Inflation and Asset Returns in a New Keynesian Model for Thailand, Including the Housing Sector*

Transcription

1 Inflaion and Asse Reurns in a New Keynesian Model for Thailand, Including he ousing Secor* Muichai Aroonrueangaram** Absrac This paper aims o invesigae he relaionships beween nominal reurns on asses and inflaion in Thailand. We consruc a New Keynesian model which includes hree ypes of asses namely sock, bond, and house. The feaure of his sudy is ha he housing secor and land facor are included in he model. This sudy examines he relaionships when he inflaion is driven by differen sources ha are echnology shock, governmen spending shock, and ineres rae shock. We caegorize inflaion ino hree ypes; normal goods inflaion, housing goods inflaion, and oal inflaion. The resuls of his paper show ha he relaionship beween inflaion and asse reurns are differen under various sources of inflaion. The economy wih all shocks a he same ime generaes weak negaive correlaion beween inflaion and all kinds of asse reurns. Finally, his paper also suggess wo ses of sraegy abou how o inves in asses by applying hese relaionships. JEL codes: Keywords: E44, G12 Asse Reurn, Inflaion edging, Real Esae, New Keynesian model (DSGE model), and Thailand. *A hesis submied in parial fulfillmen of requiremen for he degree of Maser of Ars (economics), faculy of economics, Thammasa Universiy, Thailand. **Telephone number: +66 (0) Fax number: +66 (0) muichai.fi@gmail.com

2 TABLE OF CONTENT age LIST OF TABLES... iii LIST OF FIGURES... iv CATER 1 INTRODUCTION Saemen of he roblem Objecives of he Sudy Scope of he Sudy Organizaion of he Sudy... 4 CATER 2 REVIEW OF RELATED LITERATURE Asse Reurns and Inflaion in General Equilibrium Model ousing in a General Equilibrium Model Lieraure on Case of Thailand CATER 3 TEORETICAL FRAMEWORK ouseholds Firms Wholesale Normal Goods Firms Wholesale ousing Goods Firm Law of Moion for Land and ouse rice Seing Decision of Reail Secor Dividend Governmen and Cenral Bank Asse Reurns Equilibrium arameerizaion i

3 age CATER 4 RESULTS Model roperies roduciviy Shocks Governmen Expendiure Shock Land Supply Shocks Ineres Rae Shock Inflaion and Asse Reurns Relaionship ow o Inves o edge agains Inflaion? CATER 5 CONCLUSIONS AND OLICY IMLICATIONS Conclusions olicy Implicaion Limiaions of he Sudy REFERENCES AENDICES Appendix A Appendix A Appendix A Appendix A Appendix A Appendix B ii

4 LIST OF TABLES age Table 1 arameer Values Table 2 Correlaion beween Asse Reurns and Inflaion under Differen Shocks Table 3 Correlaion beween each Exogenous Variable and Inflaion Table 4 Invesmen lan for Geing Reurn Raes wih Same Direcion as Inflaion Raes under Differen Shocks Table 5 Invesmen lan for Geing Reurns Raes Equal or Greaer han Inflaion Raes under Differen Shocks iii

5 LIST OF FIGURES age Figure 1 Impulse Response o a One Sandard Deviaion of roduciviy Shock in Normal Goods Secor Figure 2 Impulse Response o a One Sandard Deviaion of roduciviy Shock in ousing Goods Secor Figure 3 Impulse Response o a One Sandard Deviaion of Governmen Expendiure Shock Figure 4 Impulse Response o a 0.01 Sandard Deviaion of Land Supply Shock Figure 5 Impulse Response o a One Sandard Deviaion of Ineres Rae Shock iv

6 CATER 1 INTRODUCTION 1.1 Saemen of he roblem Inflaion is one of he mos serious economic problems. I can cause insabiliy and slows down he growh of economy in he long run. For households, inflaion devaluaes heir money value and hus decreases heir purchasing power and wealh. olding money does no help o mainain money value alhough i gives he liquidiy benefi. From hese reason, people begin o save heir money in he bank in form of deposi. owever, in he recen years, he inflaion rae rises oo much while he deposi rae is sill very low. Only saving money in bank canno give enough rae of reurn o figh wih he rae of inflaion. Thus, invesing in asses becomes an ineresing alernaive since i migh give he average rae of reurn greaer han rae of inflaion. Type of asses ha regularly considered for invesing is financial asse. The firs well-known risk free asse is governmen bond. Since governmen bond has low defaul risk, i also has low rae of reurn. Afer subracing he nominal rae of reurn wih he rae of inflaion, ha is he real rae of reurn, i migh be very close or lower han zero. This means ha invesing in he bond only migh no give enough rae of reurn o overcome he rae of inflaion. The noable risky asse ha is inroduced ino he invesmen decision is he common sock. Invesing in sock will ge he reurn from boh dividend and capial gain ha are generally greaer han reurns from bond. This allows households o ge he higher reurn by weighing heir invesmen beween bond and sock. One of he imporan non-financial asses for invesing is real esae. I provides housing services o he owner as one of he sandards of livings. Wih very low rae of depreciaion, house can be viewed as an asse because i remains has value afer consuming oday and has he chance ha is price will increase in he fuure. Sinai and Souleles (2003) sugges ha homeowners will face asse price risk ha comes hrough valuaion via capializaion rae changes under he influence of 1

7 inflaion. Since homeowner equiy represens he larges porion of mos households wealh accumulaion, changes in real value of house have crucial influence o personal wealh. Thus, how inflaion affecs o he house prices is one of he considerable opics. Even if people should inves in hose asses, he quesions are ha which kinds of asses, when, and how hey should inves o hedge agains inflaion under he differen economic condiions. According o he convenional wisdom, he Fisher hypohesis, Fisher (1930) indicaes he one-o-one posiive relaionship beween nominal reurn on asse and inflaion. ence holding asse migh be a good hedge agains inflaion since he nominal reurn will move ogeher wih he inflaion. Many economiss sudy on he relaionship beween asse reurns and inflaion. The resuls have boh conformed and opposed o he former belief. The examples of he auhors who claim ha asse reurns have posiive relaionship wih inflaion are Ely and Robinson (1997), Anari and Kolari (2002), Wei (2010), Adam and Frimpong (2010), Kim and Ryoo (2011), Newell (1996), Bond and Seiler (1998), Anari and Kolari (2002), Moigne and Viveiros (2008), Erol and Tiriroglu (2008), and ark and Bang (2012). Meanwhile he resuls from oher groups of auhors, which conflic o Fisher hypohesis, are composed of (1) he negaive relaionship beween asse reurns and inflaion and (2) no long run relaionship beween asse reurns and inflaion. Those lieraures are Bodie (1976), Lee(1998), Marshall (1992), Engsed and Tanggaard (2001) and Francis and Tewari (2011), ark, Muluneaux, and Chew (1990), Chan, endersho, and Sander (1990), Yobaccio, Rubens, and Kecham (1995), oesli, Macgregor, Maysiak, and Nanhakumaran (1997), and Zhou and Clemens (2010). Mos of researches employ economeric echniques for sudy. Only few researches employ general equilibrium model for his issue and almos of hem focus on sock reurns-inflaion relaion wih flexible price assumpion. In addiion, here is no research in his area ha applies general equilibrium model which includes real esae in he model. Thus, he room for his poin sill opens. Applying dynamic sochasic general equilibrium (DSGE) model in he sudy gives some advanages for analysis. I allows one o view he mechanism in he economy and examine he linkage beween adjusmens of each asse reurns more clearly. Anoher benefi is ha DSGE model allows us o creae some sochasic 2

8 shocks such as echnological change, or change in macroeconomic policy, o see adjusmen and behavior of each variable in he model. From hese reasons, using DSGE model is superior o give some explanaions on he mechanism inside he economy. As menioned above, how asse reurns correspond o he inflaion is remain ambiguous. Even if many economiss sudy on his relaionship by employing economerics, heir resuls remain canno provide any obvious explanaion. Since here is a lack of sudy in his issue which using a general equilibrium model wih housing asse, his encourages his paper o employ a DSGE model wih hree ypes of asses namely sock, bond, and house. The sylized version of DSGE model as New Keynesian Moneary Model is aken ino accoun. Finally, his paper aims o sudy he impac of inflaion on asse reurns and examines how o use each kind of asse as a hedge agains inflaion. 1.2 Objecives of he Sudy The objecives of he sudy are 1. To invesigae he heoreical relaionship beween he asse reurns and inflaion in a New Keynesian Economics Model. 2. To examine how o use each kind of asse as a hedge agains inflaion. 1.3 Scope of he Sudy This sudy employs a New Keynesian Moneary Economics Model which assumes he price rigidiy assumpion. The model focuses on hree ypes of asses namely sock, bond and house. The se of parameers ha is used in he model is from he case of Thailand. For unknown parameers, we calibrae by employing he daa se during he year

9 1.4 Organizaion of he Sudy This paper is organized as follows: Chaper 1 saes he significance of his sudy. Chaper 2 is he review of he relaed lieraure. The explanaion and seing of specific model for his sudy is in Chaper 3. The resuls of model are described in Chaper 4. Finally, Chaper 5 gives he conclusions of he sudy and some policy implicaions. 4

10 CATER 2 REVIEW OF RELATED LITERATURE This chaper provides a review of relaed lieraures on relaionship beween asse reurns and inflaion. The relaionship beween asse reurn and inflaion is firsly proposed by Fisher (1930). Afer ha, his opic becomes a popular issue in 1970s. Economiss begin o invesigae he relaionship beween asse reurns, especially sock and real esae, and inflaion. Since boh heoreical and empirical sudies are published wih he mixed resuls, several hypohesizes are proposed o explain he conflic resul. For he case of Thailand, here are only few lieraures abou his issue and none of hem employs he general equilibrium in he sudy. The lieraures migh be caegorized ino four disinc groups: (1) hypohesis of relaionship beween asse reurns and inflaion, (2) asse reurns and inflaion in general equilibrium model, (3) housing in general equilibrium model, and (4) lieraure on case of Thailand. 2.1 ypohesis of Relaionship beween Asse Reurns and Inflaion Iniially, Irving Fisher (1930) proposes he heory of ineres. e hypohesizes ha nominal ineres rae can be expressed as he sum of expeced real ineres rae and expeced inflaion rae. This proposiion can be applied o all asses. Then, he relaionship beween nominal reurn of asse j and expeced inflaion can be formulaed as j, j, E r E r E, (2.1) where r j, and r j, are respecively nominal and real rae of reurn on asse j, and is rae of inflaion. In he Fisherian view, he real secor and moneary secor are largely independen. The real reurn is deermined by real facors like produciviy, invesor ime preference, and ha real reurn is no relaed o expeced inflaion. In he efficien marke, he price of asse j or he expeced nominal reurn is he sum of appropriae equilibrium expeced real reurn and expeced inflaion. From his reason, he rae of 5

11 nominal reurn should move one-o-one wih he rae of inflaion, hus imply ha invesing in asse can hedge agains inflaion. Since 1970s, many economiss have ried o examine wheher Fisher hypohesis hold for each kind of asse. The wo popular asses has been examined are common sock and real esae. For he relaionship beween sock reurns and inflaion, Ely and Robinson (1997), Anari and Kolari (2001), Adam and Frimpong (2010), and Kim and Ryoo (2011) find supporive evidences o Fisher hypohesis. They claim ha one can hedge agains inflaion by aking long posiion of common sock or he relaionship beween sock reurns and inflaion is posiive. Meanwhile anoher group of sudies claims ha sock canno hedge agains inflaion or he relaionship beween sock reurns and inflaion is negaive, his group composes of Bodie (1976), Fama and Schwer (1977), Lin (2009), and Francis and Tewari (2011). Moreover, Barnes (1999) gives he more explanaion abou his relaion ha lowaverage-inflaion counries end o display a negaive or negaive bu insignifican linear relaionship beween reurns and inflaion, while high-average-inflaion counries ofen evince a srong posiive or posiive bu insignifican linear relaionship. To sum up, hose lieraures, which esing he Fisher hypohesis, represen ambiguous relaionship beween sock reurns and inflaion. Due o he anomalous relaionship beween sock reurns and inflaion, several hypohesizes are proposed o explain ha negaive relaion. Among hem, he main hypohesizes are popularly discussed by many auhors. Modigliani and Cohn (1979) propose he inflaion illusion hypohesis. They claim ha sock marke invesors suffer from inflaion illusion. So ha when inflaion rises, hey end o discoun expeced fuure earnings of sock more heavily by using higher nominal ineres raes. As a resul, sock prices are undervalued when inflaion is high and become overvalued when inflaion is low, hese lead o a negaive relaionship beween sock reurns and inflaion. Many economiss apply his hypohesis in many cases. Rier and Warr (2002), Campbell and Vuoleenaho (2004), and Cohen, olk, and Vuoleenaho (2005) find he compaible resul o inflaion illusion hypohesis. owever, Lee (2010) finds ha inflaion illusion can explain he pos-war negaive sock reurns-inflaion relaion, bu i is no suppor wih he pre-war posiive relaion. e also shows ha he resul occurs o every developed counry under consideraion. 6

12 This resul seems inconsisen o inflaion illusion hypohesis ha predics only he negaive relaion. Anoher imporan hypohesis is proposed by Fama (1981). e hypohesizes ha he negaive relaionship beween real sock reurns and inflaion are he consequence of proxy effec. The proxy effec hypohesis, which based on money demand model, implies ha relaion of sock reurn and inflaion come from: (1) he posiive relaion beween sock reurn and real aciviy and (2) he negaive relaion beween inflaion and real aciviy. The posiive relaionship beween sock reurns and real aciviy is driven by an expecaion of higher fuure dividends, while negaive relaionship beween inflaion and real aciviy is driven by money demand effecs arising from a raional expecaions version of he quaniy heory. Moreover, he also explains ha he spurious negaive relaions beween inflaion and real asse reurns are induced by an unexpeced characerisic of he money supply process during he pos-1953 period. The variaion in money demand in response o variaion in real aciviy has been adjused hrough variaion in inflaion raher han hrough nominal money supply growh. There are many lieraures examine ha wheher proxy effec hypohesis can explain he negaive relaionship beween sock reurns and inflaion. Mandelker and Tandon (1985), Vanderoff and Vanderoff (1986), Adrangi, Charah, and Shank (1999), Gallagher and Taylor (2002), and Erbaykal, Okuyan, and Kadioglu (2008) find he evidences ha consisen o proxy effec hypohesis, while Cochran and Defina (1993), Caporale and Jung (1997), Lee (1998) and Sari and Soyas (2005) find he evidences ha are no suppor o he proxy effec hypohesis. The esing of his hypohesis also reveals he mixed resuls. As seen from above ha relaionships beween sock reurns and inflaion have been widely sudied, he relaionships beween real esae reurns and inflaion are also received much aenion oo. The lieraures mosly use house price as reurn of real esae and consumer price index (CI) as proxy of inflaion. The resuls of sudies on real esae reurns-inflaion relaion also become mixed. Fama and Schwer (1977), Bond and Seiler (1998), Moigne and Viveiros (2008), and ark and Bang (2012) find evidence ha real esae can provide hedge abiliy agains inflaion, while ark, Mullineaux, and Chew (1990), Chan, endersho, and Sander (1990), Yobaccio, Rubens, and Kecham (1995), and Liu, arzell, oesli (1997), and Zhou 7

13 and Clemens (2010) repor he negaive relaionship beween real esae reurns and inflaion. According o hose mixed resuls, Erol and Tiriroglu (2008) sugges ha he differen relaionships migh come from he differen periods of each sudy ha infer o differen inflaion sae. They es he inflaion hedging abiliies of Turkish REITs in periods of boh high and moderae inflaion raes. The empirical resuls show ha Turkish REITs, in general, provide a beer hedge agains boh acual and expeced inflaion han do he common sock indices. Moreover, hey also indicae ha hedging abiliy of REITs is beer under high inflaion han under moderae inflaion. This explanaion seems similar o Barnes (1999) who explains ha sock and inflaion ends o has posiive relaion under high-average-inflaion counries and negaive relaion under low-average-inflaion counries. Since hose aricles mosly employ consumer price index (CI) as price variable in hose sudies, Anari and Kolari (2002) noe ha he resuls from hose sudies migh be incorrec. They sugges ha since housing coss range abou 20% - 30% of he CI, regress house price on rae of change in he CI migh be biased. To avoid poenial bias in esimaing relaionship beween inflaion and house prices, hey exclude housing cos from heir measure of goods and services prices. Thus, his curren paper will apply he measuremen of non-housing goods and services price ino model. Moreover, he relaionships beween house prices and boh CI and prices of non-housing goods and services will be invesigaed. The above lieraures illusrae he resuls which boh compaible and inconsisen o he convenional wisdom, Fisher hypohesis. Even if many lieraures ry o explain he anomalous relaionship hrough he alernaive hypohesizes, hose remain canno provide he obvious mechanism inside he economy due o he lack of quaniaive framework. Therefore, some economiss ry o sudy he relaionship beween asse reurns and inflaion in a general equilibrium model. 2.2 Asse Reurns and Inflaion in General Equilibrium Model Lieraures on his opic which using general equilibrium model mosly focus on sock reurns and inflaion relaionship. These lieraures add he role of money in o he model. This allows one o sudy he connecion beween moneary 8

14 secor and real secor which affecs he relaionship beween inflaion and asse reurns, while in he Fisherian view he moneary secor and real secor are largely independen. The aricles mosly add real cash balance direcly ino he uiliy funcion of households which Feensra (1986) has shown ha his way of incorporaing a role for money is equivalen o assuming ha money faciliaes consumpion ransacions. For relaionship beween sock reurns and inflaion, Sulz (1986) shows he negaive relaion beween sock reurns and inflaion. Danhine and Donaldson (1986) also show he similar resul. They explain ha common socks are no a good hedge agains inflaion from a nonmoneary origin, while socks will offer perfec proecion over he long run agains purely moneary inflaions. This explanaion conforms o resul of Bakshin and Chen (1996) which heir model shows ha sock reurns will be negaively correlaed wih inflaion while posiively correlaed wih money growh. Marshall (1992) also reveals negaive correlaions beween expeced asse reurns and expeced inflaion. Moreover his auhor exends he explanaion from Fama (1981) ha he asse reurns-inflaion correlaion will be more srongly negaive when inflaion is generaed by flucuaions in real economic aciviy han when i is generaed by moneary flucuaions. Moreover, due o subsanial negaive sock reurns-inflaion relaion resuls, Marshall (1992) also describes ha alhough here is no money illusion or marke inefficiency in he economy, he model remains indicae he negaive correlaions beween asse reurns and inflaion. This resul can happen because he Fisher hypohesis does no generally describe he implicaions of dynamic economic equilibriums when he ransacion role of money is explicily aken ino consideraion. The prior lieraures mosly employ a flexible price assumpion in he sudies, while more recen lieraure inroduces sicky price assumpion ino sudy. Wei (2010) applies he sandard New Keynesian model o sudy he relaionship beween common sock reurns and inflaion. Anoher feaure of his sudy is ha i uses anoher proxy of sock reurn ha is dividend yields. The model shows ha dividend yield has posiive correlaion wih rae of inflaion and echnology shocks will move boh inflaion and he dividend yield in he same direcion. Moreover he argues ha he posiive correlaion beween inflaion and he dividend yield does no 9

15 consiue evidence of inflaion illusion since a correlaion which observed in he daa is indicaed by his model, which does no include any irraionaliy. Alhough here are many researches on his opic which using general equilibrium model, almos of hem focus on relaionship beween sock reurn and inflaion. The lack of lieraure ha concenraes on real esae reurn-inflaion relaion in a general equilibrium model encourages his sudy o add real esae ino he consideraion. To undersand more abou he aspec of real esae before add i ino he model, he nex secion will provide he deail of housing in general equilibrium model and some issues abou real esae. 2.3 ousing in a General Equilibrium Model There are several ineresing dimensions abou housing such as housing prices, housing invesmen, and housing wealh. Jin and Zeng (2004) sugges one imporan aspec of house ha i depreciaes a an annual rae of 1.54% compared o he depreciaion rae of durable goods a 21%. This makes house a much beer sore of value. Iacoviello (2010) provides some facs from prior researches on housing in general equilibrium model. The movemens in he pricing of housing are only loosely conneced o movemens in oher prices. In addiion, house price inflaion is more volaile han consumer price inflaion. This auhor also poins ou abou he housing wealh effec ha housing wealh and aggregae consumpion expendiures end o move ogeher in pos-world War II U.S. hisory, while he evidence from recen years show ha he correlaion beween hem become lower. In addiion, Fisher (2007) documens ha housing invesmen leads non-housing invesmen, and is more volaile. This observaion laer has led o he famous quoe by Ed Leamar ha housing is he business cycle. As noed by Iacoviello (2010), here are many ineresing issues for fuure researches o sudy such as he role of financial inermediaion, he deerminans of house prices, how o sabilize house prices, and relaionship beween housing and labor marke. ouse can be brough ino a general equilibrium model wih many differen mehods. The examples of lieraures ha model housing in a general equilibrium model compose of Jin and Zeng (2004), Davis and eahcoe (2005), Iacoviello 10

16 (2005), Favilukis, Ludvigson, and Nieuwerburgh (2010), and Jaccard (2011). In general, house gives he sream of uiliy o households and also represens he wealh of households. The housing producion is similar o he non-housing goods producion which is normally assumed Cobb Douglas producion funcion. Jin and Zeng (2004) poin ou ha house is produced from consrucion secor which is labor inensive. The special inpu facor in housing producion is he land. As seen in Davis and eahcoe (2005) and Favilukis, Ludvigson, and Nieuwerburgh (2010), hese lieraures inroduce land as an addiional inpu facor ino housing producion. To make model more realisic, some lieraures such as Iacoviello (2005), Favilukis, Ludvigson, and Nieuwerburgh (2010) add he banking secor o capure he housing finance ha represens he credi consrain for buying house. Finally, hese researches mosly employ he business cycle model which assumes he flexible prices in housing secor. For his sudy, he model employs he general housing producion funcion. Land inpu facor is added ino housing producion and belong o governmen which similar o Favilukis, Ludvigson, and Nieuwerburgh (2010). In addiion, he sickiness of prices assumpion is added o he model for analysis is effec o he house prices. 2.4 Lieraure on Case of Thailand In he case of Thailand, almos researches focus on he relaionship beween sock reurns and inflaion. Only few lieraures provide a sudy on oher asse reurnsinflaion relaion. For he case of sock reurns and inflaion, Spyrou (2004) invesigaes he Fisher hypohesis for equiy reurns in en emerging counries. For he resul of Thailand, he negaive and saisically significan relaionship beween he changes in consumer prices and equiy reurns is found. This resul resembles o Khil and Lee (2000) who sudy real sock reurn-inflaion relaions in U.S. and 10 pacific-rim counries. This aricle exhibis a negaive relaionship beween real sock reurns and inflaion. They also explain ha real oupu disurbances drive a negaive sock reurn inflaion relaion, while moneary disurbances yield a posiive sock reurn inflaion relaion. In addiion, real disurbances appear o be more imporan ha 11

17 moneary disurbances during he sample period. Tha is he reason ha observed relaion beween sock reurns and inflaion is negaive. Meanwhile, ermpoon (2010) sudies which asse class ha can provide an effecive hedge agains inflaion. By giving he definiion of effecive hedge ha is a maximum reducion invariance of porfolio wih asse and bond, his sudy finds ha he energy and food sock can provide efficiency of inflaion hedging in Thailand. In he case of long run relaionship beween sock reurns and inflaion, Maghyereh (2006) indirecly examines he issue of poenial nonlinear long-run relaionships beween sock reurns and inflaion for 18 developing counries. The auhor does no find he long run relaionship beween sock price and inflaion for case of Thailand. Tha resul suppors o Limpanihiwa and Rungsombudpornkul (2010) who invesigae he relaionship beween inflaion and sock prices by applying he coinegraion es and vecor auoregression (VAR). This lieraure also shows ha here is no relaionship beween inflaion and sock price in Thailand for year 2000 o March The long run relaionship for sock reurns and inflaion in Thailand is also anomalous from he Fisher hypohesis. For inflaion hedging abiliy of real esae in Thailand, eungchuer (2006) employs single-deached house price (excluding land), own house price index (excluding land), and land price index which include of Bangkok and is viciniy. Inflaion is decomposed ino expeced and unexpeced inflaion. The sample period under examinaion covers April1998 Decembe2004. The resuls show ha housing markes are no a good hedge agains inflaion due o heir insignifican coefficien. While he relaionship beween reurns of land segmen and unexpeced inflaion is more ha one-o-one relaion, hus land segmen hedges agains inflaion shock or unexpeced inflaion. Ibrahim, adli, and Baharom (2009) sudy he relaionship beween housing prices and he macroeconomic and sock prices in Thailand. owever, heir resuls indicae posiive relaionships beween housing prices and macroeconomic and sock prices. They claim ha in he long run behavior of housing prices is governed by is relaionship o sock prices, real oupu, and inflaion. As similar o he previous secion, he lieraures for he case of Thailand also reveal anomalous resuls o he former belief, Fisher hypohesis. And he 12

18 limiaion of sudies in Thailand is ha here is no lieraure employed general equilibrium model o sudy his opic. To summarize his chaper, he relaionship beween asse reurns and inflaion ha is firsly proposed as Fisher hypohesis which indicaes he one-o-one posiive relaionship beween asse reurns and inflaion. Many economiss laer have examined his relaion. They especially focus on asses namely common sock and real esae. Lieraures reveal he mixed resuls which boh suppor and oppose o he former belief. In order o view he mechanism inside he economy, a group of aricles employ a general equilibrium model o sudy his opic. owever, only common sock is aken ino he sudies used general equilibrium mode. There is a lack of sudy included of housing in a general equilibrium model. Moreover, mos of heoreical lieraures employ he flexible price in he model. Furhermore, lieraures in his issue for he case of Thailand also repor he anomalous resuls for boh common sock and real esae reurns. And here is no one sudied his opic in a general equilibrium model. From above reasons, his paper employs a New Keynesian Moneary model for sudy an implicaion of asse reurns in economy wih price sickiness assumpion. In addiion, hree kinds of asses namely sock, bond, and house, are added ino he model in order o sudy he relaionship beween asse reurns and inflaion. This allows one can sudy he subsiuion effec from change in reurn of each asse or he adjusmen of households in holding each kind of asses in he model. 13

19 CATER 3 TEORETICAL FRAMEWORK This chaper provides a descripion of he model. In his sudy, he closedeconomy New Keynesian Moneary model has been employed wih he hree kinds of asses for invesing namely sock, bond, and house. The model consiss of hree pars ha are households, firms, and governmen and cenral bank. ouseholds maximize heir uiliy subjec o he budge consrain. Firms maximize heir profi subjec o producion funcion. According o addiional goods as house, firms are composed of he wo secors ha are non-housing goods secor or normal goods secor and housing goods secor. Under monopolisic assumpion, firms also have power o se prices in order o maximize heir profi subjec o he demand for goods. Governmen in his model issues bond, imposes ax, and consumes and cenral bank ses he policy ineres rae o sabilize he economy. Finally, he sandard reurns of each asse are defined o be invesigaed heir relaionships wih inflaion. 3.1 ouseholds ouseholds in his model are composed of homogeneous individual. Each of hem purchases bundle of goods, supplies labor, and invess in asses. The bundle of consumpion includes of non-housing goods or called normal goods housing goods represenaive household is C and. The supply of labor is represened by N. The uiliy of a 1 M C N C U C,, N, C 1 1. (3.1) In he uiliy funcion(3.1), represens he coefficien of relaive risk aversion. Agens gain heir uiliy from combinaion of consumpion in normal goods and housing goods. arameer C deermines he relaive weighs in uiliy beween normal goods and housing goods consumpion. Wihou one of hem, he uiliy from 14

20 consumpion will be zero. The ime for working will decrease he uiliy wih he degree of curvaure. as Then, households maximize he expeced discoun value of lifeime uiliy Max E U C,, N, (3.2) 0 subjec o he budge consrain C S B C,, S, 1 1 W N D S R B where is he discoun facor., 1 S, 1 1 1, (3.3) From he budge consrain(3.3), all erms are in form of nominal level. C, and, are he prices of normal goods and housing respecively. The prices and shares of sock are represened by S, and S respecively. B denoes amoun of nominal governmen bond ha is held by agen. ges from working and is he ax rae on income. housing sock. W is he nominal wage ha agen is he depreciaion rae of D is he dividend from holding share of equiy. Finally, 1 gross ineres rae of he governmen bond. R is he To explain household budge consrain, he oal use of wealh can be disribued o purchasing in normal goods, housing goods, sock, and bond. Meanwhile, he sources of wealh come from wage income afer ax, value of housing goods ha are held from las period, value of sock from las period and is dividend, and value of bond and is ineres income from las period. In his model, here are hree kinds of asses ha agen can inves namely sock, bond, and housing. ousing is goods for consumpion which give he uiliy o agen. Afer consuming housing in firs period, i remain has he value in he nex period bu will decay by he rae of housing depreciaion. Thus, housing goods also can be viewed as asse for invesmen. Socks are issued by firms and sold o household. For holding share of sock, household will ge he dividend from operaing firm and has he chance o ge he capial gain. Bond is sold from governmen. 15

21 olding bond will ge ineres paymen as he reurn. The rae of reurn on bond is assumed o be he same as ineres rae policy from cenral bank. The represenaive household solves problem (3.2) subjec o(3.3), hen he Lagrangian for households maximizaion problem is given by (see Appendix A1) where U C,, N L E 1W N 1, 1 S, D S 1, (3.4) 0 R 1B 1 C, C, S, S B is he Lagrange muliplier or he shadow price of resource consrain. U and U, be he marginal uiliy of consumpion in normal goods Le C, and housing. U N, is he marginal disuiliy from selling one uni of labor. ouseholds maximize uiliy by choosing level of consumpion in normal goods and housing goods, ime for working, nominal bond, and share of sock. The firs-order condiion wih respec o opimal consumpion level provide U C, 1 C, 1, 1 E UC, C,. (3.5) Equaion (3.5) denoes he marginal rae of subsiuion of consumpion beween wo periods or can be viewed as he sochasic discoun facor. Then, all firsorder condiions will be derived in he erm of marginal uiliy from normal goods consumpion (see Appendix A1). The opimal level of housing goods consumpion is deermined by U,,, 1 E, (3.6) UC, C,, Equaion (3.6) shows he relaionship beween he level of consumpion in normal goods and housing. I illusraes how o conrol he iner-emporal allocaion beween he normal goods and housing consumpion. The opimal level of working is deermined by U W N, 1. (3.7) U C, C, 16

22 The relaionship beween opimal consumpion and labor supply is shown by equaion (3.7) where he marginal rae of subsiuion beween leisure and consumpion equals o real wage. The opimal level of holding bond is deermined by E, 1R 1. (3.8) Equaion (3.8) deermines he iner-emporal allocaion beween he consumpion in normal goods and he saving by holding bond. I implies ha if households reduce consumpion oday and save in form of bond, hen he will receive gross reurn o increase level of consumpion in he fuure. Finally, he opimal level of holding share of sock is deermined by E, 1 D S, 1 1 S, 1. (3.9) Equaion (3.9) represens he real value of share of equiy. The equiy price depends on he sum of discoun fuure dividend ha flows o he share holder. 3.2 Firms Firms in his model are composed of wo secors ha are normal secor and housing secor. The firs secor produces and sells he non-housing goods or called normal goods, while he second secor produces and sells house. Each secor uses labor and capial as he common facors o produce goods. The model assumes labor inpu used in boh secors is indifferen. This assumpion is also applied o capial facor. Wih housing producion, his sudy adds land facor ino housing producion funcion as Davis and eahcoe (2005). Moreover, land in his model is assumed o belong o he governmen as Favilukis, Ludvigson, and Nieuwerburgh (2010), housing firm has o pay for he permi o using land o governmen. The model also follows Bernanke, Gerler, and Gilchris (1999) in assuming a wholesale secor for producion and reail secor for pricing. Thus firms in normal goods secor are decomposed o he wholesale normal goods firms and reail normal goods firms, and firms in housing goods secor are also decomposed o he wholesale housing goods firms and reail housing goods firms. 17

23 Finally, firms belong o households, hus we can view he profi of he firm as he dividend ha finally will go back o household who hold he share equiy Wholesale Normal Goods Firms Wholesale normal goods firms produce normal goods and sell hem o reail normal goods firms in perfecly compeiive marke. They make decisions on how much labor and capial o be used. The producion funcion is Cobb-Douglas funcion which compounds of inpus and echnology. Denoe he oupu produced by wholesale normal goods firms as Y Z K N. (3.10) C 1C WC, C, C, C, Le YWC, is level of oupu produced by wholesale normal goods firms. Z C, is sochasic echnology level in normal goods secor. The inpu facors in normal goods producion are capial and labor as represened by KC, and N C,. arameer C indicaes he share of capial in normal goods secor producion. process as where Z Assume ha he echnology level in non-housing secor follows he AR(1) Z Z ln ln Z C, C, 1 Z ZC, C ZC, 0 Z 1, (3.11) is persisence of echnology level from las period and Z, is he 2 echnology shock which follows Z, N 0, Z. C The capial in his secor has he evoluion equaion as C K C, 1 I C, 1 K KC,, (3.12) where I C, is he capial invesmen in non-housing secor and K is he depreciaion rae of he capial sock. The maximizaion problem facing he wholesale normal goods firms is, 1 WC, WC, C, C, 0 Max E Y W N I. (3.13) where WC, is he price of normal goods sold by wholesale firms. C 18

24 The wholesale normal goods firms solve heir problem (3.13) by choosing level of inpu facors subjec o (3.10) and(3.12). (see Appendix A2) The Lagrangian for normal firms maximizaion problem is L Y W N I WC, WC, C, C, FC E, 1 C 1, (3.14) C 0 MCC, ZC, KC, NC, YWC, where MCC, is he Lagrange muliplier which represens he nominal marginal cos of normal goods. Then, firms choose a level of labor o maximize profi LFC / NC, 0as W MC Y N C, WC, 1 C (3.15) WC, WC, C, Equaion (3.15) is he labor demand which indicaes he level of labor required by normal firms mus saisfy he condiion ha he marginal oupu from labor equals o he real wage of labor. Firms choose a level of capial o maximize profi LFC / KC, 1 0 as E, 1 CMCC, 1 YWC, 1 KC, 1 1K 1. (3.16) Equaion (3.16) indicaes he level of capial ha firms should choose. Since he price of uni of capial is no defined, he level of capial will be deermined a level of marginal oupu from capial equals o 1/ WC,. Since he wholesale normal goods firms sell heir normal goods o he reail normal goods firms in he perfecly compeiive marke, so hey do no have he power o se heir price of goods. The price of normal goods sold by wholesale normal goods firms saisfy he condiion MC (3.17) WC, C, Wholesale ousing Goods Firm As similar o Davis and eahcoe (2005), one imporan characerisic of house is ha i mus be buil on land, so land is added ino he housing producion funcion. In his sudy, he definiion of land is he area ha gives service for housing firms o build consrucion on i. By his definiion, he farmland, swamp, grassland, 19

25 ec, or he area ha canno give he service are no land in his model. The oal supply of land a period is defined by L which composes of available land and used land. The land ha can give service for firms o build consrucion on i is called available land, while he land ha has already been used in housing producion as used land. Since here is a consrucion on used land, i canno give any new service ha allows firm o build new consrucion. Unil he old consrucion on he used land collapses, his used land will reurn o be available land and hus can give he new service for building some consrucions on i again. Moreover, his paper assumes ha (1) land belongs o governmen and (2) housing firms have o pay o governmen for a permi o consruc he residenial, which similar o Favilukis, Ludvigson, and Nieuwerburgh (2010). Wholesale housing goods firms produce housing goods and sell hem o reail housing goods firms in perfecly compeiive marke. The producion funcion in housing secor is consised of sochasic echnology, labor, capial, and land. Denoe oupu in he wholesale housing secor as 1 1 L Y Z L K N L. (3.18) W,,,, Le W, Y be he level of housing oupu from producion. Z, is he sochasic echnology level in housing secor. The level of land used in housing producion is L which according o definiion of land in his model, only available land can be used o produce new house. K, and N, are he level of capial and labor in housing secor. arameer L denoes share of land facor in housing producion, while 1 L denoes share of consrucion componen. is share of capial in he consrucion componen of housing secor producion. The echnology level in housing secor also follows AR(1) process as Z Z ln ln Z,, 1 Z Z, Z, 0 Z 1, (3.19) 20

26 where he persisence of echnology level is assumed o be same as echnology in normal goods secor and Z, is he echnology shock which follows, N 0,. 2 Z Z C To simplify he sudy, he model assumes ha depreciaion raes of capial sock in boh secors are idenical. Then, evoluion equaion of capial sock in housing secor is K, 1 I, 1 K K,. (3.20) where I, is capial invesmen in housing secor. The housing firms maximizaion problem is, 1 W, W,, L,, 0 Max E Y W N L I. (3.21) where W, is he price of housing goods sold by wholesale housing goods firms and L, is land price. Then, he wholesale housing goods firms solve heir problem (3.21) by choosing level of inpu facors subjec o (3.18) and (3.20). (see Appendix A2) The Lagrangian for wholesale housing goods firms maximizaion problem is L Y W N L I, (3.22) L W, W,, L,, F E, L 0 MC, Z, L K, N, YW, where MC, is he Lagrange muliplier which represens he nominal marginal cos of housing goods. Wholesale housing goods firms choose a level of labor o maximize heir profi LF / N, 0 as W MC Y 1 1 N, W, L. (3.23) W, W,, Equaion (3.23) also represens he level of labor required by housing firms or labor demand mus saisfy he condiion ha marginal oupu from labor equals o he real wage of labor. For he real wage in his secor, i is calculaed from dividing wage wih housing price. 21

27 Then, wholesale housing goods firms choose a level of capial o maximize profi LF / K, 1 0as E, 1 1L MC, 1 YW, 1 K, 1 1K 1. (3.24) Equaion (3.24) is also similar o he condiion (3.16) from normal secor. I indicaes ha he level of capial demand will be deermined a level of marginal oupu from capial equals o 1/,. Finally, he wholesale housing goods firms chooses a level of land o maximize heir profi L / L 0 as F L,,, L,, MC Y. (3.25) L Equaion(3.25) represens demand for available land which is derived from he condiion ha marginal oupu from land mus equals o he real price of land ha is L, /,. The wholesale housing goods firms also sell heir goods o he reail housing goods firms in he perfecly compeiive marke, so hey do no have he power o se heir price of goods. The price of housing goods sold by wholesale housing goods firms saisfy he condiion MC (3.26) W,, Finally, he oal labor and oal capial demands from firms in hose wo secors producion are added up o N N N, (3.27) C,, K K K. (3.28) C,, Law of Moion for Land and ouse Recall equaion(3.25), he demand for available land from wholesale housing goods firms can be represened in explici form as 1 1 L LMC, Z, 1,, L, L K N 22. (3.29)

28 Le variable X L, be he accumulaed used land which can be calculaed from summaion of land used a he period 1 up o curren period. In oher words, he accumulaed used land is he accumulaion of demand for available land from period 1 up o curren period. Combining wih equaion(3.29), he accumulaed used land is (see Appendix A3) where L LMC, Z, 1 L,,, L, X K N 1 1 L LMC, 1 Z, 1 1 L, 1 K, 1 N, 1 1 K 1 1 L LMC, 2 Z, K, 2 N, 2 1 K... L, 2 2 X L L 1 L 1... L, 1 K 2 K L, K L, 1 X L 1 X, (3.30) K is he depreciaion rae of consrucion on any used land. Equaion (3.30) represens he accumulaed used land in period which composes of wo erms. The firs erm represens he demand for available land in period and he second erm represens he accumulaed used land from period -1. Noe ha he accumulaed used land from las period does no equal o is previous amoun. The accumulaed used land will decrease hrough ime by a resul of he depreciaion of consrucion on he used land. Thus on aggregae here will be available land release from he accumulaed used land by he rae of depreciaion of consrucion. In oher words, a fracion of accumulaed used land from he las period will urn o be available land in his period. The land supply, L, is assumed o follow AR(1) process as L L 1 ln L ln L L L,, 0 L 1 (3.31) 23

29 where is persisence of land supply level from las period, L is land supply a L seady sae, and L 2 is he land supply shock which follows L, N 0, L. A equilibrium, he oal supply of land will equal o he aggregae of land used from equaion (3.30) ha is 1, 1 L L X. (3.32) K L From equaion(3.32), if he addiion of new demand for available land and aggregae of land used exceeds he oal supply of land, or new demand for available land, L, exceeds amoun of available land, he price of land will increase and hen he demand for available land will decrease. Thus he land marke will be in equilibrium by adjusmen of land price. (see Appendix A3) The law of moion for he aggregae of housing sock is given by 1 Y, 1, (3.33) where L. (3.34) K Equaion (3.33) represens he level of housing in he nex period ha will equal o he summaion of he level of housing afer depreciaion rae in his period and he new housings ha are consruced in his period. The depreciaion of housing comes from he depreciaion of capial srucure in housing srucure ha same as Davis and eahcoe (2005) rice Seing Decision of Reail Secor For he reail firms, here is exis a coninuum of reailers of measure one in each goods secor. Reailers in each goods secor buy he wholesale goods in a compeiive marke and differeniae wih no resource cos. Then, hey separaely sell heir goods in he normal goods marke and housing goods marke by seing heir prices o maximize profi. ouseholds, wholesale firms and governmen hen purchase he final goods for consumpion and invesmen. 24

30 Le Y j be he quaniy of normal goods sold by firm j and j C, C, be he price of normal goods j. The oal normal goods YC, are he following composie of individual firm normal goods as C 1 C 1 C 1,, C C C 0 Y Y j dj, C 1, (3.35) where C indexes he elasiciy of subsiuion beween each normal goods. chooses price C, Given equaion(3.35), he demand facing each non-housing firm when i is C C, C, C, C, Y j Y where C, is he price se by non-housing firms. And he aggregae price for normal goods secor is C, C, 0 sold by firm j and C C j dj, (3.36). (3.37) For he housing goods secor, le Y,, j be he quaniy of housing goods j be he price of housing goods j. The oal housing goods Y, can be derived from he composiion of individual housing goods firm as where chooses price, is 1 1 1,, 0 Y Y j dj, 1, (3.38) indexes he elasiciy of subsiuion beween each housing goods. Given equaion(3.38), he demand facing each housing goods firm when i,,,, Y j Y, (3.39) 25

31 where, is he price se by housing firms. And he aggregae price for housing goods secor is ,, j dj 0. (3.40) Following he formalism proposed in Calvo (1983), each firm rese is price only wih probabiliy 1 in any given period. Thus, each period a fracion 1 of firms will rese heir prices, while a fracion will keep heir prices unchanged. The can be viewed as naural index of price sickiness which in his model is assumed o be he same for each secor. Then, he aggregae price for normal goods and housing goods from equaions (3.37) and (3.40) will become C 1 C C, C, 1 C, C 1, (3.41) ,, 1, 1. (3.42) Since he goods in each secor are heerogeneous, he firms will se prices by aking he demand funcions in boh secors as given. And assume ha all firms have he same cos srucure hey will rese heir price equal o idenical price. Then, he pricing decision facing he firms in normal goods is MC Max E k YC k j YC k j C, k0 C, k C, k k C, C, k,,,, where MCC, is he nominal marginal cos for producing one uni of normal goods. Also he pricing decisions facing he firms in housing goods secor is (3.43) MC Max E k Y k j Y k j, k0, k, k k,, k,,,, (3.44) where MC, is he nominal marginal cos for producing one uni of housing goods. 26

32 The non-housing firms solve problem(3.43) subjec o(3.36) and housing firms solve problem (3.44) subjec o(3.39) will respecively choose heir opimal price in each period o maximize heir profi as (see Appendix A4) C,, k 1 C, k C, k C, k C, k k0 k 1 C E, k C, k YC, k k 0 E MC Y C 1 C k 1 E MC Y 1, k, k, k, k k 0 k 1 E, k, k Y, k k 0, (3.45), (3.46) where he gross rae of normal goods inflaion and housing goods inflaion are respecively C, C,, (3.47) C, 1,,. (3.48), 1 The equaions (3.45) and (3.46) are he answers for he firms pricing decision problems. Each of hem will be subsiued in o equaions (3.41) and (3.42) respecively o deermine he aggregae price level in each period. Define he numeraor and de-numeraor of opimal price seing condiion for normal goods firms (3.45) as A1 C, and A 2 C,, respecively. Then, equaion (3.45) can be wrien as C, C 1 C, A 1 A C, C 2 C, (3.49) where he numeraor and de-numeraor can be wrien in recursive forms as (see Appendix A4) C A1 C, mcc, YC, E, 1 C,, 1A 1 C, 1 (3.50) C 1 A2 C, YC, E, 1 C,, 1A 2 C, 1 (3.51) 27

33 Also, define he numeraor and de-numeraor of he opimal price seing condiion (3.46) for housing goods firms as A1, and A 2, equaion (3.46) can be wrien as, respecively. Then, 1, A 1 A, 2, (3.52) where he numeraor and de-numeraor can be wrien in recursive forms as (see Appendix4.2) A1, mc, Y, E, 1,, 1A 1, 1 (3.53) 1 A2, Y, E, 1,, 1A 2, 1 (3.54) Finally, I define he oal price index for goods in economy as Y Y C, C,,, Y Y C,,, (3.55) where all variables are deermined by he equilibrium of he model, and he gross rae of inflaion equaion can be defined as. (3.56) Dividend be compued from Define profi or dividend of normal goods firms as variable D C,, profi can D Y W N I, (3.57) C, C, C, C, C, The variable D, is profi or dividend of firms from operaing in housing secor. The dividend can be compued as D Y W N L I, (3.58),,,, L,, The profi from boh firms or dividend are added up o D D D. (3.59) C,, 28

34 3.3 Governmen and Cenral Bank The governmen in his model issues he permi o housing firms for residenial consrucion on any lands as see in Favilukis, Ludvigson, and Nieuwerburgh (2010). Then he governmen budge consrain is described by he following funcion G R B N W L B. (3.60) C, 1 1 L, The oal revenue of governmen is composed of he revenue from income ax, land permi, and he ne value of bond from borrowing households. The oal expendiure in each period is composed of governmen expendiure, G, and ineres expense. To simplify sudy, he model assumes ha governmen purchases only normal goods and imposes income ax a consan rae. Assume ha he governmen expendiure follow he process G G 1 ln G ln G G where G is seady sae value of governmen expendiure, G,, 0 G 1, (3.61) G is he persisence of governmen spending from las period, and G, is he fiscal policy shock wih variance 2 G. The governmen expendiure shock allows us o generae inflaion in order o examine he asse reurns and inflaion relaionship. The cenral bank in his model responds o he deviaions of inflaion and oupu from heir seady sae value. The moneary policy rule is described by he following ineres rae reacion funcion ln R ln R 1 ln R ln ln Y Y, R 1 R Y R, where 0 R 1,, Y 0,, R, (3.62) 2 is he ineres rae policy shock wih variance R. The variables and Y are inflaion rae and level of oupu a seady sae. R is ineres rae a seady sae. ere R indexes he degree of ineres rae smoohing. The posiive guaranees ha cenral bank will raise he shor-erm 29