Business Cycle Accounting of the BRIC Economies

Munich Personal RePEc Archive

Business Cycle Accounting of the BRIC Economies

Chakraborty, Suparna and Otsu, Keisuke

University of San Francisco, University of Kent at Canterbury, UK

30 August 2012

Online at https://mpra.ub.uni-muenchen.de/47451/

MPRA Paper No. 47451, posted 07 Jun 2013 01:18 UTC

BUSINESS CYCLE ACCOUNTING OF THE BRIC ECONOMIES

Suparna Chakraborty University of San Francisco

Keisuke Otsu University of Kent June 01, 2013

1

BUSINESS CYCLE ACCOUNTING OF THE BRIC ECONOMIES

June 1, 2013

Abstract

We app^l the Business^{C l} Accoun^{t m t d}o^{l d}v^ledby Chari, Kehoe an^d McGrattan ⁽2007) to ^stdy the e ^m res^u e of Br^a i^l Russia, In^{d aad}China^{( C)}over the^last^{dad W}e^d cu^m t that^{w l}e

ciency ^{wd s d} contribute in a^{la u} part to ^uo^{w t}especi^all in Br^{a l}

adRussia, there is an increas ^{m e}ortance of inv^stm nt^we^ds espe^all in the^late2000s,^{t d}in China^adIn^{d a} The res^ltsare t ^{e all}y r^{lat d}to the^{sta s}of^d ve^lop^m t^{w t} Br^{a l}an^dRussia^moa crisis to^uo^win the2000s,^w i^{l d}ia^adChina^were on a co^mparativ^{l staluwt eat}

lat n ^wd patterns to institution^{al ad}nancia^l re^{f ums w}e n^d that

…n^{a al ma u}et ^dev^{l em} nts ^{ad o}ective vernance in BRICs in the ^last

d ad are consistent ^{w t} i^mprov^m ts in invest^m nt ^ad e ciency ^we^ds that^{l d}to^uo^wt

K wor^ds BRIC, business cyc^l accountin e ciency, ^{ma u}et frictions, tre^dshocks, invest^ment ^{ad stm} t costs

JEL Co^ds E32, E^{6 6}

At its simplest, a growth economy should be regarded as one that is likely to experience rising productivity, which, together with favorable demo- graphics, points to economic growth that outpaces the global average...So we opted for the following: any economy outside the so-called developed world that accounts for at least 1% of current global GDP should be de-

…ned as a growth economy^{. —————–}Ji ^{ON & H} of

GobaE^{c c} Research at^G Sach^!"

1 Introduction

Over the ^#ast ^$eca^$e, the avera^ge ^gro^%th rate of Bra^zi^#, Russia, In^$ia an^$ China, or BRICs, has outpace^$ the^g#oba^#avera^ge^%ith their cu^'u^#ative share in the ^%or^#$

G^{DP g}ro^%in^g fro^' about16% in 2000 to 26% in 2011^. China an^$ In^$ia stan^$ 2nd an^$ 3rd in ^%or^#$ G^DP rankin^g by ^PPP co^'parisons ^*the top spot sti^## be^#on^gs to the Unite^$ States⁺,^%hi^#e Russia an^$Bra^zi^# ranks6th an^$7th ^*Table 1^+.

<Table 1 about here>

The broa^$facts of BRIC resur^gence are^genera^##y^%e^##kno^%n^*Table 2^{1+. ,}hi^#e Bra^zi^#an^$In^$ia starte^$the1960sc^#oser to their US an^$OEC^Dcounterparts, China fa^#tere^{$2. D}urin^g the 1970s, China p^#aye^$ catch^-up an^$ Bra^zi^{# g}re^% stea^$i^#y, but In^$ia^$ec^#ine^$. The tab^#es turn in the 1980s^%ith Bra^zi^#ian^gro^%th s^#o^%in^gas In^$ia

'a^$e a co^'e^-back^. 1990s ^%ere a perio^$ of econo^'ic an^$ po^#itica^# turbu^#ence for the BRICs thou^gh the ne^gative i^'pact ^%as stron^ger in Bra^zi^# an^$ Russia^. Fina^##y,

$urin^g the ^#ast ^$eca^$e of 2000s, a^## BRIC nations ^'a^$e a re^'arkab^#e co^'e^-back surpassin^g their historica^# perfor^'ance ^%ith China in the ^#ea^$.

<Table 2 about here>

In this paper, ^%e perfor^' an e^xp^#oratory ana^#ysis of the ^‡uctuations in output of the BRIC econo^'ies over the ^#ast t^%o ^$eca^$es ^- the re^#ative sta^gnation of the 1990s fo^##o^%e^$ by the econo^'ic recovery of the 2000s usin^g the Business Cyc^#e Accountin^{g *}BCA^{+ “%}e^$ge^”'etho^$o^#o^gy for^'u^#ate^$ by Co^#e an^$ Ohanian ^*2004⁺ an^$ Chari, Kehoe an^$ McGrattan^*henceforth CKM,2007⁺a^'on^gst others^.

Takin^g a cue fro^' Ca^#vo ^*2000⁺, BCA focuses not on i^$enti^/cation of pri^'ary forces^#ike po^#icy chan^ges or institutiona^# refor^'s that a^¤ect the econo^'y, rather on

1T^{0 1 234} 1^{0 5 7} 2 are^{89: ;}the IMF an⁷ An^{< =4}M0 7 7i4: 5 >s on^{2 i}ne⁷ata resources^{? @3 A0 i2}s of the histori^{0 2A i;3 2 i}ne are in the on²ine app^{35 7}i^B?

2

Eer capita ^{F@ E <9}o^{IA J} rate is ^2:I in ^{L90 Qi 2} c^{: ;R0 93 7} to 0 < < 93< 0 A3 F@ E < 9o^{IA J 7}ue to an

3BR0 5 7 i5 <pop= 20 Ai: 5 ?

the channe^Ss throu^Th ^Uhich these factors ^Uork^V The techni^que uses an rea^S busi^X ness cyc^Se ^YRBC^Z fra^[e^Uork ^Uith four channe^Ss^\ ti^[e varyin^T pro^]uctivity ^{Y^}e^{¢ X} ciency ^Ue^]Tes^{^Z}, ^Sabor ta^_es ^{Y^S}abor ^Ue^]Tes^{^Z}, ta^_es on invest^[ent ^{Y^}invest^[ent

Ue^]Tes^{^Z} an^{] T}overn^[ent consu^[ption^{3 Y^T}overn^[ent consu^[ption ^Ue^]Te^{^ZV} The BCA^[etho^]o^So^Ty is i^[p^Se^[ente^]in t^Uo steps^V In step one, the^`rst or^]er con^]itions of a stan^]ar^] RBC ^[o^]e^S a^Son^{T U}ith ^[acroecono^[ic ^]ata is use^] to esti^[ate the

Ue^]Tes^V In step t^Uo, the esti^[ate^{] U}e^]Tes fro^[ step 1are fe^] back into the ^[o^]e^S in^]ivi^]ua^SSy an^] in ^]i^berent co^[binations to ascertain their ^[ar^Tina^S contributions in^Teneratin^T the observe^] econo^[ic outco^[e^hV

App^Sication of the BCA ^[etho^]o^So^Ty to the BRICs i^]enti^`es t^Uo ^[a^jor chan^X ne^Ss at ^Uork^\ i) Bra^ki^Sian an^] Russian crisis of the 1990s is pri^[ari^Sy the resu^St of

]istortions in invest^[ent an^{] S}abor ^[arkets ^Yparticu^Sar^Sy in Bra^ki^SZV The ^Tro^Uth of the 2000s ho^Uever is the han^]i^Uork of i^[prove^[ents in e^¢ ciencyⁿ ii) in contrast, in China an^] In^]ia, both re^Sative^Sy stab^Se in the 1^pp0s, e^¢ ciency ^Ue^]Tes p^Say an i^[portant ro^Se ti^{SS [}i^]X2000s, after ^Uhich ^]ec^Sinin^T invest^[ent ^[arket ^]istortions beca^[e increasin^TSy i^[portant for the rapi^] recovery^rV These ^{`</sup>n<sup>]</sup>in<sup>T</sup>s su<sup>TT</sup>est that institutiona<sup>S</sup>an<sup>]</sup>po<sup>S</sup>icy refor<sup>[</sup>s at the core of the BRIC resur<sup>T</sup>ence<sup>U</sup>orke<sup>]</sup>pri<sup>[</sup>ari<sup>S</sup>y by increasin<sup>T</sup> pro<sup>]</sup>uction e<sup>¢</sup> ciency an<sup>]</sup> re<sup>]</sup>ucin<sup>T</sup> invest<sup>[</sup>ent <sup>[</sup>arket frictions to ai<sup>]</sup> capita<sup>S</sup> accu<sup>[</sup>u<sup>S</sup>ation<sup>V</sup> Our pri<sup>[</sup>ary <sup>`}n^]in^Ts are robust to three a^]]itiona^S checks^X

Ya^Zintro^]uction of capita^Sa^]just^[ent costs, kno^Un to a^Ster bench^[ark BCA resu^Sts

YChristiano an^]vavis,2006);^Yb^Zfactor hoar^]in^Tto a^]]ress concerns about^[is^[an^X a^Te^[ent of e^¢ ciency^Ue^]Tes an^]Yc^Zs^[a^SS, open econo^[y settin^T as in^[ost BRICs

Uith separation of transitory an^] tren^] shocks a^bectin^T pro^]uctivity ^Y A^Tuiar an^] Gopinath, 2007^Z,

Our app^Sication a^]]s to the e^_tensive ^Siterature on BCA^YCKM, 2007ⁿ Kerstin^T, 2008ⁿChakraborty,2009ⁿKobayashi an^]Inaba, 2006ⁿCho an^]vob^Sas^XMa^]ri^]2012, Otsu 2010aⁿ La^[a2011^Z, ^Uith the e^_ception that in contrast to the e^_istin^Tstu^]ies our ob^jective is to stu^]y not^just a crisis, but the eventua^S recovery^V Secon^]Sy,^Uhi^Se China an^]In^]ia, has^Tarnere^][ost attention a^[on^Tst the BRICs^YSon^T, Stores^Setten an^{] y}i^Sibotti 2011, ^vek^Se an^{] {}an^]enbroucke 2012, Jones an^] Sahu, 2009; Hseih an^] K^Seno^U 2009^Z, ^Ue brin^T a^SS BRIC nations on the sa^[e ana^Sytica^S p^Satfor^[ to perfor^[ a ^joint ana^Sysis over an e^_ten^]e^] ti^[e perio^{] Y}1990 to 2009^ZV This turns out to be crucia^S for unearthin^T the ro^Se of invest^[ent ^[arket frictions, a channe^S

[ost^Sy i^Tnore^] in BCA ^Siterature ^Uith a fe^U e^_ceptions^V Focusin^T separate^Sy on perio^]s of crisis an^]recovery^Ue^`n^], si^[i^Sar to Cava^Scanti, E^Sose^Tui, McCan^]Sess^|

3In a^{} ~ € ‚} econ^{ ƒ}y set^„up, net^{† ˆ}orts are^{‰ ‚‚‚}to^{Š }vern^{ƒ ‹}t consŒ ƒˆŽ  ‹

For† ‰ ƒˆ ~‘ if BCA e^†ercise^{Ž‚ ‹Ž’}es^•ciency^˜e^{‚Š €}as a^ƒ‰™or p^~ayer, the interpretation is that ^{˜š‰  ›}er pri^{ƒ‰ œ} factors are respon^€Žž~ for output ^{Š œ˜š‘} they^˜ork by ^{Ž ƒˆ}ro^{›Ž ‹Š} the

‹‰ Ž  ‹Ÿs e^•ciency or pro^‚Œ}tivity^¡

£The ro^~ of ^{~‰ ž}or an^{‚ Š}v^{ œ‹ ƒ}ent consu^{ƒˆŽ  ‹ ˜}e^{‚Š €} turn out to be ^{€ ƒ˜š‰ } sensitive to

ƒ‚ ~speci^’cation^€

B^¥anco^¦2008^§, that^¨orsenin^©invest^ªent frictions can e^«p^¥ain a si^©ni^¬cant portion of business cyc^¥e^­o^¨nturns^{® ¯}e further^­etect that^­ec^¥inin^© invest^ªent frictions an^­ capita^¥ accu^ªu^¥ation can a^¥so he^¥p sustain ^©ro^¨th^® This contrasts ^¨ith the ear^¥ier

¬n^­in^©s of Jones an^­ Sahu ^¦2008^§ for In^­ia an^­ La^ªa ^¦2011^§ for Latin A^ªerica,

¨here a sa^ªp^¥e ti^{¥¥ ª}i^­°2000s un^­er^ªines the potentia^¥ ro^¥e of invest^ªent ^ªarket

±uctuations^®

Fina^¥¥y,^¨e atte^ªpt to tie the observe^­¨e^­©e patterns^¨ith so^ªe in^­ices of insti^° tutiona^¥ an^­ po^¥icy chan^©es in the BRICs^® A^©ro^¨in^©¥iterature in recent years have foun^{­ ª}icro^°¥eve^¥ evi^­ence of in^±uence of cre^­it ^ªarket ^ªove^ªents on invest^ªent an^­ econo^ªic ^©ro^¨th^¦Bekaert, Harvey an^­ Lun^­b^¥a^­, 2011^² A^¥faro, Ka^¥e^ª¥i^°O^³can an^­ Sayek, 2009^§® BRICs fo^¥¥o^¨e^­ a consistent po^¥icy of easin^© cre^­it ^¨ith priva^° ti^³ation, ^¬nancia^{¥ ¥}ibera^¥i^³ation an^­ openin^© up^´® The i^ªpact of such po^¥icies is observe^­ in i^ªprove^­ cre^­it^°ratin^©s an^­ cre^­it avai^¥abi^¥ity^® In^­ices of institutiona^¥ an^­po^¥itica^¥ refor^ªs pub^¥ishe^­by the^¯or^¥­ Bank su^©©ests i^ªprove^ªent in^©overn^°

ªent e^µectiveness in a^¥¥ BRICs an^­ po^¥itica^¥ stabi^¥ity ^¦ªost^¥y in Russia^§ that are con^­ucive to ^©ro^¨th an^­ recovery, but other areas of concern re^ªain, ^¨ith contro^¥ of corruption bein^© the Achi^¥¥es^¶hee^¥®

The re^ªain^­er of the paper is or^©ani^³e^­ as fo^¥¥o^¨s^® In section 2; ^¨e ^­escribe the business cyc^¥e accountin^{© ª}o^­e^¥® In section 3; ^¨e e^«p^¥ain the business cyc^¥e accountin^© proce^­ure an^­ present the resu^¥ts^® In section 4; ^¨e provi^­e sensitivity ana^¥ysis resu^¥ts^® In section 5; ^¨e ^­iscuss the un^­er^¥yin^© factors that can e^«p^¥ain the evo^¥ution of ^¨e^­©es^® Section6 conc^¥u^­es the paper^®

2 The Benchmark Model

BCA^ªetho^­o^¥o^©y uses a stan^­ar^­, c^¥ose^­econo^ªy neoc^¥assica^{¥ ©}ro^¨th ^ªo^­e^{¥ ¨}ith a representative househo^¥­, ^¬r^ª an^­ a ^©overn^ªent^® The representative ^¬r^ª hires

¥abor an^­ capita^¥fro^ª the househo^¥­ to pro^­uce output usin^©a constant returns to sca^¥e techno^¥o^©y, ^¨hich is a^µecte^­ by ti^ªe^°varyin^©pro^­uction e^· ciency^® The repre^° sentative househo^¥­­eci^­es on consu^ªption,^¥abor an^­invest^ªent each perio^­® The househo^¥­faces a bu^­©et constraint^¨here its e^«pen^­iture is^¥i^ªite^­by its^¥abor an^­ capita^¥inco^ªe^® In a^­­ition, as the u^¥ti^ªate o^¨ner of the^¬r^ª, the consu^ªer receives the pro^¬ts^® The consu^ªer pays^­istortionary ta^«es on ^¥abor an^­ capita^¥ inco^ªe to the^©overn^ªent^® In the BCA fra^ªe^¨ork, these ^­istortionary ta^«es represent broa^­er econo^ªic^­istortions that a^µect the factor^ªarkets^® The^©overn^ªent uses its ta^« rev^° enue to^¬nance^©overn^ªent consu^ªption^® Any re^ªainin^©a^ªount is transferre^­back to the househo^¥­s as^¥u^ªp su^ªtransfers^® E^«o^©enous shocks to pro^­uction e^· ciency,

¸

¹e^{º »¼ ½¾ ¿}n the^{ÀºÁ ¾¿½Â}in the^{Ã Ä ½¿Ä º}appe^{Ä À¿»Å}

Æovern^Çent consu^Çption an^{È È}istortionary ta^É rates are revea^Êe^È in the be^Æinnin^Æ of each perio^È an^È a^Ëect econo^Çic incentives^Ì

2.1 Firm

The representative^Ír^Çborro^Îs capita^ÊKtan^ÈÊaborLtfro^Çthe househo^ÊÈin or^Èer to pro^Èuce output Yt accor^Èin^Æ to a Cobb^ÏÐou^ÆÊas pro^Èuction function^Ñ

Yt =K_t(AtLt)¹ ;

Îhere At ^Èenotes e^Éo^Æenous pro^Èuction e^Ò ciency^Ì Labor is ^Èe^Íne^È as tota^Ê hours

Îorke^ÈÓpro^Èuct of e^Çp^Êoy^Çent an^Èhours^Îorke^Èper^Îorker^{ÔÌ Õ}ro^Èuctivity can be

Èivi^Èe^Èinto a tren^Èco^Çponent tan^Èa cyc^Êica^Êco^Çponentzt, i^Ìe^Ì At=zt t,^Îhere

Îe assu^Çe a constant^Æro^Îth rate in the tren^Èco^Çponent in the bench^Çark^Ço^Èe^ÊÌ Labor ^Æro^Îs over ti^Çe ^Èue to constant ^Æro^Îth in popu^Êation Nt at the rate of n^Ì Output an^Ècapita^ÊÆro^Îs over ti^Çe^Èue to both popu^Êation an^Èpro^Èuctivity^Æro^Îth^Ì A^ÊÊ variab^Êes are ^Èetren^Èe^È by the ^Æro^Îth tren^Ès in or^Èer to ^Èe^Íne a stationary prob^Êe^ÇÑ

yt= Yt

Nt t

; kt = Kt

Nt t

; lt= Lt

Nt

; zt= At t

: The ^Èetren^Èe^È pro^Èuction function can be re^Îritten as

yt=k_t(ztlt)¹ : ^Ó1^Ô

The ^Èetren^Èe^È pro^Ít^Ça^Éi^Çi^Öation prob^Êe^Çis

max t=yt rtkt wtlt ^Ó2^Ô

Îhere rtan^Èwt^Èenote the rea^Êreturn on capita^Êan^Èthe rea^ÊÎa^Æe respective^Êy^Ì For the bench^Çark^Ço^Èe^Ê,^Îe fo^ÊÊo^ÎCKM^Ó2007^Ôan^ÈÈe^Íne the e^Ò ciency^Îe^ÈÆes as the

Èetren^Èe^È pro^Èuctivity^Ñ

!e;t =zt: ^Ó3^Ô

2.2 The Household and Government

The representative househo^{ÊÈ Æ}ains uti^Êity fro^Ç consu^Çption ct an^{È Ê}eisure 1 lt

Îhere ^Îe assu^Çe a ^Êo^ÆÏÊinear uti^Êity function^×Ñ

u(ct;1 lt) = lnct+ (1 ) ln(1 lt):

Ø

Ùe^{Ú Û ÜÝÞÝ ßà}uct an^{áâ áãÞä Üáåä æç}Cobb^{èé Ýêë ÛÚ}s preferences^åäth hi^ëçer e^Ûasticity of substitution presente^à in the appen^{àä âì}

Tota^í hours avai^íab^íe is nor^îa^íi^ïe^ð to one^ñ The househo^{íð î}a^òi^îi^ïes its e^òpecte^ð

íifeti^îe uti^íity^ó

maxEtP

t

t[u(ct;1 lt)];

ôhere is the sub^õective^ðiscount factor^ñ The househo^íð bu^ðöet constraint is (1 l;t)wtlt+ (1 k;t)rtkt+ t+ t=ct+xt; ^÷øù

ôhere lt an^ð kt are ^ðistortionary ^íabor an^ð capita^í inco^îe ta^òes ^ôhi^íe t is the

íu^îp^úsu^{î ö}overn^îent transfers^ñ Invest^îent xt is ^ðe^ûne^ð by the capita^{í í}a^ô of ^îo^ú tion^ó

n kt+1 =xt+ (1 )kt: ^÷üù

The ^öovern^îent co^ííects ^ðistortionary ta^òes fro^î the househo^íð in or^ðer to ^ûú nance consu^îption an^ð the ba^íance is transferre^ð to the househo^íð in a ^íu^îp^úsu^î fashion^ñ Therefore, the^öovern^îent bu^ðöet constraint is^óý

gt+ t = ltwtlt+ ktrtkt: ^÷þù Co^îbinin^öthe^öovern^îent bu^ðöet constraint^÷þùan^ð the househo^íðbu^ðöet con^ú straint^{÷ø ùî}akin^öuse of the^ðe^ûnition of pro^ûts^÷2^ù,^ôe obtain the resource constraint

yt=ct+xt+gt: ^÷ÿù

Since^öovern^îent consu^îption re^ðuces the avai^íab^íe resources for the private sector in the econo^îy,^ôe^ðe^ûne this as the^öovern^îent consu^îption^ôe^ðöe fo^íío^ôin^öCKM

÷200^{ÿ ùó}

!g;t=gt: ^÷8ù

Labor an^ð invest^îent^ôe^ðöes f!l;t; !k;tg are^ðe^ûne^ð as^ó

!l;t = 1 lt;

!k;t = 1 kt:

Technica^ííy speakin^ö, lt ^ðrives a ^ôe^ðöe bet^ôeen the consu^îption^úíeisure ^îar^öina^í rate of substitution an^ð the ^îar^öina^í pro^ðuct of ^íabor ^ôhi^íe kt ^ðrives a ^ôe^ðöe bet^ôeen the interte^îpora^íîar^öina^írate of substitution an^ðthe^îar^öina^íreturn on invest^îent^ñ If there are no ^îarket ^ðistortions, lt an^ð kt ^ôou^íð be ^ïero i^îp^íyin^ö

!l;t =!k;t = 1: This^ôou^íð yie^íðthe^ûrst best outco^îe^÷as can be seen fro^îthe^ûrst or^ðer con^ðitions out^íine^ð in section 2:4^ùñ

Note that uⁿ r the^{t t} ona^l BCA architecture⁽CKM,2007) the^l or ^{nc t lw g} are^{m l}as^t es on^l or in^{c m} ancapi^{t ln c m} respectiv^le, y^lin^gthe u ^{s lg} v^nm nt bu^{g t}constrain^t

2.3 Wedges

We ^dene the e^¢ ciency, overnent consuption, investent an^d abor e^des

!t = (!e;t; !g;t; !k;t; !l;t)⁰ such that an increase in each e^de shou^d ea^d to an increase in output^. Increases in e^¢ ciency e^de ^directy increases pro^duction an^d stiuates factor ^dean^d by increasin the arina pro^duct of inputs^. On the other han^d, increases in abor 1 lt an^d investent e^des 1 kt, hich by construction ipy a ^decine in abor arket friction lt or investent arket friction kt respectivey, stiuate output by encourain the househo^d to increase suppy of factor inputs throuh an increase in the arina incoe associate^d ith the^. An increase inovernent consuptione^de increases output by increasin areate ^dean^d9. Fooin CKM 2007, e assue that the e^des are e^x- oenous an^d foo a stochastic process^{. D}enin a vector of o^-ineari^ze^d e^des,

e

!t = (g!e;t;g!g;t;g!k;t;!fl;t)⁰ here !et = ln!t ln!,e assue that thee^des foo arst or^der^VAR process^:

e

!t = P!gt 1+"t

"t N(0; V)

here "t= ("e;t; "g;t; "k;t; "l;t)⁰ are innovations to thee^des^. FooinCKM2007

e ao spi^-over of e^des throuh P an^d conteporaneous correations of inno^- vations inV^.

2.4 Equilibrium

The copetitive e^quiibriu is iven by a price vector frt; wtg an^d an aocation of^quantitiesfyt; ct; xt; lt; kt; zt; gt; t; !e;t; !g;t; !k;t; !l;tgsuch that^: athe househo^d

a^xii^zes utiity iven frt; wt; t; !k;t; !l;tg^; b the r a^xii^zes prots iven frt; wt; ztg^;ctheovernent bu^det constraint⁶ an^dthe resource constraint ⁷ ho^ds^;an^ddthee^des foothe stochastic process^. The copetitive e^quiib^- riuis characteri^ze^dby a set ofrst^-or^der con^ditionsiven by^: athe capitaEuer e^quationrst or^der con^ditionith respect to capitae^quai^zinpresent ^discounte^d vaue ofarinautiity of future consuption to itsarina cost^:

1 ct

=bEt

1 ct+1

!k;t+1

yt+1

kt+1

+ 1 ; 10

here b = _n , b the rst^-or^der con^dition ith respect to abor e^quatin arina rate of substitution beteen consuption an^d eisure to the arina pro^duct of

A is ^!of househ ^oconsu ^"private inve^! t anovernt

#en ^$%

&abor^'

1 ct

1 lt

=!l;t(1 )yt

lt

; ^*11⁺

*c⁺ the resource constraint ^{*,+ /}iven ^*0+, ^*1+ the capita^{& &}a² of ³otion ^*5+, an^{1 *}e⁺ the pro¹uction function^*1^{+ /}iven ^*3⁺⁴

3 Quantitative Analysis

3.1 Parameter Values

<e co^&&ect annua^& nationa^& accounts ¹ata for the perio¹ 1990 to 2009 fro^{3 P}enn

<or^&1 Tab^&es ^*P<T⁺ 7:0⁴, its up¹ate¹ version ^*P<T 7:1 pub^&ishe¹ in Nove³ber, 2012⁺ an¹ its e⁼tensions ³a¹e by ^>uncan Fo^&ey⁴ In a¹¹ition, ²e co^&&ect popu^&ation

1ata fro³LABORSTA¹atabase of Internationa^&Labor Or^/ani^?ation an¹househo^&1 e⁼pen¹iture ¹ata fro³ Euro³onitor G^&oba^& Market Infor³ation ¹atabase⁴ The ¹e^@ tai^&s of ¹ata construction are out^&ine¹in the ¹ata appen¹i⁼⁴ The key para³eter an¹ stea¹y state va^&ues are^&iste¹in Table 3⁴

The ^Brst step in BCA i³p^&e³entation is to obtain the para³eters of the ³o¹e^&

throu^/h usua^&ca^&ibration techni^Cues for each country⁴ Capita^&share is ca^&ibrate¹to

3atch the capita^& inco³e share¹erive¹ fro^{3 1}ata¹⁰⁴ The pro¹uctivity ^/ro²th tren¹ a is co³pute¹ as the avera^/e ^/ro²th rate of per capita output⁴ The popu^&ation

/ro²th tren¹ n is ¹irect^&y co³pute¹ fro³ a¹u^&t popu^&ation ¹ata¹¹⁴ The annua^&

1epreciation rate is co³pute¹fro³ tota^&capita^&stock an¹invest³ent¹ata¹²⁴ The preference ²ei^/ht is ca^&ibrate¹ usin^/ the stea¹y state ^&abor ^Brst or¹er con¹ition

*11⁺to³atch the avera^/e consu³ption^@output ratio an^1&abor^&eve^&in¹ata assu³in^/ that the stea¹y state^&abor²e^1/e is e^Cua^&to one¹³⁴ The stea¹y state e^E ciency²e^1/e is nor³a^&i^?e¹to one⁴ The stea¹y state ^/overn³ent consu³ption²e^1/e is ca^&ibrate¹ to³atch the avera^/e consu³ption^@output ratio an¹ invest³ent^@output ratio⁴

The ne⁼t step is to esti³ate the stochastic process of the²e^1/es^*F+for²hich²e e³p^&oy the Bayesian techni^Cues⁴ Structura^& esti³ation is necessary for the business cyc^&e accountin^/ proce¹ure since invest³ent ²e^1/es ¹epen¹ on e⁼pectations about the future state of the econo³y ²hich is not ¹irect^&y observab^&e⁴ The esti³ate¹

10

Ge f^{HI I HJ}G^{HI I K}n^{L M N N MO}an^{QR HSTU}te the^{K iR HSX}share of^{R YTK Z YI}fr^HSi YZK H iYIinc^HSXstatistics^[ These are0:474,0:475,0:294, an^Q0:401for^{\] Y^K I}, Russia,^_iQia an^QChina respectiv^{XI `[ G}e further

Y Qaust for the^{K STUZ X Q} service inco^SXfr^HSconsu^SX]QUr^YbIXfas e^hp^{I Y}ine^Q in the^{QYZ Y}appen^QKh[

11

Ge us^{X QZ HZ YI}popu^Iation for China since^Je^{Q H}not have ^{YQUI Z}popu^{I Y}tion^Qat^{Y [}

12

Ge construct the t^{HZ YI} capi^{Z YI} stock series as the su^S of net ^{jhX Q R YTK Z YI} stock ^{Y iQ} hou^fXk

pHIQQU] YbI Xf Y iQ the to^{Z YI} inve^{fZ SX i}t series as the s^US of^{r ]}oss ^{Q HSXfZ KR}capit^YI for^{S YZK H i}an^Q househ^HIQXhTen^{QK Z U]Xf}on^QUrab^Ie^f[

13This assu^{STZ K H i}is not i^STortant as the preference^{JXK r p}t^{Yi QfZXY Q}y state^{I X uXI}of^{I Yb}or^Je^QrXf

QHnot appear in the IKiXY]K ^XQf`fZ XSofXvU YZ K H if[