REIT Markes and Raonal Speculave Bubbles: An Emprcal Invesgaon George A. Waers Asssan Professor Deparmen of Economcs Illnos Sae Unversy Normal, IL 61790-4200 gawaer@lsu.edu 309-438-7301 and James E. Payne Professor and Char Deparmen of Economcs Illnos Sae Unversy Normal, IL 61790-4200 jepayne@lsu.edu 309-438-8588 December 2005 Absrac: Ths paper uses he momenum hreshold auoregressve (MTAR) model and he resduals augmened Dckey-Fuller approach o es for he presence of Evans (1991) perodcally collapsng bubbles n he domesc REIT markes. The RADF es shows evdence of bubbles, bu he resuls of he MTAR es are mxed. The MTAR es shows asymmerc adjusmen for each REIT marke, bu only morgage REITs show evdence of bubbles, whch urn ou o be negave meanng he prce falls subsanally below he level warraned by fundamenals.
REIT Markes and Raonal Speculave Bubbles: An Emprcal Invesgaon 1. Inroducon The exsence of speculave bubbles, when sock prces devae from he level suggesed by marke fundamenals, does no necessarly volae he raonal expecaons and effcen markes hypoheses. Invesors cognzan of marke overvaluaon are compensaed for he rsk of he bubble collapsng wh excess posve reurns. Whn he leraure conegraon beween prces and dvdends s ofen aken o be evdence agans he presence of bubbles. However, Evans (1991) develops a class of perodcally collapsng bubbles, whch mgh escape deecon by such ess. The presen paper exends he emprcal leraure on he deecon of perodcally collapsng bubbles by examnng four classfcaons of real esae nvesmen russ (REITs) As dscussed by Jrasakuldech e al (2005), he REIT marke serves as an neresng case for examnng he possbly of speculave bubbles due o marke lqudy ssues, nformaonal asymmeres, and marke neffcency. Frs, unlke he sock marke, he REIT markes do no provde enough lqudy o suppor shor sellng whch ofen occurs when asse prces ncrease beyond he asse s fundamenal value (L and Yung, 2004). Second, he presence of nformaonal asymmeres and marke neffcency generaes an under-prcng of REIT seasoned equy offerngs, lmng he ably o capure marke overvaluaon (Ghosh e al, 2000). The speculave bubble leraure wh respec o he REIT marke s que lmed. Jrasakuldech e al (2005) nvesgae raonal speculave bubbles n he equy REIT marke usng he Dba and Grossman (1988a) approach of un roo and conegraon 2
ess of equy REIT reurns and macro fundamenals. Jrasakuldech e al (2005) fnd ha ndeed ha equy REIT prces and he macro fundamenals are conegraed, evdence agans he presence of bubbles. However, Evans (1991) pons ou ha he Dba and Grossman approach s unable o deec a class of raonal bubbles, known as perodcally collapsng bubbles. For nsance, he collapse of a bubble may be nerpreed as mean reverson n asse prces whn he sandard conegraon framework whch would nduce a bas owards rejecon of he null hypohess of no conegraon. 1 More specfcally, he Dba and Grossman approach o bubble deecon assumes he bubble componen follows a lnear process whereas Evans (1991) argues ha he bubble componen may follow a non-lnear process. Payne and Waers (2005 a, b) explore he possbly of perodcally collapsng bubbles a la Evans (1991) wh mxed resuls. 2 In he case of he equy REIT marke, Payne and Waers (2005b) fnd mxed evdence of posve perodcally collapsng bubbles. Ths sudy exends he leraure on bubble deecon n he REIT marke n he followng ways. Frs, he Dba and Grossman approach of usng un roo and conegraon ess whn he conex of he dvdend dscoun model s examned for he followng REIT classfcaons: all, equy, morgage, and hybrd REITs. Second, unlke Payne and Waers (2005a,b), he economerc approach wll allow for eher negave, when he prce falls below he level warraned by dvdends, or posve perodcally collapsng bubbles. Two alernave mehodologes wll be used o es for perodcally 1 In he case of REITs, Payne and Zuehlke (2005) presen evdence of posve duraon dependence excep n he case of morgage REIT expansons. 2 Payne and Waers (2005a) resrc here analyss o esng for negave perodcally collapsng bubbles and fnd evdence of such bubbles n he case of morgage and hybrd REITs. As an exenson o he sudy by Jrasakuldech e al (2005), Payne and Waers (2005b) follow he leraure by resrcng her analyss n esng for posve perodcally collapsng bubbles n he equy REIT marke wh nconclusve resuls. 3
collapsng bubbles for each REIT classfcaon: he resduals-augmened Dckey-Fuller (RADF) model of Taylor and Peel (1998) and he momenum hreshold auoregressve (MTAR) model of Enders and Sklos (2001). Secon 2 provdes he heorecal framework for he emprcal analyss. Secon 3 presens he emprcal mehodology, he daa and emprcal resuls. Concludng remarks are presened n Secon 4. 2. Theorecal Framework of Perodcally Collapsng Bubbles 3 Le he asse prce P a me depend on he expecaon a me of nex perod s prce P and dvdend D such ha 1 ( 1 r) E P 1 D 1 P (1) where he dscoun facor 0 (1 r) 1 1wh he general soluon o (1) gven as follows: P j 1 j ( 1 r) E D j B. (2) The raonal bubble erm B mus sasfy he submarngale propery E B +1 = ( 1 r)b and f a ransversaly condon s mposed on (2), he bubble erm s B 0. Indeed, f hese condons hold, he asse prce P s deermned solely by expeced fuure dvdends. Whle some queson he exsence of bubbles n lgh of he condons menoned above, here has been consderable research on wheher asse prces are deermned by dvdends alone. Specfcally, Dba and Grossman (1988a) argue ha he exsence of conegraon beween P and D does no lend suppor for he exsence of bubbles. 3 The heorecal secon draws heavly from Payne and Waers (2005 a, b). However, unlke Payne and Waers (2005 a, b), here s no resrcon as o he wheher a bubble can be negave or posve. 4
However, Evans (1991) quesons he approach underaken by Dba and Grossman (1988a) n ha a class of bubbles, known as perodcally collapsng bubbles, may very well exs ha would no be deeced by smple conegraon echnques. Recognzng he ssue rased by Evans (1991), we modfy hs model o allow for he possbly of posve and negave perodcally collapsng bubbles as follows: B 1 r), f B (3a) B 1 ( B 1 1 1 ( 1 r) 1B (1 r 1 1 ), f B. (3b) The parameers n equaons (3a) and (3b) sasfy and 0 (1 r). 4 The sochasc process γ s d, has condonal expecaon E γ +1 = 1, and γ >0, whch ensures ha a bubble wll no swch sgn. The erm represens a Bernoull process ha akes he value 1 wh probably and he value 0 wh probably 1-. Equaon (3a) represens he phase when he bubble grows a mean rae 1 r bu equaon (3b) shows ha f he bubble exceeds he hreshold, explodes a mean rae 1 (1 r) However, hs phase does no las ndefnely as he bubble collapses wh probably 1- each perod. The non-lneary of he process n equaons (3a) and (3b) creaes dffcules n deecng such bubbles va sandard conegraon ess beween prces and dvdends. Wheher he bubble erm B s posve or negave depends solely on he nal value B 0. If a bubble s negave, meanng he prces fell severely below he long erm rend for dvdends, wll always be negave and smlarly for posve bubbles. 4 Charemza and Deadmen (1995) specfy a more general model of perodcally collapsng bubbles. 5
Many auhors such as Dba and Grossman (1988b) have posulaed he mpossbly of negave bubbles, reasonng ha hey would evenually lead o negave prces. In conras, Wel (1990) consrucs a general equlbrum model showng he possbly of negave bubbles. He shows ha f he presence of a bubble alers raders dscoun rae, her valuaon of fundamenals could fall leadng o a fall n he asse prce. Snce he economercan does no observe hese changes, he fallng prce appears as a negave bubble. We fnd que plausble ha raders would focus more on shor erm gans durng a bubble epsode and allow for he possbly of eher posve or negave bubbles for he emprcal ess n hs paper. 3. Mehodology, Daa, and Resuls Monhly daa on he prces and dvdends for all, equy, morgage, and hybrd REITs were obaned from he Naonal Assocaon of Real Esae Invesmen Truss (NAREIT) for he perod 1972:01 o 2005:9. The orgnal daa was deflaed by he consumer prce ndex and convered o naural logarhms. The emprcal work begns by esng he null hypohess of a un roo n he respecve real REIT prces, p, and real REIT dvdends, d, where superscrp denoes he specfc REIT marke: a (all), e (equy), m (morgage), and h (hybrd), ncorporang he possbly of srucural breaks usng Perron s (1989) un roo es. y DU DT D( T ) y c y (4) b k 1 1 where y p or d ; DU ( T ) s a pos-break consan dummy varable; s a 1 b lnear me rend; DT 1( Tb ) s a pos-break slope dummy varable; 6
D( Tb ) 1( Tb 1) s he break dummy varable; and are whe nose error erms. The null hypohess of a un roo s gven by 1. Jrasakuldech e al (2005) provde several argumens n exogenously mposng a srucural break n 1991:11. Frs, here was ncreased marke lqudy n he pos-1992 perod as he REIT marke became domnaed by large nsuonal nvesors (Chan e al, 2003). Second, here was greaer marke ransparency of he REIT marke gven he ncreased analys and meda coverage of he markes (Genry e al, 2003 and Chu e al, 2003). Thrd, n 1991 he umbrella parnershp REIT organzaon srucure was creaed, whch permed greaer flexbly n purchasng propery; however, valuaon become more dffcul gven he lack of ransparency (Damodaran e al, 1997 and Lng and Ryngaer, 1997). Table 1 repors he resuls of he un roo ess allowng for an exogenously srucural break n 1991:11. The resuls across he REIT classfcaons ndcae ha real prces and dvdends are ndeed negraed of order one. Gven he respecve prces and dvdends are negraed of he same order, he Dba and Grossman approach o bubble deecon s examned by specfyng he followng conegraon equaon represenng he relaonshp beween REIT prces, p, and dvdends, d. p d (4) As repored n Panel A of Table 2 (column CR) prces and dvdends appear conegraed n each case as evden from he sgnfcan ADF es sasc. Followng he mehodology of Dba and Grossman, he presence of a conegraed relaonshp beween prces and dvdends can be nerpreed as evdence agans he presence of speculave bubbles n he REIT marke. However, nerpreng he presence of conegraon 7
beween prce and dvdends as evdence agans bubbles assumes a lnear process for he growh of B, whch mplys normaly n he resduals. Ths nerpreaon s quesonable gven ha a prelmnary examnaon of he resduals from equaon (4) dsplays boh skewness and excess kuross n he resduals, suggesng he presence of perodcally collapsng bubbles (see Panel A of Table 2). Taylor and Peel (1998) ncorporae skewness and excess kuross n consrucng a more effcen esmaor n conegraon ess of bubbles. 5 Specfcally, ess of conegraon examne he saonary of he resduals from equaon (4) as follows: ˆ ˆ u (5) 1 where he null hypohess of no conegraon s 0 whle he alernave hypohess s a saonary resdual, 0. As poned ou by Taylor and Peel (1998), a more effcen esmaor of can be obaned by correcng he leas squares esmae n equaon (5) for skewness and excess kuross whch wll mprove he ably o deec perodcally collapsng bubbles. Moreover, he adjusmen for skewness and excess kuross has superor power over sandard conegraon ess o correcly rejec a mean-reverng error model as a bubble. 6 Taylor and Peel (1998) advocae he followng wo-sep esmaor n he consrucon of he resduals-augmened Dckey-Fuller (RADF) es of he null hypohess of no conegraon. Frs, regress he frs dfference of he resduals of he conegrang equaon on her lagged level (see equaon 5 above) and use he new resduals, û, and 5 Ths es s based on he work of Im (1996) wh respec o resduals-augmened leas squares esmaors. 6 Taylor and Peel (1998), Sarno and Taylor (1999, 2003), as well as Capelle-Blancard and Raymond (2004) consruc crcal values and analyze he power of hs es agans alernaves. 8
2 ˆ 3 2 2 2 he esmaed varance,, o consruc he vecor, w ˆ [( uˆ 3 ˆ uˆ ),( uˆ ˆ )]. Second, re-esmae equaon (5) wh he addon of he vecor, ŵ, whch correcs he esmae of for skewness and excess kuross of he resduals as follows: wˆ 1 (6) * * where s whe nose. The key es sasc s, CR ˆ / V ( ˆ ), where s he ˆ * esmaor n equaon (6). 7 Panel A of Table 2 repors he resuls of he RADF es (column CR τ ) for each of he REITs. The RADF es canno rejec he null hypohess of non-conegraon for any of he REITs, hus provdng evdence of bubble-lke behavor. Whle he RADF es suggess he possbly of bubbles n he respecve REIT markes, he MTAR model proposed by Enders and Sklos (2001) s esmaed o deermne he possble asymmeres n he adjusmen owards he long-run equlbrum relaonshp beween REIT prces and dvdends,.e. he dynamcs of perodcally collapsng bubbles. 8 The possbly of asymmerc adjusmen s underaken n he followng regresson of he resduals generaed from equaon (4). ˆ I p ˆ I ˆ ˆ 1 1 (1 ) 2 1 v 1 (7) wh he Heavsde ndcaor funcon, I, represened by: 7 * * 2 ~ 1 The covarance marx of ˆ s esmaed by ~ V ( ˆ ) ( X M X ) where A wˆ 2 A 2 2 2 6 2 4 2 4 2 4 3 ( 6 64 9 3 ) 23( 4 3 )( 43 ) ( 4 3 ) ( 4 ) 4 2 6 2 2 ( )( 6 9 ) ( 4 ) 4 6 4 5 2 3 5 3 and denoes he h cenral momen of he dempoen marx, M w ˆ, s gven by and W ~ s he marx of he cenered resduals of u. X ~ s he vecor of he lagged seres of cenered resduals and ~ ~ ~ 1 ~ M I W ( W W ) W I s he deny marx wˆ where T T ŵ. 8 Bohl (2003) uses he MTAR model wh U.S. sock marke daa. 9
1 f ˆ 1 I (8) 0 f ˆ 1 where he hreshold value s se n accordance wh mnmzaon of he resdual sum of squares. 9 The MTAR model allows he adjusmen o depend on he prevous perod s ˆ change n 1. The MTAR model s especally valuable when he adjusmen s beleved o exhb more momenum n one drecon han he oher. The null hypohess of no conegraon s esed by he resrcon, 0. If real REIT prces, 1 2 p, and dvdends, d, are conegraed, he null hypohess of symmery s esed by he resrcon, 1 2. Indeed, f he esmaed coeffcen, 1, s sascally sgnfcan and negave and larger n absolue erms relave o he esmaed coeffcen, 2, he null hypohess of symmerc adjusmen s rejeced whch would provde evdence n favor of Evans (1991) defnon of posve perodcally collapsng bubbles n REIT prces. On he oher hand, f he esmaed coeffcen, 1, s sascally sgnfcan and negave and smaller n absolue erms relave o he esmaed coeffcen, 2, he null hypohess of symmerc adjusmen s rejeced whch would provde evdence n favor of Evans (1991) defnon of negave perodcally collapsng bubbles n REIT prces. Panel B of Table 2 dsplays he resuls of he MTAR models. Noe from equaons (7) and (8), he MTAR specfcaon provdes pon esmaes of 1 and 2. Frs, he pon esmaes, 1 and 2, sasfyng he saonary (convergence) condons. The null 9 Chan (1993) requres sorng he esmaed resduals n ascendng order, elmnang 15 percen of he larges and smalles values. The hreshold parameer ha yelds he lowes sum of squared errors from he remanng 70 percen of he resduals s used n he MTAR model. We found smlar resuls usng 10 and 5 percen cuoffs. 10
hypohess of no conegraon, 0, (F C column) s rejeced for each ype of REIT. 1 2 Furhermore, he null hypohess of symmery, 1 2, s rejeced n each case wh he excepon of hybrd REITs whch dsplays symmerc adjusmen. However, upon closer nspecon of he varous REITs, appears ha 1 s posve and sascally nsgnfcan n he cases of all and equy REITs, suggesng he absence of a perodcally collapsng bubble. The equy REIT resuls confrm earler resuls repored by Payne and Waers (2005a,b) over a slghly dfferen me frame. Wh respec o morgage REITs, he esmaed coeffcen, 1, s sascally sgnfcan and negave and smaller n absolue erms relave o he esmaed coeffcen, 2, ndcave of negave perodcally collapsng bubbles, a smlar resul o Payne and Waers (2005a). Conrary o Payne and Waers (2005a), who fnd evdence of a negave bubble n hybrd REITs, he resuls repored n hs sudy do no suppor he presence of eher posve or negave perodcally collapsng bubbles. 4. Concludng Remarks Ths sudy has exended he recen work of Jrasakuldech e al (2005) as well as Payne and Waers (2005a,b) on bubble deecon n he REIT marke n he followng ways. Frs, he Dba and Grossman approach of usng un roo and conegraon ess whn he conex of he dvdend dscoun model s examned for he followng REIT classfcaons: all, equy, morgage, and hybrd REITs. Second, unlke Payne and Waers (2005a,b), he economerc approach wll allow for eher negave or posve perodcally collapsng bubbles. Whn he conegraon framework for esng for speculave bubbles, Dba and Grossman (1988) argue ha such bubbles do no exs f 11
prces and dvdends are conegraed. The Dba and Grossman approach mplcly assumes he bubble componen follows a lnear process whereas he bubble componen may very well follow a nonlnear process, known as a perodcally collapsng bubble (Evans, 1991). Two alernave economerc approaches are used o ess for he presence of Evans (1991) perodcally collapsng bubbles. Frs, he resduals-augmened Dckey-Fuller (RADF) model ncorporaes skewness and excess kuross n provdng a more effcen esmaor n conegraon ess of bubbles. Conrary o he sandard conegraon ess, he resuls of he RADF ess are unable o rejec he null hypohess of non-conegraon for each REIT classfcaon. Second, n order o capure he asymmerc adjusmen processes assocaed wh eher negave or posve perodcally collapsng bubbles, he momenum hreshold auoregressve (MTAR) model s esmaed for each REIT classfcaon. The MTAR resuls ndcae he absence of perodcally collapsng bubbles for all, equy, and hybrd REIT classfcaons; however, morgage REITs exhb behavor ndcave of negave perodcally collapsng bubbles. 12
Table 1 Perron Un Roo Tes Sascs Real REIT Prces and Dvdends 1972:1 o 2005:9 Panel A: Real All REITs p -2.44 a a d -1.50-18.60 a a -16.67 a a p d Panel B: Equy REITs p -2.54 e e d -2.26-18.40 a e -10.00 a e p d Panel C: Morgage REITs p -2.76 m m d -3.08-12.93 a m -7.04 a m p d Panel D: Hybrd REITs p -1.42 h h d -1.85-19.12 a h -9.21 a h p d Noes: Sandard errors are denoed n parenheses and probably values n brackes. Crcal values o es he null hypohess of a un roo, 1 from equaon (4) s drawn from Table VI.B p. 1377 of Perron (1989) for. 60 as follows: 1% -4.88, 5% -4.24, and 10% -3.95. 13
Table 2 MTAR and RADF Resuls 1972:1 o 2005:9 Panel A: Resduals Augmened Dckey-Fuller Resuls CR Skewness Kuross CR τ All -3.20 b -0.04 6.78-1.02 Equy -3.38 b -0.59 31.57-0.54 Morgage -4.34 a 0.27 3.80-1.92 Hybrd -3.45 b 0.80 5.00-1.12 Panel B: Momenum Threshold Auoregressve Model Resuls τ ρ 1 ρ 2 F C F A Q(5) k All 0.02 0.01-0.07 8.26 b 5.60 a 4.14 4 (0.40) (-4.04) a {0.53} Equy 0.02 0.02-0.07 9.00 a 10.70 a 2.63 1 (0.85) (-4.15) a {0.76} Morgage -0.63-0.05-0.18 12.90 a 8.59 a 1.08 4 (-2.16) b (-4.62) a {0.96} Hybrd 0.47-0.11-0.06 8.65 a 1.52 0.33 4 (-2.91) a (-2.90) a {0.99} Noes: CR s he Dckey-Fuller es sasc appled o he resduals from he conegraon equaon (4) under he null hypohess of no conegraon wh crcal values: a(1%) -3.73, b(5%) -3.17, and c(10%) -2.91 (Engle and Granger, 1987). CR τ s he resduals-augmened Dckey-Fuller es sasc appled o he resduals from he conegrang equaon (4) under he null hypohess of no conegraon wh crcal values: a(1%) -3.98, b(5%) -3.44, and c(10%) -3.13 (Capelle-Blancard and Raymond, 2004). s he esmaed hreshold. 1 and 2 are he esmaed parameers from he MTAR specfcaon. -sascs denoed by ( ), and probably values n { } where a(1%), b(5%), and b(10%). F C represens he F-sasc correspondng o he null hypohess of no conegraon (.e. 1 2 0) wh crcal values provded by Enders and Sklos (2001, Table 5, p. 172, n = 250 and four lags an one lag whch are denoed n brackes): a(1%) 8.47 [8.84], b(5%) 6.32 [6.63], and c(10%) 5.32 [5.57]. F A represens he F-sasc correspondng o he null hypohess of symmery (.e. 1 2 ) usng he sandard F dsrbuon wh crcal values a(1%) 4.61 and b(5%) 3.00. k s he number of lags n equaon (7). Q(5) denoes he Ljung-Box Q-sasc a 5 lags. 14
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