ESSAYS ON MONETARY POLICY AND INTERNATIONAL TRADE. A Dissertation HUI-CHU CHIANG

Transcription

1 ESSAYS ON MONETARY POLICY AND INTERNATIONAL TRADE A Dsseraon by HUI-CHU CHIANG Submed o he Offce of Graduae Sudes of Texas A&M Unversy n paral fulfllmen of he requremens for he degree of DOCTOR OF PHILOSOPHY May 28 Major Subjec: Economcs

2 ESSAYS ON MONETARY POLICY AND INTERNATIONAL TRADE A Dsseraon by HUI-CHU CHIANG Submed o he Offce of Graduae Sudes of Texas A&M Unversy n paral fulfllmen of he requremens for he degree of DOCTOR OF PHILOSOPHY Approved by: Char of Commee, Commee Members, Head of Deparmen, Denns W. Jansen L Gan Paula Hernandez-Verme Davd Bessler Larry Olver May 28 Major Subjec: Economcs

3 ABSTRACT Essays on Moneary Polcy and Inernaonal Trade. (May 28) Hu-Chu Chang, B.A., SooChow Unversy; M.A., Naonal Chengch Unversy Char of Advsory Commee: Dr. Denns W. Jansen The dsseraon consss of hree essays. Chaper II examnes he asymmerc effecs of moneary polcy on sock prces by usng an unobserved componens model wh Markov-swchng. My resuls show ha moneary polcy has negave effecs on sock prces, whch s conssen wh he mos recen leraure. When he ransory componen s n he low volaly sae, a conraconary moneary polcy sgnfcanly reduces sock prces. When he ransory componen s n he hgh volaly sae, he negave effec of moneary polcy becomes larger, bu he dfference of he moneary polcy effecs beween wo saes s no sgnfcan. Besdes, a conraconary moneary polcy wll lower he probably of sock prces sayng n he low volaly sae. Moneary polcy also reduces he oal volaly of sock prces and he volaly of he ransory componen of sock prces. Chaper III employs he smooh ranson auoregressve (STAR) models o nvesgae he nonlnear effec of moneary polcy on sock reurns. The change n he Federal funds rae s used as an endogenous measure of moneary polcy and he growh rae of ndusral producon s also consdered n he model. My emprcal resuls show

4 v ha excess sock reurns, he change n he Federal funds rae, and he growh rae of ndusral producon all can be expressed n he nonlnear STAR models. The esmaed coeffcens and he mpulse response funcons show ha he effec of moneary polcy on excess reurns of sock prces s sgnfcanly negave and nonlnear. The change n he Federal funds rae has a larger negave effec on excess reurns n he exreme low excess reurns regme and he effec becomes smaller when he excess reurns are greaer han he hreshold value. In chaper IV, I use a panel daa approach o nvesgae he mpac of exchange rae volaly on blaeral expors of he U.S. o he hreen major radng parners. I furher es he possbly of nonlnear effecs of exchange rae volaly on expors by usng hreshold regresson mehods for non-dynamc panels wh ndvdual-specfc fxed effecs proposed by Hansen (999). The resuls ndcae ha he effec of exchange rae volaly on blaeral expors s nonlnear. When he relave real GDP per capa of he exporng parner s lower han he hreshold value, he response of blaeral U.S. expors o exchange rae volaly s posve. Bu, exchange rae volaly decreases blaeral expors of he U.S. o he exporng parners when her relave real GDP per capa surpass he hreshold value.

5 v DEDICATION To my parens, Yn-Fu Chang and L-Me Kuo for her uncondonal love To my husband, Kuang-Chung for hs eernal encouragemen and suppor, and o my beloved daugher, Alce

6 v ACKNOWLEDGEMENTS I would lke o express my apprecaon o all hose who have provded asssance and encouragemen o hs research. Specal hanks o my commee char, Dr. Denns Jansen, for hs dedcaed aenon, gudance, and encouragemen o hs research. I also would lke o hank my oher commee members, Dr. L Gan, Dr. Paula Hernandez- Verme, and Dr. Davd Bessler, for her suppor and commens ha were very helpful durng he fnal sage of my research. I am also hankful o he Deparmen of Economcs a Texas A&M Unversy for provdng he fnancal suppor for my sudes. I am also graeful o my famly and frends for all of her uncondonal suppor and love. I am especally graeful o my husband, Kuang-Chung, for gvng me everyhng ha I need. I can sudy abroad and have fnshed my Ph.D. program all because of you.

7 v TABLE OF CONTENTS Page ABSTRACT... DEDICATION... ACKNOWLEDGEMENTS... TABLE OF CONTENTS... LIST OF FIGURES... LIST OF TABLES... v v v x x CHAPTER I INTRODUCTION... II THE EFFECT OF MONETARY POLICY ON STOCK PRICES: AN UNOBSERVED-COMPONENTS MODEL WITH MARKOV- SWITCHING Inroducon Emprcal Model Daa Esmaon Resuls The UC-MS model whou moneary polcy The UC-MS model wh moneary polcy The UC-MS model wh moneary polcy and me-varyng ranson probables Concluson III THE NONLINEAR EFFECT OF MONETARY POLICY ON STOCK RETURNS IN A SMOOTH TRANSITION AUTOREGRESSIVE MODEL Inroducon The STAR Model The basc approach Idenfyng and esmang mehods... 32

8 v CHAPTER Page 3.3 Daa and he Emprcal Model Daa The emprcal model Emprcal Resuls Impulse Response Funcons Concluson IV THE THRESHOLD EFFECTS OF EXCHANGE RATE VOLATILITY ON EXPORTS: EVIDENCE FROM U.S. BILATERAL EXPORTS Inroducon Model Specfcaon Daa Emprcal Resuls Robusness Tes Concluson... 8 V CONCLUSIONS REFERENCES VITA... 88

9 x LIST OF FIGURES FIGURE Page 2. Log lkelhood value wh dfferen σ e a Sock prces and he esmaed rend componen for Model b The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model a Sock prces and he esmaed rend componen for Model b The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model The ransory componens of Model and Model a Toal volaly of Model and Model b Dfference of oal volaly beween Model and Model a Volales of he ransory componen of Model and Model b Dfference of volaly of he ransory componen beween Model and Model The sae-dependen mpulse response funcon of he ransory componen of sock prces for small frms a Sock prces and he esmaed rend componen for Model b The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model a Toal volaly of Model 2 and Model b Dfference of oal volaly beween Model 2 and Model a Volales of he ransory componen of Model 2 and Model

10 x FIGURE Page 2.b Dfference of volaly he ransory componen beween Model 2 and Model The me seres plo of excess sock reurns, he change n he Federal funds rae, and he growh rae of ndusral producon: 954:8 25: The scaer plo of he scaer plo of excess sock reurns and he change n he Federal funds rae: 954:8 ~ 25: Tme pah of varables The logsc ranson funcon for XR equaon: 23.5 ( 2 ( 8.4 )) F [ + e XR ] The logsc ranson funcon for DFF equaon: 846 ( ' 3 (.48 )) F [ + e DFF ] The exponenal ranson funcon for Gy equaon: 2.8 ( 2 3.) F [ e XR ] Impulse response funcons for shocks o excess reurns n wo excess reurns regme Impulse response funcons for shocks o DFF n wo excess reurns regmes Impulse response funcons for shocks o Gy n wo excess reurns regmes... 57

11 x LIST OF TABLES TABLE Page 2. Maxmum lkelhood esmaes of he unobserved-componens model wh Markov-swchng heeroscedascy: 959: ~ 25: a Lneary es and deermnaon of lag order for ranson varable XR equaon b Lneary es and deermnaon of lag order for ranson varable DFF equaon c Lneary es and deermnaon of lag order for ranson varable Gy equaon Tess for he STAR specfcaon Model esmaes of excess reurns of sock prces Model esmaes of he change n Federal funds rae Model esmaes of growh n ndusral producon Lnear panel daa regresson esmaes Tes for hreshold effecs Esmaes of panel hreshold regresson model Number of observaons by hreshold and he exchange rae polcy Percenage of observaons n he hgh relave ncome regme by counry Tes for hreshold effecs for 23 counres Esmaes of panel hreshold regresson model for 23 counres Number of observaons by hreshold and he exchange rae polcy for 23 counres... 79

12 x TABLE Page 4.9 Percenage of observaons n he hgh relave ncome regme by counry for 23 counres... 8

13 CHAPTER I INTRODUCTION In hs dsseraon, I nvesgae he nonlnear relaonshp beween economcs varables n he feld of moneary economcs and nernaonal rade. Chaper II and Chaper III examne he nonlnear effec of moneary polcy on sock reurn and sock prces by usng wo dfferen knds of nonlnear models. Chaper IV dscusses he hreshold effec of real exchange rae volaly on blaeral expors. In he recen years, he global economy has experenced many mes of fnancal crashes and booms. Economss are payng more aenon on he relaonshp beween moneary polcy and fnancal marke and ryng o fnd ou f moneary polcy can affec he fnancal marke. A large number of sudes have red o nvesgae he effecs of moneary polcy on sock reurns from every perspecve. They use dfferen knd of moneary polcy varable, for example, money aggregae daa (Pesando(974), Rogalsk and Vnso(977)), he changes n marke neres rae or offcal rae (Paels (997), Perez-Quros and Tmmermann (2)), or exracng he unexpeced moneary polcy shocks, such us he orhogonalzed nnovaons from a vecor auoregressve model (Thorbecke (997), Chen(25)), ec. Some leraure use a varey of emprcal echnques, for nsance, he vecor auoregresson esmaon, generalzed mehod of momens esmaon, or an even sudy mehodology. Mos of papers dscuss he lnear response of sock reurns o moneary polcy and fnd a negave effec of moneary Ths hess follows he syle of he Journal of Moneary Economcs.

14 2 polcy on sock reurns, bu no many researchers focus on he possble nonlnear relaonshp beween moneary polcy and sock reurns, even hough mgh happen n he heorecal pon of vew. Accordng o he heorecal model, nformaon asymmery mgh exs n fnancal markes, and hen agens may behave as f hey were consraned. The fnancal consran problem could be more serous n he bad economc envronmen. Ths mples ha he moneary polcy mgh have asymmerc effecs on fnancal marke and he asymmery effecs mgh be deermned by he suaon of sock marke, he sae of economy, or moneary polcy self. However, only a few sudes examne he asymmerc effecs of moneary polcy on sock marke and hey jus use he smple dummy varables n her equaons, excep Chen (27). Chen nvesgaes he asymmerc moneary polcy effecs on sock reurns by usng Markov-swchng models. He fnds ha moneary polcy has larger effecs on sock reurns n bear marke and a conraconary moneary polcy leads o a hgher probably of swchng o he bear marke regme. The movaon of chaper II and chaper III s o dscuss he effec of moneary polcy on sock marke by usng nonlnear models. Accordng o he resuls of Summers (986), Fama and French (988), Km and Km (996), he unobserved-componens model wh Markov-swchng s a good model o llusrae sock prces. So, n chaper II, I aemp o nvesgae he asymmerc effecs of moneary polcy on sock marke by usng an unobserved-componens model wh Markov-swchng (UC-MS model). I augmen UC-MS model wh a moneary polcy varable and assume ha moneary

15 3 polcy only nfluences he ransory componen of sock prces. Frs, I esmae UC-MS model wh no moneary polcy as a benchmark model. Then, he model s augmened wh moneary polcy varable for he purpose of nvesgang he effecs of moneary polcy on sock prces. I also esmae a hrd model whch allows he ranson probably o be me-varyng, whch depends on moneary polcy shocks. Chaper III uses smooh ranson auoregressve (STAR) models o nvesgae he nonlnear effec of moneary polcy on sock reurns. I consder hree mporan varables, sock reurns, he change n he Federal funds rae, and he growh rae of oupu. Snce hree varables are all endogenously deermned, he STAR models are consruced for each varable. Besdes, sock reurns, he change n he Federal funds rae, and he growh rae of oupu are all allowed o be he possble hreshold varable whch conrols for he nonlnear dynamcs of models. By appropraely choosng he bes hreshold varable for he model of each varable and esmang he nonlnear models for hem, he nonlnear relaonshp among excess sock reurns, moneary polcy, and oupu growh can be nvesgaed. Fnally, he nonlnear mpulse response funcons are calculaed n order o undersand how hey affec o each oher. Chaper IV nvesgaes nonlnear effecs of exchange rae volaly on expors. In he prevous leraure, he effec of real exchange rae volaly on expors has been fully dscussed by usng me seres daa, bu he concluson s sll mxed, especally usng he blaeral expors daa. From he heorecal pon of vew, De Grauwe (988) argues ha he mpac of exchange rae volaly on expors depends on he degree of

16 4 rsk averson. If he rader s less rsk averse, he ncome effec mgh be greaer han he subsuon effec when exchange rae volaly ncreases, and wll ncreases expors. I aemp o reexamne he effecs of real exchange rae volaly on blaeral expors by usng panel daa approach. The daa of real blaeral expor volume from U.S. o hreen major radng parners are used. I furher es he possbly of nonlnear effecs of exchange rae volaly on expors by usng hreshold regresson mehods for non-dynamc panels wh ndvdual-specfc fxed effecs proposed by Hansen (999). Referrng o he mos emprcal papers, he blaeral exchange rae volaly s measured by usng movng sample sandard devaon mehod and he condonal sandard devaon from a GARCH (,) model. In order o check he robusness of concluson, he model s esmaed agan for op 3 major exporng parners of he Uned Saes.

17 5 CHAPTER II THE EFFECT OF MONETARY POLICY ON STOCK PRICES: AN UNOBSERVED-COMPONENTS MODEL WITH MARKOV-SWITCHING 2. Inroducon Afer he collapse of he Japanese and U.S. asse prce bubbles, he relaonshp beween moneary polcy and asse prces has brough people s new aenon. One of he mporan ssues s he role of asse prces n he moneary ransmsson mechansm. The ransmsson mechansm of moneary polcy usually comes hrough he sock marke by changng he values of prvae porfolos (he wealh effec) and he cos of capal, hus, n urn affecs he real economy. So, he purpose of hs paper s ryng o undersand he role of asse prces n he moneary ransmsson by esmang he effecs of moneary polcy on sock prces. In he early emprcal sudes, hey usually esmae he effecs of moneary polcy on asse prces by usng money aggregae daa as he moneary polcy varable. However, he resuls are no conssen among all he research. For example, Pesando (974) uses lnear regressons and fnds ha no mpacs of changes n he money supply on sock prces. Rogalsk and Vnso (977) esmae cross correlaons beween money supply and sock prces and conclude ha here s no sgnfcan forecasng power of changes n money on sock prces. Bu, Homa and Jaffee (97) fnd ha expansonary polcy ncreases sock prces by usng lnear regressons. Recenly, afer Bernanke and

18 6 Blnder (992) show ha Federal funds rae s a good ndcaor of moneary polcy acons, economss re-esmae he lnk beween moneary polcy and sock marke. Mos resuls agree ha moneary polcy helps o explan he sock prces or reurns and he effec of moneary polcy on sock marke s negave. Thorbecke (997) uses Vecor Auoregressve model and concludes ha a conraconary moneary polcy decreases sock reurns. By usng even-sudy approach, Rgobon and Sack (24) fnd an ncrease n he shor-erm neres rae has a negave mpac on sock prces; Bernanke and Kuner (25) conclude ha unexpeced cu n he Federal funds rae would lead an ncrease n sock prces. Accordng o he heorecal model, nformaon asymmery mgh exs n fnancal markes, and hen agens may behave as f hey were consraned. The fnancal consran problem could be more serous n he bear markes. Ths mples ha moneary polcy mgh have asymmerc effecs on fnancal marke beween dfferen fnancal saes. However, only some of he prevous sudes examne he asymmerc effecs of moneary polcy on sock marke and hey jus use he smple dummy varables n her equaons, excep Chen (27). Chen nvesgaes he asymmerc moneary polcy effecs on sock reurns by usng Markov-swchng models. He fnds ha moneary polcy has larger effecs on sock reurns n bear marke and a conraconary moneary polcy leads o a hgher probably of swchng o he bear-marke regme. For modelng sock prces, Summers (986) proposed an unobservedcomponens model (UC model). Summers decomposes sock prces no a sochasc rend componen and a saonary ransory componen and fnds ha he saonary

19 7 ransory componen of prces accouns for a subsanal fracon of he varaon of reurns. Fama and French (988) conclude ha he exsence of saonary ransory componens of sock prces s more sgnfcan for he porfolo of small frms han for he porfolo of large frms. Km and Km (996) hen add he Markov-swchng (MS) mehod no an UC model and use daa from 95: o 992:2. They fnd ha he UC- MS model descrbes he paern of sock prces well and can capure he quck volaly reverng of sock reurns o s normal level afer he crash. Ths paper aemps o nvesgae he asymmerc effecs of moneary polcy on sock marke by usng an unobserved-componens model wh Markov-swchng (UC-MS model) from Km and Km (996) nsead of he usual lnear model n mos prevous papers. I augmen UC-MS model wh a moneary polcy varable o dscuss he possbly of nonlnear effecs of moneary polcy on sock prces and assume ha moneary polcy only nfluences he ransory componen of sock prces. Frs, I esmae he UC-MS model wh no moneary polcy as a benchmark model. Then, he UC-MS model wh moneary polcy varable s esmaed o undersand he asymmerc effecs of moneary polcy on sock prces. In addon, I also esmae a hrd model whch allows he ranson probably o be me-varyng, where me varaon depends on moneary polcy shocks. My resuls show ha moneary polcy has negave effecs on sock prces, whch s conssen wh he mos recen leraure. When he ransory componen s n he low volaly sae, a conraconary moneary polcy reduces sock prces and he effec s sgnfcan. When he ransory componen s n he hgh volaly sae, he

20 8 negave effec of moneary polcy becomes larger, bu he dfference of he moneary polcy effecs beween wo saes s no sgnfcan. Besdes, moneary polcy can affec he dynamcs of swchng beween low volaly and hgh volaly sae. A conraconary moneary polcy wll lower he probably of sock prces sayng n he low volaly sae. Moneary polcy also reduces he oal volaly of sock prces and he volaly of he ransory componen. The remander of he chaper proceeds as follows. Secon 2 descrbes he emprcal model o be esmaed. Secon 3 conans he daa nformaon and how o measure he moneary polcy varable. Secon 4 presens he emprcal resuls. Secon 5 s he concluson. 2.2 Emprcal Model Consder an unobserved componens model wh Markov-swchng heeroscedascy (UC-MS model) from Km and Km (996): p p + p, (2.) P T p μ + v, (2.2) P P + p p φ + e, (2.3) T T T p + φ2 p 2 2 v ~ N (, σ ), v S, 2 e ~ N (, σ ), e S, σ +, v, S ( S v ) σ v S vσ v σ +, e, S ( Se ) σ e S eσ e σ > σ, (2.4) 2 2 v v σ > σ, (2.5) 2 2 e e

21 9 where p s he log of real sock prces, whch s decomposed no a sochasc rend componen P p and a saonary ransory componen T p. Equaon (2.2) means ha he sochasc rend componen p P s specfed as a random walk wh a drf erm μ. In equaon (2.3), he ransory componen s assumed o be a saonary auoregressve process. S v and S e are dscree-valued, unobserved frs-order Markov-swchng varables whch equal eher or. v, e are he nnovaons o P p and T p, whch are assumed o have Markov-swchng varances n he form of equaon (2.4) and (2.5). We assume ha he varances of v and e are larger n sae han n sae. In order o nvesgae he asymmerc effecs of moneary polcy on sock prces, I modfy he model of Km and Km (996). Equaon (2.3) s augmened as follows: p φ S + e, (2.3 ) T T T p + φ2 p 2 + β x + βx e where x s he moneary polcy varable a me -. I assume ha moneary polcy has no effec on permanen sock prces. I only changes he ransory componen of sock prces. The effec of moneary polcy mgh be asymmerc, whch depends on he sae of nnovaon e of he ransory componen. For example, when S e equals o, he effecs of x on T p s β ; when e S equals o, he effecs of x on p s β + β. T For he unobserved sae varable S v and S e, I frs assume ha hey evolve ndependenly of each oher accordng o he followng ranson probables: v P( Sv, Sv, ) p, v P( S v, S v, ) p (2.6)

22 e P( S e, S e, ) p, e P( S e, S e, ) p (2.7) v p s he probably of he rend componen of sock prces movng from sae a me - o sae a me. The sochasc processes of S v and S e are assumed o be fxed, no deermned by any oher exogenous or predeermned varables. Then, I modfy equaon (2.7) o relax he assumpon of fxed ranson probably and allow he ranson probables of he regme-swchng process of S e o be me-varyng, where me varaon depends on moneary polcy shocks. The funcons of he ranson probables are hen specfed as follows: e exp( c + a * x ) P ( S e, S e, ) p ( x ) (2.8) + exp( c + a * x ) e exp( c + a * x ) P ( S e, S e, ) p ( x ) (2.9) + exp( c + a * x ) The esmaes of a and a ndcae how moneary polcy affecs he shfs beween hgh volaly and low volaly sae of he ransory componen. For example, a < mples ha a conraconary moneary polcy x < makes he low volaly sae more possble o urn no he hgh volaly sae. In conras, a ndcaes ha a conraconary moneary polcy makes he ransory componen of sock prces more lkely o say n he low volaly sae. Before esmang he model, I need o rewre as a sae-space wh Markov swchng represenaon whch consss of a measuremen equaon and a ranson equaon. The measuremen equaon s an equaon ha descrbes he relaon beween >

23 observed varables (daa) and unobserved sae varables. The ranson equaon s an equaon ha descrbes he dynamcs of he sae varables. I ake frs dfference of equaon (2.) and subsue equaon (2.2) no o ge he measuremen equaon T p r μ + ( ) + v T p (2.) where r p p. The ranson equaon () s obaned from equaon (3). p p φ T φ2 p T p β x + βx + e + T e T 2 S (2.) Nex, hese wo equaons are esmaed by usng Km s (994) basc fler whch s a combnaon of he Kalman fler and Hamlon fler, along wh approprae approxmaons o ge he maxmum lkelhood esmaes { p v, v p, e p, e p, v σ, σ, v σ e, e σ, φ, φ 2, μ, β, β }. 2.3 Daa The daa frequency s monhly. The sock prces p are measured by he log of real sock prces ndex of New York Sock Exchange (NYSE) whch s deflaed by he CPI whch s deflaed by he CPI. For he moneary polcy varable x, I use moneary polcy shocks, he orhogonalzed nnovaons from he sandard Vecor Auoregresson See Km and Nelson (999) for more deal of esmaon and applcaons of sae-space wh Markov swchng models.

24 2 (VAR) Model proposed by Chrsano e al. (999), o avod he endogeney problem. Federal funds raes are used o be he moneary polcy nsrumen. The VAR model for exracng moneary polcy shocks s Z + u (2.2) A + AZ + A 2 Z A q Z q where Z s { Y, CPI, PCOM, FF, NBR, TR }. Y s he log of ndusral producon, prces, CPI s he log of consumer prce ndex, FF s he Federal funds rae, PCOM s he log of commody NBR s he log of non-borrowed reserves, and s he log of oal reserves. Those varables are suggesed by Chrsano e al. (999) and he order of he varables n he vecor Z s he same as he order n whch hey are lsed above. u s serally uncorrelaed and has varance-covarance marx V. The TR VAR dsurbances are assumed o be relaed o he underlyng economc shocks, ε, by u C ε (2.3) where C s lower rangular and ε has covarance marx equal o he deny marx. The VAR s esmaed over he perod from 959: o 25:2. Afer checkng he SIC, wo lags of each varable are used n he VAR model and he resduals u and he varance-covarance marx V can be obaned afer esmaon. Then, I can calculae C by he relaonshp V C C and have he underlyng economc shocks ε by he equaon ε C u. The orhogonalzed resduals of Federal funds rae, he fourh elemen ε, s used as he moneary polcy varable x

25 3 All daa are colleced from Federal Reserve Economc Daa and he Cener for Research n Secury Prces (CRSP) daabase. The orgnal daa are from 959: o 25:2. Due o he los of wo observaons for exracng Federal funds rae shocks, he sample perod for he model s from959:3 o 25: Esmaon Resuls 2.4. The UC-MS Model whou Moneary Polcy Before esmang he moneary polcy effecs on sock prces, I esmae he model whou moneary polcy n equaon (2.)-( 2.5) as a benchmark model,.e. I esmae Km and Km (996) s model by usng real sock prces ndex of NYSE for he perod 959:3 o 25:2. In he esmang process, σ e falls on he boundary value zero and makes dffcules n nverng he nformaon marx o ge he sandard errors for oher parameers. Thus, I mpose σ e o be zero and connue he opmzaon wh respec o oher parameers. To make sure ha σ e has he maxmum log lkelhood value, I resrc σ e wh dfferen values and re-esmae he model o check wheher σ e s he bes esmae. Fgure 2. shows he graph log lkelhood value wh σ e. The resul shows ha he log lkelhood value decreases when σ e ncreases. Therefore, σ e s he maxmum lkelhood esmaes. Km and Km (996) have he same resul σ e for S&P 5 sock prce ndex from 952: o

26 4 log lkelhood sgma(e) Fgure 2.. Log lkelhood value wh dfferen σ e Esmaes of he model wh no moneary polcy, named Model, are repored n he second column n Table 2.. Sae represens he low-volaly sae and sae represens he hgh-volaly sae for boh he rend componen and he ransory componen. The sandard error of he rend componen shocks s.22 n he lowvolaly sae and s.4 n he hgh-volaly sae. The esmaes of ranson probably of he rend componen ( v p and v p ) ndcae ha he probably of he rend componen of sock prces say n sae from me - o me s.99 and say n sae from me - o me s.969. The rend componen has hgh probably o say n he same sae. For he esmaes of he parameers assocaed wh he ransory componen, he sandard error of shocks σ e s zero n he low-volaly sae, whle s large and sgnfcan for he hgh-volaly sae. The resul s smlar o he esmaes of Km and Km (996) and hey explan ha he ransory componen s eher on or off

27 5 over he me perod. The esmaes of ranson probably of he ransory componen ( e p and e p ) are.984 and.59, respecvely. The expeced duraons of he lowvolaly sae s /(-.984) 62.5 monhs, bu hose of he hgh-volaly sae s only /(-.59) 2.44 monhs. I ndcaes ha he low-volaly sae domnaes he hghvolaly sae. Table 2. Maxmum lkelhood esmaes of he unobserved-componens model wh Markov-swchng heeroscedascy: 959: ~ 25:2 Model Model 2 Model 3 No moneary Has moneary Tme-varyng ransory probably polcy polcy v p v p σ v σ v e p e p σ e σ e φ φ 2 μ β β Log lkelhood value.969 (.2).99 (.7).22 (.2).4 (.2).984 (.2).59 (.7) (-).9 (.26).58 (.25) -.25 (.75).6 (.).968 (.2).99 (.7).22 (.2).4 (.2).986 (.9).652 (.72) (-).86 (.25).292 (.54) (.39).6 (.) -.2 (.4) -.7 (.4).968 (.2).99 (.7).22 (.2).4 (.22) c a (.832) (.39).523 (.358) (-).79 (.8).99 (.56) -.33 (.4).6 (.) -.2 (.5) -.2 (.7) Noe: Fgures n parenheses are approxmae sandard errors.

28 6 Fgure 2.2a shows he sock prces and he esmaed rend componen of sock prces of Model. They mach well excep some perods of me. Fgure 2.2b shows he esmaed ransory componen and he flered probables of he rend componen and he ransory componen, whch are he esmaed probables ha S a me and S e a me, respecvely. S e s generally equal o zero, bu swches o one occasonally. The ransory componen usually flucuaes around zero, bu reduces a lo n some perods and he mng s almos he same as P( S e ) jumps up. I ndcaes ha when he ransory componen of sock prce decreases more, s more lkely o be n he hgh volaly sae. I fnd ha every perod ha he ransory componen drops a lo and P( S e ) s hgh s close o one of he crashes n he sock marke, such as ol crss n 973, black Monday n 987, Asan fnancal crss n 997, and Russan fnancal crss n 998 ec. v LNRSP TREND Fgure 2.2a: Sock prces and he esmaed rend componen for Model

29 TRANSITORY PRST PRST2 Fgure 2.2b. The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model The UC-MS Model wh Moneary Polcy Nex, I consder he UC-MS model wh moneary polcy, named Model 2, o nvesgae he effecs of moneary polcy on he ransory componen of sock prces and compare he resuls wh he benchmark model. The esmaon resuls of Model 2 are repored n he hrd column n Table 2.. The sandard errors and ranson probables of he rend componen for boh volaly saes are almos he same as n Model. For he ransory componen, he sandard error of shocks σ e and ranson probables e p n he low-volaly sae are smlar o Model, bu e σ and e p n he hgh-volaly sae are a lle dfferen. Compare o he resuls of Model, afer ncludng moneary polcy, he sandard error of shocks σ e decreases a lle b and he

30 8 probably of sayng n he hgh volaly sae n he nex perod p e ncreases. I ndcaes ha moneary polcy helps o lower he volaly when sock marke s n he hgh volaly sae, bu exends he duraon of sayng n he hgh volaly sae LNRSP TREND Fgure 2.3a. Sock prces and he esmaed rend componen for Model ransory Pr(Sv) Pr(Se) Fgure 2.3b. The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model 2

31 9 Fgure 2.3a shows he sock prces and he esmaed rend componen of sock prces of Model 2. The rend componen of sock prces s sll close o he sock prces, bu no ha mach as n he Model. Fgure 2.3b shows he esmaed ransory componen and he flered probables of he rend componen and he ransory componen of Model 2. Moneary polcy ncreases he flucuaon of he ransory componen. The change can be clearly seen when I graph he ransory componens of Model and Model 2 ogeher n Fgure Transory_Model Transory_ Model 2 Fgure 2.4. The ransory componens of Model and Model 2 Moreover, he moneary polcy changes he volaly of sock prces, oo. Fgure 2.5a shows he oal volaly of Model and Model 2. Fgure 2.5b shows he dfference of oal volaly beween Model and Model 2, whch s calculaed as oal volaly of Model mnus he oal volaly of Model 2. From Fgure 2.5b, he dfference of oal volaly s usually above zero and has larger posve values on Aprl

32 2 98 and December 987, even hough s negave for some daa pons. Fgure 2.6a shows he volaly of he ransory componen of Model and Model 2. Fgure 2.6b shows he dfference of volaly of he ransory componen beween Model and Model 2, whch s calculaed as volaly of he ransory componen of Model mnus ha of Model 2. The dfference s also posve mos of he me. Therefore, my resuls ndcae ha moneary polcy can reduce he volaly of sock marke Toal_Volaly_Model Toal_Volaly_Model 2 Fgure 2.5a. Toal volaly of Model and Model 2 Dfference_oal_volaly Fgure 2.5b. Dfference of oal volaly beween Model and Model 2

33 Transory_Volaly_Model Transory_Volaly_Model 2 Fgure 2.6a. Volales of he ransory componen of Model and Model 2 Dfference_ransory_volaly Fgure 2.6b. Dfference of volaly of he ransory componen beween Model and Model 2 From he coeffcens of Federal funds rae shocks n he hrd column n Table 2., β shows ha moneary polcy shocks have sgnfcan negave effecs on he ransory componen of sock prces n he low-volaly regme, % ncrease n he Federal funds rae shocks decreases sock prces by.2%. The esmae of β shows ha moneary polcy shocks have larger negave effecs on sock prces ( β + β -

34 22.29) n he hgh-volaly sae, bu he effecs are no sgnfcanly dfferen from ha n he low volaly sae. Fgure 2.7 shows he sae-dependen mpulse response funcon of he ransory componen of sock prces o a one-sandard devaon ncrease of Federal funds rae shock n Model 2. The response of he ransory componen of sock prces o a moneary polcy shock s larger when s n he hgh-volaly sae ( S e ). For example, a one posve sandard devaon realzaon of moneary polcy shock lowers sock prce by a maxmum amoun of.78 when S e. However, when S e, he maxmum response of sock prce s much larger, reachng.88. The responses of sock prces o he moneary polcy shock converge o zero n abou hree years Se, + se Se, + se Fgure 2.7. The sae-dependen mpulse response funcon of he ransory componen of sock prces for small frms

35 The UC-MS Model wh Moneary Polcy and Tme-Varyng Transon Probables In hs secon, I esmae he UC-MS model wh moneary polcy and also allowed he ranson probables of he regme-swchng process of S e o be mevaryng as equaon (2.8) and (2.9), where me varaon depends on moneary polcy shocks. The resuls of esmaon show ha moneary polcy has no sgnfcan effec on P ( S e Se,, P ( S e Se,, ) ), suggesng ha he fxed ranson probably s bes for. So, I esmae a model, named Model 3, whch only P S e S ) s a funcon of Federal funds rae shocks. Resuls are showed n (, e, he fourh column n Table 2.. The sandard errors and ranson probables of he rend componen are all he same as Model and Model 2. For he ransory componen, a s negave and sgnfcan, whch mples ha a conraconary moneary polcy makes he ransory componen of sock prces more lkely o swch no he hgh volaly sae. β s also negave and sgnfcan. β s a small negave number, bu no sgnfcan. Thus, moneary polcy has sgnfcan negave effecs on sock prces n he low volaly sae and he effecs become a lle larger n he hgh volaly sae, however, he mpac s no dfferen beween wo saes. Fgure 2.8a shows he sock prces and he esmaed rend componen of sock prces of Model 3. Fgure 2.8b shows he esmaed ransory componen and he flered probables of he rend componen and he ransory componen of Model 3. Snce

36 24 moneary polcy can change he sae of ransory componen nex perod when s n he low volaly n hs perod, he flered probably of S becomes hgher e LNRSP TREND Fgure 2.8a. Sock prces and he esmaed rend componen for Model TRANSITORY PRST PRST2 Fgure 2.8b. The esmaed ransory componen and he flered probables of he rend componen and he ransory componen for Model 2

37 Toal_Volaly_Model 2 Toal_Volaly_Model 3 Fgure 2.9a. Toal volaly of Model 2 and Model 3 Dfference_oal_volaly Fgure 2.9b. Dfference of oal volaly beween Model 2 and Model 3

38 26 comparng o Model 2,.e. he probably of beng n hgh volaly sae a me ncreases. I s especally obvous durng Ocober 979 o November 982. Fnally, I compare he volaly of Model 3 wh Model 2. Fgure 2.9a and Fgure 2.9b show he oal volaly of sock prces of Model 2 and Model 3 and he dfference beween hese wo volales, whch s calculaed as oal volaly of sock prces of Model 2 mnus ha of Model 3. From Fgure 2.b, he dfference of oal volaly s normally around zero, bu Model 3 ncreases he volaly durng Ocober 979 o November 982. Fgure 2.a, he graph of he volaly of he ransory componen of Model 2 and Model 3, and Fgure 2.b, he graph of he dfference beween hese wo volales, show he same resuls. Therefore, Model 3 has no more explanaory ably o he volaly of sock marke han Model Transory_Volaly_Model 2 Transory_Volaly_Model 3 Fgure 2.a. Volales of he ransory componen of Model 2 and Model 3

39 27 Dfference_ransory_volaly Fgure 2.b. Dfference of volaly of he ransory componen beween Model 2 and Model Concluson There s a consderable amoun of papers nvesgang he effecs of moneary polcy on sock prces or sock reurns, bu here s sll no consensus of conclusons abou hs queson even hough mos of prevous papers fnd he mpac of moneary polcy on sock prces s negave. From he heorecal pon of vew, a conraconary moneary polcy can worse a frm s balance shee posons and can reduce a frm s ably o borrow, spend and nves. Ths cred consran problem s more lkely o happen when he fnancal marke s n a bad suaon. Ths mples ha moneary polcy mgh have asymmerc effecs on sock prces beween dfferen saes of sock markes. Ths paper aemps o nvesgae he asymmerc effecs of moneary polcy on sock marke by usng an unobserved-componens model wh Markov-swchng heeroscedascy. I decompose sock prces no he rend componen and he ransory componen and assume ha moneary polcy only nfluences he ransory componen of

40 28 sock prces. My resuls show ha moneary polcy has negave effecs on sock prces, whch s conssen wh he mos recen leraure. When he ransory componen s n he low volaly sae, a conraconary moneary polcy reduces sock prces and he effec s sgnfcan. When he ransory componen s n he hgh volaly sae, he negave effec of moneary polcy becomes larger, bu he dfference of he moneary polcy effecs beween wo saes s no sgnfcan. Besdes, moneary polcy can affec he dynamcs of swchng beween low volaly and hgh volaly sae. A conraconary moneary polcy wll lower he probably of sayng n he low volaly sae. Moneary polcy also reduces he oal volaly of sock prces and he volaly of he ransory componen.

41 29 CHAPTER III THE NONLINEAR EFFECT OF MONETARY POLICY ON STOCK RETURNS IN A SMOOTH TRANSITION AUTOREGRESSIVE MODEL 3. Inroducon The movaon of hs chaper s he same as chaper II, bu I ry o nvesgae he nonlnear effec of moneary polcy on sock marke by usng anoher emprcal model. From pervous leraure, no many paper focus on he queson of wheher moneary polcy can have dfferen effec on sock reurns n dfferen economc condon. Hermann and Frazscher (24) presen he evdence ha he sock marke response o moneary polcy s hghly asymmerc. They dvde he 5 ndvdual socks comprsng he S&P 5 no several groups accordng o he degree of fnancal consrans of frms and fnd he frms wh more fnancal consrans are affeced sgnfcanly more by moneary polcy. Chen (27) nvesgaes he asymmerc moneary polcy effecs on sock reurns by usng Markov-swchng models. He fnds ha moneary polcy has larger effecs on sock reurns n bear marke and a conraconary moneary polcy leads o a hgher probably of swchng o he bearmarke regme. Ths paper aemps o nvesgae he nonlnear effec of moneary polcy on sock reurns by usng he smooh ranson auoregressve (STAR) model. Snce oupu

42 3 has a close relaonshp wh sock reurns and moneary polcy and mgh be he reason of nonlnear effecs of moneary polcy on sock reurns, he growh rae of oupu s also ncluded n our emprcal model. The change n he Federal funds rae s used as an endogenous measure of moneary polcy. Snce sock reurns, he change n he Federal funds rae, and he growh rae of oupu are all endogenously deermned, he STAR models are consruced for all hree varables. One characersc of hs paper s ha excess sock reurns, he change n he Federal funds rae, and he growh rae of oupu are all allowed o be he possble hreshold varable whch conrols for he nonlnear dynamcs of models. Hence, hs paper consders hree asymmeres: asymmery relaed o he sae of sock marke, asymmery relaed o he drecon and sze of he moneary polcy acon, and asymmery relaed o he sae of economy. By appropraely choosng he bes hreshold varable for he model of each varable and esmang he nonlnear models for hem, he nonlnear relaonshp among excess sock reurns, moneary polcy, and oupu growh can be nvesgaed. Also, he nonlnear mpulse response funcons can help us o undersand how hey affec o each oher. My emprcal resuls show ha excess sock reurns, moneary polcy, and he growh rae of oupu all can be expressed n nonlnear STAR models. The hreshold varable for he excess sock reurns equaon s he excess reurns a lag wo, he hreshold varable for he change n he Federal funds rae equaon s s own lag a wo, and he hreshold varable for he growh rae of oupu equaon s also he excess sock reurns a lag wo, bu wh a dfferen hreshold value. The esmaed coeffcens and

43 3 he mpulse response funcons show ha he effec of moneary polcy on excess reurns of sock prces s sgnfcanly negave and nonlnear. The change n he Federal funds rae has a larger negave effec n he exreme low excess reurns regme han n he hgh excess reurn regme. The possble explanaon of hs resul mgh be ha fnancal consran of agens or frms are more lkely o be bnd when sock marke s n a bad suaon and excess reurns are exremely low, so ha moneary polcy would have larger mpac on sock reurns n he low sock reurns regme. The res of he chaper s organzed as follows. Secon 2 smply presens he framework of a STAR model ha wll be used n hs paper and nroduces he sandard esng and esmang procedures. Secon 3 s daa and he emprcal model. Secon 4 repors he emprcal resuls of esmang a se of nonlnear LSTAR models for excess reurns, he change n he Federal funds rae, and he growh rae of oupu. Impulse response funcons are repored n Secon 5. Secon 6 s he concluson. 3.2 The STAR Model 3.2. The Basc Approach The STAR model s a general form of he hreshold auoregressve model whch he ranson varable s a funcon of he hreshold varable, no jus an ndcaor varable, so ha he ranson processes beween regmes are smooh. A STAR model can be wren as y a L x a L x F z ) + α ( ) + [ + β ( ) ] ( d + ε (3.)

44 32 where y s he dependen varable, x represens all he explanaory varables, ncludng auoregressve lags of y, F( z d ) s he ranson funcon, z d s he ranson varable ha deermnes he swch beween regmes, and d s he lag lengh of he ranson varable. The dynamcs of equaon () changes wh values of he ranson varable. The nonlnear dynamcs can be expressed as α L) + β ( L) F( ). ( z d Two common specfcaons for ranson funcons are he logsc and he exponenal funcon. The logsc ranson funcon s F( z d ) [ + e γ ( z d c) ] (3.2) where γ deermnes he speed of ranson and c s he hreshold crcal value. If γ > ( γ < ), he logsc ranson funcon changes smoohly from zero o one (from one o zero) when he ranson varable z becomes ncreasngly larger han he hreshold d value c. The exponenal STAR model has he ranson funcon F( z d ) [ e γ ( z c) d 2 ], γ > (3.3) The exponenal ranson funcon smoohly approaches zero when he ranson varable varable z s close o he hreshold value c and approaches one when he ranson d z more devaes from he hreshold value c. d Idenfyng and esmang mehods Accordng o he STAR models developed by Luukkonen e al. (988), Terasvra and Anderson (992), and Terasvra (994), here are four man seps o denfy and esmae STAR models. Frs sep s o denfy and esmae a lnear

45 33 auoregressve model. The approprae lag lengh for he model should be chosen before he ess of lneary and he esmaon of he STAR models. In hs paper, I search over dfferen combnaons of lags of explanaory varables and he mulvarae lag lengh s seleced based on he Schwarz Informaon Crera (SIC). The mulvarae lag lengh wh he mnmum SIC s chosen. Second sep s o denfy possble canddaes for he ranson varable and es for he appropraeness of lneary. Terasvra and Anderson (992) propose an approxmang equaon and a procedure o es lnear AR model agans a nonlnear STAR model. The approxmang equaon of equaon () can be expressed as: y c φ L x L x z L x z L x z + v (3.4) ( ) + φ( ) d + φ2 ( ) d + φ3 ( ) d The lag lengh of x was deermned n he frs sep. For a gven ranson varable z and he amoun of delay d, equaon (4) can be esmaed and also be esed for he hypohess φ L) φ ( L) φ ( L). I repea he esmaon and hypohess esng ( 2 3 procedure for values of d from o 4 n hs paper. If here exss one or more values of d ha rejec he null hypohess of lneary, ndcaes a nonlnear STAR model and he delay d wh he lowes probably value (.e. he hghes F-sasc) s chosen. The hrd sep s o denfy he specfcaon of STAR model. If he null hypohess of lneary s rejeced and he ranson varable s deermned, he specfcaon of STAR model mus be chosen beween logsc STAR and exponenal STAR model. A sequence of hypohess ess and decson rules based on equaon (4) proposed by Terasvra and Anderson (992) are:

46 34 : φ ( L) (3.5) H, 3 H,2 2 3 : φ ( L) φ ( L) (3.6) H,3 2 3 : φ ( L) φ ( L) φ ( L) (3.7) If H, s rejeced, selec an LSTAR model. If H, s no rejeced and H,2 s rejeced, selec an ESTAR model. If H, and H,2 are no rejeced bu H,3 s rejeced, selec an LSTAR model. The fnal sep s he esmaon of he STAR model. The hreshold value c and he rae of ranson beween regmes γ are deermned by a wo-dmensonal grd search over daa pons of he ranson varable z and dfferen values of γ. The combnaon values of z and γ wh he mnmum sum of squared errors are he opmal esmaes. Then, he model can be esmaed by usng nonlnear leas squares. 3.3 Daa and he Emprcal Model 3.3. Daa Monhly daa on he Sandard and Poors 5 sock ndex s used as he sock prces. The excess reurns of sock prces ( XR ) are defned as he monhly percenage change n he S&P 5 ndex mnus he monhly yeld on 3-monh U.S. Treasury Bll. The change n he Federal funds rae ( DFF ) s used as he moneary polcy varable and s calculaed as he frs dfference of he Federal funds rae whch s already dvded by 2 for he monhly frequency. Snce oupu has a close relaonshp wh sock reurns and moneary polcy and mgh be he reason of nonlnear effecs of moneary polcy

47 35 on sock reurns, he growh rae of oupu s also ncluded n our emprcal model. Indusral producon s used as oupu for he monhly purpose, whle real Gross Domesc Produc s only avalable a quarerly frequency. The growh rae of oupu s measured by he percenage change n ndusral producon. All orgnal daa are colleced from Federal Reserve Economc Daa and he Cener for Research n Secury Prces (CRSP) daabase and sar from July 954 o December 25. Due o he los of one daa pons n calculang he change n he Federal funds rae, he values of excess reurns, he change n he Federal funds rae, and he growh rae of ndusral producon are from Augus 954 o December 25 and all expressed n percenage erms. Fgure 3. shows he me seres plo of excess sock reurns ( XR ), he change n he Federal funds rae ( DFF ), and he growh rae of oupu (Gy ) from Augus 954 o December 25. Fgure 3.2 shows he scaer plo of excess sock reurns and he change n he Federal funds rae. From Fgure he me seres plo of he change n he Federal funds rae, shows a very dfferen paern durng he perod of Ocober 979 o Ocober 982, especally he flucuaon of DFF n hs perod s larger han he res of he sample perod. Therefore, I wll nclude a dummy varable for hs specal perod n he model.

48 XR DFF Fgure 3.. The me seres plo of excess sock reurns, he change n he Federal funds rae, and he growh rae of ndusral producon: 954:8 25:2 Gy

49 37 2 XR (%) DFF (%) Fgure 3.2. The scaer plo of he scaer plo of excess sock reurns and he change n he Federal funds rae: 954:8 ~ 25:2 The oher hng s ha he monhly daa of sock reurns downloaded from CRSP daabase are values on he las day of each monh, bu he daa of Federal funds rae and ndusral producon are averages of daly fgures of a monh. When we look a he me pah n Fgure 3.3, he Federal funds rae and ndusral producon represen he values n he mddle of a monh and excess sock reurns are values n he end of a monh. Consderng he quck reacon of he sock marke, I allow he change n he Federal funds rae and he growh rae of ndusral producon can have conemporaneous effecs on he excess sock reurns n he model.

50 38 Fgure 3.3. Tme pah of varables The emprcal model Snce excess sock reurns, he change n he Federal funds rae, and he growh rae of oupu are all endogenously deermned, STAR models for hese hree varables can be wren as: * r q q p Gy Dummy DFF DFF XR a XR α α α α * [ q q p Dummy DFF DFF XR a α α α d r z F Gy, 8 ) ( ] α + ε + (3.8) r q p Gy DFF XR b DFF β β β d r q p z F Gy DFF XR b 2 2, ) ( ] [ ε β β β (3.9) * r q q p Gy Dummy DFF DFF XR c Gy γ γ γ γ FFshock Gy, XR +, FFshock Gy, + + FFshock Gy XR + XR

51 39 + [ c p3 q3 q3 + γ 5 XR + γ 6 DFF + γ 7 DFF * Dummy r3 + γ 8 Gy ] F( z3, d ) + ε 3 (3.) where rae, XR s excess reurns of sock prces, Gy s he growh rae of ndusral producon, for he specal perod Ocober 979 o Ocober 982: DFF s he change n he Federal funds Dummy s a me dummy varable Dummy, f Ocober 979 o Ocober 982, named he specal perod;, f Augus 954 o Sepember 979 and November 982 o December 25, named normal perod. p, q, r, for, 2, 3 are lag lengh of XR, DFF, and Gy n equaon (3.8), (3.9), and (3.), respecvely. z d, z d 2, and z 3 d are ranson varables for XR, DFF, and Gy equaons, respecvely. XR d, d Gy, and DFF d are all consdered as he possble ranson varable for each equaon. The lag lengh of he ranson varable d s chosen from o 4. Transon funcons F z ), F z ), and F z ) are all seleced beween he ( d ( 2 d ( 2 d logsc funcon and he exponenal funcon. For he model of excess sock reurns n equaon (3.8), he change n he Federal funds rae and he growh rae of oupu are allowed o have conemporaneous effecs on he excess sock reurns, so DFF, and Gy are ncluded n explanaory varables. Moreover, o capure he possble dfferen effecs of moneary polcy DFF on excess sock reurns beween he specal perod and he normal perod, a dummy varable Dummy s ncluded n conjuncon wh DFF. Thus, he effec of DFF on XR s

52 4 nonlnear: vares beween α 2 and α 2 + α 6 n he normal perod and vares beween α 2 + α 3 and α 2 α 3 + α 6 + α 7 + n he specal perod. funds rae For he model of Federal funds rae n equaon (3.9), he change n he Federal DFF s a funcon of lags of excess sock reurns XR, lags of he change n he Federal funds rae DFF, lags of growh rae of ndusral producongy, and he ranson varable z d 2. For dealng wh he specal perod for DFF, f coeffcens of all explanaory varables are allowed o change beween wo sample perods, here mgh be oo many regressors n he equaon. Therefore, I adop he generalzed leas squares esmaon mehod o deal wh he hgh volaly of DFF n he specal perod. I frs esmae he lnear AR model of equaon (3.9) and ge he resduals. I hen calculae he sandard devaon of he resduals for he specal perod and for he normal perod, so ha he rao of he sandard devaon of he resduals of he specal perod o he normal perod can be known. Nex, dvde each observaon (boh dependen and explanaory varables) n he specal perod by he rao n order o shrnk he hgh volaly n ha perod. Fnally, he four seps of denfyng and esmang STAR models can be appled o he ransformed dependen and explanaory varables. For he model of ndusral producon n equaon (3.), he explanaory varables of he growh rae of ndusral producon Gy are lags of excess sock reurns XR, lags of he change n he Federal funds rae DFF, lags of growh rae of ndusral producongy, and he ranson varable z 3 d. As he same season n he