US Monetary Policy and the G7 House Business Cycle: FIML Markov Switching Approach

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1 U Monear Polc and he G7 Hoe Bness Ccle: FML Markov wchng Approach Jae-Ho oon h Jun. 7 Absrac n order o deermne he effec of U monear polc o he common bness ccle beween hong prce and GDP n he G7 counres (U.. U.K. Canada German France al and Japan hs paper adoped FML Markov-swchng model of oon (6. he paper showed a posve relaonshp beween U neres rae and G7 GDP growh. U neres rae s a sgnfcan varable o he common bness ccle beween hong prce and GDP n he G7 counres. HoweverU neres rae showed a sgnfcan effec o he G7 hoe bness ccle for small shock perods no exremel large shocks perods. hs paper also found no relaonshp beween U m growh and he GDP growh rae of he G7 counres. U m growh s no a sgnfcan varable o he common bness ccle beween hong prce and GDP n he G7 counres. Kewords: neres rae m hong prce GDP FML Markov-swchng model bness ccle G7 U.. U.K. Canada German France al Japan JEL Classfcaons: C3; C3 hs paper was acceped o presen a he 4h nernaonal Assocaon for Appled Economercs (hp:// June Hokkado Unvers apporo Japan. hs paper was acceped o presen a he oce for Economc Measuremen (hp://sem.soce.cmu.edu/m.hml Jul M Cambrdge Massaches. hs paper was also acceped o presen a ngapore Economc Revew Conference (hp:// Aug ngapore. he auhor would lke o hank Lee- Jung and Eun-Jung for her valuable commens and suggesons Moble: E-mal: beowulfkorea@gmal.com. Webse: hp://ses.google.com/se/beowulfkorea/

2 . nroducon oon and Lee (4 showed ha he G7 hong prce has a procclcal movemen wh GDP durng he ol shock perods of he 97s 8s 9s and he bursng of hong bubble n 8 ng FML Markov-swchng model of oon (6. o he relaonshp beween U monear polc and hoe prces has been assumed o be posve durng shock perods. Plamen ossfov Marn Čhák and Amar hanghav (8 showed ha he shor-erm neres rae has a szable mpac on resdenal hong prces. Lasrapes W. D. ( showed ha mone suppl shocks have real effecs on he hong prces. However Denz gan and Prakash Loungan ( found ha long-run hoe prce dnamcs are mosl drven b local fundamenals such as ncome and he effec of more globall conneced facors such as neres raes appears o be less srong. Ò scar Jordà Morz chularck Alan M. alor (5 dsagree over neres raes ncrease o curb asse prce booms. Lucas R. E. Jr. (996 showed ha monear polc s neural. herefore hs paper examned wheher here reall s a posve relaonshp beween U monear polc and he G7 hoe bness ccle o esablsh a relaonshp beween U monear polc and he G7 hoe bness ccle we adoped he full nformaon maxmum lkelhood (FML Markovswchng model of oon (6. hs paper found ha U neres rae s a sgnfcan varable o he G7 GDP and he G7 hoe bness ccle. However U Δm has no sgnfcan effec o he G7 bness ccle beween hong prce and GDP n he G7 counres. he paper has been dvded n four secons. econ presens he FML Markov-swchng model. econ 3 presens he effec of U. monear polc ng FML Markov-swchng model. econ 4 concludes hs paper.. FML Markov-swchng model n order o esmae he parameers of he Markov-swchng model n he smulaneo equaons conssenl we consder he followng FML Markovswchng model: Bs Zs U U.. d. N( ( ~ where s he M marx of onl dependen varables; B s an M M marx and s nonsngular; Z s he K marx of predeermned varables; Γ s a K M

3 3 marx and rank(z = K; and Us s he M marx of he srucural dsurbances of he ssem. Consequenl he model has M equaons and observaons. M M M M M M U U E ' ( Pr( p wh N p for all. o derve he FML Markov-swchng model n he smulaneo equaons we can oban Pr( b applng a Hamlon fler (989 as follows: ep : A he begnnng of he h eraon Pr( N s gven and we calculae Pr( Pr( N N Pr( Pr( where Pr( N N are he ranson probables. ep : Consder he on condonal dens of and unobserved varable = whch s he produc of he condonal and margnal denses: Pr( ( ( f f from whch he margnal dens of s obaned b: ( ( N f f Pr( ( N f where he condonal dens ( f s obaned from (: ( f

4 M / / ( de( de( Bs exp( ( Bs zs ( Bs zs ' ( where ( Bs Zs '( Bs Zs s he h row of he marx z s he h row of he Z marx and B and Γ are obaned from (. ep 3: Once s observed a he end of me we updae he probabl erms: Pr( Pr( f ( f ( f ( f ( Pr( As a bproduc of he fler n ep we oban he log lkelhood funcon: ln L ln f ( whch can be maxmzed wh respec o he model parameers. 3. U monear polc ng FML Markov-swchng model Le consder he quarerl real GDP and Hong Prce ndex 3 n he G7 counres. We added U monear polc varables 4 o he FML Markov-swchng model. H M e (3 We obaned he G7 quarerl real GDP from he OECD daabase (hp://sas.oecd.org/ 3 ource: Naonal sources B Resdenal Proper Prce daabase (hp:// 4 We obaned Federal Funds rae and m from FRED daabase (hp://fred.slousfed.org/ 4

5 uk H uk M e uk (4 france H france M e france (5 german H german M e german (6 al H al M e al (7 canada H canada M e canada (8 apan H apan M e apan (9 where Δ s he log dfferenced real GDP and ΔH s he log dfferenced hong prce n he G7 counres. M s federal funds rae or he log dfferenced m. ( ( able : MLE of he FML Markov-swchng model (97. o 6. Parameers.59 (.3.78(.9.64(.3.45 (.6.(.8.49(.6 uk.37 (.5.49(.8.36(.5 uk.8 (.39.85(.5.8(.4 fr.53 (.9.44(.7.54(.9 fr.98 (.38.9(.44.97(.38 de. (.9.8(.8.5(.93 de.69 (.6.47(.44.67(.5.8 (.3.7(.36.75(.3.5 (.4.84(.46.95(.4 ca -.4 (. -.(. -.4(. ca.5 (.39.4(.49.3(.39 p.58 (.78.84(.68.6(.8 p.96 (.64.36(.76.95( (.59.57(.8.735(.9.64 ( (.5.47(.97 uk.536 ( ( (.7 5

6 uk.3 ( (.6.73(. fr.47 (.44.8(.56.4(.77 fr.4 ( (..445(.57 de.47 (.7.55(.4.43(.3 de.37 ( ( (.5.8 (.59.7( (..54 ( ( (.34 ca.65 (.59.66( (.94 ca.59 ( (.3.5(.86 p.469 ( (..539(.5 p.58 ( (.35.7(.7. (.8.4(.3.93(.8.85 (.75.4(.86.96(.77 uk.3 (..34(.3.8(.9 uk.56 ( ( (.39 fr.4 (..49(.9.4(. fr.484 (.77.69(.3.48(.77 de.399 ( ( (.55 de.59 ( (.35.57( ( (.45.56( (.93.36(.7.8(.89 ca.5 (.3.84(.37.3(.3 ca.45 ( (.73.35(.8 p.699 (..689( (. p.496 (.4.8( (.39 q.95 (..943(..95(. p.936 (.9.859( (.8.46 (.4 Δ m -.78 (.6 uk.8 (.4 Δ m uk -.8 (.47 fr.44 (. Δ m fr -.3 (.5 de.65 (.8 Δ m de -.7 ( (.5 Δ m -.7 (.63 ca.34 (.4 Δ m ca.8 (.53 p.44 (.3 Δ m p -.56 ( Log Lkelhood andard errors of he parameers esmaes are repored n he parenheses 6

7 able gves he esmaes from he FML Markov-swchng model ng quarerl daa for 97: o 6:. he coeffcen s sgnfcan and posve correlaed durng regme perods. he posve coeffcen showed he comovemen beween G7 hong prce and G7 GDP durng regme perods. he coeffcen β showed an upward shf durng regme perods and he degree of he upward movemen s obvo becae β > β excep Japan. Japan has been Zombe econom more han 5 ears afer hong bubble collapse n 989. he eld of hoe prce H s more unsable han he growh rae of G7 GDP becae absolue values of are smaller han. he varance σ s sgnfcan and he varance σ s also sgnfcan. he varance showed large volal durng regme perods becae σ > σ. he coeffcen neres rae (Federal Funds rae s sgnfcan and posve. However he coeffcen Δm s no sgnfcan. Fgure shows ha he nernaonal common smoohed probables Pr( mach he ol prce shock perods durng 97s 8s and 9s well. n addon here were common bness ccles durng he savngs and loan (&L crss (986:V o 988: and he hong bubble burs (8: o 9:. Fgure. Common probables 5 of regme Pr( n he G7 counres: U.. U.K. France German al Canada Japan (97: o 6: G7_PROB he resuls n able and Fgure gve evdence of a common nernaonal bness ccle beween hong prces and GDP oupu wh large shocks. Especall exremel large shocks such as ol shocks cae procclcal hong prce movemen wh GDP ncludng he bursng of hong bubble n 8. 5 For smoohed probables we followed Km s algorhm (994. 7

8 o exam he effec of U monear polc and he G7 hoe bness ccle we adoped he lkelhood rao es (LR es whch compared he goodness of f of wo models n able. he LR compared o a crcal value o decde wheher o reec he null model n favor of he alernave model n able. LR (log L( log L( ( where log L ( s a log lkelhood of he null model log L ( s a log lkelhood of he alernave model he es sasc LR s wll be asmpocall ch-squared dsrbuon wh degrees of freedom. able : he resuls of lkelhood rao es (LR es Monear polc varables Federal funds rae 7.38** Δm 6.34 ============================================================== * 5% sgnfcance level ** % sgnfcance level From he resuls of LR es n able we can found ha a posve relaonshp beween U neres rae and G7 GDP growh. However here s no relaonshp beween U Δm growh and he GDP growh rae of he G7 counres. We also have same resuls from he values of U neres rae and Δm n able. Fgure. Common probables of regme Pr( ncludng neres rae G7_PROB_N 8

9 Fgure 3. Common probables of regme Pr( ncludng Δm G7_PROB_M We can found ha Pr( ncludng U neres rae n Fgure s a lle b dfferen from Pr( n Fgure. From Fgure we can found ha U neres rae s a sgnfcan varable o he common bness ccle beween hong prce and GDP n he G7 counres. Especall neres rae showed a sgnfcan effec o he G7 hoe bness ccle for small shock perods durng he 99s. However neres rae polc showed no sgnfcan effec o he G7 hoe bness ccle for exremel large shocks such as ol shocks n 97s and he bursng of hong bubble n 8. hs resul s dfferen form Denz gan and Prakash Loungan ( who nssed he effec of neres raes less srong. Pr( ncludng Δm n Fgure 3 s no dfferen from Pr( n Fgure. From Fgure 3 we can fnd ha Δm s no a sgnfcan varable o he common hoe bness ccle. 4. Conclon Applng a FML Markov-swchng model o he G7 counres we found ha he hong prce movemen was procclcal wh GDP durng he ol shock perods of he 97s 8s and 9s and he bursng of hong bubble n 8 hs paper found ha U neres rae s a ver mporan ool o he relave small shocks. However U neres rae s no workng well for he exremel large shocks such as he bursng of hong bubble n 8 9

10 References Denz gan and Prakash Loungan ( Global hong ccles MF workng paper /7 Hamlon J.D. (989 A new approach o he economc analss of nonsaonar me seres and he bness ccle Economerca 57 ( Hamlon J.D. (994 me eres Analss Prnceon Unvers Prnceon N.J. Km C.J. (994 Dnamc facor models wh Markov swchng Journal of Economercs 6 -. Km C.J. and Nelson C.R. (999 ae-space models wh regme swchng: Classcal and Gbbs samplng approaches wh applcaons M Press Cambrdge Lasrapes W. D. ( he real prce of hong and mone suppl shocks: me seres evdence and heorecal smulaons Journal of Hong Economcs ( Lucas R. E. Jr. (996 Nobel Lecure: Monear Neural Journal of Polcal Econom Plamen ossfov Marn Čhák and Amar hanghav (8 neres Rae Elasc of Resdenal Hong Prces MF workng paper 8/47 Ò scar Jordà Morz chularck Alan M. alor (5 neres Raes and Hoe Prces: Pll or Poson? FRBF Economc Leer 5 oon J.H. (6 he co-movemen of nflaon and he real growh of oupu he Journal of he Korean Econom 7 ( 3-9 oon J.H. (9 mulaneo equaons n he Markov-swchng model Far Eas and ouh Asa Meeng of he Economerc oce oko oon J. H. and Lee J. H. (4 "he Lnked Movemen of Hoe Prces and GDP n he G7 Counres" he Korea paal Plannng Revew Vol