,-:A0 (,-70 ;=0>09?> ?30 =0>@7?> 9 ?34> .,>0 ?:?,7 & >;09/492 ;@-74. ;7@>
;=4A,?0 =0;=0>09?> ;0=.09? :1 ?30 % B34.3 =0>@7?> 49 ,9 49.=0,>0 49 7:92?0=8 2=:B?3 ,9/
49 -@>490>> ?@=9:A0= (30 =,?4: -0?B009 :->0=A0/ & 49A0>?809? ,9/ 4?> 0L.409? 4> .7:>0 ?: (34> 4> 49 7490 B4?3 ?30 .,74-=,?4:9 0C0=.4>0 :1 :90> ,9/ +4774,8> B3: F9/ =,?4:> -0?B009 ,9/
1:= ;7,@>4-70 ;,=,80?=4E,?4:9>
(: .:8;@?0 3:B ?34> ?=,9>7,?0> ?: >:.4,7 B071,=0 B0 .:8;@?0 ?30 >?0,/D >?,?0 @?474?D ,>
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?30 48;,.? :1 2=:B?3 4> <@4?0 >4294F.,?4A0 ,> 4? 4> B0423?0/ -D
B34.3 4> 34230= ?3,9 1:= ?30
.,74-=,?0/ A,7@0 :1 (34> 4> >: ,> , 34230= 2=:B?3 =,?0 ,77:B> 3:@>03:7/> ?: .:9>@80 8:=0 49 ?30 1@?@=0
> ;=0>09?0/ 49 (,-70 ?30 >:.4,7 B071,=0 49 ?30 %,=0?: :;?48,7 .,>0 4> 8:=0 ?3,9 ?480> 34230= ?3,9
49 , /0.09?=,74E0/ 0<@474-=4@8
0.&!&".
(: 84?42,?0 ?30 B071,=0 7:>> /@0 ?: ?30 >@-:;?48,7 ,77:.,?4:9 :1 =0>:@=.0> 49 ?30 /0.09?=,74E0/ 0<@474-=4@8
2:A0=9809?> 8,D >@->4/4E0 & 0C;09/4?@=0> >: ?3,? 499:A,?:=> 49?0=9,74E0 >:80 :1 ?30 >;477:A0=> /0=4A0/
1=:8 ?304= ,.?4A4?40> (30 .3,920 49 >?0,/D >?,?0 @?474?D ,> , 1@9.?4:9 :1 ?30 A,7@0 :1 4> >3:B9 49
42@=0 (30 >.,70 4> 9:=8,74E0/ >: ?3,? 4> >0? ?: ?30 -09.38,=6 .,>0 (:?,7 @?474?D 2=:B>
,> >@->4/40> 49.=0,>0 @9?47 , 8,C48@8 4> =0,.30/ ,? +0 /0F90 ?34> A,7@0 ,> ?30 J:;?48,7
>@->4/DK ?3,? 4> ?30 >@->4/D ?3,? 8,C484E0> B071,=0 @9/0= ?30 .:9>?=,49?> :1 , /0.09?=,74E0/ 0.:9:8D
(,-70 /4>;7,D> ?30 =0>@7?> 1:= ?30 .,>0 :1 9: >@->4/40> ,9/ 1:= ?30 :;?48,7 >@->4/D +309 ?30 :;?48,7
>@->4/D 4> ,;;740/ ?:?,7 & 0C;09/4?@=0> =4>0 ?: :1 ?30 % , 34230= A,7@0 ?3,9 @9 ?30 %,=0?:
0L.409? ,77:.,?4:9 ":>? :1 ?34> 49.=0,>0 4> /@0 ?: ;@-74. & B30=0,> ;=4A,?0 & 49.=0,>0>
>?48,?492 ?30 >:.4,7 =0?@=9 ?: & :90> ,9/ +4774,8> .:9.7@/0 ?3,? , J.:9>0=A,?4A0K 7:B0= -:@9/ ?: ?30
=,?4: -0?B009 :;?48,7 & 49A0>?809? ,9/ ,.?@,7 49A0>?809? B:@7/ -0 ,=:@9/ BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1009
>7423?7D :97D ,9 ,//4?4:9,7 (30 49.=0,>0 49 & >;09/492 =,4>0> 2=:B?3 ,9/ -@>490>> ?@=9:A0=
(30 90? 48;,.? :9 B071,=0 4> , ?B:1:7/ 49.=0,>0 B4?3 =0>;0.? ?: ?30 -09.38,=6 #:?B4?3>?,9/492 >:.4,7
B071,=0 B4?3 ?30 :;?48,7 >@->4/D 4> >?477 -07:B ?30 70A07 B4?3 , -090A:709? >:.4,7 ;7,990=
+3D 4> ?:?,7 & 49A0>?809? /4M0=09? B4?3 ?30 :;?48,7 >@->4/D ?3,9 @9/0= , >:.4,7 ;7,990= (34>
4> /@0 ?: ?30 1,.? ?3,? ?30 0.:9:8D 4> 1,.492 >0A0=,7 /4>?:=?4:9> >: 84?42,?492 :90 /4>?:=?4:9 8,D 70,/ ?:
, &"!&' >4?@,?4:9 42@=0 >3:B> 3:B ;@-74. >@->4/40> ,M0.? ?30 /4M0=09? .:8;:909?> :1 B071,=0
9 49.=0,>0 49 ;@-74. & =0/4=0.?> =0>:@=.0> 1=:8 .:9>@8;?4:9 ,9/ 49A0>?809? ?: 499:A,?4:9 ?3@>
=0/@.492 0M0.?4A0 :@?;@? ,9/ .:9>@8;?4:9 (34> 1,77 49 :@?;@? 1:=.0> ,209?> ?: B:=6 8:=0 3:@=> B4?3
?30 .:9>0<@09? 7:>> 49 704>@=0 @?474?D ? ?30 >,80 ?480 ?30 49.=0,>0 49 ;@-74. & 49.=0,>0> 2=:B?3
,9/ >?48@7,?0> ;=4A,?0 & (30 2=:B?3 0M0.? 4> 8:=0 >4294F.,?4A0 1:= >@->4/40> -07:B B30=0,> ?30
.:9>@8;?4:9 ,9/ 704>@=0 0M0.?> ;=0A,47 ,-:A0 ?34> >@->4/D 70A07
49,77D ,9/ 1:= ?30 8,??0= :1 .:8;,=4>:9 B0 49.7@/0 49 (,-70 ?30 ?30 .,>0 :1 9: >@->4/40> 9
?34> >4?@,?4:9 2=:B?3 ,9/ B071,=0 1,77 49 .:8;,=4>:9 ?: ?30 -09.38,=6 ,> 09?=0;=090@=> /0.4/0 ?: 49A0>?
>7423?7D 70>> ?30 /4M0=09.0 4> 49 ?30 >0.:9/ /0.48,7 ,9/ ?30=0 4> 9: ;@-74. &
0.&!&". 1"-.0. *-+*-/" 0.&!&".
& >@->4/40> ,77:B 09?=0;=090@=> ?: 49?0=9,74E0 >:80 :1 ?30 >;477:A0=> :1 499:A,?4:9 -D =0/@.492 ?304=
& >@96 .:>?> 9 ,7?0=9,?4A0 ,;;=:,.3 B:@7/ -0 ?: 49.=0,>0 ?304= ;=:>;0.?4A0 ;=:F?> >: ?3,? ?30 A,7@0
:1 -0.:8492 ?30 49.@8-09? 49 , >0.?:= 49.=0,>0> ? .,9 -0 /:90 -D >@->4/4E492 ;=:F?> := .@??492
.:=;:=,?0 ?,C0> 41 ?30D ,=0 ;=0>09?
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& $()!' '" #%"#"%'"! &(&, '+&
-**# '00 ;;09/4C (34> 4> >: 49 ?30 .:9?0C? :1 ?30 8:/07 /@0 ?: ?30 1,.? ?3,? 49.@8-09?> /: 9: =0>0,=.3 (3@> .:=;:=,?0
;=:F?> ,M0.? 0C.7@>4A07D ?30 ;=:>;0.?4A0 A,7@0 :1 -0.:8492 ?30 90C? 8:9:;:74>? 234:9 ,9/ :B4??
+0 70,A0 1:= 1@=?30= =0>0,=.3 ?30 >?@/D :1 3:B ?34> =0>@7? B:@7/ .3,920 49 ?30 .,>0 :1 &
,.?4A4?40> -D 49.@8-09?>
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(30 8,49 =0>@7?> ;=0>09?0/ 49 ?34> >0.?4:9 ,=0 =:-@>? ?: =0,>:9,-70 .3,920> 49 ;,=,80?0= A,7@0> #:?B4?3
>?,9/492 4? 4> 49?0=0>?492 ?: 0C;7:=0 B3,? 3,;;09> 49 , 0C?=080 .,>0 B30=0 .@==09? :->0=A0/ ;@-74. &
49A0>?809? .,99:? -0 .:9>4/0=0/ ,> & >@->4/40> ,9/ ?30=01:=0 4? 3,> 9: 0M0.? :9 499:A,?4:9 +0 ?309 =0.,74-=,?0 ;,=,80?0=> ,9/ ?: 0C;7,49 ?30 >?D74E0/ 1,.?> (30 A,7@0> :1 7:2 ,9/ ,=0
,9/ ,> 49 ?30 >?,9/,=/ .,>0 =0>;0.?4A07D
(,-70 >@220>?> 3:B ?30 =0>@7?> .3,920 A0=D 74??70 & 0C;09/4?@=0 @9/0= , >:.4,7 ;7,990= 4> 9:B
,9/ 4? ;=:/@.0> , 2=:B?3 =,?0 $;?48,7 & >@->4/40> ,=0 =:@237D ?30 >,80 ,> B4?3 ?30
>?,9/,=/ .,74-=,?4:9 9:B ;=:/@.492 , 34230= 0M0.? :9 -@>490>> ?@=9:A0= ,9/ 2=:B?3 9 .:9.7@>4:9 ?30
8,49 =0>@7?> :1 ?34> >0.?4:9 ?30 >@-:;?48,74?D :1 & >;09/492 ,9/ ?30 ;:>>4-474?D :1 ;,=?4,77D 84?42,?492
4? -D 49.=0,>492 ;@-74. >@->4/40> =08,49 @9,7?0=0/
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-* 4 '& ' ,=70AD F9/> , ;:>4?4A0 .:==07,?4:9 -0?B009 ?30 2=:B?3 =,?0 :1 & 0C;09/4?@=0 ,9/ % 2=:B?3
:1 > :@= 8:/07 4> 49 ;0= .,;4?, ?0=8> B0 =0.:8;@?0 ?34> .:==07,?4:9 49 ;0= .,;4?, ?0=8> 1:= ?30
2=:B?3 =,?0> :1 & ", ,9/ % "- ?: F9/ 4? ?: -0 B34.3 .:9F=8> ?30 ;=:.D.74.,74?D :1 &
(: .30.6 B30?30= ?34> ;=:.D.74.,74?D 8,D -0 =0;:=/@.0/ 49 ?30 .:9?0C? :1 :@= 8:/07 B0 .,74-=,?0 ?30
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;=0.4>07D 49 ?0=8> #% *"%! #%&"! ?0=8> ,> B0 /: 9:? 8:/07 ,9D 649/ :1 ;:;@7,?4:9 /D9,84.>
15
DOCUMENTO DE TRABAJO N.º 1009
;,=,80?0=> ,9/ :1 ?30 ?08;:=,=D ,22=02,?0 ;=:/@.?4A4?D >3:.6 . >: ?3,? ?30 8:/07 =0;74.,?0> ?30
A:7,?474?D ,9/ F=>? ,@?:.:==07,?4:9 .:0L.409? :1 ?30 % 2=:B?3 &0>@7?> 49 ?,-70 >3:B ?3,? 49 ?34> .,>0 ?30 -09.38,=6 8:/07 ;=:/@.0> , .:==07,?4:9 -0?B009 %
,9/ & :1 34230= ?3,9 ?30 :90 :->0=A0/ 49 ?30 /,?, //4?4:9,77D ?30 8:/07 2090=,?0> , A:7,?474?D
:1 & 2=:B?3 :1 =:@237D 3,71 :1 ?30 :90 :->0=A0/ 49 ?30 /,?, :8;,=0/ ?: ,=70AD B0
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% /,?, 1:= ?30 ;0=4:/ .:80> 1=:8 ?30 (%( " "!" !,&& ,?, ,-:@? .4A474,9
9:949>?4?@?4:9,7 ;:;@7,?4:9 ,20/ ,9/ :7/0= .:80> 1=:8 ?30 (%( " "% ''&'&
91:=8,?4:9 ,-:@? -@>490>> ?@=9:A0= 4> ;=:A4/0/ 1:= ?30 ;0=4:/ -D ?30 (&!&&
!&'%'"! A4/09.0 ,-:@? >@=A4A,7 =,?0> 1:= ?30 ,9/ .:3:=?> 4> :-?,490/ 1=:8 @990
&:-0=?> ,9/ ',8@07>:9 ,9/ @/=0?>.3 =0>;0.?4A07D ,?, ,-:@? & 0C;09/4?@=0> .:80> 1=:8 ?30 '"! ! "(!'"!
++")!&3 '". )! 5$0-".
(,-70 :8;,=4>:9 -0?B009 /,?, -09.38,=6 >:.4,7 :;?48@8 ,9/ :;?48,7 >@->4/D
,?,
09.38,=6
':.4,7 %7,990=
#: >@->4/D
$;?48,7 >@->4/D
% 2=:B?3
+071,=0
(@=9:A0=
& '@->4/40>
%=4A,?0 &
(:?,7 &
+071,=0 =010=> ?: ?30 >?0,/D >?,?0 @?474?D .:8;,=0/ ?: ?3,? :1 ?30 -09.38,=6
% 2=:B?3 =010=> ?: ?30 2=:B?3 :1 % ;0= B:=6492 ,20 ;:;@7,?4:9 .4A474,9 9:949>?4?@?4:9,7 ;:;@7,?4:9 D0,=> ,9/ :7/0=
(,-70 &:-@>?90>> .30.6 B309 ?30=0 ,=0 9: ;@-74. >@->4/40> 49 ?30 -09.38,=6
09.38,=6
':.4,7 %7,990=
$;?48,7 >@->4/D
% 2=:B?3
(30 -09.38,=6 =010=> ?: ?30 90B .,74-=,?4:9
BANCO DE ESPAÑA
20
DOCUMENTO DE TRABAJO N.º 1009
+071,=0
(@=9:A0=
& '@->4/40>
%=4A,?0 &
(:?,7 &
(,-70 '0.:9/ 8:809?> :1 % ,9/ & 2=:B?3
,?,
09.38,=6
09.38,=6
09.38,=6
':.4,7 %7,990=
':.4,7 %7,990=
':.4,7 %7,990=
$;?48,7 (,C
$;?48,7 (,C
$;?48,7 (,C
.
.
.
>3:.6
>3:.6
>3:.6
>3:.6
>3:.6
>3:.6
>3:.6
>3:.6
>3:.6
"- "- "- ", "- ", % ,9/ & 2=:B?3 ;0= B:=6492 ,20 ;0=>:9
/09:?0> A:7,?474?D ,9/
4> ?30 .:==07,?4:9 .:0L.409?
(,-70 D9,84. B071,=0 ,9,7D>4> B4?3 ;=:/@.?4A4?D >3:.6>
'?0,/D >?,?0 B071,=0
#: >3:.6> B071,=0
D9,84. B071,=0
D9,84. B071,=0 7:>>
09.38,=6
':.4,7 %7,990=
$;?48,7 >@->4/D
+071,=0 =010=> ?: @?474?D .:8;,=0/ ?: ?3,? :1 ?30 >?0,/D >?,?0 -09.38,=6
"0,9 A,7@0> ,1?0= ":9?0 ,=7: >48@7,?4:9> :1 7092?3 D0,=>
BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1009
1
surviving firms as a fraction of age cohort
0.9
Model, n = 10%
U.S. manufacturing firms, 1976 cohort
U.S. manufacturing firms, 1963 cohort
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2
4
6
8
10
12
years since entry
14
16
18
20
42@=0 '@=A4A,7 =,?0> :1 F=8> 49 ?30 0.:9:8D
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

42@=0 8;,.? :1 , 2090=,7 & >@->4/D :9 B071,=0
BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1009
u(C)=log(C)/(1-)
C
1.05
-10
1
-11
-12
0.95
-13
0.9
-14
0.85
0.8
-15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-16
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.7
0.8
0.9
1
0.7
0.8
0.9
1
u(G)=*log(G)/(1-)^2
G
1.026
25
24
1.024
23
1.022
22
21
1.02
20
1.018
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
19
0
0.1
0.2
0.3
0.4
0.5
0.6
u(L)=-L^(1+  )/((1-)(1+ ))
L
1.25
-7
1.2
-8
1.15
-9
1.1
-10
1.05
-11
1
0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-12
0
0.1
0.2
0.3
0.4

0.5
0.6

42@=0 8;,.? :1 , & >@->4/D :9 .:9>@8;?4:9 2=:B?3 ,9/ 7,-:=
GDP
R&D share
2.6
0.01
2.4
0
2.2
2
-0.01
1.8
-0.02
1.6
1.4
-0.03
1.2
-0.04
1
0.8
0
5
10
15
20
25
30
35
40
-0.05
0
5
10
15
Business Turnover
20
25
30
35
40
Employment
0.02
0.6
Benchmark
Optimum
0.5
0.4
0.015
0.3
0.2
0.01
0.1
0
0.005
0
5
10
15
20
years
25
30
35
40
-0.1
0
5
10
15
20
years
25
30
35
40
42@=0 8;@7>0 =0>;:9>0> ?: , ;=:/@.?4A4?D >3:.6 . 0.09?=,74E0/ 0.:9:8D H09.38,=6I A0=>@>
>:.4,7 ;7,990= H$;?48@8I
BANCO DE ESPAÑA
23
DOCUMENTO DE TRABAJO N.º 1009
GDP
R&D share
12
0.6
10
0.5
8
0.4
6
0.3
4
0.2
2
0.1
0
0
-2
0
5
10
15
20
25
30
35
40
-0.1
0
5
10
15
Business Turnover
20
25
30
35
40
Employment
0
0.6
-0.005
0.4
-0.01
0.2
-0.015
0
-0.02
-0.2
-0.025
-0.4
-0.03
-0.6
-0.035
-0.045
Benchmark
Optimum
-0.8
-0.04
0
5
10
15
20
years
25
30
35
40
-1
0
5
10
15
20
years
25
30
35
40
42@=0 8;@7>0 =0>;:9>0> ?: , >;477:A0= >3:.6 0.09?=,74E0/ 0.:9:8D H09.38,=6I A0=>@> >:.4,7
;7,990= H$;?48@8I
GDP
R&D share
2.6
0.01
2.4
0
2.2
2
-0.01
1.8
-0.02
1.6
1.4
-0.03
1.2
-0.04
1
0.8
0
5
10
15
20
25
30
35
40
-0.05
0
5
10
15
Business Turnover
0.6
0.018
0.5
0.016
0.4
0.014
0.3
0.012
0.2
0.01
0.1
0.008
0
0.006
-0.1
5
10
15
20
years
25
25
30
35
40
Employment
0.02
0
20
30
35
40
Benchmark
Optimum
0
5
10
15
20
years
25
30
35
40
42@=0 8;@7>0 =0>;:9>0> ?: , ;=:/@.?4A4?D >3:.6 . 49 ?30 .,>0 :1 :;?48,7 .:9>?,9? ?,C 0.09?=,74E0/ 0.:9:8D H09.38,=6I A0=>@> >:.4,7 ;7,990= H$;?48@8I
BANCO DE ESPAÑA
24
DOCUMENTO DE TRABAJO N.º 1009
BANCO DE ESPAÑA PUBLICATIONS
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0909 JAVIER MENCÍA AND ENRIQUE SENTANA: Multivariate location-scale mixtures of normals and mean-varianceskewness portfolio allocation.
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0917 MAXIMO CAMACHO, GABRIEL PEREZ-QUIROS AND HUGO RODRÍGUEZ MENDIZÁBAL: High-growth
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0919 JESÚS VÁZQUEZ, RAMÓN MARÍA-DOLORES AND JUAN-MIGUEL LONDOÑO: On the informational role of
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0920 PALOMA LÓPEZ-GARCÍA AND SERGIO PUENTE: What makes a high-growth firm? A probit analysis using
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0921 FABIO CANOVA, MATTEO CICCARELLI AND EVA ORTEGA: Do institutional changes affect business cycles?
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0922 GALO NUÑO: Technology, convergence and business cycles.
0923 FRANCISCO DE CASTRO AND JOSÉ LUIS FERNÁNDEZ: The relationship between public and private saving in
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0924 GONZALO FERNÁNDEZ-DE-CÓRDOBA, JAVIER J. PÉREZ AND JOSÉ L. TORRES: Public and private sector
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0926 JUANA ALEDO, FERNANDO GARCÍA-MARTÍNEZ AND JUAN M. MARÍN DIAZARAQUE: Firm-specific factors
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0928 MAX GILLMAN AND ANTON NAKOV: Monetary effects on nominal oil prices.
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0932 ANTON NAKOV AND GALO NUÑO: Oilgopoly: a general equilibrium model of the oil-macroeconomy nexus.
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1006 GIUSEPPE BERTOLA, AURELIJUS DABUSINSKAS, MARCO HOEBERICHTS, MARIO IZQUIERDO, CLAUDIA
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1008 ALFREDO MARTÍN-OLIVER: From proximity to distant banking: Spanish banks in the EMU.
1009 GALO NUÑO: Optimal research and development expenditure: a general equilibrium approach.
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