China s Model of Managing the Financial System

Transcription

1 Chna s odel of anagng the Fnancal System arkus K. Brunnermeer Professor of Economcs, Prnceton Unversty chael Sockn Assstant Professor of Fnance, Unversty of Texas at Austn We Xong Professor of Economcs, Prnceton Unversty Presented at the Federal Reserve Bank of Atlanta 07 Fnancal arkets Conference anagng Global Fnancal Rsks: Shftng Sands and Shock Waves Amela Island, Georga ay 9, 07

2 Chna s odel of anagng the Fnancal System arkus K. Brunnermeer y chael Sockn z We Xong x February 07 Abstract Chna s economc model nvolves actve government nterventon n nancal markets. It relaxes/tghtens market regulatons and even drects asset tradng wth the objectve to mantan market stablty. We develop a theoretcal framework that anchors government nterventon on a msson to prevent market breakdown and the exploson of volatlty caused by the reluctance of short-term nvestors to trade aganst nose traders when the rsk of tradng aganst them s su cently large. In the presence of realstc nformaton frctons about unobservable asset fundamentals, our framework shows that the government can alter market dynamcs by makng nose n ts nterventon program an addtonal factor drvng asset prces, and can dvert nvestor attenton toward acqurng nformaton about ths nose rather than fundamentals. Through ths latter channel, the wdely-adopted objectve of government nterventon to reduce asset prce volatlty may exacerbate, rather than mprove, the nformaton e cency of asset prces. We are grateful to Wll Cong, Darrell Du e, Debbe Lucas, Lyan Yang, Haoxang Zhu, and semnar partcpants at 07 Amercan Economc Assocaton eetngs, NBER Chnese Economy eetng, 06 Rksbank acroprudental Conference, the nd Bank of Canada-Unversty of Toronto Conference on Chnese Economy, the nd Chna-Europe Conference on Transparency, Economc Insttutons and Governance, the 6th JRC Center Conference n Prnceton Unversty, and Unversty of Toronto for helpful comments and suggestons. y Prnceton Unversty and NBER. Emal: markus@prnceton.edu. z Unversty of Texas at Austn. Emal: chael.sockn@mccombs.utexas.edu. x Prnceton Unversty and NBER. Emal: wxong@prnceton.edu.

3 Introducton Chna has experenced rapd growth n the last three decades, and has become an mportant part of the global economy. Its underdeveloped nancal system, however, has recently been a source of great anxety for nvestors and polcy makers across the world. Ths anxety has been drven, n part, by the turmol n ts stock markets n 05, the sudden devaluaton of ts currency n 05 that rased doubts about the government s ablty to manage ts exchange rate, ts overheatng housng markets, and ts growng leverage at a natonal level. To fully understand these ssues, t s mportant to systematcally examne the dstnct structures and features of the Chnese economy and nancal system. A strkng feature of the Chnese nancal system s how actvely Chna s government manages t n order to promote nancal stablty. The government does so through frequent polcy changes, usng a wde array of polcy tools rangng from changes n nterest rates and bank reserve requrements to stamp taxes on stock tradng, suspensons and quota controls on IPO ssuances, rules on mortgage rates and rst payment requrements, provdng publc gudance through o cal meda outlets, and drect tradng n asset markets through government sponsored nsttutons. As potental just caton for such large-scale, actve nterventons, Chna s nancal markets are hghly speculatve, and largely populated by nexperenced retal nvestors. 3 Its markets experence hgh prce volatlty and the hghest turnover rate among major stock markets n the world. In addton, the Chnese government s paternalstc culture motvates t to vew stablzng markets and protectng retal nvestors as a prorty. Whle hghly relevant for nvestors and polcy makers, the mpact of such actve government nterventon n asset markets s stll not well understood. Even wthn the OECD, governments engaged n unconventonal monetary polcy wth large-scale asset purchases durng the nancal crss and subsequent recesson. Understandng ts tradeo s, consequently, See, for nstance, Song, Storesletten, and Zlbott (0) for a theoretcal model of how the nancal system asymmetrcally provdes credt to the state and non-state sectors n Chna. As evdence of ths, e, Schenkman, and Xong (009) llustrate how speculatve tradng by Chnese nvestors mght have contrbuted to a systematc devaton n the prces of A and B shares ssued by the same Chnese companes. The key d erence between these shares s that A shares can only be held by Chnese nvestors, whle B shares can only be held by foregn nvestors before 00. Furthermore, Xong and Yu (0) document a spectacular bubble n Chnese warrants from , durng whch Chnese nvestors actvely traded a set of deep out-of-money put warrants that had zero fundamental value. 3 Retal nvestors n Chna s stock markets hold about 50% of ts tradable shares and contrbute to about 90% of ts tradng volume.

4 s mportant not only for promotng stablty n the Chnese nancal system, but also for navgatng the post nancal crss envronment, n whch even governments n the OECD may be prepared to ntervene after epsodes of hgh volatlty or severe market dysfuncton. We develop a conceptual framework to analyze these nterventons, and, specally, government nterventon through drectly tradng aganst nose traders n asset markets. To do ths, we buld on the standard nosy ratonal expectatons models of asset markets wth asymmetrc nformaton, such as Grossman and Stgltz (980) and Hellwg (980), and ther dynamc versons, such as He and Wang (995) and Allen, orrs, and Shn (006). In these models, nose traders create short-term prce uctuatons and a group of ratonal nvestors, each acqurng a pece of prvate nformaton, trade aganst these nose traders to provde lqudty and to speculate on ther prvate nformaton. Our settng ncludes a new player, a government, whch s prepared to trade aganst the nose traders subject to a penalty on ts tradng actvty. That the asset fundamental n our settng s unobservable re ects realstc nformaton frctons faced by nvestors and polcy makers n the Chnese economy. To capture addtonal realstc features of the Chnese economy, we assume that nvestors are myopc to re ect the hghly speculatve nature of Chnese nvestors. Nose tradng n our framework arses as a result of nexperenced retal nvestors n the Chnese markets, who contrbute to prce volatlty and nstablty. Realstc nformaton frctons and moral hazard also ntroduce unntended nose nto the government s nterventon, wth the magntude of ths nose ncreasng wth the ntensty of government s nterventon. In addton, each nvestor has to choose between acqurng a prvate sgnal about the asset fundamental or about ths government nose before tradng. Ths nformaton acquston decson re ects the xed costs and lmts to nvestor attenton assocated wth acqurng nformaton. In accordance wth the Chnese government s paternalstc culture n mantanng market stablty, the government n our framework adopts a weghted objectve of mprovng nformaton e cency of the asset prce and reducng asset prce volatlty. These crtera are wdely used n government nterventon not only n Chna but also n many other countres. A conventonal wsdom posts that reducng prce volatlty, whch s easly mplementable, s consstent wth a more fundamental, yet d cult to mplement, objectve of mprovng the nformaton e cency of asset prces. Ths occurs because the government s tradng aganst nose traders smultaneously reduces prce volatlty and mproves prce e cency.

5 Wth these elements, we buld up our analyss n several steps. Frst, we characterze a benchmark economy wth perfect nformaton, n whch all nvestors and the government observe the fundamental. We show that, n the absence of government nterventon, the asset prce volatlty may explode and the market may even break down when the volatlty of nose tradng becomes su cently hgh. Ths market breakdown occurs because of the myopa of nvestors. As nvestors are concerned only wth the short-term return from tradng the asset, ther requred return ncreases wth the volatlty of nose tradng, and ths, n turn, makes the asset prce more senstve to nose tradng. As a result, the volatlty of the asset prce rses wth nose tradng volatlty, and may explode when t becomes su cently large, whch further rases the return requred by nvestors to provde lqudty to nose traders. Ths feedback process can cause the market to break down because there may not exst any rsk premum that can nduce the nvestors to trade. Such a market breakdown ntroduces a role for the government to reduce market volatlty and stablze the market. In ths envronment, the government s objectve of reducng prce volatlty s fully consstent wth mprovng prce e cency. We then consder an extended settng n whch the asset fundamental s unobservable to both nvestors and the government. We rst llustrate that, n the absence of government nterventon, reducng prce volatlty ntroduced by nose traders s consstent wth mprovng prce e cency. We then show that ntroducng government nterventon can gve rse to several unntended consequences. As a large player n the asset market, the government unavodably makes the nose n ts nterventon an addtonal prcng factor n asset prces, even though t nternalzes ts mpact on asset prces. Ths new prcng factor, n turn, can attract speculaton by nvestors n the presence of nformatonal frctons, who may choose to acqure prvate nformaton about the government s nose and, as a result, be dstracted from acqurng nformaton about the fundamental. In dong so, the nvestors speculaton about the government s nose can further mtgate the prce volatlty caused by nose traders, but can exacerbate the nformaton e cency of the asset prce. 4 Whether nvestors focus on acqurng nformaton about the asset fundamental or the 4 There s a growng lterature that explores how uncertanty about government polcy ntroduces a nonfundamental factor nto asset prces. See, for nstance, Salm (006) and Pastor and Verones (0, 03). Our focus here s not on provdng a mcrofoundaton for ths uncertanty, whch we take as gven, but n demonstratng how such uncertanty nteracts wth nvestor ncentves to acqure nformaton. A prevous draft of ths paper, whch had qualtatvely smlar nsghts, mcrofounded the uncertanty as nose n prvate sgnals that the government receves about the asset fundamental. 3

6 government nose determnes the behavor of asset prces, and can gve rse to two types of equlbrum, whch we label "fundamental-centrc" and "government-centrc", respectvely. In the fundamental-centrc equlbrum, nvestors each acqure a prvate sgnal about the fundamental and the asset prce aggregates ther nformaton to partally reveal the fundamental. In ths equlbrum, the government trades aganst both the nose traders, to mnmze ther prce dstorton, and aganst the nvestors, based on ther respectve prvate nformaton. In the government-centrc equlbrum, the nvestors focus on learnng about the government s nose, and share a smlar belef wth each other and wth the government about the fundamental. Consequently, they tend to trade alongsde the government aganst the nose traders, whch renforces the government s e ort to reduce prce volatlty and renders the government nterventon more e ectve n reducng the prce dstorton of the nose traders. The reduced prce volatlty, however, comes at the expense of asset prces beng less nformatve about the fundamental. Generally speakng, whether a fundamental-centrc or government-centrc equlbrum appears depends on the scale of the government s nterventon. There s a tendency n our economy for the market to shft from a fundamental-centrc equlbrum to a government centrc equlbrum as the government s nterventon ntens es beyond a certan threshold, and the nose the government ntroduces plays a su cently large role n asset prces. Ths occurs, for nstance, when the government assgns a su cently large weght to reducng prce volatlty, or when there s su cent volatlty from nose tradng n the market. Overall, our model delvers several key nsghts not only for government nterventon n Chna but also more generally for nterventon programs n other countres. Frst, t demonstrates that, even n the absence of nformaton frctons, there can be a role for government nterventon to reduce prce volatlty and mtgate the possblty of a market breakdown. Second, such nterventon can make the government nose an addtonal factor n asset prces, and ths addtonal factor may attract the speculaton of nvestors and dstract them from acqurng prvate nformaton about the fundamental. Ths speculaton, n turn, renforces the mpact of nose n the government s polcy on asset prces. These two mplcatons capture mportant observatons about Chna s nancal markets speculaton about government polces plays a central role n drvng market dynamcs and market partcpants pay great attenton to government polces, although less so to economc fundamentals. A lterature revew follows. Secton sets up the model wth perfect nformaton, and 4

7 derves the equlbra wth and wthout government nterventon. Our analyss here llustrates how a market breakdown can be avoded by the latter. Secton 3 extends the settng to ncorporate nformaton frctons, derves the new equlbra under d erent settngs wthout and wth government nterventon, and analyzes the e ects of government nterventon. Secton 4 concludes wth some addtonal dscusson. We cover the salent features of the equlbra under d erent settngs n the man text, whle leavng more detaled descrptons of the equlbra and the key steps for dervng the equlbra n the appendx. We also provde a separate onlne appendx that contans all techncal proofs nvolved n our analyss.. Related Lterature Our work contrbutes to the growng lterature on the mpact of polcy uncertanty on asset prces and the macroeconomy. Pastor and Verones (0, 03) explore the asset prcng mplcatons of uncertanty about government polcy outcomes and potental changes to polcy regmes. Fernandez-Vllaverde et al (03) nvestgates the macroeconomc consequences of uncertanty n scal polces. Salm (006) analyzes the asset prcng mplcatons of uncertanty about nvestor taxaton n an endowment economy, whle Croce, Kung, Nguyen, and Schmd (0) assesses ts role n a producton economy wth recursve preferences. Croce, Nguyen, and Schmd (0) examnes the nteracton between scal uncertanty and long-run growth when agents also face model uncertanty, and Ulrch (03) studes how bond markets respond to Knghtan uncertanty over the e ectveness of government polces. Baker, Bloom, and Davs (05) emprcally lnks government polcy uncertanty to busness cycle uctuatons. Our work extends ths lterature by studyng polcy uncertanty n the context of government nterventons n nancal markets. Our work also contrbutes to the lterature on dynamc models of asymmetrc nformaton n asset markets, whch ncludes Wang (994), He and Wang (995), Allen, orrs, and Shn (006), and Bacchetta and van Wncoop (006, 008). D erent from these studes, our model features a large agent (.e., the government) wth prce mpact, n addton to a contnuum of small nvestors, each possessng prvate nformaton. In our settng, nose n the government s tradng becomes an addtonal prcng factor, and, more nterestngly, a target of speculaton by the nvestors. We also contrbute to the lterature on the nancal market mplcatons of government nterventon. Gertler and Kyotak (03) constructs a framework for analyzng the macro- 5

8 economc mpact of large scale asset purchases by central banks. Bond and Goldsten (05) studes the mpact on nformaton aggregaton n prces when uncertan, future government nterventon n uences a rm s real outcomes. Boyarchenko, Lucca, and Veldkamp (06) study the mpact on nformaton d uson and propagaton, and Treasury aucton revenues, when the government can choose the form of the aucton, and consequently the market structure. Cong, Grenader, and Hu (07) explore the nformaton externalty of government nterventon n money market mutual funds n a global games envronment n whch nvestors face strategc coordnaton ssues and nterventon changes the nformaton publcly avalable to them. In contrast to these studes, we focus on the ncentves for nformaton acquston among market partcpants when there s uncertanty about the scope of government nterventon n nancal markets through large-scale asset purchases. 5 Our work also relates to the growng lterature on the role of the government n shapng the nformaton envronment of market partcpants. Goldsten and Letner (05) and Castro, artnez, and Phlppon (05), for nstance, consder the mpact of strategc publc dsclosure of the results of bank stress tests by an nformed polcy maker. Angeletos, Hellwg, and Pavan (006) and Goldsten and Huang (06) consder nformaton desgn by an nformed polcy maker that can send messages through ts actons to coordnate the response of prvate agents n a global games settng. 6 Smlar to Cong, Grenader, and Hu (07), we do not assume the polcy maker has an nformatonal advantage to market partcpants, and that t shapes the endogenous nformatveness of prces through ts dstortonary actons that do not a ect the underlyng cash ows of nancal assets. Our study helps to understand how the government, by nternalzng what nformaton nvestors acqure, can change the nformaton re ected n nancal markets by shftng the fundamentals that nvestors coordnate on learnng, whch can be to the potental detrment of market e cency. Sten and Sundarem (06) develops a model to analyze the communcaton between the Federal Reserve and the bond market. By assumng that the Fed has an objectve to mnmze the volatlty of long-term nterest rate, the model shows that a sgnal jammng mechansm may operate that renders the Fed ne ectve n communcatng nformaton to the market and makng bond prces more nformatve. Our model also hghlghts a tenson between 5 Smlar to Goldsten and Yang (05), prces n our settng can aggregate nformaton about multple fundamentals, and the fundamentals that nvestors care about can be d erent from those the government nds most relevant. 6 As n Angeletos, Hellwg, and Pavan (006), the government n our framework faces a tme-consstency ssue when t lacks commtment. We take up ths ssue n Secton

9 the government s objectve n reducng prce volatlty and mprovng nformaton e cency, albet through a d erent mechansm related to the nformaton acquston decsons of nvestors. arket Breakdown n a Perfect-Informaton odel Consder an n nte horzon economy n dscrete tme wth n ntely many perods: t = 0; ; :::. There s a rsky asset, whch can be vewed as stock ssued by a rm that has a stream of cash ows D t over tme: D t = t + D " D t : The components t s a persstent component of the fundamentals, whle " D t s ndependent and dentcal cash ow nose wth a Gaussan dstrbuton of N (0; ) and D > 0 measures the volatlty of cash ow nose. Government polces n practce may a ect asset markets through several channels. The government can drectly a ect the pro tablty of rms. We do not focus on ths drect channel snce we do not nclude an addtonal government cash ow term beyond t + " D t. The lterature has already studed ths drect e ect. 7 Instead, we ntend to analyze a d erent channel, through whch the government nterventon can mpact the market dynamcs even when t does not drectly a ect the rm s cash ow. Spec cally, we assume that the asset s cash ow s fully determned by an exogenous fundamental t ; whch follows an AR() process: t = t + " t ; where (0; ) measures the persstence of the asset fundamental, > 0 measures the fundamental volatlty, and " t s N (0; ) s ndependently and dentcally dstrbuted shocks to the asset fundamental. 7 For example, f the government faces a tme-varyng cost n mplementng such a polcy, the cost of the government polcy can become an mportant factor n drvng the stock cash ow and thus prce dynamcs. See Pastor and Verones (0, 03) for recent studes that explore ths channel. In addton, when government polces a ect the cash ow of publcly traded rms, Bond and Goldsten (05) shows that such nterventon feeds back nto how market partcpants trade on ther prvate nformaton. Ths results n socally ne cent aggregaton of prvate nformaton about the unobservable fundamental t nto asset prces, whch can mpede polcymakng f the government also nfers relevant nformaton about t from the traded asset prce n determnng the scale of ts nterventon. 7

10 In ths secton, we assume that at tme t, t+ s observable to all agents n the economy. Ths settng serves as a benchmark for examnng the role of government nterventon. 8 wll remove ths assumpton n the next secton to make t+ We unobservable to both the government and nvestors n the next secton to dscuss how government nterventon a ects the nvestors nformaton acquston. For smplcty, suppose that there s also a rskfree asset n elastc supply that pays a constant gross nterest rate > : In what follows, we de ne R t+ to be the excess payo to holdng the rsky asset: R t+ = D t+ + P t+ P t : There are three types of agents n the asset market: nose traders, nvestors, and the government, whch we descrbe below.. Nose Traders It s wdely observed that there s a large number of nexperenced retal nvestors n Chna s stock markets. otvated by ths observaton, we assume that n each perod, these nexperenced nvestors, whom we call nose traders, submt exogenous market orders nto the asset market. 9 AR() process: We denote the quantty of ther orders by N t and assume that N t also follows an N t = N N t + N " N t ; where N (0; ) measures the persstence of nose tradng, N > 0 measures the volatlty of nose tradng (or nose trader rsk n ths market), and " N t s N (0; ) s ndependently and dentcally dstrbuted shocks to nose traders. The presence of nose traders creates ncentves for other nvestors to trade n the asset market. To the extent that nvestors may not be able to fully elmnate the market mpact of nose traders, ths also just es government nterventon to further dampen the mpact of nose traders. 8 We make t+ ; not just t, observable at tme t so that ths benchmark s exactly the lmtng case of the settng n the next secton when we allow the precson of each nvestor s prvate nformaton about t+ to rse to n nty. 9 Ths way of modelng nose tradng s standard n the market mcrostructure lterature. See Black (986) for a classc reference. Even though we do not explctly model ther orgnaton, we thnk of these random orders as emanatng from uctuatons n the retal nvestors sentment and overreactons to relevant or rrelevant nformaton. 8

11 . Investors Problem There are a contnuum of nvestors n the market who trade the asset on each date t: We assume that these nvestors are myopc and lve for only one perod. That s, n each perod a group of new nvestors wth measure jon the market, replacng the group from the prevous perod. We ndex an ndvdual nvestor by [0; ] : Investor born at date t s endowed wth wealth W and has constant absolute rsk averson CARA preferences wth coe cent of rsk averson over ts next-perod wealth W t+: U t = E exp W t+ j Ft : It purchases X t shares of the asset and nvests the rest n the rskfree asset at a constant rate, so that W t+ s gven by W t+ = W + X t R t+ : The nvestors have symmetrc, perfect nformaton, and ther expectatons are all taken wth respect to the full-nformaton set F t = f s+ ; N s ; D s g st n ths secton. As a result of CARA preferences, an ndvdual nvestor s tradng behavor s nsenstve to hs ntal wealth level. The assumpton of nvestor myopa s commonly used n dynamc models of assset markets wth nformatonal frctons for smplcty, e.g., Allen, orrs, and Shn (006) and Bacchetta and van Wncoop (006). In our settng, ths assumpton also serves to capture the speculatve nature of Chnese nvestors, whch s mportant for generatng market breakdown when nose trader rsk becomes su cently large..3 Equlbrum wthout Government To facltate our dscusson of ths perfect-nformaton settng, we rst characterze the ratonal expectatons equlbrum wthout government nterventon. Because nvestors are rskaverse, the market can only bear a lmted amount of nose trader rsk. In what follows, we derve the equlbrum prce and show formally that the market breaks down whenever the nose trader rsk N rses above a certan threshold. oreover, we show that the excess return volatlty n equlbrum s ncreasng n N, and the rate of ths volatlty ncrease grows explosvely as N approaches the threshold. 9

12 We conjecture a lnear ratonal expectatons equlbrum and then verfy that there cannot be any nonlnear equlbrum see Appendx A for more detals of the equlbrum constructon. In ths equlbrum, the asset prce P t s a lnear functon of the fundamental t+ and the nose trader shock N t : P t = t+ + p N N t ; where t+ s the expected present value of cash ows from the asset. Ths conjecture mples that the condtonal excess return varance s gven by V ar (R t+ jf t ) = D + + p N N: Snce all nvestors are symmetrcally nformed and have CARA utlty wth normally dstrbuted payo s, they wll have dentcal demand for the rsky asset Xt: Xt = p N N N t : D + + p N N Each myopc nvestor s demand trades o the expected asset return wth the return varance over the subsequent perod. Then, mposng market-clearng n the asset market X t = N t leads to a quadratc equaton that pns down the prce coe cent p N. Note that there exst two negatve roots to p N : Smlar to Bacchetta and van Wncoop (006, 008), we focus on the less negatve root of the two. Bacchetta and van Wncoop (003) establsh that the less negatve root s the only stable root wth common knowledge, and we nd ths choce also sensble snce as N! 0 (.e., nose trader rsk vanshes from the economy), the less negatve root has a nce property of p N N! 0 (.e., the prce mpact of nose traders dmnshes), whle the more negatve root dverges. In addton, ths root corresponds to the prce that has a lower condtonal prce varance. We always focus on ths more stable root of the two n our analyss, hereafter. The followng proposton, wth detals provded n the Appendx, shows that the equlbrum does not exst f N s hgher than a threshold: N = N r : () D + Proposton If the nose trader rsk N N ; an equlbrum exsts ar(r t+jf t)) N 0, ar(r t+jf t))! N! N mplyng that the asset return varance s hghest at N N = N wth a value of D +. If N > N, no equlbrum exsts. 0

13 Fgure : Asset prce varance wth and wthout government nterventon wth respect to the varance of nose tradng N. The sold lne represents the case wthout government nterventon, and the dashed lne represents the case wth government nterventon at a gven ntensty of # N = 0:. Ths gure s based on the followng model parameters: = ; = :0; = 0:75; = 0:0; D = 0:08; N = 0; # N = 0:: The proposton shows that the asset return varance ncreases wth the nose trader rsk N and the rate of ths ncrease explodes as N gets close to the threshold N : Fgure llustrates the explosve return varance as N approaches N : Furthermore, ths proposton establshes that the market breaks down when N rses above N : Intutvely, snce the nvestors are myopc and care only about the rsk and return over the subsequent one perod, they become ncreasngly reluctant to trade aganst nose traders as N rses. As N rses, nvestors would demand a hgher rsk premum to take on a poston aganst nose traders, re ected n a larger coe cent p N, whch, n turn, leads to a hgher asset return volatlty. Through ths feedback process, once N gets larger than N ; the asset return volatlty becomes so large that the nvestors are not wllng to take on any poston regardless of the rsk premum. In ths settng, the myopa of nvestors and the prce-nsenstve tradng of nose traders jontly lead to the market breakdown. If the nvestors have longer horzons, they would be wllng to take on a poston despte the large return volatlty over the short-term, whch would, n turn, stablze the prce mpact of nose traders. As such, the reluctance of shortterm nvestors to trade aganst nose traders s remnscent of the classc result hghlghted

14 by De Long, et al (990), whch shows that nose traders can create ther own space n asset prces n the presence of myopc arbtrageurs. The nose traders prce-nsenstve trades serve to capture market rgdty that sometmes occurs as a result of ether forced re sales or panck sellng durng market turmol. If the nose traders have a prce-senstve supply curve, there would always be a market-clearng prce. Nevertheless, n such a case, the tradng of the nose traders would stll lead to hgher asset prce volatlty, whch rsk-averse nvestors would not be able to fully remove, and thus would nevertheless motvate government nterventon. 0.4 Equlbrum wth Government Interventon We now augment the baselne settng to nclude a government that actvely ntervenes n the asset market. Spec cally, we assume that the government s asset tradng follows a lnear tradng rule: X G t = # N;t N t + q V ar [# N;t N t j F t ]G t ; where the coe cent # N;t represents the government s nterventon strategy n tradng aganst the nose traders, and p V ar [# N;t N t j F t ]G t s an unntended nose component that arses from frctons n the nterventon process, such as behavoral bases, lobbyng e ort, or nformaton frctons. Spec cally, G t = G " G t wth " G t s N (0; ) as ndependently and dentcally dstrbuted shocks and G as a volatlty parameter. The magntude of ths nose component scales up wth the condtonal volatlty of the ntended nterventon strategy p V ar [#N;t N t j F t ]; whch s equal to N # N;t wth perfect nformaton. Ths spec caton s reasonable as t s easer for frctons to a ect the government nterventon when the nterventon strategy requres more ntensve tradng. Furthermore, the government can nether correct nor trade aganst ts own nose, because the nose orgnates from ts own system. Instead, as we wll analyze later, the government can nternalze the amount of nose by lmtng ts tradng ntensty. We assume the government ntervenes wth a benevolent objectve of stablzng the market, whch s consstent wth what s often stated by the Chnese government. There are two d erent varatons n mplementng ths general objectve n practce: one s to mnmze 0 The presence of hgh prce volatlty n Chna s nancal markets, whch s possbly drven by the large number of retal nvestors and the short-termsm of other nvestors, also makes t d cult for a nancal nsttuton to pursue a long-term nvestment strategy as a result of the agency problems hghlghted by Shlefer and Vshny (997). Ths ssue, whle not explctly modeled n our settng, also motvates government nterventon to reduce prce volatlty.

15 the devaton of asset prces from fundamentals; the other s smply to mnmze asset prce volatlty. Each of these two objectves has ts own appeal and can be mcro-founded under sutable assumptons. The former s consstent wth makng asset prces more nformatve and thus more e cent n gudng resource allocaton n the economy, whle the latter s consstent wth reducng destablzng e ects of asset prce volatlty on leveraged nvestors and rms. These two objectves are closely related and are often treated as consstent wth each other n government nterventon. Ths s because by reducng the prce mpact of nose traders, government nterventon reduces both asset prce devaton from fundamentals and prce volatlty. As n practce prce volatlty s easy to measure whle asset prce devaton from fundamentals s d cult to detect, reducng asset prce volatlty s more appealng and ndeed s wdely adopted. Our analyss ntends to compare these two objectves and show that they may devate from each other n the presence of nformaton frctons. Spec cally, we adopt the followng general spec caton to represent the government s myopc preference for nterventon n the asset market at date t: Ut G = mn V ar [P t (# N;t ) jf t ] + V ar P t (# N;t ) # N;t t+ jf t The rst term V ar [P t (# N;t ) jf t ] captures a goal to mnmze the condtonal asset prce varance, wth the coe cent 0 measurng the government s averson to prce volatlty. h The second term V ar P t (# N;t ) t+ jf t captures a goal to reduce prce ne - cency, wth the coe cent 0 measurng the government s averson to the condtonal varance of the asset prce devaton from the asset s fundamental value t+. In choosng # N;t, the government recognzes that ts nterventon drectly a ects the asset prce P t # ^N;t. In other words, the government s a large player that nternalzes ts mpact on the asset market. There are several notable ponts about ths objectve functon. Frst, snce the two components n the government s objectve are both second moments, we shall consder only statonary polces, # N;t = # N : Second, ths objectve functon can be scaled up or down by any postve constant wthout a ectng the government s optmal choce. Thrd, ths objectve functon does not contan any cost for government nterventon. Interestngly, despte the absence of any nterventon cost, there s an nteror optmum to the government s nterventon strategy, because the government nternalzes the amount of nose that ts nterventon For example, a recent study by Sten and Sunderam (06) adopts reducng volatlty of long-term nterest rate as the objectve of the Federal Reserve Board n managng ts monetary polcy n the U.S. 3 :

16 ntroduces nto the market. As the government trades alongsde nvestors to accommodate the tradng of nose traders, the market-clearng condton R 0 X td+x G t = N t mples the followng equlbrum asset prce functon wth the government nose as an addtonal factor: P t = t+ + p N N t + P g G t : In Appendx A, we show that a market equlbrum exsts when where N N < ( # N ) s + N # N # N G N () s gven n equaton (). The more aggressvely the government trades to accommodate nose tradng, the closer s # N to, and the slacker s the equlbrum exstence condton compared to the case wthout the government nterventon (.e., # N = 0:) Ths s shown n Fgure, whch depcts the shft n the market breakdown upper-bound and also the reduced asset prce volatlty before N reaches the upper-bound. To the extent that the asset prce varance and the varance of the asset prce from ts fundamental value both explode when the market breaks down, the government s averson to any of these outcomes would motvate the government to choose a su cently large # N so that the condton n () s sats ed. Thus, a market equlbrum always prevals. Furthermore, the government objectve of mprovng prce e cency s qualtatvely consstent wth an alternatve of reducng prce volatlty. Taken together, government nterventon n asset markets can help to ensure market stablty, especally durng tmes of extreme market dysfuncton, when nose trader rsk s hgh. Wth nformatonal frctons, however, the nterventon to stablze asset prces has addtonal e ects on market dynamcs, whch we llustrate n the next secton. 3 An Extended odel wth Informaton Frctons We now extend the model to ntroduce realstc nformaton frctons that nvestors and the government face n nancal markets, whle keepng the market structure and the tradng preferences of nvestors and the government smlar. Spec cally, we assume that the asset fundamental t+ and nose tradng N t are both unobservable at tme t to all agents n the economy. Ths extended model allows us to analyze how government nterventon 4

17 nteracts wth both tradng and nformaton acquston of nvestors, ultmately a ectng the nformaton e cency of asset prces. Furthermore, for smpl caton, we assume that the nose n government tradng G t s publcly observable at date t; albet not before t. As the government nose a ects the asset prce n equlbrum, nvestors have an ncentve to acqure nformaton about the next-perod s government nose, and ths ncentve may be even greater than the ncentve to acqure nformaton about the asset fundamental. Indeed, our model shows that whle government nterventon dampens prce volatlty when ths occurs, t may exacerbate rather than mprove the nformaton e cency of the asset prce. 3. Informaton and Equlbrum Ths subsecton descrbes the nformaton structure of the economy wth nformaton frctons, buldng on the prmtves of the model and the preferences of the varous economc agents n the perfect nformaton settng. 3.. Publc arket Informaton All market partcpants observe the full hstory of all publc nformaton, whch ncludes all past dvdends, asset prces, and government nose: F t = fd s ; P s ; G s g st ; whch we wll hereafter refer to as the "market" nformaton set. We de ne ^ t+ = E t+ j F t as the condtonal expectaton of t+ wth respect to F t. The government needs to trade aganst the nose tradng based on ts condtonal expectaton of N t. Wthout any prvate nformaton, ts expectaton of N t s equal to the expectaton condtonal on F t rsk of abusng notaton, we de ne. At the ^N t = E N t j F t : Importantly, ^N t represents expectaton of the current-perod N t rather than N t+ : Furthermore, we de ne ^G t+ = E G t+ j F t In an earler draft of the paper, we have analyzed the case wth G t beng unobservable even after t. The results are qualtatvely smlar to our current settng, although the analyss s substantally more complex. 5

18 as the market s condtonal expectaton of the next-perod G t+ : These three belef varables, ^ t+; ^N t ; and ^G t+; are tme-t expectatons of t+, N t, and G t+, respectvely. Together wth the publcly observed current-perod G t, they summarze the publc nformaton at tme t regardng the aggregate state of the market. We collect these varables as a state vector 3.. Government t = h ^ t+ ^N t G t ^G t+ : At date t, the government s nformaton set contans only the publcly avalable nformaton F t. 3 Lke before, we assume that the government has an nterventon program, whch s nsttuted to trade aganst the nose traders based on the condtonal market expectaton ^N t : r h Xt G = # ^N;t ^N t + V ar # ^N;t ^N t j Ft G t : (3) Furthermore, the government has a smlar myopc objectve as before n choosng ts nterventon strategy at date t: U G t = mn V ar hp t # ^N;t # ^N;t j F t + V ar P t # ^N;t t+ j Ft : (4) As both of these varance terms are condtonal on the government s nformaton set F t ; one can vew the government as choosng ts nterventon strategy # ^N;t at date t before the nvestors observe any prvate nformaton. The two terms n the government s objectve are all centered second moments, whch are determnstc n our Gaussan settng, thus they are all computable despte the non-nestng of nformaton sets between the government and the nvestors. In maxmzng (4), the government s fully aware of how ts tradng mpacts the asset prce and, through ths channel, the nformatveness of the asset prce as a sgnal about t and G t : Ths nformatveness of the asset prce mpacts not only the government s ablty to learn from the asset prce, but also that of the nvestors. Importantly, the government also 3 In a prevous draft, we adopted an alternatve settng, n whch the government possesses prvate sgnals about the fundamental. Ths prvate nformaton causes the government to hold d erent belefs about the fundamental and nose tradng from nvestors and, more mportantly, makes the government s tradng not fully observable to the nvestors. Through ths latter channel, the nose n the government s sgnals endogenzes the government nose G t. Such a structure substantally complcates the analyss by ntroducng a double learnng problem for the nvestors to acqure nformaton about the government s belef, whch s tself the outcome of a learnng process. It s reassurng that ths more elaborate settng gves smlar results as our current settng wth exogenous government nose. 6

19 nternalzes ts mpact on the nformaton acquston decsons of the nvestors. As such, one can vew the government s nterventon program as an nformaton desgn problem n whch the government selects an nformaton structure for the asset prce that s ncentve compatble wth the tradng and nformaton acquston actons of the nvestors. Snce the government possesses nferor nformaton to prvate agents, our settng represents a correlated equlbrum n a Bayesan game wth coordnaton, n the sprt of yerson (994), rather than a game of Bayesan Persuason by an nformed polcy maker, e.g., Kamenca and Gentzkow (0) Investors In each perod, the nvestors face uncertanty n the asset fundamental, the nose tradng, and the government nose. Spec cally, at date t; each nvestor can choose to acqure a prvate sgnal ether about the next-perod asset fundamental t+ or about the next-perod government nose G t+ : We denote the nvestor s choce as a t f0; g ; wth representng the choce of a fundamental sgnal and 0 the choce of a sgnal about the government nose. When the nvestor chooses a t = ; the fundamental sgnal s where " s; t s t = t+ + a t s = " s; t ; s N (0; ) s sgnal nose, ndependent of all other random varables n the settng, and s represents the precson of the sgnal f chosen. When the nvestor chooses a t = 0, the government sgnal s where " g; t g t = G t+ + a = t g " g; t ; s N (0; ) s sgnal nose, ndependent of all other random varables n the settng, and g represents the precson of the sgnal f chosen. These sgnals allow the nvestor to better predct the next-perod asset return by formng more precse belefs about t+ and G t+. otvated by lmted nvestor attenton and realstc xed cost n nformaton acquston, we assume that each nvestor needs to choose one and only one of these two sgnals. 4 At date t; each nvestor rst makes hs nformaton acquston choce a t based on the publc nformaton set F t from the prevous perod. After recevng hs prvate nformaton 4 Generally speakng, the nvestors may also acqure prvate nformaton about nose tradng, rather than asset fundamental and government nose. Introducng such a thrd type of prvate nformaton complcates the analyss wthout a partcular gan n nsght. In our current settng, each nvestor can ndrectly nfer the value of nose tradng through the publcly observed asset prce. 7

20 a ts t + ( a t) g t and the publc nformaton D t, P t, and G t released durng the perod, the nvestor chooses hs asset poston X t t + : to maxmze hs expected utlty over hs wealth at Ut = max E max E exp W a t f0;g Xt t+ j F t j F t where the nvestor s full nformaton set F t s F t = F t _ a ts t + a t g t : The nvestor s objectve guarantees sequental ratonalty of hs nformaton acquston and tradng decsons. Gven hs belefs about how he wll trade at date t; the nvestor chooses what nformaton to acqure based on publc nformaton up to t tradng strategy Nosy Ratonal Expectatons Equlbrum ; ; and then chooses hs arket clearng of the asset market requres that the net demand from the nvestors and the government equals the supply of the nose traders at each date t: R 0 X td + X G t = N t : We assume that the supply of rskless debt s elastc, and therefore the credt market clears automatcally. We also assume that the nvestors and the government have an ntal pror wth Gaussan dstrbutons at t = 0: ( 0 ; N 0 ) s N ; N " # ; 0 ; where = : Note that the 0 N 0 varables n both Ft and Ft all have Gaussan dstrbutons. Thus, condtonal belefs of the nvestors and the government about t and N t under any of the nformaton sets are always Gaussan. Furthermore, the varances of these condtonal belefs follow determnstc dynamcs over tme and wll converge to ther respectve steady-state levels at exponental rates. Throughout our analyss, we wll focus on steady-state equlbra, n whch the belef varances of the government and nvestors have reached ther respectve steady-state levels and ther polces are tme homogeneous. At tme t, a Nosy Ratonal Expectatons Equlbrum s a lst of polcy functons, X G ( t), a ( t ) ; and X ( t; a ts t + ( a t) g t; P t ) ; and a prce functon P ( t; t ; N t ; G t+ ), whch jontly satsfy the followng: Government optmzaton: Before the nvestors choose ther optmal nformaton acquston polces fa tg and optmal tradng polces fx tg, the government chooses ts 8

21 nterventon polcy X G ( t) = # ^N;t ^N t + r chosen based on ts ex ante nformaton set F t V ar h# ^N;t ^N t j F t ; fa tg G t wth # ^N;t to maxmze ts objectve, takng nto account the mpact of ths choce on the nvestors nformaton acquston and tradng strateges. Investor optmzaton: An ndvdual nvestor takes as gven the government s nterventon strategy to make hs nformaton acquston choce a t = a ( t ) based on hs ex ante nformaton set F t and then makes hs nvestment choce X ( t; a ts t + ( a t) g t; P t ) based on other nvestors nformaton acquston choces a t and hs full nformaton set F t : arket clearng: Z 0 X t; a ts t + a t g t ; P t d + X G ( t) = N t : Consstency: nvestor and the government form ther expectatons about t+ and N t based on ther nformaton sets F t and F t ; respectvely, accordng to Bayes Rule. In the man part of our analyss, we assume that the government can commt to an nterventon strategy, as de ned above, by choosng ts nterventon strategy before the nvestors choose ther nformaton and tradng strateges. We also dscuss a tme-nconsstency problem f the government cannot commt n Secton A Benchmark wthout Government Interventon Before we analyze the e ects of government nterventon, we rst descrbe a benchmark equlbrum n the absence of government nterventon. We arrve at ths benchmark by lettng = = 0. In ths case, the government would not ntervene at all. Consequently, the nvestors would all acqure nformaton about the asset fundamental. Wth each nvestor possessng a prvate sgnal about the asset fundamental, the settng n each perod resembles that of Hellwg (980). We systematcally derve the market equlbrum n Appendx B. In ths subsecton we hghlght a few key steps for dervng the equlbrum, as we wll also follow the same steps, albet wth more complexty, n dervng the equlbrum wth government nterventon. Frst, ^ t+; the condtonal expectaton of the fundamental based on the publc market nformaton set Ft ; represents an anchor of the fundamental before each nvestor condtons 9

22 on hs prvate sgnal. Second, after an ndvdual nvestor receves hs prvate sgnal s t, hs condtonal belef s updated to ^ t+ = E t+ jft = E t+ jft _ s t = ^ t+ + Cov t+ ; s tjft V ar [s tjft ] s t ^ t+ : Thrd, n a lnear asset market equlbrum, the nvestor s expected excess asset return s a lnear functon that ncreases wth ^ t+ and decreases wth the asset prce P t. Fourth, the nvestor s preference mples that hs optmal asset poston lnearly ncreases wth hs expected excess asset return and s thus a lnear functon that ncreases wth s t ^ t+ and decreases wth P t. Ffth, gven the symmetry among all nvestors, ther aggregate asset poston s a lnear functon, ncreasng wth ther aggregate sgnal R s 0 t ^ t+ d; whch s exactly t+ ^ t+ accordng to the Law of Large Numbers, and decreasng wth P t. Fnally, the market clearng condton of equatng the nvestors aggregate asset poston to the supply of nose traders leads to the equlbrum asset prce: P t = ^ t+ + p t+ ^ t+ + p N N t ; (5) where the rst component ^ t+ s the expected asset fundamental based on the market nformaton, and the second component represents nformaton aggregaton through the nvestors tradng, and the thrd component represents the prce mpact of nose traders. The presence of nose tradng prevents the asset prce from fully revealng the asset fundamental t+, whle the nvestors tradng mtgates the prce mpact of nose tradng. The weghts of these two components, p and p N, are endogenously determned n the equlbrum by varous model parameters, such as the nvestors rsk averson, sgnal precson and the nose trader rsk. We derve these coe cents n the appendx, and demonstrate that p s always below ; ts value n the perfect-nformaton settng. Importantly, the asset prce P t s a key source of market nformaton n determnng ^ t+ n the rst step. We start by conjecturng the lnear prce functon n (5) and carryng the unknown coe cents p and p N through the aforementoned steps untl we solve them through the market clearng condton n the nal step. Ths benchmark equlbrum shows that when the nvestors each acqure a prvate sgnal about the fundamental, the equlbrum asset prce aggregates ther prvate sgnals and partally reveals the fundamental. Fgure llustrates ths benchmark equlbrum. Panel A compares the asset prce varance V ar P t j F t n the presence and absence of nformaton frctons by varyng the nose 0

23 Fgure : The benchmark equlbrum wthout government nterventon across d erent values of nose trader rsk. Panel A depcts asset prce varance V ar P t j Ft for the symmetrc nformaton case n the dashed lne and for the asymmetrc nformaton case n the sold lne. Panel B depcts, for the asymmetrc nformaton case, asset prce varance h n the sold lne and the condtonal varance of prce devaton from the fundamental V ar P t t+ j F t n the dashed lne. Ths gure s based on the followng model parameters: = ; = :0; = 0:75; = 0:0; D = 0:08; N = 0; s = 500: trader rsk N : As n the full nformaton case, a market breakdown can stll occur, and t does so for an even lower threshold n nose trader rsk. Ths earler breakdown, whch s caused by the larger rsk that nvestors have to take n the presence of nformaton frctons, holds for many d erent constellatons of model parameters we have examned. Panel B of Fgure shows that n the presence of nformaton frctons the condtonal h varance of the prce devaton from ts fundamental value V ar P t t+ j F t and the condtonal asset prce varance V ar P t j Ft are both monotoncally ncreasng wth nose trader rsk N. Ths pattern s consstent wth the conventonal wsdom that n tradng aganst nose traders, the government s objectve n mprovng nformaton e cency of asset prces (.e., reducng prce devaton from asset fundamentals) s consstent wth reducng prce volatlty. As we wll show later, however, ths conventonal wsdom may not hold when nvestors can choose to acqure nformaton about the asset fundamental or nose n the government nterventon.

24 3.3 Equlbrum wth Government Interventon We now analyze the man settng wth the government tradng along wth the nvestors. As noted prevously, wth the government nterventon ntroducng nose G t nto the equlbrum asset prce as an addtonal factor, each nvestor faces a choce at date t n whether to acqure prvate nformaton about ether the next-perod fundamental t+ or government nose G t+. When all nvestors choose to acqure nformaton about the government nose, the asset prce does not aggregate any prvate nformaton about t+ but rather brngs the next-perod government nose nto the current-perod asset prce. Ths outcome may thus compromse the nformaton e cency of the asset prce. The dervaton of the equlbrum follows smlar steps as dervng the benchmark equlbrum n the prevous subsecton, albet wth addtonal complexty as a result of the government s nterventon and the nvestors speculaton of the nose n government nterventon. To smplfy the presentaton, we descrbe key elements of the equlbrum n ths subsecton n order to convey the key economc mechansm of the model. We provde the complete steps and formulas n Appendx C Prce Conjecture and Equlbrum Belefs We begn by conjecturng a lnear asset prce functon: P t = ^ t+ + p g G t + p ^G ^G t+ + p t+ ^ t+ + p G G t+ ^Gt+ + p N N t : (6) The rst term ^ t+ s the expected asset fundamental condtonal on the market nformaton Ft at date t, the term p g G t re ects the nose ntroduced by the government nto the asset demand n the current perod, whle the term p ^G ^G t+ re ects the market expectaton of the government nose n the next perod. These three peces serve as anchors n the asset prce based on the publc nformaton. The fourth term p t+ captures the fundamental nformaton aggregated through the nvestors tradng, smlar to the benchmark wthout the government nterventon. Note that f all nvestors choose to acqure nformaton about the next-perod government nose, rather than the asset fundamental, the coe cent of ths term p would be zero. The fth term p G G t+ ^G t+ captures the nvestors prvate nformaton about the next-perod government nose aggregated through ther tradng. 5 5 Note that there s no need to ncorporate a term related to nvestors cross-belefs about t+ or G t+ because R 0 a ts td = t+ and R a 0 t g t d = G t+ by the Law of Large Numbers. ^ t+