The co-movement of inflation and the real growth of output

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Myles Horace Booker
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1 he co-movemen of inflaion and he real growh of o Jae Ho oon PC Research nsie PR 47 amsng-dong Gangnam-g eol Korea (jhyoon@osri.re.kr Absrac n order o find o wheher here really are co-movemens beween inflaion and he real growh of o for he os-ww eriod his aer ados F arkov- wiching odel o solve he eqaion of Phillis Crve and he eqaion of kn s aw ogeher. he findings of his aer are as follows: inflaion is rocyclical in movemen wih he real growh of o dring he Korean War and he wo il hock eriods; and here is relaively lile evidence of co-movemen beween inflaion and real growh of o wih he exceions of he Korean War and he wo il hock eriods. Keyword: F arkov-wiching odel Hamilon filer Phillis Crve kn s aw co-movemen Korean War il hock inflaion Corresonding Ahor : Phone: ; fax: beowlfkorea@hanmail.ne

2 . nrodcion he relaionshi beween inflaion and he real growh of o has been assmed o be osiive and sable. ills (946 ichell (95 Kznes (93 fond a srong b no erfec conformiy in he movemens of rices and o boh for shor erm conracion and longer erm cycles. For he os-ww eriod cas (97 observed ha inflaion and nemloymen rae are negaively correlaed hs indicaing a sable Phillis Crve. However Cooley and hanian (99 arged ha wih he exceions of he wo world wars ariclarly dring he eriod of he Grea Deression ( and ar of he lae 9 h cenry here was relaively lile evidence of rocyclical rices over he las cenry and a half inclding he os-ww eriod. Cooley and hanian s (99 findings are qie differen from ankiw (989 who claimed ha in he absence of idenifiable real shocks sch as PEC oil rice changes inflaion ends o rise dring booms and fall dring recessions. Cooley and hanian s findings are also differen from Den Haan ( who fond ha he co-movemen beween o and rices is osiive in he shor rn and negaive in he long rn sing a VAR model. hs he rose of his aer is o find o wheher here really are co-movemens beween inflaion and real growh of o for he os-ww eriod. o esablish he relaionshi beween inflaion and he real growh of o we ado F arkov-wiching odel by oon (4 and agnolo F. Psaradakis. and ola. (5 o solve he eqaion of Phillis Crve and he eqaion of kn s aw ogeher. he meri of he F arkov-wiching odel is ha we can deal wih he roblem of simlaneos eqaions based on he Hamilon filer (989. he findings of his aer are as follows: inflaion is rocyclical in movemen wih he real growh of o dring he Korean War and he wo il hock eriods for he os-ww eriod; and here was relaively lile evidence of co-movemen beween inflaion and he real growh of o wih he exceions of he Korean War and he wo il hock eriods. he aer has been divided in 4 secions. ecion resens F arkov-wiching odel. ecion 3 smmarizes he emirical resls. ecion 4 concldes his aer.. F arkov-wiching odel n order o ge he consisen esimaion of he arameers of he arkov-swiching model in he simlaneos eqaions we consider he following F arkov- wiching odel.

3 3 U s Bs Γ + (... ~ N d i i U Σ ( where y y y Bs K K K z z z Γ K K K s ( U ( ( ' E U U E Σ is he x marix of joinly deenden variables B is an x marix and nonsinglar. is he x K marix of redeermined variables Γs is K x marix and rank( K. Us is x marix of he srcral disrbances of he sysem. hs he model has eqaions and observaions. he srcral errors are assmed as a nonsinglar -variae normal (Gassian disribion. is he covariance of he error erms. Σ is an x marix and osiive definie and no resricions are laced on i. is assmed ha all eqaions saisfy he rank condiion for idenificaion. Also if

4 lagged endogenos variables are inclded as redeermined variables he sysem is assmed o be sable. An orhogonaliy assmion E( U beween he redeermined variables and srcral errors is reqired and we assme he resence of conemoraneos correlaion b no ineremoral correlaion in (. f we assme ha he single arkov-swiching variable has an N-sae firs-order arkov rocess hen we can wrie he ransiion robabiliy marix in he following way: N N N N NN N ij j where ij Pr( j i wih for all i f or model involves only wo nobserved wo-sae firs order arkov-swiching variables sch as and he dynamics of arkov-swiching variables can be reresened by a single arkov-swiching variable in he following manner: if and if and 3 if and 4 if and 4 wih ij Pr( j i ij j o derive he F arkov-wiching odel in he simlaneos eqaions we can obain Pr( j ψ by alying a Hamilon filer (989 as follows: e : A he beginning of he h ieraion Pr( i ψ i N is given. And we calclae Pr( N i j ψ Pr( i j ψ 4

5 N i Pr( j ψ i Pr( i where Pr( j i i N j N are he ransiion robabiliies. e : Consider he join condiional densiy of y and nobserved which is he rodc of he condiional and marginal densiies: j variable f ( y j ψ f ( y j ψ Pr( j ψ from which he marginal densiy of y is obained by: N f ( y ψ f ( y j ψ j N f ( y j ψ Pr( j ψ j where he condiional densiy f y j ψ is obained from ( : ( f ( y j ψ / / (π de( Σ de( Bs ex( ( y Bs + zγs Σ ( y Bs + zγs ' ( where Σ ( Bs + Γs '( Bs + Γs y is he h row of he marix. z is he h row of he marix. Bs and Γ s is obained from (. e 3 : nce y is observed a he end of ime we dae he robabiliy erms: Pr( j ψ Pr( j ψ y f ( j y ψ f ( y ψ 5

6 f ( y j ψ Pr( f ( y ψ j ψ As a byrodc of he above filer in e we obain he log likelihood fncion: ln ln f ( y ψ which can be maximized in resec o he arameers of he model. 3. Emirical Resls e s consider he Phillis Crve. An regression for 949 o 4 sing annal daa for inflaion ( π and nemloymen rae in year is given by eqaion ( π π + e (3 (. (. (. where sandard errors of he arameers esimaes are reored in he arenheses. he regression (3 reveals saisically insignifican evidence of an inflaionnemloymen rade-off becase he arameer of nemloymen rae in he eqaion (3 reveals saisically insignifican. Figre deics he relaionshi beween inflaion π and nemloymen rae. Figre. inflaion π and nemloymen rae UNEP NFA 6

7 5 NFA UNEP From he eqaion (3 and Figre we can find ha he shor rn Phillis Crve does no remain sable. hese resls sgges s o ilize a arkov-wiching odel for he nsable Phillis Crve for he os WW eriod. o find o he relaionshi beween nemloymen and he real growh of o he eqaion of kn s aw for 949 o 4 is given by eqaion ( ν (4 y (.3 (.3 where y is he annal real growh of GDP is changes in he nemloymen rae in year. he eqaion of kn s aw in (4 reveals saisically significan evidence beween changes in he nemloymen rae and real growh of GDP. Figre. changes in he nemloymen rae and real growh of GDP DUNEP RGDP 7

8 5 RGDP DUNEP From he eqaion (4 and Figre we can find ha he sable kn s aw for he os-ww eriod. For he esimaion of Phillis Crve and kn s aw ogeher he roosed F arkov-wiching odel was alied which ados a simle wo-sae arkov swiching arameers in he simlaneos eqaions. π + e (5 α + + π φ + φ y + ν + φ + φ y + ν (6 where α α + α( + ( Pr( q Pr( q e ~ i. i. d. N( Σ q ν o solve he eqaion (5 and (6 ogeher we can rewrie i as follows: [ π ] [ ] [ ] * π y * φ α φ ν e where ~ i. i. d. N( Σ ν e 8

9 Σ ( Bs + Γs '( Bs + Γs α α + α( + ( q Pr( q Pr( q able reors esimaion resls sing annal daa for ABE : AXU KEHD EAN F HE DE: (949~4 π + e ( + {.95.9( } +.68π (3.37 (. (.57 (. ( y + ν (.3 (.3 Pr(.96 Pr(. 85 (.4 (.4 og ikelihood -65. andard errors of he arameers esimaes are reored in he arenheses he coefficien. 95 is negaive dring regime eriod. However.9 is negaive saisically insignifican dring he regime eriod. Figre 3. Probabiliies of regime Pr( for 949~ PRB_Phillis Crve From Figre 3 he inferred robabiliies Pr( accord qie well wih he Korean War (95 and he wo il hock eriods ( Alhogh he resls of in able seems o be saisically meaningfl dring 9

10 regime eriod sing annal daa we esimae he model again wih qarerly daa becase qarerly daa has more recise informaion han annal daa. We can idenify regime swiching robabiliies more concisely wih qarerly daa which may be missed by annal daa for he nsable Phillis Crve. We obained seasonally adjsed qarerly daa of he nemloymen rae and he consmer rice index for he U.. from he Brea of abor aisics and seasonally adjsed qarerly GDP ercen change based on he chained dollars from he Brea of Economic Analysis. nflaion raes are calclaed from he log differenced consmer rice index. he samle eriod is from 949: o 4:V. able reors esimaion resls sing qarerly daa for 949:~4:V. ABE : AXU KEHD EAN F HE DE: (949:~4:V π + e ( + {.4.38( } +.36π +. 3π (.46 (.7 (.68 (.36 (.6 ( y + ν (.7 (.5 Pr(.99 Pr(. 96 (. (.3 og ikelihood andard errors of he arameers esimaes are reored in he arenheses From able he coefficien. 4 is negaively significan dring he regime eriod. From his resl we can find ha here is an inflaion-nemloymen rade-off dring he regime eriod.. 38 is negaively and saisically insignifican dring he regime eriod. Figre 4. Probabiliies of regime Pr( for 949:~4:V PRB_Phillis Crve

11 Figre 4 show ha he inferred robabiliies Pr( accord qie well wih he Korean War (95:-95: and he wo il hock eriods (974:- 975:V 978:-984:. From. 4 in he able and Figre 4 we can conclde ha inflaion is rocyclical in movemen wih he real growh of o dring he Korean War and wo il hock eriods. As he resls of in he able and able are saisically insignifican here was relaively lile evidence of co-movemen beween inflaion and he real growh of o wih he exceion of he Korean War and he wo il hock eriods. 4 Conclsion As he eqaions of he Phillis Crve wih kn s aw was alied o he F arkov-wiching odel for he os-ww eriod he findings of his aer are as follows: inflaion is rocyclical in movemen wih he real growh of o dring he Korean War and he wo il hock eriods for he os-ww eriod; and here was relaively lile evidence of co-movemen beween inflaion and he real growh of o wih he exceions of he Korean War and he wo il hock eriods. hese resls sgges anoher exlanaion ha when here are exremely large shocks sch as big wars or oil shocks inflaion is rocyclical in movemen wih he real growh of o and he rocyclical movemen occrs in conjncion wih he big shocks exiss no only re-ww eriod b also os-ww eriod which is he differen resl from Cooley and hanian s findings. Acknowledgemens he ahor wold like o hank o-ong n for her valable commens.

12 References Cooley. F. and hanian. E.(99 he cyclical behavior of rices Jornal of oneary Economics Den Haan W. J.( he comovemen beween o and rices Jornal of oneary Economics Hamilon J.D. (989 A new aroach o he economic analysis of nonsaionary ime series and he bsiness cycle Economerica 57 ( Kznes imon (93 eclar movemens in rodcion and rices NBER N cas R. E. (97 Economeric esing of he naral rae hyohesis in: o Eckseined.he economerics of rice deerminaion Board Governor he Federal Reserve ysem ills F. C. (946 Prices qaniy ineracion in bsiness cycles NBER N ichell W. C. (95 Wha haens dring bsiness cycles Hoghon ifflin Co. ankiw N. Gregory (989 Real bsiness cycles: A new Keynesian ersecive Economic Persecive agnolo F. Psaradakis. and ola. (5 esing he Unbiased Forward Exchange Rae Hyohesis Using. a arkov wiching odel and nsrmenal Variables Jornal of Alied Economerics ( oon J. H. (4 imlaneos eqaions in he markov-swiching model PC Research nsie working aer

The Co-movement of Inflation and the Real Growth of Output *

The Co-movement of Inflation and the Real Growth of Output * THE JOURNAL OF THE KOREAN ECONOMY, Vol. 7, No. 2 (Winer 26), 23-229 The Co-movemen of Inflaion and he Real Growh of Oupu * Jae Ho Yoon ** In order o find ou wheher here really are co-movemens beween inflaion