Malthus to Solow - Federal Reserve Bank of Minneapolis

!"#$
%&'(
)*&"+$
%
&,
(-(&(,*
,
, .
* /00 * ,*, , 1. . "21
3**
,*,*"4,**
,*
.,"-3
53.3
. " - 3 5 " 4
*,
3,33
,*3
,,,,")
3,,
*,..3.,"63
.
*,*"
$4*,1
.(7
"4
,!,&
,*3
-8"-
*1
"
-
3
.
33*/003
*.
9"+/003
,*,:*,33
,*"33;,,*
,"63
1
**,*
,*"63,
*
..
,3
.3,
,*"633,
<.,3,3=35.
.5"
-*.*,**
"-,*
>/003*."-
.,*,,5.,*?
< @=A"-,..,
,*1,."23
*3.3.
"#3*
,,
*"(331.
"-3
31."+.
.,3*1,.
,"
4*,5.,*3,
,
*.*,",
,3*,*3
,
")
3.*,,*3*,.,."
-3
.."(3
,.,
3,*,*
"63.
*,*3
*"
-
.>.,
533
,**
.
*,"-3*
,
..
"&*3<
03"@=3*
,,
3B,*C
.,
,**,"D-
,.,,**,
*,,3*
3*,
,*
"-1,*,
,,*>
,
>
"-
,
,,*"
23,
3*.*313
."-
*,,.
"-
3*
3
<.=*"(< 0=
3,
.,*
"2
3*,.,.3
,B,.,D
,,*"
-
,'<
"'<
/=3.
/=*1,
3
3,
"63'<
/=3,
,
,
31.
"-.'<
33-<
/=
0=3*9
"63
"6.3
*.
,*,*,
,5,
"-*
5.3"
'<
/=1*
,
"'35.
*>
1
,
3
,
3>
,
*"
#*
3>
,'F
,,*"#3,*
5.*"
-,9*"613*
,"-
"6E335.
9"-*5..
G"4*3*
*.!4< /=-< /=
,9,,"
E
*"3,
@"
-.*.
),0
/00"63*,3,3
,
"6.*,
.,
,*3
,",
3*,1,,.*
1"-*."1
*.*3*,*,.
"-
.
;*"4*
*
,
"
,*,@H/00"E-,*
*,
"-+>*#< @=1
**,"-*,/03"
,,,3"1",3
,,1."-
.*,
,...+>*#
< @=5,"#*
3
E>
,*"
E
-),&< /=@HE4,"< =GH/00"
-*,&< /.=31*,
+>*#< @="-
.9.00@
.
,#>+*,00"
G
&#'
!"#$%
E0
E00
0
00
0
00
0
0
0
*,
E0
G0
0
@0
0
,*
*,"
-.00.
*,"2.,
3*,"-.
*,
*,.,3*,3
"
(*"
,),
@H/00
,"G-.
,*"4*
,3"43
"
G
-),1
,"-&< /="(,3
.9.
00@
.,#>+*,00"
&#'
!
00
0
00
0
0
0
E0
G0
0
@0
0
!!
.5/003*.*.
),
"'.
3*
**,3,*"
+,
,"
--.3*),.
"-,.
.
.
.*/0 / "-.*,.
...
"
**,.,.
,
5*
,
1"I<
I<
=1"%,,,3
=,,
,,1"',,*
13.,01"I
<
=,,*.*@/00"
@
(
%"8"+
'
J
!+K#
+"
< /L%""=
<=
00
0"/
/"G
/0
0"/G
"
/0
"
"
/0
"
E"G
/ 0
"/@
E"
E
E"@E
G"@
G"/
G"
E/
G" G"
@0
/"
"G
/
/"
"
:< 3"GH3@="
:< 3"3E0HE ="
4.003/03
/0;6
"-
,
/03/ 03 E3< =
**6"%"8".
*6*"0%"8"
.
*6"
"
#$$%
&' !!
(
,
<!I+=/03
.3
"-."
(
%""M
!I+
J
+,
/0
//
00
/
E
0
0
0
:%""&
< ="
0
.8)3
NO.1"",",
P"-
/0
..,//
.,3,"6
003
,*//
"
- *
.,,,..
"-.
*3*
,3..
0"-
!I+///0
0
,"
)
->,3*>
F< @=
,,"63**
3.3."63**
;.,"-
**:
/
( ) * + <=
( ) * "
<=
#3.*"-
.
(, 3 ) , 3 * , 3 + , <,Q3=33.3
,"-
,*
,"
6.,,,,
*3,
39
9.1"-
.,"-*33
"#33
.
"-*,*
*
"&*3*
"63*,33*
13"
2.
"&
"@#3
,
.
- ) ( ( "
<E=
63*
,*
"-,"45
,**3.."13
,*
*.,3,.,3,*
*,"
@
6.13*.E"#3
00."
'1:."
495."63
"
1.3*3
3;
,"!
*,
<=3< ) =3< + =3,
*,.:
1R(, * , ) ) , + + , S3
, 3
<G=
.;<=<="
.&/
#
*
"63,.
9.*,:
# <
3 = , , "
<=
#3 , ."
-... * 3*
* <
= * "
<@=
*,< /=3*,*
,
3**,,"-
*.."
(*
**,*
"' ...,
,
.# <
3 = 0 <
= 3*#,
.,"
63 .,"63
, # <
3 = 0 "-5.
. <
= 3*
0
-< 0 =** )0 K * 0 + K * 0 "-3
3,"),**
.."-..,
3**
*"-3,19<=.;
*,.,:
1 ) 1 <+ = "
<=
-*1*.
)+<+Q=
."-"
-&/%"&
!
* 0 3 1 0 3 0 <* * 0 0 =3
5.
5 0 3R 3 3 ) 3 + ST3
R ) 3 ) 3 * 3 * 3 ( 3 ( ST3R 3 3 1 3 S3
*,:
" !
53
.
5<G="
" !
5319<=.;<="
E" : ) ) * 1 * * *
* ( ( * * * 1 "
G" * <
= * "
* * <
= * "4
1,3*
."
!"
#
$
" " %
&
'
(
! "#"$
%!
%
&
)"
&!'(") %
!* )" (
("!"
%
'*
%
#
+%
&,
' ' + " ' &
-"
65</=35.*,
*>"65</=3.
5."
4-35.
*"#3*.3
*,.
:/
( < ) 3 * 3 = 1 < ) ) = < * * = ) * "
0 ) )
0 * *
<0=
-,
. ) * "-3.;
3
1"-
1
.;
5"635.*,
*>.
) * < = ) * ) ) * ) * <=
+ < = ) * "
!
)3*3.
535.
*,3*3
< ) 3 ) 3 * 3 * ="
/
23
19.*."
#*
35</=3 ) * 50"
E
4*F9.3*19<=
.;<="-> 1 .,
*,1:
<=
) + "
<E=
63.,>,
) * < = "
<G=
!
3 ) 3 * 3 35<=3<=3<@=3<G=
. 3 ) 3 + 3 3 * 3 ) "I13,
3<=<E=
. "!
0 3 )0 3 * 0 3 0 333.
.5,
.,"-
..3,3**.1
.3*,
"-
0 .3*
3.,53 0
3
5."4,
5.G"
:;%
&
M 0 )0 .5=3*,
13,
,"63 )0 5 0 ,
,*>*,"-,*
< =
,*< 0 ="-5,*.5
< = "63,,,3333
G
,*"-*,"63
3
,"-,>,*<.,,
.=1
"
' .
,>,*"*>
3* <
= 5<@= <
= < = "
*,,>.,*3*
,*
., "?5</="A23
,*.,
,**,,
<
= 5<@="2
3
3.
,3,*3*
9"(3*.
*>"-3
*
,,*,* 3 3 ) * 3 ( * 3 ,*
< = ) "%,,*3
,
,
"
49**,:
/<$4 <
= < = 5&/
</=
&/$
#3*
."
*+!
-5.
,5
,
.,
.*)3*
3 0 "63*.**. 0 3*5
0
5.5"-533
, 0 ,
) 3.5<G=3
.*9"-*
,
,
0 "#3,5.
13*..,,3.
15."
-&*"
, )0 * 0 ..
, 0 U0 3* U0 >
,>,*3*5
,.
5 U 3 )U 3 *U 0
"-<= U .
,
., ) ,
"6 U .,
3*
*,
U0 "6 U .,3**
*
"-,,3*
.
0 *
"-
U0 .
5 0
T3* 0 U0 "
(,5<E=33...5
53*,.
"#3.3
*..55.*,
."63*5 U 3 )U 3 *U 0 **. 0 ,,,;."
U
U
U
U
-
)0 * 0 55
)0 * 0 ,"-
5 0
."!
53,5.
5.,5.,"
(
,,,533.
.,9"-.
@
>
." *3*
*,3,.
*5."!
135..
*,"!
,
,35.
) * .,,
"
,-
-"
(,>3*
5..
..
*"0-.<=>
*,*.,),/003<=*>
,*.,H446693
<E=,*,,
,'<
/=3
<G=.,
."
5<=.
3 3 3*5<=
,
"!
*
,
3*.F50"@.3*
50"@0"G3
"41*
*
3*
0"1"-F
>0"E"
6>/003*3.'<
/=3
,*.0"E
,"6
>,
.E3*
-5. ?03 < =A "
0
0
0
+**.3,
<=
,9"
0E
"
"4. ,*!I+*"
- /
"
"
4 5"-
..*GG"**
,
"
'<
/=
,*,!I+
,*0"4.
,*3 <
= "63,*
*.,
<
E="2
,,*3
,<
=."(3,*
,1/**
"4
,*."-
,
*, <
= :
< = @
< =
/
"
/
,E, <
= ,
"
/
<=
!." / 0 1
"
"0
"
"0
0"
0"0
0
0
0 0
)
2
4.,,* 0 3*
*,*
",G**
.,
<.=
"-,*
*,
*"
2!
"
"0
0"/
0"@
0"G
8
0"
I
0"0
>
>G
>E
>
>
0
*
E
G
2,H0",3
*,3*"2
.,
3*,*,,")
3,*
*
,39,*>"
3!! 4
@
G
E
0
>
>G
>E
>
>
0
E
G
,*,.,3,*
3*,"(03,*
3*,*"<,@3**,.
9"=->/00),3
*-."
0
!
0
4,
/
+
@
G
0
>
>G
>E
>
>
0
E
G
#
63,*
"(,3,*.
%*"<-."=
627-3!
0"E0
0"
0"0
0"
0"0
0"0
0"00
>
>G
>E
>
>
0
E
G
5
3,/*,*"6.,,
1
3*.,
E>"-
,*
,
"
!.
"
"0
"
"0
0"
0"0
>
>G
>E
>
>
0
E
G
@
%
#+
1,,**
3.*,*.,"
-..1,,3*< =3
*,,*3< /@='< //="-
11*.,3
*"?'<
/="A63*
,*
*,*."-
3
35.
*"
4
1
,,
< @="4.*,*
5.,"43*
3*,9
91,*V,*
*1,,,*31"23
9+HE3,
,F"
< /=9*
,
3,*
"-,
9
<
= 5<="#*
3,*
,
"2*
"3< @0='<
/=3
,
.5>5>.*.
"2.3
13*,,
."-3
** 0 /0.
.,*
,
"4
*1"
3*
1,,*5
*,"13++<
=
*
*,"
,3*5</=33*
<
=
"-
),&3*
.*,
.,3
*"
E
2
3!" @0"()("6)3"3
.&/
%
&
-./-3=-
#:*>-&&%
&
"+3I"":+
%
+3"0 HG0"
3!"38
"3.-"
0"#&33
)!*"?
%
& /<2.3"=:HE"
&3!,"
/".:4)
W
%.<%
&3
="
&3!,"
/."I(,4,),30H/0"
%.<%
&3
="
3+(" @"I.I!*"=&
%
&
@<.=:@H0"
!323
I"4"
/"+3-,3!*:
,,-"%.<*
%
="
'3"
/"&,)!*"%.
<%
,="
'3.)"3" //"2)
$?
%
&
<=:EHG"
'3.)"3"
/"7@32"%.
<%
&,="
3(,"
".&
2
-/./&3=+@-&/
0"21I*J:21%
+"
3-" /"=%
//"21:21
%
+<
E,="
G
3"
0"+@
3
-%
&
$
21I*J:21%
+"
I34"
"24,&W-
#',,,,I"6-"."!3"3
%
&
*43I)64"&,
':%
&,+3
"/3" H"
+3'"3)*&"+"
",:("
E@3
"
+>*3#3M"#" @"
&+
&.3&4F4,>"%
&
E: @HE"
3+" /@"6,',>!*"?
%
&
G<2.=:00H0E"
*3." "-&,(,,,+"@
%
&
E <(,=:EHE0"
-3."
/"(,6:#&9"
%.<&%
="
%""&" "A
#-&
!' "
"4,3"&":%""!
+,2"
4,3)"("T""
T")"2T""3"
"%/
A2&2&@
<'$I*J&.,:&.,
%
+"