Business cycle

56 Economic Perspectives

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Introduction and summary

!""#$%&'()*$)+#$,"+-.)/0$1"*&(0$/-23&/-'$)$(*-)/$3+4#-/'.)+#&+5$"%$.6-$7"/8&+5'$"%$.6-$-("+",09$-'1-4(&)**0$76).$#/&:-'$.6-$;3'&+-''$(0(*-<.6-$1-/&"#&(31'$)+#$#"7+'$&+$-("+",&($)(.&:&.0=$>&+(-$).$*-)'..6-$*).-$?@AA'9$)$%3**$'7&+5$%/",$.6-$'.)/.$"%$)+$-("4+",&($-B1)+'&"+$."$)$/-(-''&"+$)+#$;)(8$."$.6-$'.)/."%$)+".6-/$-B1)+'&"+$6)'$5-+-/)**0$.)8-+$;-.7--+.7"$)+#$-&56.$0-)/'=$C:-/0$(&.&D-+$&'$8--+*0$)7)/-$"%.6-$'.).-$"%$.6-$-("+",09$76-.6-/$&.$&'$&+$1/"'1-/&.0"/$/-(-''&"+=

C:-/0"+-$&'$'"$("+'(&"3'$"%$.6-$;3'&+-''$(0(*-;-()3'-$,"'.$'-(."/'$"%$.6-$-("+",0$,":-$31$)+##"7+$."5-.6-/=!$E6&'$16-+",-+"+9$/-%-//-#$."$)'!"#"$%#%&'9$&'$)$(-+./)*$1)/.$"%$.6-$"%%&(&)*$#-%&+&.&"+"%$.6-$;3'&+-''$(0(*-=$E6-$#-%&+&.&"+$&'$'-.$;0$.6-$F)4.&"+)*$G3/-)3$"%$C("+",&($H-'-)/(6$IFGCHJ9$76&(6#-(&#-'$76-+$/-(-''&"+'$;-5&+$)+#$-+#=$K+#-/$.6-FGCHL'$#-%&+&.&"+9

M===$)$/-(-''&"+$&'$)$N1-/'&'.-+.O$1-/&"#$"%$#-(*&+-&+$.".)*$"3.13.9$&+(",-9$-,1*"0,-+.9$)+#$./)#-9$3'34)**0$*)'.&+5$%/",$'&B$,"+.6'$."$)$0-)/9$)+#$#()*%+,-./0+%12)%(+,!"&')(!'0"&1,0&,#(&.,1%!'")1,"3,'4%%!"&"#.=P"

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&+./"#3(-#9$&+$.6-$*).-$?RSA'$)+#$-)/*0$?R@A'9$.6-$'.).-"%$,)(/"-("+",&('$6)'$)#:)+(-#$/)1&#*0=$E6-$("+4(-1.3)*$)+#$(",13.).&"+)*$;)//&-/'$."$.6&+8&+5$);"3.,3*.&1*-$'-(."/'$)/-$23&(8*0$%)**&+5$)7)0=$T'$)$/-'3*.9/-(-+.$0-)/'$6):-$7&.+-''-#$)$/-+-7-#$&+.-/-'.$&+3+#-/'.)+#&+5$(",":-,-+.=

U-$6):-$.7"$";V-(.&:-'$&+$.6&'$)/.&(*-=$E6-$%&/'.&'$."$#"(3,-+.$;3'&+-''$(0(*-$(",":-,-+.=$U--B),&+-$#).)$"+$6"3/'$7"/8-#$&+$)$(/"''$'-(.&"+$"%-("+",&($'-(."/'=$U-$-B),&+-$.6-$;3'&+-''$(0(*-(",1"+-+.'$"%$.6-'-$#).)$)+#$'6"7$.6).$.6-$#-5/--"%$(",":-,-+.$&'$'3;'.)+.&)*=$W3/$'-("+#$";V-(.&:-&'$."$)+)*0D-$-B1*)+).&"+'$%"/$.6&'$(",":-,-+.=$U-%&+#$.6).$+"+-$&'$(",1*-.-*0$').&'%)(."/0=$>.&**9$.6&'&'$)$5/"7&+5$)/-)$"%$/-'-)/(69$)+#$7-$)/-$'--&+5'",-$1/"5/-''=

Identifying comovement

E"$'.3#0$(",":-,-+.$)(/"''$'-(."/'$":-/$.6-;3'&+-''$(0(*-9$7-$+--#$.6-$%"**"7&+5$.7"$.6&+5'X$),-)'3/-$"%$.6-$*-:-*$"%$-("+",&($)(.&:&.0$&+$.6-$:)/&4"3'$'-(."/'$"%$.6-$-("+",0Y$)+#$)$1/-(&'-$#-%&+&.&"+"%$76).$7-$,-)+$;0$.6-$;3'&+-''$(0(*-$(",1"+-+.$"%.6-$#).)=$G-*"79$7-$)##/-''$.6-'-$.7"$&''3-'=$T%.-/.6).9$7-$1/-'-+.$"3/$/-'3*.'9$(6)/)(.-/&D&+5$.6-$#-5/--"%$(",":-,-+.$&+$.6-$#).)=

57Federal Reserve Bank of Chicago

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TABLE 1

Variable Relative Relative Business cyclenumber Hours worked variable magnitude volatility comovement

1 To t a l priva t e 1 . 0 0 1 . 0 0 . 0 02 Goods -produc ing indus tries . 3 3 3 . 9 1 . 9 93 M in ing . 0 3 5 . 4 6 . 3 84 Cons truc t ion . 1 7 6 . 7 5 . 8 85 Manu f a c turing . 8 0 3 . 9 2 . 9 76 Durab le goods . 5 8 6 . 9 0 . 9 77 Lumber and wood products . 0 6 1 0 . 1 8 . 8 98 Furn iture and f ixtures . 0 4 8 . 1 4 . 9 49 Stone , clay, and glass products . 0 5 4 . 9 8 . 9 5

1 0 Primar y me t a l indus tri es . 0 9 9 . 8 9 . 8 61 1 Fabrica ted me ta l products . 1 3 7 . 2 1 . 9 61 2 Mach inery, except e lectrica l . 1 9 1 1 . 1 0 . 9 31 3 E lectrica l and e lectron ic equ ipment . 1 5 8 . 7 5 . 8 81 4 Transpor t a t ion equ ipmen t . 1 7 7 . 8 3 . 8 91 5 Ins truments and re la ted products . 0 8 5 . 0 3 . 7 61 6 M isce l laneous manufa cturing . 0 4 3 . 2 3 . 9 01 7 Nondurab le goods . 4 2 1 . 3 9 . 9 11 8 Food and k indred products . 2 1 . 1 6 . 5 01 9 Tobacco manufactures . 0 1 1 . 8 3 . 0 82 0 Text i le m i l l products . 1 1 3 . 9 2 . 7 62 1 Appare l and other text i le products . 1 5 2 . 6 4 . 8 52 2 Paper and a l l ied products . 0 9 1 . 9 7 . 8 52 3 Print ing and pub l ish ing . 1 6 . 9 1 . 9 02 4 Chem ica ls and a l l ied products . 1 3 1 . 0 1 . 8 02 5 Pe tro leum and coa l products . 0 2 2 . 0 2 . 1 62 6 Rubber and m isc . p las t ics products . 0 9 7 . 8 2 . 8 92 7 Lea ther and lea ther products . 0 3 2 . 7 1 . 6 42 8 Servic e -produc ing indus tries . 6 7 . 2 5 . 9 32 9 Transpor t a t ion and pub l ic ut i l it ies . 1 0 . 8 7 . 9 53 0 Who lesa le trade . 1 0 . 6 5 . 8 73 1 Re t a i l trade . 3 1 . 3 6 . 8 73 2 Finance , insurance , and rea l esta te . 1 0 . 3 5 . 4 83 3 S e rv i c e s . 3 8 . 1 9 . 4 9

Notes: The column labe led “Re lative magnitude” reports an indication of the re lative magnitude of each sector. Any given row reports the average number of peopleemployed in that sector divided by the average number of people employed in the sectora l aggregate to which that sector be longs , for example , 58 percent ofmanufacturing employment is in the durable goods sector and 42 percent is in the nondurable goods sector. The column labe led “Re la tive vola tility” reports thevariance of the bus iness cycle component of the logarithm of hours worked in the indicated row variable divided by the variance of the bus iness cycle component ofthe logarithm of tota l priva te hours worked. The column labe led “Bus iness cycle comovement” is ca lcula ted us ing the process des cribed in note 6 of the article .Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .


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logarithmA. Total hours worked

FIGURE 1

logarithmB. Total hours worked—High-pass and business cycle components

TrendData

Businesscycle

component

High-pass

Note: Shaded areas indicate recessions as determined by theNationa l Bureau of Economic Research.Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .

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Measuring business cycle comovement

b-'1&.-$.6-$:-/0$'3;'.)+.&)*$#&%%-/-+(-'$&+$.6-./-+#'$"%$.6-$#).)$'-/&-'$'6"7+$&+$%&53/-$\9$.6-&/$,":-4,-+.'$":-/$.6-$;3'&+-''$(0(*-$)/-$23&.-$'&,&*)/=$̂ &53/-$a&**3'./).-'$.6-$;3'&+-''$(0(*-$(",1"+-+.'$"%$.6-$'),-:)/&);*-'$3'-#$&+$%&53/-$\=$Q+$-)(6$()'-9$7-$(",13.-#.6-$;3'&+-''$(0(*-$(",1"+-+.$3'&+5$-B)(.*0$.6-$'),-,-.6"#$3+#-/*0&+5$.6-$()*(3*).&"+'$&+$1)+-*$G$"%$%&543/-$?=$C)(6$5/)16$("+.)&+'$.6-$;3'&+-''$(0(*-$(",1"4+-+.$"%$.6-$:)/&);*-$&+#&().-#$)+#$.6-$;3'&+-''$(0(*-(",1"+-+.$%"/$.".)*$1/&:).-$6"3/'=$E6&'$7)'$.)8-+#&/-(.*0$%/",$1)+-*$G$"%$%&53/-$?=

Q+$,"'.$"%$.6-$'-/&-'$&+$%&53/-$a9$.6-$#).)$,":-31$)+#$#"7+$(*"'-*0$7&.6$.6-$;3'&+-''$(0(*-$(",1"4+-+.$"%$.".)*$6"3/'$7"/8-#=$E6-/-$)/-$'",-$-B(-1.&"+'=^"/$-B),1*-9$.6-$;3'&+-''$(0(*-$,":-,-+.'$&+$,&+&+5;-)/$*&..*-$/-'-,;*)+(-$."$.6-$;3'&+-''$(0(*-$,":-4,-+.'$&+$.".)*$6"3/'$7"/8-#=$T.$.6-$'),-$.&,-9$,&+&+5/-1/-'-+.'$)$:-/0$',)**$1)/.$"%$.6-$1/&:).-$-("+",0)+#$-,1*"0'$"+*0$a$1-/(-+.$"%$7"/8-/'$&+$.6-$5""#'41/"#3(&+5$&+#3'./0=$T+".6-/$-B(-1.&"+$&'$.6-$%&+)+(-9&+'3/)+(-9$)+#$/-)*$-'.).-$I^QHCJ$&+#3'./09$76"'-;3'&+-''$(0(*-$(",1"+-+.$-B6&;&.'$/-)'"+);*0$6&56

(",":-,-+.$7&.6$)55/-5).-$-,1*"0,-+.$3+.&*$.6-?R@A'9$)%.-/$76&(6$.6&'$/-*).&"+'6&1$;/-)8'$#"7+=

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̂ QHC9$)+#$'-/:&(-'$'-(4."/'=$W:-/)**9$6"7-:-/9$.6-$#-5/--$"%$(",":-,-+.$;0.6&'$,-)'3/-$&'$6&56=

!"&+5$"+-$'.-1$%3/.6-/$&+$.6-$*-:-*$"%$#&')55/-5)4.&"+9$7-$()+$5-.$)+$&#-)$);"3.$.6-$(",":-,-+.$&+$.6-(",1"+-+.'$"%$#3/);*-$)+#$+"+#3/);*-$,)+3%)(.3/4&+5=$^&53/-$[9$1)+-*$T$#&'1*)0'$.6-$;3'&+-''$(0(*-,":-,-+.'$&+$.6-$(",1"+-+.'$"%$#3/);*-$,)+3%)(4.3/&+5$'-(."/'=$c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

^&53/-$[9$1)+-*$T$'6"7'$.6).$.6-$(",":-,-+.),"+5$'-(."/'$&+$#3/);*-$,)+3%)(.3/&+5$&'$:-/0$6&56=U&.6$"+*0$"+-$,&+"/$-B(-1.&"+9$.6-$:)/&);*-'$,":-(*"'-*0$7&.6$-)(6$".6-/$)+#$7&.6$)55/-5).-$-,1*"04,-+.=$E6-$-B(-1.&"+$&'$.6).$&+'./3,-+.'$)+#$/-*).-#1/"#3(.'9$'-/&-'$?Z9$#"-'$+".$,":-$(*"'-*0$7&.6$.6-".6-/$:)/&);*-'$#3/&+5$?R@S9$76-+$.6-$".6-/$;3'&+-''(0(*-$(",1"+-+.'$)/-$'&5+)*&+5$)$/-(-''&"+=$`"7-:-/9":-/)**$.6-$#-5/--$"%$(",":-,-+.$&'$'./&8&+5*0$6&56=^&53/-$[9$1)+-*$G$'6"7'$.6).$.6-$;3'&+-''$(0(*-$("4,":-,-+.$&+$.6-$+"+#3/);*-$5""#'$,)+3%)(.3/&+5&+#3'./&-'$&'$*"7-/$.6)+$&+$.6-$#3/);*-$5""#'$'-(."/=E7"$:)/&);*-'$.6).$#"$+".$(",":-$(*"'-*0$7&.6$.6-".6-/'$).$;3'&+-''$(0(*-$%/-23-+(&-'$)/-$.";)(("$,)+43%)(.3/-'9$'-/&-'$?R9$)+#$1-./"*-3,$)+#$(")*$1/"#3(.'9'-/&-'$\Z=$G".6$.6-'-$:)/&);*-'$)/-$/&'&+5$&+$.6-$%&/'.)+#$*)'.$FGCH$/-(-''&"+$1-/&"#'$&+$"3/$#).)=$E6-

60

Eco

nom

ic Persp

ectives

FIGURE 2

8#-"()3#"4%5)'.)97"'#-()(%/&#"(:);7&7)7.5)&"%.5(

logarithmA. Goods-producing industries

logarithmD. Mining

logarithmG. Service-producing industries

logarithmJ. Retail trade

logarithmB. Manufacturing, durable goods

logarithmE. Construction

logarithmH. Transportation and utilities

logarithmK. Finance, insurance, and real estate

logarithmC. Manufacturing, nondurable goods

logarithmF. Wholesale trade

logarithmI. Services

Trend

Data

Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .

→

61

Federal R

eserve Ban

k o

f Chicag

o

FIGURE 3

<-('.%(()/0/1%)/#2$#.%.&)/#2$7"'(#.:)6#&71)+#-"()3#"4%5)9%"(-()+#-"()3#"4%5)'.)97"'#-()(%/&#"(

logarithmA. Goods-producing industries

logarithmD. Mining

logarithmG. Service-producing industries

logarithmJ. Retail trade

logarithmB. Manufacturing, durable goods

logarithmE. Construction

logarithmH. Transportation and utilities

logarithmK. Finance, insurance, and real estate

logarithmC. Manufacturing, nondurable goods

logarithmF. Wholesale trade

logarithmI. Services

Total

Note: The information displayed in the “tota l hours worked” line is “business cycle component,” taken from figure 1 , pane l B.Source: Authors’ ca lculations from data of DRI Basic Economics database , 1964–96 .

Subsector


FIGURE 4

<-('.%(()/0/1%)/#2$#.%.&)#*)&#&71)+#-"()3#"4%5)7.5)+#-"()3#"4%5'.)97"'#-()27.-*7/&-"'.=)(-,(%/&#"(

A. Two-digit manufacturing durableand total hours worked

B. Two-digit manufacturing nondurableand total hours worked

1

16

15

14

13

12

1110

9

87

1

27

2625

24

232221

2019

18

Notes: The number on the right indicates the variable sector from table 1 that is be ing highlighted. Pane l A shows:1—tota l private hours; 7—lumber and wood products; 8—furniture and fixtures; 9—stone , clay, and glass products;10—primary me ta l industries; 11—fabrica ted me ta l products; 12—machinery, except e lectrica l; 13—e lectrica l and e lectronicequipment; 14—transportation equipment; 15—instruments and re lated products; and 16—misce llaneous manufacturing.Pane l B shows: 1—tota l priva te hours; 18—food and kindred products; 19—tobacco manufactures; 20—textile mill products;21—appare l and other textile products; 22—paper and a llied products; 23—printing and publishing; 24—chemica ls and a lliedproducts; 25—petroleum and coa l products; 26—rubber and misce llaneous plastics products; and 27—leather and leather products .Each variable has been sca led by its sample standard deviation and a constant has been added in order to spread out the data in the pane ls . Shaded areas indicate recessions as determined by the Nationa l Bureau of Economic Research.Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .

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Q+$("+(*3'&"+9$7-$%&+#$.6).$.6-/-$&'$'3;'.)+.&)*;3'&+-''$(0(*-$(",":-,-+.$&+$.6-$#).)=$W+*0$.7"$/-*4).&:-*0$',)**$'-(."/'<.";)(("$,)+3%)(.3/-'$)+#$1-4./"*-3,$)+#$(")*$1/"#3(.'<-B6&;&.$*&..*-$.-+#-+(0$.",":-$31$)+#$#"7+$7&.6$5-+-/)*$;3'&+-''$("+#&.&"+'":-/$.6-$;3'&+-''$(0(*-=

Explaining business cycle comovement

U6).$&'$&.$.6).$).$.&,-'$13**'$,"'.$'-(."/'$"%$.6--("+",0$319$)+#$).$".6-/$.&,-'$13'6-'$.6-,$#"7+)5)&+]$E6&'$&'$"+-$"%$.6-$(-+./)*$23-'.&"+'$&+$;3'&4+-''$(0(*-$)+)*0'&'=$T*.6"356$-("+",&'.'$6):-$#-4:-*"1-#$)$+3,;-/$"%$1"''&;*-$-B1*)+).&"+'9$.6-16-+",-+"+$/-,)&+'$)$13DD*-=

Q+$)$(*)''&($)/.&(*-$#-:".-#$."$.6&'$13DD*-9$H";-/.C=$i3()'9$j/=9$("+V-(.3/-'$.6).$.6-$/-'"*3.&"+$,3'.$*&-&+$'",-$'"/.$"%$'6"(8$.6).$6&.'$)**$'-(."/'$"%$.6-$-("+4",09$)$'"4()**-#$)55/-5).-$'6"(8$Ii3()'9$?R@?J=k)+0$-("+",&'.'$."#)0$7"3*#$1/";);*0$)5/--$7&.6.6&'$("+V-(.3/-=$E6).$&'$7609$&+$1/)(.&(-9$.6-$'-)/(6$%"/.6-$3*.&,).-$()3'-$"%$;3'&+-''$(0(*-'$"%.-+$%"(3'-'

FIGURE 5

frequency

;'(&"',-&'#.)#*)/#""%17&'#.(),%&3%%.),-('.%(()/0/1%)/#2$#.%.&()#*)+#-"()3#"4%5)'.)97"'#-()(%/&#"(

A. All sectors and all sectors without mining (3), tobacco manufactures (19),and petroleum and coal products (25)

–0.4 –0.2 0.2 0.40.0 0.6 0.8 1.0

0.0 0.5 1.0 1.00.0 0.5 1.00.0 0.5

corre lation

frequencyB. Two-digit durable manufacturing

frequencyC. Two-digit nondurable manufacturing

frequencyD. Service-producing

corre lation corre lation corre lation

All sectors (0 .55)

All sectors minus three (0 .68)

All sectors (0 .82) All sectors (0 .46)All sectors minus (19)and (25) (0 .66)

All sectors (0 .63)

Notes: Whole numbers in parentheses represent the variable sector des ignated in table 1 . Decima ls in parentheses representmean over indica ted se t of corre la tions .Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .


"+$&#-+.&%0&+5$)+$)55/-5).-$'6"(8=$`"7-:-/9$/-4'-)/(6$("+#3(.-#$'&+(-$i3()'$13;*&'6-#$6&'$)/.&(*-'355-'.'$.6).$&#-+.&%0&+5$.6-$!(61%$"%$;3'&+-''$(0(*-',)0$+".$;-$'"$'&,1*-=

^&/'.9$-:-+$&%$7-$#"$,)+)5-$."$&#-+.&%0$)$'6"(8.6).$(*-)/*0$)%%-(.'$.6-$76"*-$-("+",09$&.$#"-'$+".+-(-'')/&*0$%"**"7$.6).$'6"(8$&'$/-'1"+'&;*-$%"/$.6-;3'&+-''$(0(*-=$T$'6"(8$,&56.$7-**$;-$-B1-/&-+(-#$;0)**$'-(."/'$"%$.6-$-("+",09$;3.$.6-0$+--#$+".$)**$)%712"&+$&+$.6-$'),-$7)0=$E6-$;3'&+-''$(0(*-$'6"(89$&%&+#--#$.6-/-$&'$"+*0$"+-9$'--,'$."$*-)#$."$)$'0+(6/"4+&D-#$/-'1"+'-$)(/"''$'-(."/'=$>-("+#9$7-$+"7$8+"7.6).$.6-$'-)/(6$%"/$)$'&+5*-$)55/-5).-$'6"(8$,)0$&.'-*%;-$"%%$;)'-=$^"**"7&+5$.6-$7"/8$"%$i"+5$)+#$c*"''-/I?R@aJ9$7-$8+"7$.6).9$).$*-)'.$&+$.6-"/09$#&'.3/;)+(-'."$&+#&:&#3)*$&+#3'./&-'9$-:-+$&%$.6-0$)/-$3+("//-*).-#)(/"''$&+#3'./&-'9$("3*#$/-'3*.$&+$(",":-,-+.=

h3//-+.*09$.6-/-$&'$+"$("+'-+'3'$),"+5$-("+"4,&'.'$)'$."$76).$()3'-'$;3'&+-''$(0(*-'$)+#9$&+$1)/.&(43*)/9$.6-&/$8-0$%-).3/-9$(",":-,-+.=$T.$.6-$'),-$.&,-9/-'-)/(6-/'$)/-$-B1*"/&+5$)$*)/5-$/)+5-$"%$1"''&;&*&.&-'=F-B.9$7-$1/":&#-$)$'-*-(.&:-$":-/:&-7$"%$.6&'$/-'-)/(6=

T$+).3/)*$'.)/.&+5$1"&+.$&'$76).$&'$1-/6)1'$.6-,"'.$.6"/"356*0$#-:-*"1-#$.6-"/0$"%$;3'&+-''$(0(*-'9.6-$)%(5,-610&%11,!.!5%$.6-"/0$)''"(&).-#$7&.6$l0#*)+#)+#$c/-'("..$I?R@\J9$i"+5$)+#$c*"''-/$I?R@aJ9$)+#c/-'("..$I?R@_J=!!$U-$%"(3'$'1-(&%&()**0$"+$.6-$1'(&7+()+,)%(5,-610&%11,!.!5%,#"+%59$#-:-*"1-#$&+$`)+'-+I?R@ZJ$)+#$)+)*0D-#$&+$c/-'("..$I?R@_J=$T*.6"356$.6).,"#-*$1"'&.'$)+$)55/-5).-$'6"(89$&.$&'$&+("+'&'.-+.7&.6$;3'&+-''$(0(*-$(",":-,-+.=$U-$.6-+$-B1*"/-.7"$'-.'$"%$,"#&%&().&"+'$."$.6&'$,"#-*=$E6-$%&/'.$()+;-$:&-7-#$)'$+).3/)*$-B.-+'&"+'$"%$.6-$,"#-*=$E6-'-("+#$#-1)/.$,"/-$'&5+&%&()+.*0$%/",$.6-$,"#-*L')''3,1.&"+'=

Standard real business cycle theory12

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Natural extensions of the standard theory

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comovement

FIGURE 6

importance of intermedia te goods channe l to investment sector (lc )

Printing (0 .02)Transportation, communication,and public utilities (0 .13)

Apparel (0.02) Reta iltrade (0.07)

Paper (0.02)Chemicals (0 .03)

Rubber (0.02)

Textiles(0.01)Leather products (0.00)

Services (0 .28)

Finance, insurance,and real estate (0.21)

Food (0.06)

Tobacco (0.01)

Agriculture (0 .04)

Mining (0.02)

Petroleum (0.02)

Wholesaletrade (0.07)

Note: Plot of sector is ca lcula ted us ing the comovement sta tistic reported intable 1 and as expla ined in note 6 . The number in parentheses following the sectorname indica tes the re la tive s ize of tha t sector.Source: Authors’ ca lculations from data of DRI Bas ic Economics database , 1964–96 .


TABLE 2

>?72$1%)#*)(&"7&%='/)/#2$1%2%.&7"'&0

Person B

H igh e ffor t Low e ffor t

Person A H igh e ffor t (5 , 5) (–5 , 0)Low e ffor t (0 , –5) (2 , 2)

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3 0) [ ( )cos( ) ( )sin( )] ,x a t b t dt = ! +ω ω ω ω ωπ

76-/-$-IωJ$)+#$4IωJ$)/-$%3+(.&"+'$"%$ω=$Q+$:&-7$"%.6-'-$";'-/:).&"+'9$&.$&'$1-/6)1'$+".$'3/1/&'&+5$.6).

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4) [ ( )cos( ) ( ) sin( )] .y a t b t dt = ! +ω ω ω ω ωωω

Q.$&'$7-**$8+"7+$.6).$+!$()+$;-$(",13.-#$)'$)$1)/4.&(3*)/$(-+.-/-#$,":&+5$):-/)5-$"%$";'-/:).&"+'$"+.6-$";'-/:-#$#).)9$5!

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76-/-

61 2

0

)

sin( ) sin( ) , , , ...

.

B B j jj

j

B

j j= =−

=

=−

−

ω ω

πω ω

π

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7 0 1 1 1) ( )

( ).

y B x B x x

B x xt t t t

K t K t K

= + + +

+ +

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t tE y y=

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9 0 112 0 1 2 1

) , , ...,

... .

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B B B B Bj j

K K

= = −

= − + + + + −

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a t x

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j T j tt

T

j T j tt

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=

2

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ω

ω

G1(":

a t x T

b x T

T T tt

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T tt

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TECHNICAL APPENDIX 2

Comovement and the elasticityof substitution

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EC L

t

t t t0

0

111

βσ

ψ σ

=

∞−

∑−

−

( ),


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c k k k L zt t t t t t+ − − ≤ − +!"##

$%&&+

− − −

1

1 1 11 1( ) ( ) .δ α α

ν

ν

ν

ν

ν

ν

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log( ) log( ) , ,z zt t t= + < <−ρ ε ρ1 0 1

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αψν ν

νCL

z CL LC c i

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1

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α

ψ

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ε=

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TECHNICAL APPENDIX 3

Analysis of the input–output tables

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TABLE A1

I–O industry number I–O industry title

1+2+3+4 Agriculture , forestry, and fisheries 0.060 0.894 0.052 –0.0065+6+7+8+9+10 Mining 0.207 0.893 0.181 –0.28214 Food and k indred products 0.018 0.962 0.041 –0.02115 Tobacco products 0.000 0.914 0.000 0.08616+17 Textile mill products 0.185 0.995 0.072 –0.25218+19 Appare l and other textile products 0.037 1.284 0.041 –0.36224+25 Paper and a llied products 0.103 0.833 0.112 –0.04726A+26B Printing and publishing 0.058 0.795 0.121 0.02627A+27B+28 Chemica ls and a llied products 0.180 0.698 0.138 –0.01631 Pe troleum re fining and re la ted products 0.105 0.782 0.145 –0.03232 Rubber and misce llaneous plastics products 0.246 0.761 0.127 –0.13433+34 Footwear, lea ther, and lea ther products 0.031 2.154 0.037 –1.22265A+...+68C Transpor ta tion, communica tions , and utilities 0.107 0.740 0.123 0.02969A Wholesa le trade 0.232 0.589 0.098 0.08269B Re ta il trade 0.066 0.919 0.015 0.00070A+70B+71A+71B Finance , insurance , and rea l esta te 0.061 0.877 0.043 0 .02072A+...+77B Services 0.076 0.879 0.044 0.002

Notes: Yi measures amount of gross output of industry in indica ted row sent directly or indirectly to industry i, where i = I f, C, G , O .Row numbers are sca led so they sum to unity.Source: Authors’ ca lculations based on data from U.S . Department of Commerce , Bureau of Economic Ana lys is , 1992 ,Survey of Current Bus iness , Volume 72 , Number 4 , April.


/(.-0).+,%"+&%&*%&.-'1)#%&

TABLE A2

I–O industrynumber I–O industry title

11 New construction 0.805 0.000 0.195 0.00012 Ma intenance and repa ir construction 0.180 0.574 0.243 0.00213 Ordnance and accessories 0.011 0.051 0.838 0.10020+21 Lumber and wood products 0.542 0.340 0.169 –0.05122+23 Furniture and fixtures 0.477 0.585 0.067 –0.12829A Drugs 0.018 0.963 0.125 –0.10729B C leaning and toile t prepara tions 0.018 0.949 0.033 0.00030 Pa ints and a llied products 0.422 0.445 0.168 –0.03635 Glass and glass products 0.202 0.798 0.116 –0.11636 Stone and clay products 0.575 0.314 0.206 –0.09537 Primary iron and stee l manufacturing 0.515 0.501 0.207 –0.22338 Primary nonferrous me ta ls manufacturing 0.400 0.485 0.247 –0.13239 Meta l conta iners 0.057 0.891 0.064 –0.01240 Hea ting, plumbing, and fabrica ted structura l me ta l products 0.604 0.201 0.198 –0.00241 Screw machine products and stampings 0.358 0.641 0.132 –0.13142 Other fabrica ted me ta l products 0.377 0.573 0.175 –0.12443 Engines and turbines 0.377 0.362 0.246 0.01544+45 Farm, construction, and mining machinery 0.731 0.151 0.097 0.02146 Ma teria ls handling machinery and equipment 0.876 0.134 0.105 –0.11547 Me ta lworking machinery and equipment 0.779 0.261 0.108 –0.14748 Specia l industry machinery and equipment 0.962 0.154 0.028 –0.14549 Genera l industria l machinery and equipment 0.729 0.305 0.130 –0.16450 Misce llaneous machinery, except e lectrica l 0.309 0.438 0.258 –0.00651 Computer and office equipment 0.786 0.148 0.156 –0.09052 Service industry machinery 0.636 0.289 0.120 –0.04553 E lectrica l industria l equipment and appara tus 0.639 0.308 0.168 –0.11454 Household appliances 0.242 0.842 0.045 –0.12955 E lectric lighting and wiring equipment 0.471 0.447 0.185 –0.10456 Audio, video, and communica tion equipment 0.626 0.564 0.206 –0.39657 Electronic components and accessories 0.338 0.437 0.322 –0.09758 Misce llaneous e lectrica l machinery and supplies 0.321 0.687 0.148 –0.15659A Motor vehicles (passenger cars and trucks) 0.478 0.776 0.051 –0.30459B Truck and bus bodies , tra ilers , and motor vehicles par ts 0.437 0.746 0.080 –0.26360 Aircra ft and parts 0.134 0.049 0.546 0.27061 Other transporta tion equipment 0.145 0.543 0.336 –0.02462 Scientific and controlling instruments 0.442 0.166 0.372 0.02063 Ophtha lmic and photographic equipment 0.347 0.590 0.228 –0.16564 Misce llaneous manufacturing 0.175 1.121 0.071 –0.36878 Federa l government enterprises 0.079 0.814 0.104 0.00379 Sta te and loca l government enterprises 0.033 0.928 0.043 –0.00380 Noncomparable imports 0.000 0.000 0.000 0.00081 Scrap, used, and secondhand goods –9.699 7.493 1.830 1.37782 Genera l government industry 0.000 0.000 1.000 0.00083 Rest of the world adjustment to fina l uses 0.000 0.000 0.000 0.00084 Household industry 0.000 1.000 0.000 0.00085 Inventory va lua tion adjustment 0.000 0.000 0.000 1.000

Notes: Yi measures amount of gross output of industry in indica ted row sent directly or indirectly to industry i , where i = I f, C , G , O .Row numbers are sca led so they sum to unity.Source: Authors’ ca lculations based on U.S . Department of Commerce , Bureau of Economic Ana lys is , 1992 ,Survey of Current Bus iness , Volume 72 , Number 4 , April.


NOTES

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αψ

ξ

CL

CL Lc c i

=− −( )

.1

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α

ψξ( ) .1− − =L L Lc i c

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α

ξξ( ) .1− − − =L L L Lc i x c

[=);$*#1@:%*"I%)#%)(%?"(()<1$%/"0%<"#&%9+%'*;%9#%#"%<$%?0"5@51)65'1:%'(%1"*2%'(%9-%)(%(7//)5)$*#1@%5"7*#$05@51)5'13

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)%9!/ψC+B%O%ψ,`:%I&$0$%ψ:%ψ

)%k%.%'*;%8%)(%'%5"*6

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ψ3%47<(#)#7#)*2%#&)(%)*#"%#&$%$8?1"@8$*#%5"*;)#)"*%)*%*"#$BY%0$(71#(%)*

α ψ ψCL

L Lc

c i= +0 ( ) .

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